UNIVERSIDAD COMPLUTENSE DE MADRID FACULTAD DE CIENCIAS FÍSICAS TESIS DOCTORAL The lithium-age relation: Calibration with open clusters and associations La relación litio-edad: calibración con cúmulos abiertos y asociaciones MEMORIA PARA OPTAR AL GRADO DE DOCTOR PRESENTADA POR Marta Lúthien Gutiérrez Albarrán Director David Montes Gutiérrez Madrid © Marta Lúthien Gutiérrez Albarrán, 2022 Marta Lúthien Gutiérrez Albarrán David Montes Gutiérrez Madrid, enero 2022 Memoria presentada para aspirar al grado de Doctora en Astrofísica en la Facultad de CC. Físicas Departamento de Física de la Tierra y Astrofísica Madrid, enero de 2022 Supervisor:Memoria que presenta: The lithium-age relation: Calibration with open clusters and associations La relación litio-edad: Calibración con cúmulos abiertos y asociaciones Marta Lúthien Gutiérrez Albarrán David Montes Gutiérrez TESIS DOCTORAL iv Some of the figures and material included in this document have already been published in the Astronomy & Astrophysics. journal (DOI 10.1051/0004-6361/202037620) This document has been created with a modified version of TEXiS v.1.0+. Spitzer Space Telescope (SST) image of NGC 2244. Credit: NASA/JPL-Caltech/Univ.of Ariz To my inner circle. And to all my fellow women in science. Hey, do you mind if I tell you a story? One you might not have heard. All the elements in your body were forged many, many millions of years ago, in the heart of a far away star that exploded and died. That explosion scattered those elements across the desolations of deep space. After so, so many millions of years, these elements came together to form new stars and new planets. And on and on it went. The elements came together and burst apart, forming shoes and ships and sealing wax, and cabbages and kings. Until eventually, they came together to make you. You are unique in the universe. The Doctor in The Rings of Akhaten (Doctor Who) Acknowledgements None of us know for sure what’s out there. That’s why we keep looking. Travel hopefully. The universe will surprise you... constantly. The Thirteenth Doctor (Doctor Who) This thesis is the result of years of effort and determination, sorting out tables upon tables of data, plotting countless figures, waiting for new data releases from GES and Gaia to surface, upgrading and expanding analyses, and delving one step at a time into the mysteries of lithium and the fascinating complexities of stellar evolution. To quote the Doctor, the universe will keep surprising us constantly (although preferably not with new variants in the pandemic that we are all braving), and hopefully we will also keep understanding the many enigmas of stellar lithium more and more each time as well! But just as the Doctor needs her companions to travel space and time and see the wonders of the universe, so I truly need to thank the people and inspirations around me who have made the completion of this thesis fully possible: First of all, I have to thank my supervisor, Dr. David Montes Gutiérrez, for giving me the opportunity and the trust to delve into the world of stellar Astrophysics, firstly during my Mas- ter’s thesis, and then during all the years of this PhD program. Immersed in the analysis of stellar spectra and GES data from the start, I must thank him for welcoming me into the UCM GES node, and also for all the suggestions and revisions over the years. I would also like to express my gratitude to many of the professors and colleagues in the department for their support and the important role they played in my Astrophysics journey from my degree years up till now. I cannot mention them all here, but among them I especially give my thanks to Profa. Dra. Elisa de Castro, Profa. Dra. María José Fernández-Figueroa, Prof. Dr Manuel Rego, Dra. África Castillo, Dr. José Antonio Caballero, Dr. Jesús Gallego, Dr. Nicolás Cardiel, and Dr. Francisco Javier Gorgas. I would also like to mention Dr. Benjamín Montesinos, whose seminaries and courses at CosmoCaixa Madrid were a crucial and fondly re- membered part of my growing interest in Astronomy and Astrophysics during my High School years. And, of course, I want to mention all my fellow PhD students and recently graduated doctors who I have met over the years, sharing both our science pursuits and our technical and academic woes, from Miriam, Hugo, Miguel, Víctor and Flory to Emilio. It is of course necessary for me to highlight the work of the Gaia-ESO Survey and the GES consortium, without which this work would not exist. The invaluable data from GES and from the Gaia mission have allowed me and many other people to keep exploring the workings of the stars with the aid of increasingly large and precise sets of data. Regarding the work of the GES UCM node, I also have to acknowledge the financial support provided by the Universidad Com- plutense de Madrid and by the Spanish Ministry of Economy and Competitiveness (MINECO) xi xii Acknowledgements from project AYA2016-79425-C3-1-P. I have come a long way in the path to study science from that little girl who drew stars and purple Saturns (it was a design choice) in Primary School and wanted to be an astronomer — as well as an artist, an archaeologist and a writer, and, judging from a school assignment that included a hilariously tightly organized schedule, that would have definitely required a well- functioning TARDIS to achieve! And my feminist self would be remiss to forget to mention the ongoing inspiration not only of all the remarkable historical figures of women who defied the system to pursue their scientific aptitudes, but especially of all my fellow women in STEM in the present day, who continue to be bold and brilliant and prove gender roles and the system wrong every single time. The scientific world is still some way of being completely diverse and inclusive, but every time I see a fellow woman in science I have hope that it is becoming steadily better. Thank you for inspiring me to follow in your steps. Another source of inspiration and support that I would like to mention here are my many fandoms and hobbies, and the groups and people that I have met thanks to them. From Doctor Who to Tolkien, Good Omens, Star Trek and the MCU, fandoms have inspired me to ask more questions about the universe, and provided a way to find comfort from the harsher realities of the world with countless characters and realities. I want to mention all the fandom friends and connections who have offered helpful evasion and support from the daily grind, from the online social media world to the Spanish Tolkien Society (STE). I would also like to mention the friends I met years ago thanks to our common interest in the Irish language, as well as the importance of music and art to give the mind a respite between one analysis and the next, and tackle the work at hand with renewed strength. And last but definitely not least, my thanks go to my family, parents and inner circle, who have supported me through these years, and especially during these last intense few months. Special mentions go to Tarmariel, my beta reader (thank you for reading it all!), who shares my daily study life with her own interests and pursuits, has supported me in everything that I have aspired to do in life, and joined many lunch breaks watching the classic series of Doctor Who; and to Héctor, fellow Astrophysicist, who has offered both sporadic (but very helpful) tech support and constant encouragement, as well as joining in many discussions about fandoms and activism and science and a bit of everything. Thank you both for supporting me and sharing so many nice moments. And finally, I would like to dedicate this work to you, reader. Thank you for being here, and I hope you will enjoy this journey across the stars. Resumen El litio es un elemento muy frágil que se destruye fácilmente en los interiores estelares. La abundancia superficial de litio disminuye lentamente con el tiempo en estrellas de tipo solar y estrellas poco masivas. Es por esta razón que el litio puede usarse para estudiar la evolución estelar, y es particularmente relevante a la hora de determinar la edad de cúmulos estelares. Las abundancias de litio (derivadas de la línea de Li en 6707.76 Å) observadas para estrellas de tipo tardío dependen fuertemente de la edad, pero también muestran un patrón complejo que depende de diferentes parámetros, desde la rotación, a la actividad cromosférica, la metalicidad, los mecanismos de mezcla, la estructura convectiva o la actividad magnética. La mejor forma de poder calibrar estos efectos es analizando en detalle conjuntos de estrellas de la misma edad, como los cúmulos abiertos y las asociaciones estelares. Este proyecto se ha desarrollado haciendo uso de los datos proporcionados por Gaia-ESO (GES), una gran exploración espectroscópica pública que proporciona una visión homogénea de la distribución de la cinemática y la estructura dinámica y química de la Galaxia. GES ha tomado datos de una gran cantidad de estrellas y de casi 100 cúmulos estelares, desde 2011 hasta 2018. Esta exploración usa el espectrógrafo multi-objeto FLAMES del Very Large Telescope (ESO, Chile) para obtener tanto espectros de alta resolución con UVES (Ultraviolet and Visual Echelle Spectrograph), como de resolución media con el espectrógrafo GIRAFFE. Como parte del nodo de GES de la UCM, en la primera etapa de este proyecto de tesis estuve realizando un extenso trabajo de medida de las anchuras equivalentes (la línea de Li I en 6707.76 Å y la línea adyacente de Fe I en 6707.43 Å) de los espectros de UVES, con vistas a la homo- geneización del entonces cuarto lanzamiento de GES (iDR4). Para todo el análisis del proyecto, sin embargo, hemos actualizado todos los resultados haciendo uso del último lanzamiento de GES, iDR6, además de los datos proporcionados por Gaia EDR3. Esta tesis, titulada La relación litio-edad: Calibración con cúmulos abiertos y asociaciones, se enmarca dentro de un estudio a gran escala que hace uso de una serie de 42 cúmulos abiertos y asociaciones observados por GES, en un rango de edades desde 1 Myr a 5 Gyr, con el objetivo de estudiar el litio como indicador de edad para estrellas de tipos tardíos FGK en la pre-secuencia principal y secuencia principal, y de esta forma llegar a una calibración empírica de la relación Li-edad. Comenzamos el estudio realizando un detallado análisis de pertenencia para obtener listas de estrellas candidatas para cada uno de los 42 cúmulos de la muestra, utilizando todos los parámetros disponibles, y basándonos en los siguientes criterios: En primer lugar, se lleva a cabo un estudio cinemático de las distribuciones de velocidades radiales, y se combina con el análisis de los movimientos propios y las paralajes proporcionadas por Gaia. Se utilizan indicadores de gravedad como log g y el índice γ para descartar contaminantes gigantes de campo, y de esta xiii xiv Resumen forma obtenemos, como resultado paralelo, un número de gigantes ricas en Li que listamos por su interés. Reforzamos las selecciones astrométricas utilizando la fotometría de Gaia en dia- gramas color−magnitud, y usamos también la metalicidad [Fe/H] para descartar contaminantes que pudieran quedar en la selección. Con todo esto, terminamos estudiando las candidatas en diagramas de EW (Li) frente a Teff , y por fin obtenemos listas finales de candidatas. Todos estos análisis de pertenencia se han complementado con una minuciosa búsqueda bibliográfica de los cúmulos de la muestra, recopilando todos los datos previos sobre abundancias de Li, estimaciones de edades, velocidades y metalicidades, y estudios previos de pertenencia. Obtenidas las selecciones de candidatas para todos los cúmulos de la muestra, a continuación hemos llevado a cabo un estudio comparativo para poder cuantificar las dispersiones de Li ob- servadas en cada cúmulo, y analizar su dependencia con diferentes parámetros derivados de las observaciones espectroscópicas de GES: rotación, indicadores de acreción, actividad cromosférica (Hα) y metalicidad. Para el estudio de la rotación usamos tanto las velocidades de rotación pro- porcionadas por GES (vsini), como una serie de períodos obtenidos de la literatura, incluyendo datos de CoRoT, Kepler, K2 y TESS. Con la ayuda de diferentes tipos de gráficas y figuras, hemos estudiado y confirmado varias correlaciones y comportamientos descritos en la literatura: Observamos, por ejemplo, que candidatas con más litio tienden a ser más rápidas rotadoras y usualmente también presentan niveles más altos de actividad. Por último, hemos observado también cómo la metalicidad puede influir en el nivel de disminución de Li para cúmulos de las mismas edades según sean más o menos metálicos. Con toda esta información y teniendo todos estos efectos en cuenta, pasamos a la última parte del proyecto, la de calibrar una relación Li-edad. Para ello hemos creado una serie de envolventes empíricas de litio para edades claves de cúmulos de nuestra muestra, desde unos pocos Myr a varios Gyr. Para obtener envolventes de la manera más completa posible, hemos delimitado también la zona de la LDB (el límite de disminución de litio) para los cúmulos con edades de 15-500 Myr, con ayuda de varios modelos. Una aplicación de estas envolventes a la hora de usar el litio como indicador de edad es poder representar estrellas de edad desconocida en diagramas de EW (Li) frente a Teff y usarlas como guía para estimar sus edades. Como trabajo futuro, tenemos como objetivo principal utilizar esta relación Li-edad y las envolventes que hemos obtenido para poder estimar las edades de estrellas de campo observadas por GES cuya edad es aún desconocida, y así también confirmar su pertenencia a diferentes grupos cinemáticos estelares de diferentes edades. Otro punto de interés adicional es el estudio de las gigantes ricas en litio observadas en el campo de estos cúmulos durante el análisis de pertenencia, dada la naturaleza excepcional de estas estrellas y su utilidad a la hora de entender el comportamiento del litio estelar. Abstract Lithium is a very fragile element that is easily destroyed in stellar interiors. In solar-type and lower mass stars, lithium is slowly being depleted and its surface abundance decreases over time. For this reason, lithium is a very sensitive tracer of stellar evolution, and is especially relevant in the determination of the age of stellar clusters. The lithium abundance (derived from the Li 6707.76 Å line) observed in late-type stars is strongly age-dependent, but also shows a complex pattern depending on several parameters such as rotation, chromospheric activity, metallicity, mixing mechanisms, convection structure, and magnetic activity. The best way to calibrate these effects is to analyse and calibrate coeval groups of stars, such as open clusters and associations. This project has made use of data provided by the Gaia-ESO Survey (GES), a large, public spectroscopic survey that provides an homogeneous overview of the distribution of kinematics, dynamical structure and chemical compositions in the Galaxy. GES has measured data for a great number of stars, as well as near 100 open clusters, from 2011 until 2018. This survey uses the multi-object spectrograph FLAMES on the Very Large Telescope (ESO, Chile) to ob- tain both high resolution spectra with UVES (Ultraviolet and Visual Echelle Spectrograph) and medium resolution spectra with GIRAFFE. As part of the UCM GES node, in the first stages of this thesis project I performed an exten- sive analysis of the UVES spectra, manually measuring the equivalent widths (both the Li I line at 6707.76 Å and the adjacent Fe I line at 6707.43 Å) for all UVES spectra, in the context of the homogenization of what then was the fourth data release of GES (iDR4). For all the analysis in the present project, however, we have updated all results using the last GES data release, iDR6, as well as the data provided by Gaia EDR3. The present thesis, entitled The lithium-age relation: Calibration with open clusters and as- sociations, is a large scale work in which we use a series of 42 open clusters and associations observed by GES, ranging in ages from 1 Myr to 5 Gyr, with the aim of studying lithium as an age indicator for pre- and main-sequence FGK late-type stars, and in this way calibrating an empirical Li-age relation. Our first step in this study was to perform a thorough membership analysis in order to obtain lists of candidate members for all 42 clusters in our sample, making use of all available GES pa- rameters, and based on the following criteria: Firstly, we studied the radial velocity distributions of each cluster to obtain probable kinematic members, and we combined this kinematic selection with an analysis of the proper motions and parallaxes provided by Gaia. Gravity indicators such as log g and the γ index enabled us to discard field giant contaminants, and in this way we also obtained, as an additional result of the membership analysis, a series of Li-rich giant stars that we have listed in this work given their interest. We also used photometry from Gaia in colour−magnitude diagrams (CMDs) to confirm the membership of the astrometric selections, as xv xvi Abstract well as [Fe/H] metallicity, which helped rule out further contaminants which might still remain in the list. Finally, we studied lithium as a final criterion by plotting the candidates in EW (Li) vs Teff diagrams, and thus obtained the final lists of candidate stars. All these membership analyses were complemented with detailed bibliographical searches for all clusters in the sample, compil- ing all previous data regarding Li abundances, age estimations, velocities and metallicities, as well as existing membership studies. Having obtained the member selections for all clusters in the sample, our next step was to conduct a comparative study that allowed us to quantify the observable lithium dispersion in each cluster, and analyse in detail its dependence with several other stellar parameters derived from the GES spectroscopic observations: rotation, accretion indicators, the level of chromospheric activity (Hα), and metallicity. For the study of rotation, we used both rotational velocities provided by GES (vsini), as well as a series of periods obtained from the literature, including CoRoT, Kepler, K2 and TESS measurements. With the aid of several types of figures and dia- grams, we studied and confirmed the findings and correlations described in former publications: We found, for example, that members with higher values of Li tended to be faster rotators and often also had higher levels of activity. Lastly, we additionally observed the effects of metallicity in the Li depletion of coeval clusters for those which are metal-rich or metal-poor. Taking all these effects into account, all this information allowed us to finally calibrate a Li-age relation as the final part of this project. In order to do so, we created a series of empirical lithium envelopes for key ages in our cluster sample, from a few Myr to several Gyr. And to be able to obtain the most complete envelopes possible, we have also constrained the lithium depletion boundary (LDB) for those clusters in the 15-500 Myr age range, with the aid of several models. One of the applications of these lithium envelopes when it comes to using lithium as an effective age indicator is to plot field stars whose age is yet unknown in EW (Li) vs Teff diagrams, and so use them as references and a guide to estimate their ages. Regarding future work, our main objective is to use this Li-age relation and the envelopes we have obtained to estimate age ranges for GES field stars whose ages are still unknown, as well as confirm the membership of these field stars to stellar kinematic groups of different ages. An additional point of interest is the study of the unknown Li-rich giant stars observed in the field of these clusters, given their exceptional nature and their usefulness to further understand lithium in stars. Contents Acknowledgements xi Resumen xiii Abstract xv List of Figures xix List of Tables xxv 1 Introduction 1 1.1 Lithium as an age indicator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Stellar nucleosynthesis and Li production . . . . . . . . . . . . . . . . . . 1 1.1.2 Lithium depletion for FGKM stars . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 The lithium depletion boundary (LDB) . . . . . . . . . . . . . . . . . . . 8 1.1.4 Open clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.1.5 Li-rich giants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2 Calibrating the Li-age relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.1 Lithium and rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.2.2 Lithium and activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2.3 Lithium and accretion processes . . . . . . . . . . . . . . . . . . . . . . . . 22 1.2.4 Lithium and metallicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.3 Data surveys and missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.3.1 The Gaia-ESO Survey (GES) . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.3.2 Gaia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.3.3 CoRoT, Kepler, K2, and TESS . . . . . . . . . . . . . . . . . . . . . . . . 29 1.4 Description of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2 Cluster sample and membership selections 33 2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.1.1 GES spectra and data reduction . . . . . . . . . . . . . . . . . . . . . . . 33 2.1.2 Cluster sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.2 Selection criteria and membership analysis . . . . . . . . . . . . . . . . . . . . . . 42 2.2.1 Kinematic selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.2.2 Proper motions and parallaxes . . . . . . . . . . . . . . . . . . . . . . . . 48 2.2.3 Colour-magnitude diagrams (CMDs) . . . . . . . . . . . . . . . . . . . . . 53 2.2.4 Gravity indicators: Kiel diagram and γ index . . . . . . . . . . . . . . . . 54 2.2.5 Metallicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.2.6 Lithium content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.2.7 Comparison with other Gaia studies . . . . . . . . . . . . . . . . . . . . . 63 2.3 Identification of giant and non-giant contaminants . . . . . . . . . . . . . . . . . 65 xvii xviii Contents 2.4 Cluster member selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.4.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3 Dependence with rotation, activity and metallicity 77 3.1 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.1.1 vsini and Prot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.1.2 The Li-rotation relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.2 Chromospheric activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.2.1 The Li-activity relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.3 Colour-rotation and colour-activity diagrams . . . . . . . . . . . . . . . . . . . . 91 3.4 [Fe/H] metallicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4 The Li-age relation: Creating Li envelopes 105 4.1 Empirical lithium envelopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.2 Evolutionary models and the LDB . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5 Summary, conclusions and future work 125 5.1 Results and scientific prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 A List of publications 135 A.1 In this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 A.1.1 Published in refereed journals . . . . . . . . . . . . . . . . . . . . . . . . . 135 A.1.2 Conference proceedings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 A.2 Additional publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.2.1 Published in refereed journals . . . . . . . . . . . . . . . . . . . . . . . . . 136 B Cluster selections: Individual notes of Chapter 2 and 3 137 B.1 SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) . . . . . . . . . . . 137 B.2 Intermediate-age clusters (age= 50–700 Myr) . . . . . . . . . . . . . . . . . . . . 158 B.3 Old clusters (age > 700 Myr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 C Individual figures of Chapter 2 189 C.1 Young clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 C.2 Intermediate-age clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 C.3 Old clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 D Long tables of Chapter 2 233 E Individual figures of Chapter 3 241 E.1 Young clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 E.2 Intermediate-age clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 E.3 Old clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 F Tables for the empirical Li envelopes of Chapter 4 287 Bibliography 297 List of Figures 1.1 Primordial nucleosynthesis and the creation of Li . . . . . . . . . . . . . . . . . 1 1.2 The Li Ispectral line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Stellar spectral types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Lithium depletion as a function of colour and spectral type . . . . . . . . . . . 4 1.5 Timescales of Li depletion (I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.6 Timescales of Li depletion (II) . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.7 Li abundance as a function of age for solar-type stars . . . . . . . . . . . . . . 7 1.8 The Lithium depletion boundary (LDB) . . . . . . . . . . . . . . . . . . . . . . 8 1.9 Locating the LDB for NGC 2547 . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.10 The Pleiades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.11 HR diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.12 Study of Li-rich giants in Magrini et al. (2021b) . . . . . . . . . . . . . . . . . 12 1.13 Calibrating the ages of stars with a Li-age relation . . . . . . . . . . . . . . . . 14 1.14 The Li-rotation connection for the Pleiades (I) . . . . . . . . . . . . . . . . . . 15 1.15 The Li-rotation connection for the Pleiades (II) . . . . . . . . . . . . . . . . . . 16 1.16 The Li-rotation connection for PMS stars . . . . . . . . . . . . . . . . . . . . . 17 1.17 The Li-activity connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.18 Rotation-activity connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.19 Li-activity connection for IC 4665 and the Pleiades . . . . . . . . . . . . . . . . 21 1.20 Enhancement of the Li Iline due to accretion . . . . . . . . . . . . . . . . . . . 23 1.21 Li abundance as a function of cluster metallicity from Randich et al. (2020) . . 25 1.22 Map of observed GES targets on the sky. . . . . . . . . . . . . . . . . . . . . . 26 1.23 The outputs of the complementary GES and Gaia surveys. . . . . . . . . . . . 27 1.24 An artist’s concept of the Gaia spacecraft. . . . . . . . . . . . . . . . . . . . . 28 1.25 An illustration of the Transiting Exoplanet Survey Satellite (TESS). . . . . . . 30 2.1 FLAMES and UVES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 Giraffe spectrograph general layout. . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3 Gaia-ESO Survey data flow schematic. . . . . . . . . . . . . . . . . . . . . . . . 35 2.4 An overview of the Gaia-ESO Survey data flow system. . . . . . . . . . . . . . 36 2.5 Example of the initial TAME measurements of the Li Iline for iDR4 NGC 6705 spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.6 The Li Iand Fe Ilines in two NGC 6705 iDR4 spectra plotted with IRAF. . . . 38 2.7 RV selection for stars in NGC 6705. . . . . . . . . . . . . . . . . . . . . . . . . 44 2.8 Gaussian fit of the RV distribution for NGC 6705 members . . . . . . . . . . . 45 2.9 Example of the use of the boxplot command. . . . . . . . . . . . . . . . . . . . 45 2.10 pmra-versus-pmdec proper motions diagram for NGC 2516. . . . . . . . . . . . 49 2.11 Distributions of parallaxes for NGC 2516. . . . . . . . . . . . . . . . . . . . . . 51 2.12 CMD showing the final candidate selection of IC 2602. . . . . . . . . . . . . . . 53 2.13 Kiel diagram for Trumpler 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.14 Spectral index γ as a function of Teff for IC 2602. . . . . . . . . . . . . . . . . 55 xix xx List of figures 2.15 Histograms of metallicity for NGC 6705. . . . . . . . . . . . . . . . . . . . . . . 56 2.16 Distributions of metallicity for NGC 6705. . . . . . . . . . . . . . . . . . . . . 57 2.17 EW (Li)-versus-Teff diagram for IC 2602. . . . . . . . . . . . . . . . . . . . . . 60 2.18 EW (Li)-versus-Teff diagram for NGC 6633. . . . . . . . . . . . . . . . . . . . . 61 2.19 Strong accretors in EW (Li)-versus-Teff diagram for NGC 2264. . . . . . . . . . 62 2.20 EW (Li)-versus-Teff diagram for the Li-rich giant outliers. . . . . . . . . . . . . 65 2.21 Li-rich giant outliers in Kiel and γ index-versus-Teff diagrams. . . . . . . . . . 66 2.22 Giant and NG contaminants in the field of the young iDR4 cluster sample . . . 68 2.23 Giant and NG contaminants in the field of the intermediate-age and old iDR4 cluster sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.24 EW (Li)-versus-Teff diagrams for all clusters . . . . . . . . . . . . . . . . . . . . 72 2.25 γ as a function of Teff and Kiel diagrams for all clusters of the sample . . . . . 73 3.1 Prot-versus-vsini for NGC 2264. . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.2 Prot-versus-vsini for NGC 2516. . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3 EW (Li)-versus-Teff diagram colour-coded by Prot for NGC 2264 . . . . . . . . 80 3.4 EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2264. . . . . . . . 80 3.5 EW (Li)-versus-Teff diagram colour-coded by vsini for IC 2391, IC 2602 and IC 4665 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.6 EW (Li)-versus-Teff diagram colour-coded by Prot for NGC 2547 . . . . . . . . 83 3.7 EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2547 . . . . . . . . 83 3.8 EW (Li)-versus-Teff diagram colour-coded by Prot for NGC 2516 . . . . . . . . 84 3.9 EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2516 . . . . . . . . 84 3.10 EW (Li)-versus-Teff diagram colour-coded by Prot for NGC 3532 . . . . . . . . 85 3.11 EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 3532 . . . . . . . . 85 3.12 EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2355 . . . . . . . . 86 3.13 EW (Li)-versus-Teff diagram colour-coded by vsini for Trumpler 20 . . . . . . . 86 3.14 EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2243 . . . . . . . . 87 3.15 EW (Li)-versus-Teff diagram colour-coded by vsini for M67 . . . . . . . . . . . 87 3.16 EW (Li)-versus-Teff diagram colour-coded by Hα for NGC 2264 . . . . . . . . . 89 3.17 EW (Li)-versus-Teff diagram colour-coded by Hα for IC 2391, IC 2602 and IC 4665 89 3.18 EW (Li)-versus-Teff diagram colour-coded by Hα for NGC 2516 . . . . . . . . . 90 3.19 EW (Li)-versus-Teff diagram colour-coded by Hα for Trumpler 20 . . . . . . . . 91 3.20 EW (Li)-versus-Teff diagram colour-coded by Hα for NGC 2243 . . . . . . . . . 91 3.21 Rotation as a function of age . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.22 Colour-rotation and colour-period diagrams for the young clusters . . . . . . . 94 3.23 Colour-rotation and colour-period diagrams for the intermediate-age clusters . 95 3.24 Colour-rotation and colour-period diagrams for the old clusters . . . . . . . . . 96 3.25 Example of a rotation period distribution in Popinchalk et al. (2021) . . . . . . 100 3.26 Influence of metallicity: NGC 2244 and NGC 2264 . . . . . . . . . . . . . . . . 101 3.27 Influence of metallicity: NGC 6705 and NGC 3532 . . . . . . . . . . . . . . . . 101 3.28 Influence of metallicity: NGC 6633 and Hyades . . . . . . . . . . . . . . . . . . 102 3.29 Influence of metallicity: NGC 2355 and NGC 6802 . . . . . . . . . . . . . . . . 102 3.30 Influence of metallicity: Pismis 15 and Trumpler 20 . . . . . . . . . . . . . . . 103 3.31 Influence of metallicity: NGC 2243 and M67 . . . . . . . . . . . . . . . . . . . 103 4.1 Previous empirical Li envelopes used in this work . . . . . . . . . . . . . . . . . 105 4.2 Empirical Li envelopes for the SFR cluster sample . . . . . . . . . . . . . . . . 107 4.3 Empirical Li envelopes for the young cluster sample . . . . . . . . . . . . . . . 108 4.4 Empirical Li envelopes for the intermediate-age cluster sample . . . . . . . . . 109 List of figures xxi 4.5 Empirical Li envelopes for the old cluster sample . . . . . . . . . . . . . . . . . 110 4.6 Empirical Li envelopes for the young, intermediate-age and old clusters . . . . 118 4.7 Empirical Li envelopes obtained for the whole cluster sample . . . . . . . . . . 119 4.8 Evolutionary models from Baraffe et al. (2015) . . . . . . . . . . . . . . . . . . 120 4.9 Li envelope and LDB region for IC 2391, IC 2602 and IC 4665 . . . . . . . . . 122 5.1 Young associations and stellar kinematic groups in (U, V) Galactic velocity plane131 5.2 Effect of rotation and starspot coverage . . . . . . . . . . . . . . . . . . . . . . 132 B.1 Image of Rho Oph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 B.2 Image of Trumpler 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 B.3 Image of NGC 2244 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 B.4 Image of NGC 2264 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 B.5 Image of NGC 2547 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 B.6 Image of NGC 6405 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 B.7 Image of NGC 6705 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 B.8 Image of NGC 3532 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 B.9 Image of NGC 2477 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 B.10 Image of Trumpler 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 C.1 Individual figures for NGC 6530 . . . . . . . . . . . . . . . . . . . . . . . . . . 190 C.7 Individual figures for ρ Oph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 C.13 Individual figures for Trumpler 14 . . . . . . . . . . . . . . . . . . . . . . . . . 192 C.19 Individual figures for Cha I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 C.25 Individual figures for NGC 2244 . . . . . . . . . . . . . . . . . . . . . . . . . . 194 C.31 Individual figures for NGC 2264 . . . . . . . . . . . . . . . . . . . . . . . . . . 195 C.37 Individual figures for λ Ori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 C.43 Individual figures for Col 197 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 C.49 Individual figures for γ Vel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 C.53 Individual figures for NGC 2232 . . . . . . . . . . . . . . . . . . . . . . . . . . 199 C.59 Individual figures for NGC 2547 . . . . . . . . . . . . . . . . . . . . . . . . . . 200 C.63 Individual figures for IC 2391 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 C.69 Individual figures for IC 2602 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 C.75 Individual figures for IC 4665 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 C.81 Individual figures for NGC 2451 A and B . . . . . . . . . . . . . . . . . . . . . 204 C.85 Individual figures for NGC 6405 . . . . . . . . . . . . . . . . . . . . . . . . . . 206 C.91 Individual figures for Blanco 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 C.97 Individual figures for NGC 6067 . . . . . . . . . . . . . . . . . . . . . . . . . . 208 C.103 Individual figures for NGC 6649 . . . . . . . . . . . . . . . . . . . . . . . . . . 209 C.107 Individual figures for NGC 2516 . . . . . . . . . . . . . . . . . . . . . . . . . . 210 C.113 Individual figures for NGC 6709 . . . . . . . . . . . . . . . . . . . . . . . . . . 211 C.119 Individual figures for NGC 6259 . . . . . . . . . . . . . . . . . . . . . . . . . . 212 C.125 Individual figures for NGC 6705 . . . . . . . . . . . . . . . . . . . . . . . . . . 213 C.131 Individual figures for Berkeley 30 . . . . . . . . . . . . . . . . . . . . . . . . . . 214 C.137 Individual figures for NGC 6281 . . . . . . . . . . . . . . . . . . . . . . . . . . 215 C.143 Individual figures for NGC 3532 . . . . . . . . . . . . . . . . . . . . . . . . . . 216 C.149 Individual figures for NGC 4815 . . . . . . . . . . . . . . . . . . . . . . . . . . 217 C.155 Individual figures for NGC 6633 . . . . . . . . . . . . . . . . . . . . . . . . . . 218 C.161 Individual figures for NGC 2477 . . . . . . . . . . . . . . . . . . . . . . . . . . 220 C.167 Individual figures for Trumpler 23 . . . . . . . . . . . . . . . . . . . . . . . . . 221 xxii List of figures C.173 Individual figures for Berkeley 81 . . . . . . . . . . . . . . . . . . . . . . . . . . 222 C.179 Individual figures for NGC 2355 . . . . . . . . . . . . . . . . . . . . . . . . . . 223 C.185 Individual figures for NGC 6802 . . . . . . . . . . . . . . . . . . . . . . . . . . 224 C.191 Individual figures for NGC 6005 . . . . . . . . . . . . . . . . . . . . . . . . . . 225 C.197 Individual figures for Pismis 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 C.203 Individual figures for Melotte 71 . . . . . . . . . . . . . . . . . . . . . . . . . . 227 C.209 Individual figures for Pismis 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 C.215 Individual figures for Trumpler 20 . . . . . . . . . . . . . . . . . . . . . . . . . 229 C.221 Individual figures for Berkeley 44 . . . . . . . . . . . . . . . . . . . . . . . . . . 230 C.227 Individual figures for NGC 2243 . . . . . . . . . . . . . . . . . . . . . . . . . . 231 C.233 Individual figures for M67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 E.1 Rotation and activity: NGC 6530. . . . . . . . . . . . . . . . . . . . . . . . . . 242 E.2 Rotation and activity: ρ Oph. . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 E.3 Rotation: Trumpler 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 E.4 Rotation and activity: Cha I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 E.5 Rotation and activity: NGC 2244. . . . . . . . . . . . . . . . . . . . . . . . . . 246 E.6 Rotation and activity: NGC 2264. . . . . . . . . . . . . . . . . . . . . . . . . . 247 E.7 Rotation and activity: λ Ori. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 E.8 Rotation and activity: Col 197. . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 E.9 Rotation and activity: γ Vel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 E.10 Rotation and activity: γ Vel A. . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 E.12 Rotation and activity: γ Vel B. . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 E.14 Rotation and activity: NGC 2232. . . . . . . . . . . . . . . . . . . . . . . . . . 252 E.15 Rotation and activity: NGC 2547. . . . . . . . . . . . . . . . . . . . . . . . . . 253 E.16 Rotation and activity: NGC 2547 A. . . . . . . . . . . . . . . . . . . . . . . . . 254 E.17 Rotation and activity: NGC 2547 B. . . . . . . . . . . . . . . . . . . . . . . . . 255 E.18 Rotation and activity: IC 2391. . . . . . . . . . . . . . . . . . . . . . . . . . . 256 E.19 Rotation and activity: IC 2602. . . . . . . . . . . . . . . . . . . . . . . . . . . 257 E.20 Rotation and activity: IC 4665. . . . . . . . . . . . . . . . . . . . . . . . . . . 258 E.21 Rotation and activity: NGC 2451. . . . . . . . . . . . . . . . . . . . . . . . . . 259 E.22 Rotation and activity: NGC 2451 A. . . . . . . . . . . . . . . . . . . . . . . . . 260 E.24 Rotation and activity: NGC 2451 B. . . . . . . . . . . . . . . . . . . . . . . . . 260 E.26 Rotation and activity: NGC 6405. . . . . . . . . . . . . . . . . . . . . . . . . . 261 E.27 Rotation and activity: Blanco 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 262 E.28 Rotation and activity: NGC 6067. . . . . . . . . . . . . . . . . . . . . . . . . . 263 E.29 Rotation: NGC 6649. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 E.30 Rotation and activity: NGC 2516. . . . . . . . . . . . . . . . . . . . . . . . . . 265 E.31 Rotation and activity: NGC 6709. . . . . . . . . . . . . . . . . . . . . . . . . . 266 E.32 Rotation and activity: NGC 6259. . . . . . . . . . . . . . . . . . . . . . . . . . 267 E.33 Rotation and activity: NGC 6705. . . . . . . . . . . . . . . . . . . . . . . . . . 268 E.34 Rotation: Berkeley 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 E.35 Rotation: NGC 6281. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 E.36 Rotation and activity: NGC 3532. . . . . . . . . . . . . . . . . . . . . . . . . . 270 E.37 Rotation: NGC 4815. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 E.38 Rotation and activity: NGC 6633. . . . . . . . . . . . . . . . . . . . . . . . . . 272 E.39 Rotation and activity: NGC 2477. . . . . . . . . . . . . . . . . . . . . . . . . . 274 E.40 Rotation: Trumpler 23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 E.41 Rotation and activity: Berkeley 81. . . . . . . . . . . . . . . . . . . . . . . . . 276 E.42 Rotation: NGC 2355. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 List of tables xxiii E.43 Rotation and activity: NGC 6802. . . . . . . . . . . . . . . . . . . . . . . . . . 278 E.44 Rotation and activity: NGC 6005. . . . . . . . . . . . . . . . . . . . . . . . . . 279 E.45 Rotation and activity: Pismis 18. . . . . . . . . . . . . . . . . . . . . . . . . . 280 E.46 Rotation: Melotte 71. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 E.47 Rotation and activity: Pismis 15. . . . . . . . . . . . . . . . . . . . . . . . . . 282 E.48 Rotation and activity: Trumpler 20. . . . . . . . . . . . . . . . . . . . . . . . . 283 E.49 Rotation: Berkeley 44. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 E.50 Rotation and activity: NGC 2243. . . . . . . . . . . . . . . . . . . . . . . . . . 285 E.51 Rotation and activity: M67. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 List of Tables 1.1 Structure of late-type ZAMS stars. . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1 WG11 and WG12 nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2 Age estimates, reddening, distance to the Sun, and GES and Gaia membership studies from the literature for the 15 SFRs and young clusters in our sample. . . 40 2.3 Age estimates, reddening, distance to the Sun, and GES and Gaia membership studies from the literature for the 26 intermediate-age and old clusters in our sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4 Fit parameters and RV members for the sample clusters. . . . . . . . . . . . . . 48 2.5 Fit parameters and parallax membership for the sample clusters. . . . . . . . . . 52 2.6 Fit parameters and metallicity membership for the sample clusters. . . . . . . . 59 2.7 Criteria for giant and non-giant outliers. . . . . . . . . . . . . . . . . . . . . . . . 67 2.8 Main results for the 42 open clusters analysed. . . . . . . . . . . . . . . . . . . . 74 2.9 Results and member percentages for the cluster sample. . . . . . . . . . . . . . . 75 3.1 Prot measurements from the literature. . . . . . . . . . . . . . . . . . . . . . . . . 77 4.1 Teff values from the evolutionary models of Baraffe et al. (2015) used in Chapter 4 to delimit the LDB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 D.1 Tables of Chapter 2: GES parameters . . . . . . . . . . . . . . . . . . . . . . . . 234 D.2 Tables of Chapter 2: Gaia parameters and Prot measurements . . . . . . . . . . 235 D.3 Tables of Chapter 2: Membership analysis and candidate selections . . . . . . . 235 D.4 NGC 2516 GES parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 D.6 NGC 2516 Gaia parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 D.7 NGC 2516 Prot measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 D.8 NGC 2516 membership analysis and selection . . . . . . . . . . . . . . . . . . . . 240 F.1 Upper Li envelope for NGC 6530 . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 F.2 Upper Li envelope for Rho Oph . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 F.3 Upper Li envelope for Trumpler 14 . . . . . . . . . . . . . . . . . . . . . . . . . . 288 F.4 Upper Li envelope for Cha I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 F.5 Upper Li envelope for NGC 2244 . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 F.6 Upper Li envelope for NGC 2264 . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 F.7 Upper Li envelope for λ Ori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 F.8 Upper Li envelope for Col 197 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 F.9 Upper Li envelope for γ Vel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 F.10 Lower Li envelope for γ Vel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 F.11 Upper Li envelope for NGC 2232 . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 F.12 Upper Li envelope for NGC 2547 A . . . . . . . . . . . . . . . . . . . . . . . . . 291 F.13 Upper Li envelope for NGC 2547 B . . . . . . . . . . . . . . . . . . . . . . . . . 291 F.14 Upper Li envelope for IC 2391, IC 2602 and IC 4665 . . . . . . . . . . . . . . . . 291 xxv xxvi List of tables F.15 Upper Li envelope for Blanco 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 F.16 Lower Li envelope for Blanco 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 F.17 Upper Li envelope for NGC 2516 . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 F.18 Lower Li envelope for NGC 2516 . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 F.19 Upper Li envelope for NGC 6709 . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 F.20 Lower Li envelope for NGC 6709 . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 F.21 Upper Li envelope for NGC 6705 . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 F.22 Lower Li envelope for NGC 6705 . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 F.23 Upper Li envelope for NGC 3532 . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 F.24 Lower Li envelope for NGC 3532 . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 F.25 Upper Li envelope for NGC 6633 . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 F.26 Upper Li envelope for NGC 2355 . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 F.27 Upper Li envelope for NGC 6802 . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 F.28 Upper Li envelope for NGC 6005 . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 F.29 Upper Li envelope for Pismis 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 F.30 Upper Li envelope for Trumpler 20 . . . . . . . . . . . . . . . . . . . . . . . . . . 296 F.31 Upper Li envelope for NGC 2243 . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 F.32 Upper Li envelope for M67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Chapter 1 Introduction 1.1 Lithium as an age indicator 1.1.1 Stellar nucleosynthesis and Li production Lithium (henceforth, Li), in the form of its main isotope 7Li, has the most complex origin and evolution out of all the elements in the periodic table. Li is one of the few chemical elements, alongside hydrogen (H) and helium (He), to be created in the first instants after the Big Bang, by means of the process known as primordial nucleosynthesis (see Fig. 1.1) (e.g., Pallavicini et al., 1990; Jeffries, 2014; Lyubimkov, 2016; Magrini et al., 2021b; Randich & Magrini, 2021; Romano et al., 2021). All elements heavier than Li were produced afterwards, mainly during the nucleosynthesis occurring in the stellar interiors. Figure 1.1: Creation of Li, alongside H and He, during primordial nucleosynthesis. Unstable nuclear species are marked by dashed boxes. Credit: Rauscher & Patkós (2011). The Li abundance measured today, however, is only in part the primordial one synthesized in the first few minutes of the Universe, as many destructive (see the process of Li depletion below in Subsect. 1.1.2) as well as constructive processes have occurred since (e.g., Magrini et al., 2021b; Randich & Magrini, 2021; Romano et al., 2021). The current Li abundance in the Universe, as observed in meteorites and young T-Tauri stars, has increased from the primordial value by means of a probable combination of stellar nucleosynthesis and spalliation processes in the in- terstellar medium (ISM) (e.g., Romano et al., 2021). Very young disc stars in the solar vicinity 1 2 Chapter 1. Introduction have Li abundances up to A(Li)=3.2, the modern Li abundance for Main Sequence (MS) stars (e.g., Jeffries, 2014; Lyubimkov, 2016; Randich & Magrini, 2021). As described in detail in studies such as Romano et al. (2021) and Randich & Magrini (2021), several sources of production for 7Li have been proposed to account for the increase from the Big Bang A(Li) to the meteoritic value, including the following: stellar nucleosynthesis through intermediate production of 7Be, later decaying to 7Li as the stellar convection carries it to cooler layers — this is the so-called Cameron-Fowler mechanism (also see the discussion on Li-rich giants and internal Li production below in Subsect. 1.1.5); Li production with the catalysis of a flux of neutrinos resulting from supernovas; thermonuclear runaways during classical nova explosions; red giants and ejecta from giant stars in the asymptotic giant branch (AGB); and spalliation of atoms in the ISM by cosmic rays (also see Lyubimkov, 2016; Magrini et al., 2021b). It is worth noting that none of these production mechanisms of Li have been accurately assessed as yet, and the study of the reconstruction of the history of Li enrichment of the Galaxy is still ongoing (Romano et al., 2021). Li continues to be one of the most mysterious chemical elements in the Universe, as its observ- able abundance in the atmosphere of different types of stars constantly comes into conflict with theoretical predictions (e.g., Pallavicini et al., 1990; Lyubimkov, 2016). A well-known unresolved issue regarding the Li abundance values in the Universe is the ‘Cosmological Li problem’, arising from the difference between the primordial abundance of Li predicted by the Big Bang nucle- osynthesis (BBN) and standard model of the Big Bang (SMBB), A(Li)=2.7, and the abundance inferred from observations of old Galactic halo stars that should not have depleted their 7Li, A(Li)=2.1–2.2, known as the ‘Lithium plateau’. (e.g., Jeffries, 2014; Lyubimkov, 2016; Randich & Magrini, 2021; Romano et al., 2021). Figure 1.2: This figure from López-Santiago et al. (2003) displays stellar spectra for the young star PW And (above), indicating a significant Li I line at 6707.76 Å, as well as the reference star GJ 706 (below), where we can also see the adjacent Fe I line at 6707.43 Å. Li is mainly observable through the spectral resonance lines of neutral Li, forming a doublet at 6707.76 Å and 6707.89 Å. The 6707.76 Å Li I line is also often blended with a Fe I line at 6707.43 Å (see Sect. 2.1) as exemplified in Fig. 1.2 (e.g., Pallavicini et al., 1992; Soderblom, 2010; Soderblom et al., 2014; Lyubimkov, 2016; Randich & Magrini, 2021). The strength of this Li doublet depends on the temperature and chemical abundances of the star. As we will see in the following Subsect. 1.1.2 when discussing Li depletion for late-type stars, the Li feature is strong 1.1. Lithium as an age indicator 3 for cool stars with a high Li content, and weaker for warmer stars which have experienced a higher amount of Li depletion. Due to its low ionization potential of 5.39 eV, a large fraction of stellar Li is in its ionized form, and the Li I lines are only observable in stars later than the A2–A3 spectral type (e.g., Randich & Magrini, 2021). Li is usually determined by measuring equivalent widths (EW (Li), see Sect. 2.1), and Li abundances, A(Li), can also be derived with the use of evolutionary models and curves of growth (see Sects. 2.1 and 4). Figure 1.3: Stellar spectral types, indicating for reference Teff ranges and key absorption line features. 1.1.2 Lithium depletion for FGKM stars Li is a very fragile element that is easily destroyed in stellar interiors, burning at temperatures above ∼ 2.5–3 x 106 K, corresponding to the temperature at the base of the convective zone of a solar-mass star on the zero-age main sequence (ZAMS) (e.g., Pallavicini et al., 1990; Siess et al., 2000; Casey et al., 2016; Castro et al., 2016; Magrini et al., 2021b; Randich & Magrini, 2021). For this reason, Li is slowly being depleted and its surface abundance decreases over time in solar-type and lower mass stars (Bouvier, 2008; Jeffries et al., 2014; Soderblom et al., 2014; Lyubimkov, 2016; Randich & Magrini, 2021). Given its fragility, Li is depleted from stellar atmospheres with the presence of any mechanism able to transport material from the photosphere and outer layers of the star to the hotter stellar interior. These transport mechanisms include convection, rotation-induced mixing, thermohaline instability (also see Subsect. 1.1.5), atomic difussion, overshooting, and mixing by internal grav- ity waves or magneto-hydrodynamic instabilities (e.g., Magrini et al., 2021b; Randich & Magrini, 2021; Romano et al., 2021). Because it only survives in the outer layers of a star, Li is a very sensitive tracer of stellar physics and evolution for PMS (pre-Main Sequence), MS and post-MS star. Li abundances are also particularly helpful to study the mixing mechanisms and transport processes at work in stellar interiors, including both convection (the sole process considered by the standard models) and non-standard mechanisms (see Sect. 1.2), given that more Li depletion will be observable with more vigorous internal transport processes to the hot central regions of the star (e.g., Sestito & Randich, 2005; Castro et al., 2016; Bouvier et al., 2018; Dumont et al., 2021a,b; Magrini et al., 2021b; Randich & Magrini, 2021). 4 Chapter 1. Introduction Figure 1.4: EW (Li) as a function of colour (left) and spectral type (right, a proxy of colour). The left diagram shows confirmed members of the β Pictoris association from Messina et al. (2016), while the figure on the right shows a selection of PMS stars, compared to the Li envelopes of well-known clusters (see Chapter 4), from Montes et al. (2009). Both figures reflect how stars from different spectral types deplete Li in a different way, with low values for F-type stars, maximum around GK stars, and a decrease for M-dwarfs until complete Li depletion. The plot from Messina et al. (2016) additionally shows undepleted M-type stars in the upper right of the figure (see Subsect. 1.1.3), while the diagram from Montes et al. (2009) also includes the regions for weak-line T-Tauri stars (WTTS), and post T-Tauri stars (PTTS). Table 1.1: Structure of late-type ZAMS stars. Spectral type Mass Structure Tsp > M3.5–M4 M< 0.35 M⊙ Fully convective M3.5–M4 > Tsp > F2 0.35 1.2 M⊙ Convective core, radiative envelope It is well-known that Li depletion depends on both age and mass (as well as metallicity and several other stellar parameters and mechanisms, as we will see in Sect. 1.2). For this reason, Li is one of the most sensitive indicators of stellar evolution, and it is particularly relevant for the study of the evolution of low-mass stars and for the determination of the age of stellar clusters (e.g., Soderblom et al., 1983; Barrado y Navascués, 2004; Soderblom, 2010; Jeffries et al., 2014; Soderblom et al., 2014; Castro et al., 2016; Lyubimkov, 2016; Rigliaco et al., 2016; Bouvier et al., 2018; Dumont et al., 2021b; Franciosini et al., 2021; Randich & Magrini, 2021). Given that Li starts to be depleted during the PMS phase and that young FGKM stars seem to always show a strong lithium feature (e.g., Soderblom, 2010; Soderblom et al., 2014), the presence of Li in stellar spectra is a relevant indicator of youth in late-type stars (see Fig. 1.2 for the distinct Li I line in the spectrum of a young star). Li being considered an excellent age calibrator for both PMS young low-mass stars and older MS solar-type stars, it has been extensively used to identify and characterize star-forming regions and young stellar populations (see Sect. 2.2.6), and also to derive cluster ages using the LDB method, as discussed in Subsect. 1.1.3 (e.g., Randich & Magrini, 2021). 1.1. Lithium as an age indicator 5 Figure 1.5: EW (Li) as a function of colour and spectral type for groups of stars, from Soderblom et al. (2014). This figure illustrates the empirical progression of Li depletion with age, observing that: i) The youngest stars (2–10 Myr) show negligible Li depletion; ii) M-dwarfs experience rapid depletion between 10 and 50 Myr; iii) K stars experience Li depletion on longer timescales, with increased scattering; iv) Little depletion occurs for G stars in the first 100 Myr. Because Li depletion increases with age and depends directly on temperature and mass, and thus, on spectral type (see Fig. 1.3), late-type FGKM stars will show different timescales and varying degrees of Li depletion depending on their temperature, their mass and their internal structure. For reference, Table 1.1 summarizes the differing internal structures of cool low-mass FGKM stars, from the completely convective mid- and late-M dwarfs, to the FGK stars with a radiative core and convective envelope (the majority of stars we will be studying in this work), the more massive F stars with a convective core and radiative envelope. Stellar mass is the primary parameter controlling Li depletion, followed by age as the sec- ond parameter, and chemical composition as the third (e.g., Soderblom et al., 1993; Barrado y Navascués, 2004; Franciosini et al., 2021). According to standard stellar models, at a given age solar-like and lower-mass FGKM stars show Li depletion increasing with decreasing mass (due to thicker convective envelopes), while stars more massive than the Sun undergo little or no de- pletion (e.g., Pallavicini et al., 1990; Umezu & Saio, 2000; Wilden et al., 2002; Soderblom, 2010; Soderblom et al., 2014; Dumont et al., 2021b; Randich & Magrini, 2021). For the lower-mass M stars, the surface abundance of Li is rapidly depleted when the core reaches the Li-burning temperature, and fully convective mid- to late-M dwarfs show no depletion at all, given that their central temperature never reaches the Li burning point (e.g., Jones et al., 1999; Soderblom et al., 2014; Franciosini et al., 2021) (also see the LDB in Subsect. 1.1.3). Two examples of the progression of Li depletion depending on mass and spectral type are illustrated in Fig. 1.4. Figs. 1.5 and 1.6 further show the progression of Li depletion with age, and also the effective- ness of Li depletion as an age indicator depending on spectral type (Randich, 2009; Soderblom, 2010; Soderblom et al., 2014). Li depletion is characterized by different timescales in the various age ranges, as follows: At very low ages (< 10 Myr) little or no depletion is expected. The timescale for significant lithium depletion for ages > 10 Myr ranges from 10–20 Myr in M-type 6 Chapter 1. Introduction Figure 1.6: EW (Li) as a function of colour for several clusters, from Soderblom (2010), showing the empirical progression of Li depletion with age from the SFR NGC 2264 (5 Myr), to the young clusters IC 2391, IC 2602, IC 4665 and NGC 2547 (30–50 Myr), the Pleiades (100 Myr), and the Hyades (625 Myr). T Tauri stars are undepleted in Li and show little scatter in EW (Li), while the Pleiades have a significant scatter. stars, ∼ 100 Myr in K-type stars, to ∼ 1 Gyr in F- and G-type stars (e.g., Soderblom et al., 1983; Sestito & Randich, 2005; Randich, 2009; Soderblom, 2010; Delgado Mena et al., 2015; Jeffries et al., 2014; Soderblom et al., 2014; Rigliaco et al., 2016; Franciosini et al., 2021). Regarding the use of Li depletion as an age calibrator, we also note that for undepleted stars only an upper limit to an age can be estimated, while for completely depleted stars only a lower limit is possible (Jeffries, 2014; Soderblom et al., 2014). Classical stellar evolution predicts a noticeable level of Li depletion during the PMS phase for the lower-mass stars, at a rate that strongly increases for late-K and M dwarfs, the lowest- mass stars for which the base of the convective envelope is deep enough to reach the Li-burning temperature. On the other hand, F and G-type stars show very weak levels of Li destruction and seem to retain essentially their primordial Li abundance even well after their arrival on the ZAMS (thus, Li depletion can rarely be used to estimate reliable ages for F and early-G stars in this phase) (also see Bouvier et al., 2018). As mentioned earlier, fully convective M-type stars start to deplete Li at ages 5–10 Myr and destroy it completely in the span of a few Myr, while Li remains undepleted for very low-mass stars unable to reach the Li-burning temperature (this is discussed in more detail in the following Subsect. 1.1.3 on the LDB). As they contract towards 1.1. Lithium as an age indicator 7 Figure 1.7: Li abundance as a function of age for solar-type stars, from Randich (2009). Open symbols and filled circles indicate cluster targets from Sestito & Randich (2005) and Randich (2009), respectively. The figure shows the patterns of negligible Li depletion for stars up to 100 Myr, followed by the trend of Li depletion increasing with age until 1 Gyr, when the trend becomes bimodal. the ZAMS, the stellar interiors of the higher-mass PMS stars reach temperatures high enough to burn Li, with a focus on K dwarfs, resulting in rapid mixing and Li destruction, although the creation of a radiative core only results in a partial and mass-dependent depletion of pho- tospheric Li (e.g., Zapatero Osorio et al., 2002; Barrado y Navascués, 2004; Sestito & Randich, 2005; Soderblom, 2010; Jeffries, 2014; Soderblom et al., 2014; Castro et al., 2016; Lyubimkov, 2016; Dumont et al., 2021b; Franciosini et al., 2021; Randich & Magrini, 2021; Binks et al., 2022, in prep.). In the PMS phase, the trend of declining Li abundance with age is particularly strong for the K dwarfs, and in later stages stars in this spectral type are key to estimate ages in a wide age range from 20–50 Myr till the complete depletion of Li at 500 Myr (Soderblom et al., 2014). Most Li depletion occurs before stars reach the ZAMS, with some continuing depletion up to 1–2 Gyr at most (e.g., Wilden et al., 2002; Sestito & Randich, 2005; Soderblom, 2010). On reaching the ZAMS, G and early-K stars show steadily lower Li abundances for increasingly older cluster ages, while the more massive F-type stars do not present significant Li depletion due to their higher masses and thinner convective envelopes. In general, little change is seen in the Li abundances of late-F and early-G stars with age (e.g., Pallavicini et al., 1992; Martín & Montes, 1997; Soderblom et al., 1993; Barrado y Navascués, 2004; Sestito & Randich, 2005; Soderblom, 2010; Soderblom et al., 2014; Castro et al., 2016; Dumont et al., 2021b). For stars in the MS phase, standard evolutionary models yield too much Li depletion, and so non-convective extra mixing processes are needed to be taken into account in order to explain the observable Li abundances of FGKM stars in clusters of different ages (see Sect. 1.2) (e.g., Umezu & Saio, 2000; Barrado y Navascués, 2004; Randich, 2009; Soderblom, 2010; Jeffries, 2014). In addition to the general decline of surface Li abundance for GK stars with age during the ZAMS and MS phases, a group of F-type stars with Teff in the narrow range of 6400–6800 K fall into the so-called ‘Li dip’, which appears in clusters older than 200 Myr, and whose depth increases with the age of the clusters. This phenomenon is still not well understood, but it 8 Chapter 1. Introduction probably involves rotation-driven non-convective mixing (e.g., Umezu & Saio, 2000; Sestito & Randich, 2005; Jeffries, 2014; Delgado Mena et al., 2015; Barrado et al., 2016; Lyubimkov, 2016; Anthony-Twarog et al., 2018; Twarog et al., 2020; Dumont et al., 2021b; Randich & Magrini, 2021). Cooler stars with spectral types after late-F become fainter and are harder to study in progressively older clusters (e.g., Jeffries, 2014). Beyond 1 Gyr, Li depletion becomes bimodal, with a fraction of stars not undergoing any additional depletion, while others continue to deplete Li at a rapid rate (see Fig. 1.7). The reason for this dychotomy is as yet unclear (e.g., Sestito & Randich, 2005; Randich, 2009; Jeffries, 2014). The destruction of Li also becomes particularly important after the MS, with Li abundances decreasing by a factor from 30 to 60 in what is known as the first dredge-up event (e.g., Magrini et al., 2021b; Randich & Magrini, 2021). Standard stellar evolution models predict that the Li abundance of a star should continue to decrease as it ascends the red giant branch (RGB), reaching A(Li)<1.5 (e.g., Casey et al., 2016; Lyubimkov, 2016; Randich & Magrini, 2021). The existence of Li-rich giants would thus require of non-standard models to be able to explain the synthesis of new Li for these stars, as further discussed in Subsect. 1.1.5 (e.g., Umezu & Saio, 2000; Casey et al., 2016; Lyubimkov, 2016). We also note that GK stars also present a substantial spread of Li at a given temperature, particularly for young and intermediate-age clusters in a 10–150 Myr age range (see Fig. 1.6). This scatter is something which standard evolutionary models also fail to predict, and it is not a result of surface inhomogeneities such as starspots or the presence of planets, but instead appears to be a real dispersion that can be explained by taking into account non-standard models and the influence on Li depletion of stellar parameters such as rotation (see Sect. 1.2) (e.g., Simon et al., 1985; Randich & Pallavicini, 1991; Sestito & Randich, 2005; Soderblom, 2010; Jeffries, 2014; Soderblom et al., 2014; Flores Soriano et al., 2015). 1.1.3 The lithium depletion boundary (LDB) Figure 1.8: The Lithium depletion boundary (LDB): A(Li)-versus-Teff for the Pleiades, α Persei and IC 2391 (left), and location of the LDB and its relation with cluster age (right), from Barrado y Navascués et al. (2011). The LDB is clearly marked, corresponding to very narrow ranges of Teff values or magnitudes (in a CMD, see Fig. 1.9). The lithium depletion boundary (henceforth, LDB) technique refers to a method to calibrate 1.1. Lithium as an age indicator 9 the ages of open clusters based on the determination of the Li abundances of those cluster stars whose masses are at the hydrogen-burning limit. As PMS low-mass stars (with masses < 0.6M⊙) contract towards the ZAMS, their core temperatures rise, and, if these stars have masses higher than 0.06 M⊙, they will become hot enough to burn Li. In fully convective stars the PMS phase is additionally short, and so Li depletion occurs rapidly. On the other hand, very low-mass M-type stars with masses < 0.06 M⊙ never reach the sufficient temperature in their cores to destroy their Li, and so these stars retain all their original Li content (e.g., Burke et al., 2004; Cargile et al., 2010; Soderblom, 2010; Jeffries, 2014; Soderblom et al., 2014; Binks et al., 2022, in prep.). The LDB thus refers to the luminosity at the sharp, age-dependent transition between the low-mass, low-luminosity stars with undepleted Li, and the slightly more massive and more luminous stars with total Li depletion (see Figs. 1.8 and 1.9). Figure 1.9: Locating the LDB for NGC 2547 in a CMD, from Soderblom et al. (2014). The figure shows three dashed loci corresponding to LDB ages of 30, 40 and 50 Myr. Cluster members of NGC 2547 with depleted Li are marked as open squares, while filled squares indicate members with undepleted Li. The sharp transition between the two groups of depleted and undepleted cluster members clearly points to the location of the LDB. Determining the luminosity at the LDB is considered to be one of the most accurate age indicators for open clusters in an age range of 20–200 Myr (e.g., Burke et al., 2004; Cargile et al., 2010; Soderblom, 2010; Barrado y Navascués et al., 2011; Soderblom et al., 2014). The age-LDB luminosity method is semi-fundamental, involving few prior assumptions, and relying on the well-understood physics on contracting, fully convective low-mass stars. In addition, this method seems to be remarkably insensitive to various observational uncertainties and to variations in assumed opacities, metallicity, convective efficiency, equation of state and stellar rotation, making it notably more reliable than other methods. It is also a very precise technique, requiring minimal analysis of interpretation to detect the clear boundary between low-luminosity stars with undepleted levels of Li and those with slightly higher luminosities which have already depleted their superficial Li content (Hobbs & Pilachowski, 1986; Burke et al., 2004; Soderblom, 2009; Barrado y Navascués et al., 2011; Jeffries, 2014; Soderblom et al., 2014). In spite of this, LDB ages have been determined for only a very small number of nearby clusters (e.g., Oliveira et al., 2003; Burke et al., 2004; Cargile et al., 2010; Barrado y Navascués et al., 2011; Soderblom 10 Chapter 1. Introduction et al., 2014; Messina et al., 2016), and this is generally due to the necessity of higher resolution spectra to detect the very faint, cool mid- to late-M dwarfs (e.g., Cargile et al., 2010; Soderblom et al., 2014). The LDB method is most sensitive for clusters in an age range of 20–200 Myr, a range which does not cover SFRs or stars past the ZAMS (Burke et al., 2004; Cargile et al., 2010; Jeffries, 2014; Soderblom et al., 2014). Other studies such as Barrado y Navascués et al. (2011) also give an age range of 15–500 Myr for the determination of the LDB. The reason for this limited age range is that significant Li depletion has not yet started for younger clusters, while stars with masses > 0.06 M⊙ older than 500 Myr would have already completely depleted their Li content (Barrado y Navascués et al., 2011). As we will see in Sect. 4.2 of this work, we note that the coolest stars in our data sample are typically limited to 3000 K, and so we were unable to fully delimit the LDB for clusters older than 50–80 Myr. For ages in a 90–570 Myr range we could only mark the starting point of this region, indicating the transition between the depleted and undepleted low-mass stars without being able to observe the reappearance of stars showing undepleted Li at cooler temperatures than were available in the data sample. 1.1.4 Open clusters Figure 1.10: The Pleiades, a 78–125 Myr intermediate-age open cluster. Credit: NASA, ESA, AURA/Caltech, Palomar Observatory. As most stars do not form individually, but inside clusters and associations, the study of clusters of different ages and chemical compositions is essential to understanding star formation and evolution (e.g., Gilmore et al., 2012; Smiljanic et al., 2014; Spina et al., 2014b; Magrini et al., 2014; Tautvaišienė et al., 2015; Magrini et al., 2015; Sacco et al., 2017; Tang et al., 2017; Bragaglia et al., 2021; Dumont et al., 2021a; Randich & Magrini, 2021; Gilmore et al., 2022, submitted; Randich et al., 2022, submitted). Open clusters (OCs) are also very useful tracers to study the properties of planetary systems observed in the Galactic field (Sacco et al., 2017), as well as the formation and evolution of the Galaxy as a whole, especially the spatial distri- bution of elemental abundances in the Galactic thin disc and their evolution with time (e.g., Gilmore et al., 2012; Netopil & Paunzen, 2013; Randich et al., 2013; Magrini et al., 2014; Smil- janic et al., 2014; Magrini et al., 2015; Tang et al., 2017; Casali et al., 2019; Bragaglia et al., 2021). Because the stars in open clusters share the same origin, having been formed in the same protocloud of gas and dust, the study of OCs is so vital because it involves the analysis of stars 1.1. Lithium as an age indicator 11 with the same age, distance, proper motions, radial velocity distribution, and metallicity (e.g., Tautvaišienė et al., 2015; Tang et al., 2017). Among all OCs, the SFRs and young PMS clusters are particularly interesting as they are still close to their birthplaces and contain a homogeneous stellar population. These young OCs are, for example, key objects in order to trace the current chemical composition of the Solar neighbourhood and its evolution in space and time (Spina et al., 2014b). As we will see in Sect. 1.3 below, the Gaia-ESO Survey (GES) has put a special focus on targeting open clusters covering a wide age range, due to their crucial use to under- stand this wide array of stellar and Galactic issues (Bragaglia et al., 2021; Gilmore et al., 2022, submitted; Randich et al., 2013, 2022, submitted). Figure 1.11: The Hertzprung-Russell (HR) diagram. The colour-magnitude diagram (CMD) is the observational counterpart. Credit: ESO. As we will discuss in detail in the following chapters, regarding the specific aims of this project we note that the membership analysis and calibration of the ages of open clusters and associations is also of particular importance to constrain a lithium-age relation. OCs are crucial both in the study of Li depletion and in the calibration and determination of stellar ages, serving as benchmarks to calibrate practically every stellar age except that of the Sun (e.g., Soderblom, 2010; Soderblom et al., 2014). One of the essential tools to study the age and evolution of open clusters is the colour-magnitude diagram (CMD), the observational counterpart of the Hertzsprung-Russell (HR) diagram (see Sect. 2.2.3). In a CMD open cluster stars are plotted in terms of their brightness (a proxy of luminosity) and colour (a proxy of effective temperature), and their evolution can be studied depending on their location in the well-known distinct areas of this diagram, reflecting the different stellar evolutionary stages (see Fig. 1.11). Finally, we also note that open clusters and associations are also the ideal laboratory to calibrate the effects of different stellar parameters on Li depletion (see Sect. 1.2 below). 1.1.5 Li-rich giants The study of Li-rich giants is of great interest for the further understanding of the behaviour of stellar Li and the Li enrichment of the Galaxy (e.g., Casey et al., 2016; Lyubimkov, 2016; 12 Chapter 1. Introduction Randich & Magrini, 2021; Romano et al., 2021). Even though they can be found ubiquitously in a number of different environments – from open clusters, to globular clusters, the Galactic Bulge, and even dwarf galaxies (e.g., Casey et al., 2016; Smiljanic et al., 2016) –, most Li-rich giant stars are still not well understood and their existence remains a compelling mystery that has not yet been resolved (e.g., Lyubimkov, 2016; Smiljanic et al., 2018; Magrini et al., 2021a,b; Randich & Magrini, 2021). These objects can appear both at the RGB (red giant branch) and AGB (asymptotic giant branch) for low- and intermediate-mass stars, respectively (Smiljanic et al., 2016). Li-rich giants comprise approximately 1–2% of FGK giants and supergiants (e.g., Casey et al., 2016; Lyubimkov, 2016; Smiljanic et al., 2016; Gao, 2018), and are typically defined as those that have A(Li)≥1.5 (Lagarde et al., 2012; Delgado Mena et al., 2016; Smiljanic et al., 2016, 2018; Gao, 2018; Twarog et al., 2020; Magrini et al., 2021b) (also see Sect. 2.3). According to standard evolutionary models, this limit refers to the post-dredge up Li abundance of a low-mass star (Lagarde et al., 2012; Smiljanic et al., 2016). Some studies, such as (e.g., Casey et al., 2016; Lyu- bimkov, 2016), define Li-rich giants as those giants with slightly higher abundances of A(Li)≥ 2. Lyubimkov (2016) further defines the even scarcer group of the so-called ‘super Li-rich giants’ as those with A(Li)=3.5–4.3. Figure 1.12: Study of Li-rich giants in Magrini et al. (2021b). This figure displays the luminosity versus A(Li) for cluster candidates with masses in the range of 1–1.8 M⊙, showing models for rotation-induced mixing (red curves) and thermohaline mixing (green curves), as well as the limit for Li-rich giants with A(Li)≥1.5 (vertical black line). The existence of Li-rich giants cannot be explained in terms of the standard theory of stellar evolution. As stars leave the MS towards the RGB, the Li that had been stored in the outer con- vective zone is mixed with the hotter interior when they experience the first dredge-up, resulting in lower Li abundances, generally below A(Li)= 1.5 (e.g., Casey et al., 2016; Delgado Mena et al., 2016; Lyubimkov, 2016; Smiljanic et al., 2018). Given the low temperatures necessary to destroy lithium in stellar interiors, the existence and properties of these stars contradict expectations from standard stellar evolution models (which only include convection as a mixing mechanism), 1.2. Calibrating the Li-age relation 13 and would require extra non-standard mixing mechanisms to account for the additional lithium synthesis detected on their surfaces, such as rotation-induced mixing in the more massive stars, or thermohaline instability for the less massive giants (e.g., Casey et al., 2016; Delgado Mena et al., 2016; Lyubimkov, 2016; Smiljanic et al., 2016; Magrini et al., 2021a,b; Randich & Magrini, 2021, and references therein). Li-rich giants additionally seem to be more common among fast rotating stars, and Li-rich giants displaying higher levels of chromospheric activity and the presence of strong magnetic fields have also been detected (Lyubimkov, 2016; Smiljanic et al., 2016). This seems to be in agreement with all the literature studies proposing a connection between Li enrichment, fast rotation and chromospheric activity (see Sects. 1.2.1 and 1.2.2 below), and may be a factor that contributes to the high Li abundances of these objects. Several scenarios and sources of Li-enrichment have been proposed to explain the unexpect- edly high Li abundances of these stars, usually divided into those which propose Li enrichment through external contamination, and those requiring an internal production of Li (e.g., Smiljanic et al., 2018; Randich & Magrini, 2021). Many studies have proposed that Li enrichment could be caused by planet engulfment, which would also result in these giants spinning up, and in an increase of their magnetic fields (Casey et al., 2016; Delgado Mena et al., 2016; Lyubimkov, 2016; Smiljanic et al., 2016). Planet accretion, and also the external contamination of interstellar gas enriched by supernova explosions (Delgado Mena et al., 2016), might enhance internal Li pro- duction and increase the Li content in the photosphere. However, planetary engulfment should not only cause the enhacement of Li, but also of other light elements such as Be, and this is something which has very rarely been detected in Li-rich giants (Smiljanic et al., 2016, 2018). On the other hand, internal Li production by means of the Cameron-Fowler mechanism (e.g., Casey et al., 2016; Delgado Mena et al., 2016; Lyubimkov, 2016; Smiljanic et al., 2018; Magrini et al., 2021b; Romano et al., 2021, and references therein), can lead to an increase in Li abundance for giant stars more massive than 1.5 M⊙. For less massive stars, however, a non-standard mixing process (such as thermohaline mixing) would be required to bring fresh Li up to the surface, and the extra mixing required might also be induced by external phenomena, as discussed above (Casey et al., 2016; Delgado Mena et al., 2016; Lyubimkov, 2016; Smiljanic et al., 2018). 1.2 Calibrating the Li-age relation Standard models of stellar evolution including convection as the only mixing mechanism predict that stellar Li abundances should only be a function of effective temperature, mass and age (e.g., Soderblom et al., 1990; Barrado y Navascués et al., 2001a; Soderblom, 2010; Dumont et al., 2021b; Randich & Magrini, 2021). Consequently, stars with similar effective temperatures in a given cluster should have undergone the same amount of Li depletion, and similarly, for a given mass stellar ages could be derived with a direct calibration between age and Li abundance (e.g., Pallavicini et al., 1992; Randich & Magrini, 2021). However, the measured Li abundances in various studies for late-type stars in open clusters of different ages have revealed a complex be- haviour of Li depletion with significant scattering, showing a significant spread in Li abundance at a given colour (or mass) which could not be attributed to observational errors (e.g., Dun- can, 1981; Soderblom et al., 1993; Martín & Claret, 1996; Stout-Batalha et al., 2000; Barrado y Navascués et al., 2001a; Wilden et al., 2002; Jeffries, 2014; Jeffries et al., 2014; Barrado et al., 2016; Castro et al., 2016; Bouvier et al., 2018; Binks et al., 2022, in prep.). Observations of solar and late-type stars in open clusters of different ages show that both 14 Chapter 1. Introduction Figure 1.13: Li abundances for field stars, with superimposed curves of growth obtained as a result of a calibration of the Li-age relation for solar-mass stars, from Soderblom et al. (1983). These isochrones enable the calibration of age ranges for the plotted field stars. PMS and MS Li depletion are significantly more complex than the prediction of standard mod- els, and that depletion is not a simple function of mass and stellar age only, but also depends on a series of other factors and parameters, such as rotation, angular momentum loss, activ- ity, metallicity, accretion, mass loss and magnetic activity, as well as convection structure and non-standard mixing mechanisms and transport processes (e.g., Duncan, 1981; Soderblom et al., 1993; García López et al., 1994; Jones et al., 1999; Randich et al., 2002; Charbonnel & Talon, 2005; Pallavicini et al., 2005; Bouvier, 2008; Soderblom et al., 2014; Barrado et al., 2016; Castro et al., 2016; Lyubimkov, 2016; Dumont et al., 2021b; Randich & Magrini, 2021; Romano et al., 2021). This indicates the presence of a variety of additional non-standard mixing processes, in addi- tion to convection, that would account for the observed behaviour of Li in PMS and MS FGKM stars, and for the enhanced Li spread in otherwise similar stars with the same temperature and at the same age. These non-standard processes include rotational mixing, convective overshooting, microscopic diffusion, mass loss through stellar winds, planet accretion, internal gravitational waves, tachocline mixing, penetrative convection, and magnetic fields (e.g., Soderblom et al., 1990; Pallavicini et al., 1997; Umezu & Saio, 2000; Sestito & Randich, 2005; Jeffries, 2014; Bou- vier et al., 2016, 2018; Dumont et al., 2021a,b; Randich & Magrini, 2021; Romano et al., 2021). Even though a large amount of theoretical and observational work has been dedicated to the understanding of Li and its evolution, the complex pattern of Li depletion in pre- and main- sequence stars is not yet well understood, preventing a more precise and quantitative use of Li as an age tracer, which would be particularly ideal in order to infer ages for solar-like MW field stars (e.g., Sestito & Randich, 2005; Randich & Magrini, 2021). The most precise way to calibrate these effects — including the characterization of the de- pendence of Li depletion on several stellar parameters, and the study of non-convective mixing processes — and derive a reliable Li-age relation is to conduct a comprehensive study of stel- lar groups with similar ages, such as open clusters, associations, and kinematic groups (e.g., Soderblom et al., 1983; Soderblom, 2010; Castro et al., 2016; Randich & Magrini, 2021). One 1.2. Calibrating the Li-age relation 15 such Li-age calibration was performed by Soderblom et al. (1983), who established a Li-age re- lation to estimate ages for solar-mass field stars by deriving a series of curves of growth using Li abundances for open cluster stars and the Sun (see Fig. 1.13). While additionally doing a preliminary study of the Li-rotation and Li-activity relations, the Li-age relation obtained in this study was also based on three simplified assumptions, namely that all stars have the same initial Li abundance, that the Li depletion rate depends only on stellar mass, and that the Sun is a typical star regarding its mass and age. In this work (see Chapters 3, 4 and Sect. 5.3), we have done a characterization of the de- pendence of Li depletion with several parameters in order to calibrate a Li-age relation using EW (Li) values from open clusters. And in order to optimally contextualize this characterization, in the following subsections we will proceed to discuss the dependence of Li on rotation, activity, accretion and metallicity: 1.2.1 Lithium and rotation Figure 1.14: Left: EW (Li) equivalent widths versus unreddened (B-V) colour for stars of the Pleiades, from Soderblom et al. (1993). The size of the circles plotted increases with the observed vsini in the manner indicated; Right: EW (Li) equivalent widths versus bolometric luminosity for high probability member stars of the Pleiades, from Barrado et al. (2016). Li-rich stars are indicated with large, open diamonds. In both cases we can see the Li-rotation connection with the more Li rich stars tending to be faster rotators. Rotation is a very important stellar parameter, with a dependence on mass, age and other factors that is still not fully understood. The best way to do so is to characterize said dependence with the study of member stars of open clusters, covering a range of different ages and metallici- ties. Because Li abundance depends on mass (see Subsect. 1.1.2), the analysis of the dependence of Li and rotation is crucial to characterize both the behaviour of stellar rotation, and the depen- dence of rotation on Li depletion (e.g., Barrado y Navascués et al., 2001a). Over the years, many studies from the literature have consequently reported a clear and enduring connection between Li abundance and rotation rates for cluster stars. This Li-rotation connection has been clearly observed for SFRs as young as 3–6 Myr, to intermediate-age clusters up to 170 Myr, and a weak Li-rotation connection has also been suggested in the case of older clusters around the age of the Hyades (750 Myr) (e.g., Soderblom et al., 1983; Randich & Pallavicini, 1991; Soderblom et al., 16 Chapter 1. Introduction 1993; Martín & Claret, 1996; King et al., 2000; Barrado y Navascués et al., 2001a; Sestito & Randich, 2005; Jeffries, 2014; Soderblom et al., 2014; Barrado et al., 2016; Bouvier et al., 2016; Anthony-Twarog et al., 2018; Bouvier et al., 2018; Arancibia-Silva et al., 2020; Twarog et al., 2020; Constantino et al., 2021; Franciosini et al., 2021; Llorente de Andrés et al., 2021; Randich & Magrini, 2021; Binks et al., 2022, in prep.). Figure 1.15: A(Li) abundances as a function of Teff for the Pleiades, from Bouvier et al. (2018). The auxiliary axis colour-codes the stars according to their angular velocities. A large scatter of A(Li) at fixed Teff is clearly visible in the 4000–5300 K range, strongly correlated with the stellar spin rate especially from 4400 K to 5300 K. Soderblom et al. (1993) was one of the first studies to empirically confirm that rotation could have an appreciable effect on the Li abundance of solar-type stars at an evolutionary stage as early as the ZAMS, concluding that fast rotators were systematically more Li-rich than their slower rotating counterparts (see Fig. 1.14, left). This work analysed a series of FGK stars from the Pleiades and observed a large spread in Li abundances, particularly for early to mid-K stars (late-K and M dwarfs are heavily depleted at this age, as discussed in Subsect. 1.1.2), confirming that this was indeed a genuine intrinsic scatter in Li abundances, and was not due to spurious effects caused by other factors, such as the presence of starspots (also see, Bouvier et al., 2018). Soderblom et al. (1993) claimed that this Li dispersion could be explained with the observable connection between rapid rotation and reduced Li depletion (also see, Barrado et al., 2016; Bou- vier et al., 2018). This observed anti-correlation between rotation and Li depletion seemed originally counter- intuitive, seeing as rotational mixing was thought to be directly correlated with surface rotation, and, according to this theory, fast rotating stars would consequently deplete Li more rapidly than slow rotators — the opposite trend to what was observed in the Pleiades (e.g., Soderblom et al., 1983; Bouvier et al., 2018; Arancibia-Silva et al., 2020; Llorente de Andrés et al., 2021). The trend with fast rotating stars being systematically more Li-rich compared to slower rotating ones has been confirmed in various additional studies on the Pleiades (e.g., Martín & Claret, 1996; King et al., 2000; Barrado et al., 2016; Bouvier et al., 2018), with one example from Barrado et al. (2016) shown in the right figure in Fig. 1.14. These studies typically reinforced the initial results from Soderblom et al. (1993), suggesting that the observable spread in Li is strongly cor- related with the cumulative rotational history of the solar-type cluster stars, starting at the PMS phase (also see Anthony-Twarog et al., 2018). Bouvier et al. (2018) confirmed the findings of 1.2. Calibrating the Li-age relation 17 Figure 1.16: EW (Li)-versus-Teff diagram for weak-line T-Tauri, from Bouvier et al. (2016). The trend of decreasing EW (Li) with higher Teff continues up to 6600 K, (see Subsect. 1.1.2). The colour scale is representative of the rotational periods, with a clear trend of faster rotators among the more Li-rich stars. earlier studies by observing a tight relationship between Li content and rotational rates especially among low-mass early-K stars, in a restricted range of effective temperatures from 4400 K to 5300 K (see Fig. 1.15), while more massive stars at higher temperature ranges showed a weaker connection in spite of a visible residual rotational scatter. Other studies from the literature additionally arrived to the same Li-rotation connection to that of the Pleiades for cooler, low-mass stars in NGC 2516 (125–138 Myr) (Jeffries et al., 1998) and M35 (175 Myr) (e.g., Barrado y Navascués et al., 2001a; Anthony-Twarog et al., 2018; Jack- son et al., 2020; Jeffries et al., 2020; Randich & Magrini, 2021), two intermediate-age clusters somewhat older than the Pleiades. In addition, the Li-rotation connection has also been observed in different types of stellar groups with similar ages to the Pleiades, such as the stellar stream Psc-Eri (Arancibia-Silva et al., 2020). Regarding M35, Barrado y Navascués et al. (2001a) ad- ditionally concluded that most of the large spread in Li abundances in the Pleiades was for the most part no longer observed, potentially as a result of the evolution of rotation rates with age (see. 3.3). Anthony-Twarog et al. (2018), however, partly attributed this less noticeable spread in Li abundances for the slightly older M35 to the lack of a sufficiently large sample of cluster stars, and concluded that, even with a smaller sample, the rapid rotators tended to be Li-rich stars, and the resulting distribution seemed to be compatible with the scatter found in the Pleiades. Additional studies showed that this Li-rotation connection could also be a factor to explain the dispersion in Li observed for low-mass stars in appreciably younger clusters than the Pleiades, as early as SFRs such as the 3–5 Myr-old NGC 2264 (Bouvier et al., 2016) or the 3 Myr-old σ Ori (Llorente de Andrés et al., 2021). In addition, the Li-rotation connection is also observable for different young moving groups and associations, such as β Pic (21 Myr) (Messina et al., 2016). Even though the difference in Li between faster and slower rotators was smaller than what was observed for older clusters in an age range coeval to the Pleiades, the anti-correlation between Li depletion and rotation seems to be already established early on during PMS evolution for low-mass stars, as shown in Fig. 1.16 from Bouvier et al. (2016), with the faster rotating stars 18 Chapter 1. Introduction in NGC 2264 being more Li-rich than slower ones (see also, e.g., Martín & Claret, 1996; Binks et al., 2022, in prep.). In agreement to what we have just discussed, the recent study by Arancibia-Silva et al. (2020) stated that the Li-rotation connection seems to be universal for a restricted temperature range for low-mass stars at or close to the ZAMS and does not depend on environmental conditions, having been reported in various SFRs, young moving groups, and young and intermediate-age open clusters in an age range from 3 Myr (corresponding to σ Ori) to 175 Myr (correspond- ing to M35). Regarding older clusters, Martín & Claret (1996) suggested that some memory of the Li-rotation connection observable throughout the PMS and ZAMS phases may be still retained in the low-mass stars of the Hyades. Twarog et al. (2020) also studied the evolution of Li during the MS phase, and concluded that both rotation and rotational evolution (namely, the rotational spin-down occurring throughout the MS) appeared to be critical factors for the appearance of the Li-dip for F-type stars (see Subsect. 1.1.2) (see also Randich & Magrini, 2021). Rotation is thought to directly impact the Li depletion rate in stars with thick convective envelopes either through structural changes during the PMS, or by reducing the penetrative convection into the radiative core, resulting in reduced Li depletion for faster rotators (e.g., Bouvier et al., 2018; Arancibia-Silva et al., 2020; Llorente de Andrés et al., 2021). Angular momentum loss as a result of disc locking during the PMS phase can also initiate the Li spread by enhacing Li depletion in slower rotating stars with long-lived circumstellar discs (see Sub- sect. 1.2.3). In addition, stellar magnetic fields can reduce Li depletion by diminishing the rate of energy transport in the outer convective layers, resulting in a lower temperature at the base of the convective zone and an inflated stellar radius. Radius inflation is a vital factor to explain the observed spread in Li abundances not only for PMS stars in young clusters, but also for older clusters like the Pleiades (e.g., Jackson et al., 2016; Anthony-Twarog et al., 2018; Bouvier et al., 2018; Jackson et al., 2018; Arancibia-Silva et al., 2020; Randich & Magrini, 2021). Finally, studies like Randich & Magrini (2021) additionally comment on the importance of also taking rotational mixing into account in the PMS phase, as well as the effect of accretion discs. Given the saturation of magnetic activity and the inhibition of Li depletion at very young ages (see Subsect. 1.2.2), additional mixing might account for the enhanced Li depletion for the slower rotating stars which are undergoing angular momentum loss (also see Jeffries et al., 2020). Various studies have proposed various explanations to account for the Li-rotation connection and the observable spread in Li abundances by developing models which make use of non-standard transport processes to explore the influence of rotation on the structure of late-type young stars and on Li depletion, as well as characterize stellar angular momentum loss and rotational evo- lution (see Sect. 3.3). Furthermore, as mentioned above, and as we will discuss in more detail in Subsect. 1.2.2, rotation is also directly linked to stellar activity, and so many of these models characterize the Li-rotation connection by taking magnetic fields and chromospheric activity into account as well (e.g., Soderblom et al., 1993; Wright et al., 2011; Bouvier et al., 2016; Franciosini et al., 2021; Johnstone et al., 2021; Randich & Magrini, 2021). These models include the study of the influence of circumstellar accretion discs for T-Tauri stars in SFRs and the impact of disc lifetimes on rotational mixing (see Subsect. 1.2.3); the analysis of angular momentum evolution (e.g., Soderblom et al., 1983; Dumont et al., 2021a,b); rotational mixing and convective instability (e.g., Constantino et al., 2021); rotational evolution linked with high-energy X-ray, extreme ultraviolet (EUV) and Ly-α emission for FGKM stars (e.g., Johnstone et al., 2021); the evaluation of the effects of starspot coverage on the Li spread of 1.2. Calibrating the Li-age relation 19 low-mass stars (e.g., Somers & Pinsonneault, 2015a; Somers et al., 2020; Franciosini et al., 2021); and the dependence and the exploration of structural changes due to magnetic fields and activity, resulting in inflated radii and, consequently, reduced Li depletion (e.g., Soderblom et al., 1983; Somers & Pinsonneault, 2014, 2015b; Messina et al., 2016; Jeffries et al., 2017; Somers et al., 2020; Dumont et al., 2021a,b; Franciosini et al., 2021; Binks et al., 2022, in prep.). These latter models also make a connection between inflated radii and the Li-rotation relation. As mentioned above, fast rotators tend to display the most inflated radii, resulting in less effective convection mixing, and, consequently, reduced Li burning (e.g., Somers & Pinsonneault, 2015b; Barrado et al., 2016; Bouvier et al., 2016; Randich & Magrini, 2021; Binks et al., 2022, in prep.). 1.2.2 Lithium and activity Figure 1.17: Li abundances versus Teff for chromospherically active stars, from Randich & Pallavicini (1991). Most of the stars plotted in this figure are Li-rich, in agreement with the often seen correlation between high levels of Hα and a Li excess for late-type stars. As in the case of rotation (see Subsect. 1.2.1), and as we will further be discussing in Sect. 3.2, several studies have consistently observed an anti-correlation between Li depletion and Hα emis- sion for late-type low-mass stars, where active stars tend to be more Li-rich than their less active counterparts (e.g., Duncan, 1981; Baliunas & Vaughan, 1985; Simon et al., 1985; Pallavicini et al., 1990; Randich & Pallavicini, 1991; Soderblom et al., 1993; Martín & Montes, 1997; Zapa- tero Osorio et al., 2002; Hall, 2008; Martínez Arnáiz, 2011; Wright et al., 2011; Mishenina et al., 2012; Soderblom et al., 2014; Frasca et al., 2015; Flores Soriano et al., 2015; Johnstone et al., 2021). Solar-type and later-type stars have chromospheres, regions with a positive temperature gra- dient which lie above the photosphere and below the corona, and are characterized by a prominent departure from radiative equilibrium (RE) (e.g., Baliunas & Vaughan, 1985; Hall, 2008). Indi- cators of chromospheric emission, including broad stellar spectra emission features in the optical range, such as the Hα Balmer line and the Ca II H and K lines, point to these departures of RE in the stellar atmospheres, due to the existence of additional heating mechanisms and a wide range of phenomena that are generally referred to as stellar activity (e.g., Baliunas & Vaughan, 20 Chapter 1. Introduction Figure 1.18: This figure from Baliunas & Vaughan (1985) shows ⟨R′ HK⟩ (the chromospheric radiative loss relative to the stellar bolometric magnitude) as a function of the Rossby number (the ratio of the observed rotational period to the convective turnover time, τc). The small scatter observed in this figure points to rotation-activity relation, and the fact that rotation can be predicted given the average chromospheric emission strength, as well as colour information. 1985; Pallavicini et al., 1990; Randich & Pallavicini, 1991; Hall, 2008; Martínez Arnáiz, 2011; Wright et al., 2011). Chromospheric magnetic activity is common among cool solar-type and later-type FGKM stars sharing subphotospheric convection zones of increasing depth, driven by differential rotation. Activity is tightly related to changes in the stellar magnetic field, produced through a self-sustaining dynamo mechanism, which in turn is also caused by this differential rotation in the stellar interior (e.g., Randich & Pallavicini, 1991; Hall, 2008; Martínez Arnáiz, 2011; Wright et al., 2011; Frasca et al., 2015). Chromospheric activity is tightly correlated to the age of a star — The more active stars are typically younger, making chromospheric emission a tracer of stellar youth. Additionally, more active stars tend to show less Li depletion, while stars with weak chromospheric emission are often appreciably depleted in Li, pointing to an additional correlation between Li excess (another marker of youth) and high levels of chromospheric activity, as illustrated in Fig. 1.17 (e.g., Dun- can, 1981; Simon et al., 1985; Pallavicini et al., 1990; Randich & Pallavicini, 1991; Pallavicini et al., 1992; Soderblom et al., 1993; Mallik, 1998; Zapatero Osorio et al., 2002; Martínez Arnáiz, 2011; Soderblom et al., 2014). However, it is important to note that neither chromospheric emis- sion nor high levels of Li abundance are always necessarily connected to the youth of an star, as evolved Li-rich and/or chromospherically active stars have also been observed. For example, a high level of chromospheric emission could be observed in fast-rotating evolved stars with a convection zone that is sufficiently deep (e.g., Randich & Pallavicini, 1991; Soderblom et al., 1993; Mallik, 1998). Thus, because the mechanics of Li depletion depend on a variety of factors and parameters (see the introduction of Sect. 1.2 above), activity or rotation alone are not able to account for the observable spread in Li for young and intermediate-age clusters. Even though a number of stud- ies from the literature have reported a correlation between Li excess and high activity emissions, 1.2. Calibrating the Li-age relation 21 Figure 1.19: Correlation between Li abundances and Hα excess emission for stars in IC 4665 (diagonal crosses) and the Pleiades (open pentagons), from Martín & Montes (1997). as well as a correlation between Li excess and high rotation rates, not every star with Li excess will always necessarily show both a high chromospheric emission and a high rotation rate. There does not seem to be a one-to-one correlation between Li abundance and chromospheric activity, and appreciable spreads in Li abundance for both active and inactive stars have been reported (e.g., Duncan, 1981; Soderblom et al., 1993; Mallik, 1998; Flores Soriano et al., 2015; Barrado et al., 2016). As exemplified in Fig. 1.18, activity and rotation are instead intrinsically inter- connected through the stellar dynamo mechanism, with fast rotation resulting in strong stellar magnetic fields, consequently making rotation a key factor in the physical processes responsible for both Li abundance and chromospheric activity (see also Sects. 1.1.2 and 1.2.1), and result- ing in a Li-rotation-activity connection, which can be explored by studying open cluster stars (e.g., Duncan, 1981; Baliunas & Vaughan, 1985; Simon et al., 1985; Randich & Pallavicini, 1991; Soderblom et al., 1993; Martín & Montes, 1997; Mallik, 1998; Martínez Arnáiz, 2011; Mishenina et al., 2012; Johnstone et al., 2021). This Li-rotation-activity connection has been clearly established for the Pleiades, with stud- ies such as Soderblom et al. (1993) observing that FGKM cluster candidates exhibited a large spread in Li, rotation and chromospheric activity, and that cluster stars rotating faster tended to have both higher Li abundances and stronger chromospheric emission (CE) at any given colour. Indeed, most of the Li-rich stars had the highest values of CE for their corresponding colour, whereas the Li-poor stars tended to be much less chromospherically active. This Li-rotation- activity relation is also maintained for younger clusters, such as the 35–38 Myr-old IC 4665 (see Fig. 1.19), whose low-mass stars display a similarly large spread in both Li abundance and chro- mospheric activity compared to that of the Pleiades, increasing for Teff < 5500 (e.g., Martín & Montes, 1997). The Li-activity relation additionally holds for early PMS stars in SFRs, which also tend to exhibit a particularly broad and variable range of activity at a given age, partly as a result of the accretion processes experienced by very young T-Tauri stars (e.g., Martín & Montes, 1997; 22 Chapter 1. Introduction Soderblom, 2010; Soderblom et al., 2014; Frasca et al., 2015; Johnstone et al., 2021) (also see Subsect. 1.2.3). In addition, for very fast rotators, the rotation-activity relation seems to break down, with chromospheric and coronal activity emissions reaching a saturation level that has been confirmed for members of young star clusters, and extends from G-type stars to the lowest- mass M-dwarfs. This saturation level is additionally reached at a rotation period that increases towards later types (e.g., Soderblom, 2010; Martínez Arnáiz, 2011; Wright et al., 2011; Soderblom et al., 2014). Lastly, regarding MS stars, it has been observed that the level of chromospheric activity decays with age as a result of magnetic braking, and also related to angular momentum loss due to the activity-rotation connection. This decrease in activity continues steadily up to 2 Gyr according to recent indications, with a nearly constant behaviour for older ages (e.g., Duncan, 1981; Baliunas & Vaughan, 1985; Simon et al., 1985; Martínez Arnáiz, 2011; Wright et al., 2011; Frasca et al., 2015). The timescale for activity evolution additionally depends on mass, as well as age and rota- tional evolution, with lower-mass stars remaining active for longer periods of time (e.g., Johnstone et al., 2021). For all age ranges, but particularly so for younger clusters, Hα emission thus tends to increase towards later types and cooler temperatures, with a trend of more active stars towards redder colours (e.g., Martín & Montes, 1997; Lamm et al., 2005; Mishenina et al., 2012; Rebull et al., 2018). Finally, we briefly mention how some studies have also explored the possibility of fresh Li being produced as a result of flares (e.g., Montes & Ramsey, 1998; Flores Soriano et al., 2015). These studies reported the potential enhancement of the Li I line at 6707.76 Å during optical flares of young and chromospherically active stars. While no significant variations were detected in other photospheric lines, appreciable changes were observed in the intensity of the EW (Li) measurements, with the largest value corresponding to the point just after the maximum level of chromospheric emission of the flare. A significant increase of 6Li/7Li isotopic ratio was also detected. These Li line variations could not be attributed to either starspots or line blends, and they may potentially be a result of spalliation reactions during the flares. 1.2.3 Lithium and accretion processes The accretion of material from circumstellar discs is another factor that can account for the observable dispersion in Li for very young PMS late-type stars in star-forming regions (SFRs). During the PMS evolutionary phase, solar-like and lower mass stars experience complex changes regarding their internal structure, temperature, radius and rotation, with several phenomena and circumstellar environments affecting their atmospheric layers and resulting in noticeable effects on their spectral lines. Mass accretion is also directly responsible for a significant fraction of the final stellar mass, and the time dependence of the accretion rates also determines the evolution of the disc (e.g., Frasca et al., 2015). Early PMS Li depletion additionally experiences repeated bursts of accretion which can also result in an increase of the Li depletion rates, and a young stellar population may consequently exhibit a significant scatter in Li depending on the individ- ual accretion history of its member stars (e.g., Bouvier et al., 2016). Circumstellar discs regulate the stellar rotation of PMS stars up to the first few 5–6 Myr of their life. The phenomenon of disc-locking and the magnetic interaction of stars with their ac- cretion discs appreciably affect the angular momentum of these stars, resulting in notably slower rotation rates for those PMS stars with accretion discs. After 5–7 Myr (up to 8–10 Myr at the ut- 1.2. Calibrating the Li-age relation 23 Figure 1.20: Enhancement of the Li I and K I photospheric lines due to the effect of circumstellar accretion for classical T-Tauri stars, from Stout-Batalha et al. (2000). most, with Llorente de Andrés et al. (2021) giving an age of approximately 9 Myr for the lifetime of circumstellar discs), the discs dissipate quickly, and this disc decoupling process also results in increased rotation rates for the contracting PMS stars until they reach the ZAMS (e.g., Barnes et al., 1999; Lamm et al., 2005; Frasca et al., 2015; Rebull et al., 2018; Arancibia-Silva et al., 2020; Bonito et al., 2020; Fritzewski et al., 2020; Llorente de Andrés et al., 2021; Popinchalk et al., 2021). The influence of circumstellar accretion discs on the rotation rates of PMS stars is also directly correlated with the Li-rotation relation (see Subsect. 1.2.1), where slower rotating stars also deplete Li more rapidly as a result. Thus, the long-lasting impact of the disc lifetimes on the rotation profile for solar-type PMS stars seem to contribute in a significant way to the observable Li spread observed in the ZAMS and beyond (e.g., Barnes et al., 1999; Bouvier et al., 2016; Arancibia-Silva et al., 2020).In Sect. 3.3, we discuss gyrochronology and the evolution of rotation with age in more detail, including the influence of circumstellar discs and the loss of angular momentum due to disc coupling for the stars in the early phases of the PMS. Accretion processes have an appreciable effect on the stellar spectra as well, appearing as strong and broad emission lines (e.g., Stout-Batalha et al., 2000; Frasca et al., 2015; Bonito et al., 2020). Accretion can have a notable effect on the spectral diagnostics of the Hα chromospheric emission lines, and conversely, chromospheric emission can also be a source of contamination in the measurements of mass accretion rates (e.g., Frasca et al., 2015). For SFRs such as Cha I (see the individual notes of Appendix B), studied by Frasca et al. (2015), oftentimes the highest fluxes of Hα can be due to accretion, rather than to chromospheric activity. Similarly, Li lines of very accreting T-Tauri stars in SFRs can be appreciably enhanced as a result of accretion, resulting in significant overestimated values of surface Li abundances. Studies such as Stout-Batalha et al. (2000) analysed this effect by making use of a number of spectra for classical T-Tauri stars (CTTS), substracting the continuum veiling emission to recover the underlying photospheric spectrum, and observing that the Li I and K I photospheric lines were 24 Chapter 1. Introduction notably enhanced as a result of the accretion process (see Fig. 1.20). The study concluded that the measurements of surface Li abundances for strong accreting T-Tauri stars are likely to be overestimated as a result. On the other hand, strong accretion rates can also cause the Li con- tent of PMS stars to be underestimated due to the veiling factor (Stout-Batalha et al., 2000; Frasca et al., 2015; Bonito et al., 2020). We further discuss the effects of accretion on the Li lines in regards to our target sample in Sects. 2.2.6, 3.1, and 3.2 (as well as the individual notes of Appendix B). As we will see in this work, we note that 4 Myr-old SFR NGC 2264 offers a particularly clear example of the effects of accretion-induced enhancement on the Li lines of their very young T-Tauri candidate members (Bonito et al., 2020). Some studies have also investigated whether the accretion of planetesimals from a surrounding disc might be an additional factor to characterize the observable spread in Li for GK stars with similar temperature in intermediate-age clusters. Such a correlation would imply that these stars would be able to replenish their surface Li by accreting hydrogen-depleted material from a circumstellar disc, in a similar way to the accreting processes of SFRs and their influence on Li, which would result in the observed dispersion. Studies such as Wilden et al. (2002) analysed the scatter of Li abundance for GK stars in the Pleiades, and concluded that the accretion of hydrogen-depleted planetesimals does not seem to play a significant role in the dispersion in Li of these stars. 1.2.4 Lithium and metallicity Several studies from the literature have studied the effect of metallicity (using [Fe/H] as a proxy for the overall metallicity of the cluster stars) on Li depletion (e.g., Randich & Pallavicini, 1991; Umezu & Saio, 2000; Barrado y Navascués et al., 2001a; Jeffries et al., 2002; Wilden et al., 2002; Mishenina et al., 2012; Jeffries, 2014; Delgado Mena et al., 2015; Randich et al., 2020; Twarog et al., 2020; Dumont et al., 2021a; Randich & Magrini, 2021), resulting in two main hypotheses which we will now briefly describe. Some of these studies state that Galactic Li decreases at high metallicity (e.g., Randich & Pallavicini, 1991; Umezu & Saio, 2000; Jeffries, 2014; Delgado Mena et al., 2015; Dumont et al., 2021a), while others claim that the distribution is flat or even increases (Twarog et al., 2020; Randich & Magrini, 2021). All these studies tend to agree, how- ever, on the fact that metallicity can have small observable effects on the Li depletion of clusters (e.g., Jeffries et al., 2002; Jeffries, 2014), even though overall it only seems to have a minimal effect on Li depletion, and its determination does not greatly increase the precision of age es- timations using Li (e.g., Umezu & Saio, 2000; Zapatero Osorio et al., 2002; Sestito & Randich, 2005; Mishenina et al., 2012; Jeffries, 2014). We also refer here to Sect. 3.4 for the analysis of the dependence of our cluster selections with metallicity. Randich et al. (2020), also addressed in Randich & Magrini (2021), is one of the most recent studies which analysed the evolution of the upper envelope of Li abundance versus metallicity for an open cluster sample, with the aim of tracing the Galactic evolution of Li at high metallicity and constraining the sources of Li-enrichment in the ISM. According to this study, metal-rich clusters tend to show higher Li abundances than their metal-poor counterparts, with clusters with [Fe/H]< −0.1 showing a maximum values of A(Li)∼ 3.1, while stars with solar and super- solar metallicities all having higher values, peaking at A(Li)∼ 3.4 (see Fig. 1.21. Randich et al. (2020) concluded that Li does not decrease in the ISM at supersolar metallicities, as is suggested in several other studies (see below), and the trend of A(Li) with Galactrocentric distance was shown to even show a potential mild increase at high metallicity. Other studies such as Twarog et al. (2020) have also stated that more metal-deficient stars should present higher levels of Li 1.3. Data surveys and missions 25 depletion than metal-rich stars of a similar age. Figure 1.21: A diagram of the average maximum Li abundance for the open clusters (colour- coded by age) studied by Randich et al. (2020) as a function of cluster metallicity. On the other hand, other studies have suggested the opposite of this hypothesis, stating that Li rather decreases at high metallicity (e.g., Umezu & Saio, 2000; Jeffries et al., 2002; Wilden et al., 2002; Delgado Mena et al., 2015; Dumont et al., 2021a). This differing hypothesis links stars with high metallicity with a more efficient convection zone, and as a result stars in more metal-rich clusters would appear to deplete more Li than their metal-poor counterparts. One of the most recent studies addressing this interpretation is that of Dumont et al. (2021a), who anal- ysed the chemical and rotational evolution of low-mass PMS and MS stars for different masses and metallicities for a sample of Galactic open clusters. Different transport sources in the star interiors depend on both mass and metallicity, and according to the findings of this study, when metallicity decreases for a given mass the convective envelope that affects PMS depletion retracts more rapidly and becomes thinner in the MS, leading to a lower Li depletion. The study con- cluded that an anti-correlation between metallicity and Li depletion was observed, with stronger Li depletion levels for more metal-rich stars, and additionally suggested that the dependence of metallicity on Li depletion seemed to be more relevant than was formerly predicted. However, Randich et al. (2020) claimed that they did not find any evidence of a Li decline at high metallicities, and suggested that these differing findings and discrepancies were affected by selection biases in the samples, and that the Li abundance in the ISM may actually rather increase (see above). They remarked that the measured Li of the metal-rich population for many stars does not represent the initial ISM abundance, given that these stars have already undergone a partial Li depletion, and so they only considered in their study cluster members that had presumably not have undergone any Li depletion and retained their original Li content (Randich & Magrini, 2021). These studies thus concluded that the previously observed decrease in Li for metal-rich field stars was not real, and was instead affected both by sample selection effects and by stellar evolution and Li depletion mechanisms. 1.3 Data surveys and missions After an overview of the basics of lithium as an age indicator and a summarized discussion of the many complexities the Li-age relation entails, this last section will introduce the Gaia-ESO 26 Chapter 1. Introduction Survey and Gaia as the main data surveys we have used in this project, as well as any other explorations and missions which have provided data for the analysis of this work. 1.3.1 The Gaia-ESO Survey (GES) The Gaia-ESO Survey (GES – Gilmore et al., 2012; Randich et al., 2013; Gilmore et al., 2022, submitted; Randich et al., 2022, submitted)1 is a large, public spectroscopic survey that system- atically covers all major components of the Milky Way (from the ancient halo stars, to the bulge, thick and thin disc, and star forming regions), and thus provides a homogeneous and ambitious overview of the distribution of kinematics, dynamical structure and chemical compositions in the Galaxy (Bergemann et al., 2014; Smiljanic et al., 2014). The goals of GES have been challeng- ing in their scope, encompassing a wide range of stellar ages and spectral types B-M, and all stellar populations, field and clusters, open and globular (Gilmore et al., 2022, submitted). This exploration aspires to revolutionize our knowledge of Galactic and stellar evolution, and while its great science potential is yet to be fully exploited, this can already be exemplified by the significant scientific results delivered in more than 100 papers already published by the commu- nity, using GES data to focus on different topics seeking to study the formation, evolution and dynamics of the Galaxy and its stars (e.g., Magrini et al., 2021b; Gilmore et al., 2022, submitted). Figure 1.22: Map of observed GES targets on the sky. Observations shown are those included in internal data release 6 (iDR6), covering the entire observing period of the Survey, from 31/12/2011-26/01/2018. Key: MW= Milky Way, CL= Cluster, SD= Standard. Credit: GES. GES uses the multi-object spectrograph FLAMES on the Very Large Telescope (VLT at ESO, Chile) to obtain both high resolution spectra with UVES (Ultraviolet and Visual Echelle Spectrograph) and medium resolution spectra with GIRAFFE (see Sect. 2.1 for more details on the GES spectrographs). The observations, which started in December 2011 and were completed 1https://www.gaia-eso.eu/ https://www.gaia-eso.eu/ 1.3. Data surveys and missions 27 in January 2018, provided high-quality, uniformly calibrated spectroscopy of about 105 stars and a sample of 65 (plus 18–20 archive) open clusters (OCs) and star-forming regions (SFRs) of all ages, metallicities and stellar masses (Bragaglia et al., 2021; Gilmore et al., 2022, submitted; Randich et al., 2022, submitted). The targets include early- and late-type stars, giant and dwarf stars, and pre-main-sequence stars (Smiljanic et al., 2014). In addition to its measured spectra, this exploration uses well-defined samples from photometric surveys, such as VISTA (Sutherland et al., 2015), 2MASS (Skrutskie et al., 2006) and a variety of photometric surveys of open clusters that cover all the major components of the Galaxy (Gilmore et al., 2012; Bragaglia et al., 2021). While we note that there are also a number of wide field large spectroscopic surveys with different properties which already offer comprehensive data, such as APOGEE (Dawson et al., 2013), GALAH (De Silva et al., 2015), LAMOST (Deng et al., 2012) or RAVE (Kunder et al., 2017), among others, GES is unique among other surveys for its depth, its high spectroscopy UVES observations, its systematic coverage of all populations and spectral types in the Milky Way, its emphasis on obtaining comprehensive data for a large sample of open clusters, and its homogenized data results (Randich et al., 2022, submitted). Combined with precision astrome- try and spectrophotometry provided by Gaia, which is delivering accurate parallaxes and proper motions, GES provides a rich dataset yielding 3D spatial distributions, 3D kinematics, individual chemical abundances, and improved fundamental parameters for all target objects (e.g., Beccari et al., 2018; Cantat-Gaudin et al., 2018; Randich et al., 2018; Roccatagliata et al., 2018; Soubiran et al., 2018; Cánovas et al., 2019; Bossini et al., 2019). Figure 1.23: The outputs of the complementary GES and Gaia surveys. Credit: Gilmore et al. (2012) Thus, the goal of GES was to provide a large set of complementary spectroscopic data to the astrometry of Gaia, including radial and rotational velocities, effective temperatures, gravity indi- cators, metallicity, and elemental abundances for several chemical elements (Gilmore et al., 2022, submitted). In regards to our study of lithium, we note the importance of the high-resolution UVES spectroscopy of this survey allowing us to obtain and make use of a high number of lithium equivalent widths (EW (Li)) and abundances. And particularly in the field of dozens of open clusters covering an extensive age range, which have been a special focus of this survey as a result of them being crucial to understand a variety of scientific issues, from the formation and evolution of the clusters themselves, to stellar evolution and star formation as a whole, the evolution and 28 Chapter 1. Introduction metallicity distribution of the disc of the Galaxy, and the calibration and determination of stellar ages (Bragaglia et al., 2021; Randich et al., 2013; Gilmore et al., 2022, submitted; Randich et al., 2022, submitted). As discussed earlier in this chapter, open clusters are not only one of the best options in our astrophysical arsenal in order to calibrate stellar ages, they are also the best option to study the behaviour of lithium depletion and the Li-age relation, the main focus of this project. All the data obtained by the survey has been homogeneously analysed and reduced by the GES consortium (a community including some 450 co-investigators from more than 110 insti- tutes), providing internally-consistent results calibrated on benchmark stars and star clusters (Gilmore et al., 2022, submitted), and several data releases (from iDR1 to iDR6) including homogenized recommended astrophysical parameters and elemental abundances were produced during the years to be made publicly available to the scientific community (e.g., Smiljanic et al., 2014; Gilmore et al., 2022, submitted). Next chapter (specifically Sect. 2.1) will start by ad- dressing the work of the GES consortium in closer detail as regards its working groups (WGs), its analysis strategy, and a description of the latest internal data release, iDR6. 1.3.2 Gaia Figure 1.24: An artist’s concept of the Gaia spacecraft. Credit: ESA Gaia (Gaia Collaboration et al., 2016b)2 is an ongoing ambitious global space-astrometry ESA mission which launched in 2013 and started scientific operations in mid-2014. Initially a five-year mission, in 2018 the Gaia mission was extended to 2020, and currently Gaia has been firmly extended until the end of 2022, with an indicative approval until the end of 2025 (Gaia Collaboration et al., 2021). Its primary science goal is to chart a three-dimensional map of the Galaxy, providing photometry and astrometry of unprecedented precision for most stars brighter than G=20 mag, as well as obtaining low- and medium-resolution spectroscopy data for most stars brighter than G=17 mag (Gilmore et al., 2012; Gaia Collaboration et al., 2016b). Gaia provides a large stellar census that allows for an extensive overview of the origin, composition, formation and evolution of the Galaxy, producing a stereoscopic dataset which include positions, proper motions, parallaxes, radial velocities, brightness and astrophysical parameters of about 2https://sci.esa.int/web/gaia https://sci.esa.int/web/gaia 1.3. Data surveys and missions 29 one billion stars and other astronomical objects in the Milky Way and throughout the Local Group. Similar to its predecessor Hipparcos (operational 1989–1993), albeit with a precision of a hundred times better, the spacecraft of Gaia contains two optical telescopes, functioning with three science instruments in order to determine the location, motions and velocities of stars with very high precision. The astrometric instrument collects data in the G-band (330–1050 nm), while the blue (BP, 330–680 nm) and red (RP, 640–1050 nm) prism photometers obtain low resolution spectrophotometric data for additional analysis, and the radial velocity spectrometer collects medium resolution (R=11, 700) spectra (845–872 nm) (Gaia Collaboration et al., 2016b, 2021). Gaia maps the stars from a L2 Lagrangian point, keeping pace with the Earth in its orbit around the Sun. This orbit, in contrast to an orbit around the Earth, provides a more stable viewpoint and a clearer view of the target space skies. During its mission, the spacecraft rotates continuously around an axis perpendicular to the line of sight of both telescopes, and as a result of this the instruments repeatedly measure the position of each object, detecting any changes in the motion of the objects through space (Gaia Collaboration et al., 2016b). As mentioned earlier, space missions like Gaia, with its high precision astrometry and pho- tometry, can be optimally complemented with data from surveys like GES and its large ground- based telescope data, which offers superior spectroscopic capabilities in contrast to the more limited resolution of the Gaia spectra. As illustrated in Fig. 1.23, Gaia and GES complement each other to obtain high-quality data, starting with the revolutionary high-precision astrometry of Gaia to provide positions, proper motions and parallaxes of an object, and then combining said astrometry information with the high-resolution spectroscopy of GES, supplementing radial velocities, astrophysical parameters and abundances (Gilmore et al., 2012). The responsibility of the Gaia data processing is entrusted to the Data Processing and Anal- ysis Consortium (DPAC) (Gaia Collaboration et al., 2016b). The data catalogues are released in stages containing increasing amounts of information, and so far they comprise three data releases, from Gaia DR1 and Gaia DR2 to the Gaia Early Data Release 3 (EDR3)3. The first data release, Gaia DR1 (Gaia Collaboration et al., 2016a), was based on 14 months of observations and took place on September 2016, while Gaia DR2 was released on April 2018, based on 22 months of observations (Gaia Collaboration et al., 2018b). In combination with GES iDR6, in the present project we have made use of the proper motions, parallaxes and photometry provided by the first installment of the third intermediate data release, Gaia EDR3, based on the data of the first 34 months of the mission. The full third data release is expected in 2022 (Gaia Collaboration et al., 2021). Gaia EDR3 provides, with increased precision and accuracy, an updated source list, astrometry, and broad photometry in the G, GBP and GRP bands, as well as an updated list of radial velocities (Gaia Collaboration et al., 2021). As for future releases, Gaia DR3 is expected in the second quarter of 2022, covering 34 months of data, and Gaia DR4 will be based on 66 months of data. Pending further approvals of mission extensions, additional releases will also take place. Gaia DR5 is currently anticipated to contain all collected data. 1.3.3 CoRoT, Kepler, K2, and TESS We finish this introductory chapter by further acknowledging that for our analysis in Chapter 3 we also made use of several sets of rotational periods (Prot) provided by missions such as CoRoT, Kepler, K2, and TESS. 3See https://www.cosmos.esa.int/web/gaia/earlydr3 to access Gaia EDR3 https://www.cosmos.esa.int/web/gaia/earlydr3 30 Chapter 1. Introduction Figure 1.25: An illustration of the Transiting Exoplanet Survey Satellite (TESS). Credits: NASA CoRoT (Convection, Rotation et Transits planétaires – Auvergne et al., 2009)4 was a 30- centimetre space telescope mission operating from 2006 until 2013. This mission had the ob- jectives of searching for rocky exoplanets with short orbital periods, in particular those with terrestrial size, as well as performing asteroseismology by measuring solar-like oscillation in stars and thus enabling the calculation of their mass, age and chemical compositions. CoRoT was the first spacecraft dedicated to the detection of transiting extrasolar planets, paving the way for more advanced missions such as Kepler and TESS. The main objective of the Kepler mission (Borucki, 2016)5, a space observatory launched in 2009 by NASA, was to explore the structure and diversity of planetary systems, and determine the frequency of Earth-size and larger planets in and near the habitable zone of Sun-like stars. Kepler surveyed a large sample of stars, applying the transit method in order to obtain the size and orbital distributions of transiting exoplanets, as well as studying the type of stars they orbit. K2 (Howell et al., 2014) was the second mission of Kepler, which started in 2013 as a result of a malfunction in the Kepler spacecraft, and allowed the Kepler space telescope to continue its observations until its retirement in 2018. Finally, TESS (Transiting Exoplanet Survey Satellite – Ricker et al., 2015)6 is a space tele- scope launched by NASA in 2018 which is also designed to search for exoplanets using the tran- sit method, in an area 400 larger than that covered by the Kepler mission, making it the first spaceborne all-sky transit survey. TESS is cataloguing the nearest and brightest stars hosting transiting planets, highly interesting targets for a number of investigations. 4https://www.esa.int/Science_Exploration/Space_Science/COROT_overview 5https://www.nasa.gov/mission_pages/kepler/overview/index.html 6https://tess.mit.edu/ https://www.esa.int/Science_Exploration/Space_Science/COROT_overview https://www.nasa.gov/mission_pages/kepler/overview/index.html https://tess.mit.edu/ 1.4. Description of the work 31 1.4 Description of the work In the present thesis, we calibrate a series of 42 open clusters and associations observed by GES iDR6, covering an age range from 1 Myr to 5 Gyr, in order to study lithium as an age indicator for pre- and main-sequence FGKM late-type stars, with the ultimate aim of calibrating an em- pirical Li-age relation. This work is organized as follows: In Chapter 2 we describe the cluster sample and constrain the cluster membership to obtain lists of candidate members for all target clusters, updating and expanding the work already published in Gutiérrez Albarrán et al. (2020). We begin with a general overview of the instru- ments, analysis strategy and data reduction of GES, and we describe the cluster sample used throughout this work in Sect. 2.1. In Sect. 2.2 we describe the criteria used in the membership analysis to identify likely cluster members, from radial velocity distributions to proper motions and parallaxes provided by Gaia, gravity indicators (log g and the γ index), colour−magnitude diagrams (CMDs) using photometry from Gaia, [Fe/H] metallicity, and lithium in EW (Li) vs Teff diagrams. Sect. 2.3 we discuss the selection of giant and non-giant (NG) outlier contaminants, particularly Li-rich giants, obtained as an additional result of the membership process. And lastly, in Sect. 2.4 we present our lists of candidate members for all clusters, and present some further discussion of our results. Individual cluster notes with more detailed information on the membership process for each of the clusters in the sample can be also found in Appendix B, and all individual figures from this chapter can be found in Appendix C. Finally, the description and links for the online long tables from this chapter are shown in Appendix D. In Chapter 3 we conduct a comparative study to quantify the observable lithium dispersion in the final candidate selection for each cluster, and analyse its dependence with a series of pa- rameters with the aim of confirming the correlations and findings of earlier publications. Firstly, we study the effects of rotation, using both vsini data from GES as well as several measurements of rotation periods (Prot) provided by Kepler, K2 and TESS (Sect. 3.1). Secondly, we study the effects of chromospheric activity (Hα) on the Li dispersion in the final cluster selections (Sect. 3.2). In both sections, we also address the effects of accretion in the case of the very young SFRs. The third section of this chapter concludes the study of the first two sections with a general overview of the evolution of rotation and activity across age and their dependence with colour and stellar mass, making use of rotation-colour and activity-colour diagrams (Sect. 3.3). Finally, we observe the effects of [Fe/H] metallicity on the Li envelopes of coeval clusters which present sufficiently differing values of [Fe/H], and assess the effects of significantly metal-rich and metal-poor clusters on the level of Li depletion (Sect. 3.4). We give a more detailed report of the effects of rotation, activity and metallicity for each cluster in the individual cluster notes in Appendix B, and all individual figures from this chapter can also be found in Appendix E. With the results from Chapter 2 and Chapter 3, having obtained lists of candidate members and established their dependence on several parameters, in Chapter 4 we calibrate a Li-age relation, creating empirical lithium envelopes for several key ages in our cluster sample. We display and discuss in detail these Li envelopes obtained as a result of this project in Sect. 4.1, and show the values we used to construct them in Appendix F. Additionally, in Sect. 4.2 we briefly discuss the LDB for those clusters in the 10–600 Myr range and the use of models such as (Baraffe et al., 2015; Somers et al., 2020) in order to characterize this area. Finally, we summarize our results and discuss our future work in Chapter 5. Chapter 2 Cluster sample and membership selections 2.1 Data 2.1.1 GES spectra and data reduction Figure 2.1: FLAMES and UVES. Credit: ESO GES observations are performed with the optical spectrograph FLAMES (Fibre Large Array Multi Element Spectrograph) at the VLT (Pasquini et al., 2002; Gilmore et al., 2022, submitted). FLAMES is a multi-object system feeding two different spectrograph covering the whole visual spectral range: GIRAFFE and UVES. UVES provides high-resolution spectra (R=50, 000) of mainly single FGKM stars (e.g., Smiljanic et al., 2014; Frasca et al., 2015; Lanzafame et al., 2015), but can only access up to eight objects at a time. GIRAFFE, for its part, obtains medium-resolution spectra (R=5, 000–20, 000) of up to 130 targets at the time and integral field spectroscopy, usually of late-type (F to M) stars in the PMS or MS phase (Gilmore et al., 2022, submitted). Supplemented by UVES spectra, GIRAFFE spectra in two settings have been obtained for statistically significant samples of stars in all major stellar populations. Additionally, several GIRAFFE settings, optimized for the astrophysical parameters of each target and also combined 33 34 Chapter 2. Cluster sample and membership selections Figure 2.2: Giraffe spectrograph general layout. Credit: ESO with parallel UVES spectra, have been obtained for each cluster in the GES sample. (Gilmore et al., 2022, submitted). Because open clusters show a large variety of ages, spectral types and luminosities, and evolutionary phases, the choice of which instrument and setup to use in each case must take all these aspects into account. Brighter cluster stars (PMS members and evolved giants) tend to be measured employing the UVES/U580 setting, while GIRAFFE/HR15N (and occasionally GIRAFFE/HR09B) is typically used to measure cool stars and fainter cluster mem- bers (PMS or turn-of stars) (e.g., Gilmore et al., 2022, submitted). The GIRAFFE/HR15N setup is particularly useful for the study of young stars, considering that it covers both the Hα and Li (6707.84 Å) spectral regions. However, fundamental parameters such as Teff , log g and [Fe/H] are less well determined in this wavelength range than in other settings (e.g., Lanzafame et al., 2015). The GES consortium is structured in 19 working groups (WGs), WG0 to WG18, organized in a workflow and dedicated to different survey tasks (see Fig. 2.3) (e.g., Gilmore et al., 2012; Lanzafame et al., 2015; Sacco et al., 2015; Gilmore et al., 2022, submitted). All work respon- sibilities are distributed to teams with relevant expertise and appropriate resources, and each active participant group includes a number of Co-Investigators (Co-Is). The two Co-Principal Investigators (Co-PIs) of the consortium are the point of contact to ESO, and are assisted by a steering committee. The structure of the WGs ensures a close coordination between the teams with well-established and documented methodologies. The tasks of the WGs are to implement the data flow, from target selection and characterization to, among others, observing, pipeline data processing, spectral analysis to derive abundances, astrophysical parameters and stellar properties, parameter checking and homogenization, then science quality control, preparation and documentation, and, finally, delivery of the external data products to both ESO and the public archive1 (e.g., Gilmore et al., 2022, submitted). In addition to the WGs, a significant num- ber of GES Builders have also provided numerous efforts to deliver GES data analysis and results. Among these WGs, WG10 and WG11 are focused on the spectroscopic analysis of the GI- RAFFE and UVES FGKM late-type stars, respectively (e.g., Gilmore et al., 2012; Sacco et al., 2015), while WG12 is dedicated to the analysis of PMS stars in the fields of young clusters using both UVES and GIRAFFE data. Each WG is divided into several nodes, each of which pro- cesses sets of spectra using the similar approaches, models and methodology, but also combining 1https://www.gaia-eso.eu/ https://www.gaia-eso.eu/ 2.1. Data 35 Figure 2.3: Gaia-ESO Survey data flow schematic, summarizing the roles of all WGs and the steps from pre-observation target selection to data processing, data spectrum analysis, astro- physical parameter determinations, calibration, homogenization, and the delivery of science data for verification analysis. Credit: Gilmore et al. (2012) Table 2.1: WG11 and WG12 nodes Node name Institute Bologna Space Science observatory of Bologna (OAS) OACT Osservatorio Astrofisico di Catania CAUP Centro de Astrofísica da Universidade do Porto Concepción Universidad de Concepción, Departamento de Astronomía EPINARBO ESO-Padova-Indiana-Arcetri-Bologna IAC-AIP IAC — Instituto de Astrofísica de Canarias; AIP — Leibniz Institue for Astrophysics Postdam Liège Centre Spatial de Liège LUMBA Lund-Uppsala-MPA-Bordeaux-ANU Nice Nice Observatory, Observatoire de la Côte d’Azur Paris-Heidelberg Paris — Institut Astrophysique de Paris; Heidelberg — Center for Astronomy of Heidelberg University UCM Universidad Complutense de Madrid ULB Université Libre de Bruxelles, Institut d’Astronomie et d’Astrophysique Vilnius Institute of Theoretical Physics and Astronomy of Vilnius University INAF-Arcetri Osservatorio Astrofisico di Arcetri INAF-Palermo (OAPA) Osservatorio Astrofisico di Palermo ETH Institute for Particle Physics and Astrophysics of Zürich different analysis methods and software (Smiljanic et al., 2014; Lanzafame et al., 2015; Gilmore et al., 2022, submitted). The UVES data of late-type stars in WG11 are analysed in paral- lel by 13 different nodes (Bologna, OACT, CAUP, Concepcion, EPINARBO, IAC-AIP, Liège, LUMBA, Nice, Paris-Heidelberg, UCM, ULB, and Vilnius; see Table 2.1) (Smiljanic et al., 2014) , and the analysis of PMS stars in WG12 are carried out by six nodes (INAF-Arcetri, CAUP, OACT, INAF-Palermo (OAPA), UCM, and ETH; see Table 2.1) (Lanzafame et al., 2015). For more specific and extensive details on the methodology and the codes employed by each node, see Smiljanic et al. (2014) (WG11), Lanzafame et al. (2015) (WG12), and Gilmore et al. (2022, 36 Chapter 2. Cluster sample and membership selections submitted) (all WGs). As we will see below in some more detail, our UCM node is part of both WG11 and WG12, and we have determined atmospheric parameters by employing the code stepar (Tabernero et al., 2019), based on equivalent widths automatizing the use of moog code (Sneden et al., 2012) and measured with the automatic tool tame (Tool for Automatic Measure- ment of Equivalent Widths – Kang & Lee, 2012; Tabernero et al., 2019). Figure 2.4: An overview of the Gaia-ESO Survey data flow system. Credit: GES Although a detailed discussion of all WGs is beyond the scope of this section (see, for ex- ample, Gilmore et al. (2022, submitted) and (Randich et al., 2022, submitted)), we would also like to briefly mention the role of WG1, WG4 and WG6, discussed in detail by Bragaglia et al. (2021), as regards the preparation of the observations and the selection of the most probable targets within each of the open clusters (OCs, also see Sect. 1.3). Candidate target selection for GES, conducted before the data from Gaia DR2 was available, was based on public and private photometry, as well as ground-based proper motions, radial velocities, lithium abundance, chro- mospheric activity and X-ray properties, when available, with the aim of studying the targets in colour-magnitude diagrams (CMDs). Previous information on secure membership was used for UVES target stars, while GIRAFFE targets were selected in an unbiased way from the CMDs, rather than limiting the selection to high probability members. The selection of targets in gen- eral was meant to be as unbiased and inclusive as possible, observing at least a representative fraction of all targets. The 65 OCs ultimately observed by GES include young clusters with a majority of PMS stars (as well as some MS stars), and intermediate-age and old clusters hosting mainly evolved stars (Bragaglia et al., 2021). An important focus of GES is to be able to provide astrophysical parameters on the widest possible range of stellar populations, and ensure that said parameters are both consistently de- rived and consistently calibrated (Gilmore et al., 2022, submitted). GES analyses are performed in cycles, after the reduction of new observed spectra (Lanzafame et al., 2015; Sacco et al., 2015). As additional input we can also list photometric data, the radial and rotational velocities derived 2.1. Data 37 by WG8, and first guess atmospheric parameters derived by WG9, as well as cluster distances and reddening (Gilmore et al., 2022, submitted). Recommended parameters are defined by im- proving upon each new analysis by means of updated input and methods, using a calibration strategy described in Pancino et al. (2017). The data analysis from each cycle is distributed and duplicated among all contributing nodes, and more than one WG analyses and produces results for the same survey targets. The outcome of all these cycles are then homogenized into the final recommended parameters and updated abundances, after a rigurous process of quality control and other internal checks following the data homogenization (in coordination with WG15) (e.g., Gilmore et al., 2022, submitted; Randich et al., 2022, submitted). As a result of all this process, an internal data release (iDR) is produced and made available first to the GES consortium, and then publicly through the ESO archive (e.g., Lanzafame et al., 2015; Gilmore et al., 2022, sub- mitted; Randich et al., 2022, submitted). The output parameters resulting from the spectroscopic analyses of the WGs are divided into raw, fundamental and derived parameters (e.g., Lanzafame et al., 2015; Gilmore et al., 2022, submitted): Raw parameters, such as Hα emission and Li equivalent widths (EW s), are directly measured on the input spectra and do not require any prior information. Their values are used in the case of groups such as WG12 to optimize the evaluation of the fundamental parame- ters, which include Teff , log g, [Fe/H], projected rotational velocity (v sin i), veiling (r), and the gravity-sensitive spectral index γ (Damiani et al., 2014). Lastly, derived parameters, such as elemental abundances and chromospheric activity indices, are those that require prior knowledge of the fundamental parameters (Lanzafame et al., 2015; Gilmore et al., 2022, submitted). Smil- janic et al. (2014) derived parameters for UVES spectra of FGKM stars, while Lanzafame et al. (2015) did the same specifically for PMS stellar spectra. Six analysis cycles and internal releases have been carried out by GES, from iDR1 to iDR62. These releases include stacked spectra and tables of metadata derived from all the observations collected until the completion of the survey in January 2018 (Randich et al., 2022, submitted): iDR1, the first data release, includes the analysis of the first six months of observations (up to June 2012), and it was released to the consortium in August 2013. iDR2, which includes the analysis of the first 18 months of observations (up to June 2013), was released in July 2014. This was the first time that astrophysical parameters and radial velocities were homogenized. No updates were made to methods and tools for iDR3, released to the consortium in January 2015 and containing analysis of spectra obtained between July-December 2013. iDR4 (the data release we initially used in Gutiérrez Albarrán et al. (2020)) includes the analysis of the first 31 months of observations (up to July 2014) and was made available to the consortium in February 2016. For this release homogenization of abundances was achieved for the first time, as well as improved recommended parameters. No changes were introduced to the line list and synthetic spectra with respect for iDR5, comprising the analysis of the first 48 months of observations (up to December 2015), and was released in November 2017 (Randich et al., 2022, submitted). For all the following analysis presented in this paper we used the data provided by the sixth and last internal data release of GES (iDR6). iDR6 is a full release, including all observations from the beginning of the Survey until its completion in January 2018 (Gilmore et al., 2022, submitted; Randich et al., 2022, submitted). Similarly to iDR5, the same line list and grid of synthetic spectra used for iDR4 were employed in this final release as well. The analysis took considerably longer than with former releases, due in part to the larger dataset, and partly as a consequence of a more detailed quality control. This final GES catalogue provides results for 2See https://www.gaia-eso.eu/data-products for all public and internal GES releases https://www.gaia-eso.eu/data-products 38 Chapter 2. Cluster sample and membership selections 114, 917 targets and includes data on velocities, stellar parameters, and abundances for up to 32 elements (Randich et al., 2022, submitted). Figure 2.5: Example of the initial TAME measurements of the Li I line for iDR4 NGC 6705 spectra. Figure 2.6: The Li I and Fe I lines in two NGC 6705 iDR4 spectra plotted with IRAF. The left panel shows an example of a spectrum showing distinguishable lines that can be deblended, while the right panel is an example of spectra for which only EW (Li I + Fe I) can be measured. Before delving fully into a description of the cluster sample used throughout this work, we end this subsection by briefly adding some more details on the measurements of the equivalent widths of UVES spectra conducted by the GES UCM node as part of WG11 and WG12. In the first stages of this thesis project, I performed an extensive analysis of a large number of UVES spectra, manually measuring the equivalent widths (EW s), both the Li I line at 6707.76 Å and the adjacent Fe I line at 6707.43 Å (EW (Fe)), as part of the work to deliver results for iDR4. As 2.1. Data 39 mentioned earlier, the initial EW s were measured with the automatic tool tame (see Fig. 2.5) (Kang & Lee, 2012; Tabernero et al., 2019). This tool allowed us to discard all spectra with EW (Li)<5 mÅ. We then performed an individual analysis of each of the remaining spectra by measuring the EW (Li) and EW (Fe) lines manually with the iraf task splot (e.g., Smiljanic et al., 2014; Lanzafame et al., 2015), using the tame values for comparison purposes. With enough resolution (among other factors such as the lack of broadening because of rotation), the Li line and the nearby blends are distinguishable, and so the EW (Li) and EW (Fe) lines can be measured individually (see Fig. 2.6, left panel), deblending and adopting a Gaussian fitting to the line profile. However, in the case of lower resolution spectra, only EW (Li I + Fe I) can be measured (see Fig. 2.6, right panel). EW s were corrected as EW (Li) = EW (Li I + Fe I)−EW (Fe) in those cases where the Li and Fe lines could not be resolved. For these spectra, EW (Fe) was estimated using the ewfind driver within moog code (Sneden et al., 2012), adopt- ing the recommended stellar parameters3. 2.1.2 Cluster sample Our present sample from GES iDR6 includes 114, 325 UVES and GIRAFFE spectra of 42 open clusters ranging in ages from 1 Myr to 4.5 Gyr4. This is a larger and improved sample compared to the one used in Gutiérrez Albarrán et al. (2020). We now list the changes and improvements of the updated iDR6 sample used in this work, in contrast to the former iDR4 cluster sample: ∗ The number of stars in the current iDR6 sample is considerably larger than the 12, 493 UVES and GIRAFFE spectra we had at our disposal for our first preliminary results of our cluster calibrations. This larger number of stars in the fields of many of our sample clusters has improved our membership analysis and increased the number of final candidates in more than one case. ∗ Several issues have also been solved thanks to this larger sample, such as the fact that with our former iDR4 file only a few UVES Li values were listed for many of the intermediate-age and old clusters, especially in the 3000–4000 K age range (M-type stars, more difficult to measure in those age ranges). Thus, we had to make additional use of the individual lithium measurements derived by the OACT (Osservatorio Astrofisico di Catania) node, adding to our sample a num- ber of GIRAFFE stars which had no recommended EW (Li) values in the iDR4 file. We note that, even considering the list of spectra which were deprecated in the working version of iDR6 released to the consortium in December 2020, we have observed no such lack with our present sample, and our former member lists have either been typically enlarged, or at least have stayed with approximately the same number of candidate stars. ∗ In addition to the larger number of spectra overall, we now count with 86 open clusters in the current iDR6, 38 more than in iDR4. Our former iDR4 sample offered a total of 38 clusters, 26 of them being open clusters, and the remaining 12 of them being globular, which we discarded. We do not consider any iDR6 globular cluster in this updated analysis either, as lithium cannot be used as a youth indicator in those cases. 3More details about how the final recommended EW s were determined, as well as the associated errors, can be found in, e.g. Smiljanic et al. (2014), Lanzafame et al. (2015), and Tabernero et al. (2019) 4See http://ges.ast.cam.ac.uk/GESwiki/GeSDR6/DataProducts for the iDR6 data products released to the GES consortium http://ges.ast.cam.ac.uk/GESwiki/GeSDR6/DataProducts 40 Chapter 2. Cluster sample and membership selections Table 2.2: Age estimates, reddening, distance to the Sun, and GES and Gaia membership studies from the literature for the 15 SFRs and young clusters in our sample. Cluster Age E(B-V)a Distance References References GES and Gaia membership name (Myr) (dex) (kpc) Ages Distance studies NGC 6530 1–2 0.44± 0.10 1.33 3, 4, 18, 19, 20, 33 18, 19, 20, 21 2, 3, 16, 18, 19, 22 ρ Oph 1–3 0.76± 0.13 0.13± 0.01 1, 2, 3, 4, 5, 33, 61 1, 2, 6 1, 2, 3, 6 Trumpler 14 1–3 0.61± 0.10 2.90 3, 4, 13, 33 13, 14 2, 3, 15, 17 Cha I 2 0.18± 0.08 0.16± 0.02 3, 4, 7, 8, 9, 33 7, 8, 10, 11 2, 3, 7, 8, 10, 11b, 12 NGC 2244 4 0.49± 0.09 1.59 3, 23, 24, 33 21, 23, 24, 25 3, 15, 24, 26 NGC 2264 4 0.05± 0.05 0.76 2, 3, 4, 27, 28, 29, 30, 33 2, 15, 25, 28, 29 2, 3, 15, 31, 32 λ Ori 6 0.09± 0.04 0.41 3, 43 34 3, 15 Col 197 13 0.64± 0.07 0.80–0.90 3, 5, 13, 35, 36, 37 13, 25, 35, 36, 37 3, 15 γ Vel 10–20 0.04± 0.03 0.35–0.40 2, 3, 8, 10, 38, 39, 40, 41, 42 8, 10, 38, 40, 41 2, 3, 8, 10, 38, 39, 40, 41, 44, 45, 46 NGC 2232 18–32 0.04± 0.03 0.32 3, 5, 43, 47, 48 13, 25, 48 3, 15, 43, 48 NGC 2547 20–45 0.06± 0.03 0.36± 0.02 2, 3, 5, 8, 32, 41, 48, 49, 50, 51, 63 2, 8, 41, 48 2, 3, 8, 15, 32, 48, 49, 52 IC 2391 36± 2 c 0.03± 0.01 0.16± 0.01 3, 48, 51, 53 2, 48, 54, 55, 56 2, 3, 15, 49, 52, 62 IC 2602 35± 1 c 0.04± 0.02 0.15± 0.01 3, 5, 48, 51 2, 48, 56 2, 3, 15, 49, 52, 62 IC 4665 38± 3 c 0.15± 0.02 0.36± 0.01 3, 5, 48, 51 2, 48, 57, 58 2, 3, 15, 48, 49, 52, 62 NGC 2451 B 39± 1 c 0.10± 0.03 0.36 3, 42, 48, 49, 51, 59, 60 48, 59 2, 3, 15, 48, 49 NGC 2451 A 44± 2 c 0.02± 0.02 0.19 3, 42, 48, 49, 51, 59, 60 48, 59 2, 3, 15, 48, 49 a References for the E(B-V) reddening adopted from Jackson et al. (2021) for all clusters ; b GES studies that reference the clusters and/or study them without taking membership analysis primarily into account; c Updated cluster ages using Gaia data, as listed by Bossini et al. (2019) References. For the cluster ages, reddening and distances shown here we chose the most recent or most robust estimates for each cluster, but several studies are further cited here, and larger ranges taking into account more than one literature value are additionally cited in the individual notes of Appendix B: (1) Rigliaco et al. (2016); (2) Spina et al. (2017); (3) Jackson et al. (2021); (4) Randich et al. (2020); (5) Romano et al. (2021); (6) Cánovas et al. (2019); (7) Spina et al. (2014a); (8) Sacco et al. (2015); (9) López Martí, Belén and Jiménez-Esteban, Francisco and Bayo, Amelia and others; (10) Frasca et al. (2015); (11) Roccatagliata et al. (2018); (12) Galli et al. (2021); (13) Sampedro et al. (2017); (14) Mel’nik & Dambis (2017); (15) Cantat-Gaudin et al. (2018); (16) Castro-Ginard et al. (2020); (17) Damiani et al. (2017); (18) Wright et al. (2019); (19) Damiani et al. (2019); (20) Prisinzano et al. (2005); (21) Kuhn et al. (2019); (22) Prisinzano et al. (2019); (23) Mužić et al. (2019); (24) Michalska (2019); (25) Kharchenko et al. (2005); (26) Carrera et al. (2019); (27) Arancibia-Silva et al. (2020); (28) Bonito et al. (2020); (29) Gillen et al. (2020); (30) Venuti et al. (2019); (31) Maíz Apellániz (2019); (32) Jackson et al. (2016); (33) Randich et al. (2022, submitted); (34) Dib et al. (2018); (35) Dias et al. (2019); (36) Bonatto & Bica (2010); (37) Vande Putte et al. (2010); (38) Jeffries et al. (2014); (39) Spina et al. (2014b); (40) Franciosini et al. (2018); (41) Beccari et al. (2018); (42) Franciosini et al. (2021); (43) Binks et al. (2022, in prep.); (44) Damiani et al. (2014); (45) Prisinzano et al. (2016); (46) Cantat-Gaudin et al. (2019); (47) Liu & Pang (2019); (48) Pang et al. (2021); (49) Randich et al. (2018); (50) Sestito & Randich (2005); (51) Bossini et al. (2019); (52) Bravi et al. (2018); (53) Dumont et al. (2021b); (54) Platais et al. (2007); (55) De Silva et al. (2013); (56) Smiljanic et al. (2011); (57) Martín & Montes (1997); (58) Jeffries et al. (2009a); (59) Silaj & Landstreet (2014); (60) Netopil & Paunzen (2013); (61) Kiman et al. (2021); (62) Gómez Garrido (2015); (63) Oliveira et al. (2003). ∗ In our current iDR6 sample, the data for the open clusters which were suffering from the contamination of nebular lines, which can affect the radial velocity distributions and therefore the final membership analysis (e.g., Bonito et al., 2013, 2020), have been corrected by recalculating the radial velocities and applying an alternative different sky background substraction (Gilmore et al., 2022, submitted). Thus, we have been able to add to our sample a number of young and intermediate-age clusters we had to formerly discard because they exhibited high differential nebulosity (such as NGC 2264, NGC 2451 A and B, NGC 3532, NGC 6530, and Trumpler 145). ∗ Finally, we also note that, seeing as we focus in this study on FGKM stars, we discarded all stars with Teff > 7500 K from the cluster sample in all cases. Given the nature of our mem- bership criteria (see Sect. 2.2), for each cluster we have also deprecated from our membership 5The reason this improved sky background substraction could not be done for earlier releases to the level iDR6 has finally achieved is that the Survey being fiber-fed, substraction of the nebular sky background is not a straightforward procedure (Bonito et al., 2020) 2.1. Data 41 Table 2.3: Age estimates, reddening, distance to the Sun, and GES and Gaia membership studies from the literature for the 26 intermediate-age and old clusters in our sample. Cluster Age E(B-V)a Distance References References GES and Gaia membership name (Myr) (dex) (kpc) Ages Distance studies NGC 6405 94 0.14± 0.04 0.46 1, 2, 3 2, 3, 4, 5 1, 3, 6 Blanco 1 94± 5 c −0.01± 0.03 0.23–0.24 1, 10, 15, 16, 17, 18 17, 18 1, 18 NGC 6067 120 0.34± 0.04 1.4–1.7 1, 7, 8, 9, 10, 11 4, 5 1, 6, 11 NGC 6649 120 1.43± 0.05 1.8± 0.1 12, 13, 14 12, 14 1, 6 NGC 2516 125–138 0.11± 0.03 0.41 1, 9, 19, 21, 22 23, 24 1, 6, 20, 25, 26, 27, 28 NGC 6709 173± 34 c 0.27± 0.02 1.1 1, 10, 15, 29 4, 29 1, 6 NGC 6259 210 0.63± 0.09 1.9 1, 9, 30, 31 4, 29 1, 6 NGC 6705 280 0.40± 0.06 1.88 1, 9, 10, 26, 27 4, 24 1, 6, 26, 27, 32, 33, 34b Berkeley 30 300 0.51± 0.04 4.7–4.9 1, 4, 10, 30 4, 30 1, 6 NGC 6281 314 0.18± 0.02 0.47–0.51 1, 24, 30, 36 4, 30, 36 1, 6 NGC 3532 399± 5 c 0.05± 0.02 0.48–0.49 1, 10, 15, 28, 35 4, 28 1, 6, 28, 36, 37 NGC 4815 560 0.70± 0.07 2.40–2.90 1, 26, 27, 31, 37 24, 37 1, 6, 26, 27, 32, 33, 34, 37 NGC 6633 575 0.15± 0.04 0.39 1, 26, 27, 31, 38 4, 24 1, 6, 20, 26, 27 NGC 2477 700 0.31 1.4 39 3, 4, 6, 12, 39 6, 40 Trumpler 23 800 0.68± 0.04 2.20 1, 26, 27, 31, 43 24, 43 1, 26, 27, 42 Berkeley 81 860± 100 0.85± 0.04 3.00 1, 10, 26, 27, 31, 34, 45 24, 45 1, 6, 26, 27 NGC 2355 900 0.13± 0.03 1.80± 0.07 1, 4, 10, 30 42 1, 6, NGC 6802 900 0.79± 0.06 1.80 1, 10, 26, 27, 31, 44 24 1, 6, 26, 27, 44 NGC 6005 973± 4 c 0.49± 0.06 2.70 1, 15, 26, 27, 31 4, 24 1, 6, 26, 27 Pismis 18 1200± 400 +0.22± 0.04 2.20 27, 28, 31 24 1, 27, 28 Melotte 71 1294± 89 c 0.11 2.2–3.2 8, 15 4, 42 6 Pismis 15 1300 0.56± 0.05 2.6–2.9 1, 4, 30 4, 30 1, 6 Trumpler 20 1400 0.37± 0.03 3.00 1, 10, 26, 27, 41 24, 41 1, 6, 26, 27, 33, 41, 46 Berkeley 44 1600 0.90± 0.07 1.80–3.10 1, 10, 26, 27, 31, 47 24, 47 1, 6, 26, 27 NGC 2243 4000± 120 0.04± 0.04 4.50 1, 10, 27, 31, 48, 49, 50 24, 32, 49 1, 6, 27 M67 4000–4500 0.059 0.90 21, 38, 51, 52 4, 12 40 a References for the E(B-V) reddening adopted from Jackson et al. (2021) for all clusters except for NGC 2477 Rain et al. (2021); b GES studies that reference the clusters and/or study them without taking membership analysis primarily into account; c Updated cluster ages using Gaia data, as listed by Bossini et al. (2019). References. For the cluster ages, reddening and distances shown here we chose the most recent or most robust estimates for each cluster. Several studies are further cited here, and larger ranges taking into account more than one literature value are additionally cited in Appendix B: (1) Jackson et al. (2021); (2) Kılıçoğlu et al. (2016); (3) Gao (2018); (4) Kharchenko et al. (2005); (5) Mel’nik & Dambis (2017); (6) Cantat-Gaudin et al. (2018); (7) Frinchaboy & Majewski (2008); (8) Netopil et al. (2016); (9) Randich et al. (2020); (10) Romano et al. (2021); (11) Rangwal et al. (2019); (12) Dib et al. (2018); (13) Liu & Pang (2019); (14) Alonso-Santiago et al. (2020); (15) Bossini et al. (2019); (16) Pang et al. (2021); (17) Gillen et al. (2020); (18) Zhang et al. (2020); (19) Binks et al. (2022, in prep.); (20) Randich et al. (2018); (21) Dumont et al. (2021b); (22) Franciosini et al. (2021); (23) Jeffries et al. (2001); (24) Dias et al. (2002); (25) Jackson et al. (2016); (26) Jacobson et al. (2016); (27) Magrini et al. (2017); (28) Fritzewski et al. (2019); (29) Vande Putte et al. (2010); (30) Sampedro et al. (2017); (31) Magrini et al. (2018); (32) Magrini et al. (2014); (33) Tautvaišienė et al. (2015); (34) Magrini et al. (2015); (35) Dobbie et al. (2012); (36) Fritzewski et al. (2021); (35) Hetem & Gregorio-Hetem (2019); (36) Joshi et al. (2016); (37) Friel et al. (2014); (38) Sestito & Randich (2005); (39) Rain et al. (2021); (40) Jadhav et al. (2021); (41) Donati et al. (2014b); (42) Buckner & Froebrich (2014); (43) Overbeek et al. (2017); (44) Tang et al. (2017); (45) Donati et al. (2014a); (46) Smiljanic et al. (2016); (47) Hayes & Friel (2014); (48) Heiter et al. (2014); (49) Jacobson et al. (2011); (50) Friel & Janes (1993); (51) Pallavicini et al. (2005); (52) Richer et al. (1998). study all stars with no measurements of RV s (VRAD in the iDR6 file), either Teff (TEFF ) or the newly measured infrared photometric temperatures (TEFF_IRFM ), and/or EW (Li) (be it the corrected equivalent widths, EWC_LI, or the improved EW s with an additional veiling correction, EW_LI_UNVEIL). Out of the 86 open clusters measured in the iDR6 file, we have discarded all clusters with less than 100 stars, in order to have a sufficient minimum number of stars in each cluster to ensure a better membership analysis. On the other hand, old clusters with ages older than 2 Gyr are of 42 Chapter 2. Cluster sample and membership selections less interest for our study of the Li-age relation than young and intermediate-age clusters, due to lithium depletion being virtually negligible for older age ranges, especially for GKM-type stars. For this reason, we have not taken into account any old clusters in the iDR6 file with ages older than 2 Gyr, other than the ones we had already analysed in Gutiérrez Albarrán et al. (2020). We have also only analysed four additional clusters in the 0.8–2 Gyr age range, as we already counted with nine old clusters in our first sample selection with ages 0.8–4.5 Gyr, and preferred rather to add more new young and intermediate-age clusters to our updated study, adding to the age ranges where lithium is increasingly relevant for the analysis at hand. This criteria leaves us with 42 clusters constituting our current sample, including seven star-forming regions (SFRs, 1–6 Myr) and nine young clusters (10–50 Myr), along with 13 intermediate-age clusters (90–575 Myr), and 13 old clusters (0.7–4.5 Gyr). In the next Sect. 2.2 we will be discussing the membership criteria followed to present the lists of candidate members for all the clusters included in this sample. A number of membership studies have already been conducted, and potential members have been identified for all 42 clusters selected in the present paper. These studies, particularly those who have made use of GES data and specifically iDR6 data, have been of great use to evaluate the goodness of our membership analysis by comparing our final candidates with previous membership lists. We show all these studies in Tables 2.2 and 2.3. We divided the sample clusters into groups according to age, and show them in two tables for convenience due to their length: Table 2.2 lists the young (1–50 Myr) clusters, while Table 2.3 lists the intermediate-age (50–700 Myr) and old clusters (> 700 Myr). As indicated in the table footnotes, we also differentiate between publications that include membership studies, and the few that only mention them and/or study them without taking membership analysis primarily into account. In the individual notes of Appendix B, where we present our results of cluster membership, we reference these studies in greater detail for each of the clusters. Tables 2.2 and 2.3 also list the age estimates, distances and reddening values from the literature for all clusters, and we additionally refer to Table 2.4 for radial velocities (RV s) from the literature, to Table 2.5 for proper motions (pmra and pmdec) and parallaxes (π) from Gaia, and to Table 2.6 for [Fe/H] metallicities from the literature. 2.2 Selection criteria and membership analysis To obtain final lists of candidate members for the 42 clusters in our sample, we conducted a homogeneous and coherent analysis of their membership according to the following criteria: • RV analysis (Sect. 2.2.1): We studied the radial velocity distribution of each cluster by applying a two-sigma clipping procedure and adopting a certain limit about the cluster mean yielded by the Gaussian fit to identify the most likely kinematic members. • Gaia astrometry (Sect. 2.2.2): As the next step we reinforce the kinematic selection and obtain lists of probable astrometric members with the aid of the proper motions and par- allaxes provided by Gaia EDR3, analysing the locus of probable members in pmra-versus- pmdec diagrams, and studying the parallax distributions with a Gaussian fit, similarly to the case of RV s. • Gaia photometry (Sect. 2.2.3): We also made use of Gaia EDR3 photometry to analyse the goodness of the astrometric candidates and discard field contaminants in G-versus- GBP−RP colour-magnitude diagrams (CMDs). 2.2. Selection criteria and membership analysis 43 • Gravity indicators (Sect. 2.2.4): We use the Kiel (log g-versus-Teff) diagram to identify outliers, such as lithium-rich giant stars and other field contaminants, which we disregard hereafter during our analysis. In the case of young clusters, we mainly use the gravity indicator γ to effectively discard giant contaminants as a first step of the membership process. Regarding the order of criteria, for the young clusters we discarded all giant contaminants using the γ index before performing the RV and astrometric analyses, due to their appreciable field contamination. • Metallicity (Sect. 2.2.5): An analysis of the metallicity distributions for each cluster, similarly to the analysis of both RV s and parallaxes, provides further confirmation of the membership of the candidate stars. • Lithium content (Sect. 2.2.6): Probable candidates are considered lithium members ac- cording to their locus in the EW (Li)-versus-Teff diagrams. Seeing as our work revolves around the calibration of lithium and its observable dispersion, this is one of the final cri- teria so as to already count with a robust list of probable cluster members and add the least bias to our study in this respect. • Other Gaia membership studies (Sect. 2.2.7): Finally, we made use of additional studies conducted from Gaia DR1, DR2 and EDR3 data (e.g., Cantat-Gaudin et al., 2018; Randich et al., 2018; Soubiran et al., 2018; Bossini et al., 2019; Jackson et al., 2021) to better confirm the robustness of our final candidate selections. These studies were also of great help to decide on the membership of marginal members according to one of more criteria. We also note that for all clusters we identified and discarded a series of binary stars, both SB1 (single line spectroscopic binaries) and SB2/3/4 (double and multiple line spectroscopic binaries), which can add significant contamination to our analysis. SB1s were excluded from our kinematic analysis, as they can strongly affect the observed RV distributions, but we included them in the rest of our membership analysis because lithium measurements are not affected. On the other hand, SB2/3/4s were fully discarded from our data sample for all clusters. These binary stars were identified using the iDR6 data release metadata (via the column PECULI ) (e.g., Gilmore et al., 2022, submitted), as well as existing studies (Merle et al., 2017, 2020). SB1 and SB2/3/4 stars are listed in the long tables of Appendix D. 2.2.1 Kinematic selection The aim of the GES target lists for open clusters is to produce unbiased catalogues of stars with selection criteria based on homogeneous photometric data covering a large area of the cluster field (e.g., Spina et al., 2014b). However, despite the fact that the spectroscopic targets in the field of the clusters we are studying were photometrically selected to be likely members, the GES sample also suffers from significant field star contamination. A large number of potential contaminants are also observed and have to be identified and separated from the cluster stars a posteriori, on the basis of their RV and astrometry measurements (e.g., Friel et al., 2014; Cantat-Gaudin et al., 2018). Thus, the analysis of the distributions of radial velocity (and astrometric criteria as well, as we will see in Sect. 2.2.2) is decisive in order to estimate the cluster membership on the basis of a first selection of their potential kinematic candidates. We obtained kinematic candidates for each cluster by studying the velocity distributions of the RV measurements derived from both the iDR6 UVES and GIRAFFE spectra. For this, we used RStudio, an integrated development environment (IDE) for R, a programming language for 44 Chapter 2. Cluster sample and membership selections RV [km/s] N −50 0 50 100 150 0. 00 0 0. 01 5 0. 03 0 RV [km/s] N 30 35 40 0. 00 0. 10 0. 20 RV [km/s] N 32 34 36 38 40 0. 00 0. 10 0. 20 Figure 2.7: Example of the distribution of radial velocities and RV selection for stars in the field of the cluster NGC 6705. The top panel shows the initial RV distribution for all the GES sources. We discard a few contaminants at the tails using the RStudio boxplot command (middle panel), and we show the Gaussian fit of the peak of the distribution using the 2σ clipping procedure around the median (bottom panel). statistical computing and graphics. First, we discarded initial field outliers at the tails of each of the RV distributions using the boxplot command (see Fig. 2.9). This tool shows the interquartile range (IQR) in a box-and-whisker plot, indicating the spread of the values in the distribution and the most probable outliers. The demarcation line for outliers is 1.5xIQR, that is, any value lying more than 1.5 times the length of the box from either end is considered to be a clear outlier 2.2. Selection criteria and membership analysis 45 RV [km/s] N 30 32 34 36 38 40 42 0. 00 0. 10 0. 20 Figure 2.8: Example of the gaussian fit of the RV distribution for a member selection of the cluster NGC 6705 resulting from our membership analysis. of the distribution. Figure 2.9: Example of the use of the boxplot command, showing probable field outliers at the tails of the RV distribution for the cluster NGC 6705. We then fitted a Gaussian curve to the resulting distribution by applying an iterative two- sigma clipping procedure on the median (e.g., Donati et al., 2014b; Friel et al., 2014). The 2σ clipping algorithm proceeds as follows: Firstly, we fitted the distribution with a Gaussian curve to calculate its median (m) and standard deviation (σ). All points smaller or larger than m±2σ are then disregarded. This is repeated in an iterative manner until convergence is reached and the obtained σ remains within a certain tolerance level of the previous one. In each iteration, the range of input data decreases, and so outliers can be effectively removed from the distri- bution. In the same way as the analysis carried out by studies such as Friel et al. (2014), we minimize the influence of the field star contaminants that could affect the estimate of the average value by relying on the median of the distribution, a more robust measure of the cluster velocity than the mean, which is more significantly affected by the presence of outliers in the distribution. After convergence is reached, this method results in final average velocities and dispersions 46 Chapter 2. Cluster sample and membership selections for each cluster. We consider as RV members all stars with RV s lying within 2σ from the av- erage cluster velocity provided by the fit. In several clusters we also encounter a series of stars which are marginal kinematic members according to this criteria, with RV s deviating from the limits established by this 2σ interval by 5 to 10 km s−1. We include these borderline kinematic members as part of our selection by considering a larger σ interval for these stars, given that they also fulfil the rest of our membership criteria, find them to be good spectroscopic candidates, and particularly, when they are found to be robust astrometric members (see Sect. 2.2.2). We discuss these instances in more detail for each cluster in the individual notes of Sect. B. We report all the mean RV values and their associated dispersions in Table 2.4, and we also present the kinematic distributions for all clusters in our sample in Appendix C. Regarding the specific case of those clusters that display two peaks in their RV distributions (γ Vel and NGC 2547), we note that in this analysis we relied primarily on the member selections presented in the literature, and we have done similarly with NGC 2451 A and B (Damiani et al., 2014; Jeffries et al., 2014; Spina et al., 2014b; Frasca et al., 2015; Sacco et al., 2015; Jackson et al., 2016; Prisinzano et al., 2016; Beccari et al., 2018; Bravi et al., 2018; Cantat-Gaudin et al., 2018; Franciosini et al., 2018; Randich et al., 2018; Jackson et al., 2021; Pang et al., 2021), as listed in Table 2.2. For the remaining 38 clusters analysed here, Table 2.4 presents mean RV values from the literature, and the mean velocities, dispersions and RV membership intervals rendered by each fit, as well as the number of resulting RV members. As an example, Fig. 2.7 displays the RV histogram at different stages of the analysis leading to the selection of sources belonging to the one of the clusters in our sample, intermediate- age cluster NGC 6705. The top panel shows the initial RV distribution for all GES targets in this cluster field. The distribution is broad, an indicator of contamination by field outliers, and presents an increasing dispersion with distance far away from the cluster centre, where the contaminants dominate. The red markings provide an additional visualisation of how the data points are spread out. The middle panel exemplifies how we discarded a series of field stars with the RStudio boxplot tool, as a result of which the distribution becomes less broad at smaller distances, with the cluster members starting to predominate over the field contaminants (e.g., Friel et al., 2014). Finally, the bottom panel shows the fitted RV distribution following the two-sigma clipping procedure around the median. The solid line indicates the Gaussian fit of the peak of the distribution, which identifies the signature of the cluster with respect to the field contaminants, and gives the central mean velocity and dispersion σ. As also presented in the last two columns of Table 2.4, after applying all membership criteria and concluding our membership analysis (see Sect. 2.4), we also obtained mean RV s and disper- sions for the velocity distributions of the final candidates for all clusters. For each cluster, our final mean RV value is in agreement with that reported in the literature (the only exceptions are Berkeley 30, a cluster for which we could not find any prior RV measurement in the literature; and Col 197, the only cluster in our sample whose estimated RV is not in agreement with the literature. See Appendix B for more details on this cluster). While every study made use of their own methods and criteria, a comparison with these previous literature values can be useful to further assess the goodness of our results. We also note that, depending on a series of factors, from the number of stars in the sample to the quality of the data, some distributions exhibit more dispersion than others, and thus, larger values of σ, even after discarding field outliers with the two-sigma-clipping procedure. However, the velocity intervals, defined by σ to ascertain whether or not the stars of the sample are RV members, do include in all cases the reference RV values from the literature for each cluster. As an example of these final fits, Figure 2.8 displays the RV 2.2. Selection criteria and membership analysis 47 distribution and Gaussian fit of the final candidate selection for NGC 6705, after applying all criteria resulting from our membership analysis. Regarding the SFRs and young clusters in our sample, we also recall that we discarded all giant contaminants using gravity indicators (Sect 2.2.4) before applying any other kinematic or astrometric criteria, due to the large number of outliers in these fields. Thus, we only took the non-giant (NG) stars in the sample into account to study the velocity distribution and obtain RV members for all of the 15 young clusters in the sample. This initial filter minimized the presence of field outliers and appreciably reduced the dispersions of the velocity distributions, which resulted in improved values of σ obtained from the Gaussian fits. Finally, we also note that in this study we discarded these evolved stars in the field of young clusters without taking into account small effects, such as different initial accretion patterns which can potentially lead to gravity spreads in this age range, and thus to the possibility of biasing the sample to only objects with a particular accretion history. 48 Chapter 2. Cluster sample and membership selections Table 2.4: Fit parameters and RV members for the sample clusters. Clustera RV b 2σ clipping 2σ membership No. RV Final fit of member list (km s −1) ⟨RV ⟩ (km s −1) σ (km s −1) intervals members ⟨RV ⟩ (km s −1) σ (km s −1) NGC 6530 −1.9± 7.2 1 0.3 2.1 [−3.8, 4.6] 477 0.0 2.5 ρ Oph −7.0± 0.2 2 −6.4 2.1 [−10.6, −2.2] 48 −6.6 1.0 Trumpler 14 −10.5± 6.9 3 −7.9 2.9 [−13.7, −2.1] 231 −8.4 3.0 Cha I 14.6± 1.2 4 15.7 1.1 [13.5, 17.9] 102 15.6 1.1 NGC 2244 33.6± 0.7 5 30.7 2.7 [25.3, 36.1] 143 30.5 2.7 NGC 2264 20.2± 6.4 3 20.2 2.5 [15.2, 25.2] 618 19.9 2.2 λ Ori 27.5± 0.4 5 27.1 1.0 [25.1, 29.1] 208 27.3 1.0 Col 197 35.8± 2.3 3 20.8 1.1 [18.6, 23.0] 124 20.7 1.1 NGC 2232 25.4± 0.9 3 29.7 14.1 [−0.2, 56.2] 750 25.3 0.6 IC 2391 15.3± 0.2 3 15.4 2.3 [10.5, 19.7] 55 14.6 0.7 IC 2602 17.4± 0.2 3 13.2 10.2 [−8.0, 34.0] 309 17.5 0.6 IC 4665 −14.4± 0.8 3 −13.4 14.8 [−43.0, 16.2] 233 −14.0 0.7 NGC 6405 −9.2± 0.8 6 −9.0 6.5 [−22.0, 4.0] 251 −8.8 0.8 Blanco 1 5.8± 0.1 6 5.8 0.7 [4.4, 7.2] 141 5.8 0.6 NGC 6067 −39.9± 0.2 1 −38.1 3.3 [−44.7, −31.5] 209 −37.8 2.0 NGC 6649 −8.9± 0.5 3 −10.3 3.8 [−18.7, −1.9] 32 . . . c . . . NGC 2516 23.8± 0.2 3 23.6 0.7 [22.3, 25.1] 460 23.8 0.8 NGC 6709 −7.8± 5 1 −7.7 10.3 [−28.3, 12.9] 322 −9.4 0.7 NGC 6259 −32.8± 0.4 3 −32.2 3.3 [−38.8, −25.6] 125 −32.5 2.5 NGC 6705 36.0± 0.2 3 35.6 1.9 [31.8, 39.4] 391 35.4 1.8 Berkeley 30 . . . d 47.7 3.6 [40.5, 54.9] 78 48.1 3.0 NGC 6281 −5.0± 0.1 3 −4.8 1.9 [−8.6, −1.0] 82 −4.5 0.7 NGC 3532 5.4± 0.2 3 5.3 0.9 [3.5, 7.1] 518 5.4 0.9 NGC 4815 −29.8± 0.3 3 −29.0 3.4 [−36.4, −22.8] 68 −27.6 4.0 NGC 6633 −28.6± 0.1 3 −22.4 13.2 [−49.0, 0.0] 617 −28.3 0.9 NGC 2477 7.9± 0.1 3 8.1 1.0 [6.1, 10.1] 86 7.2 2.1 Trumpler 23 −61.4± 0.5 3 −61.3 1.8 [−57.7, −64.9] 51 −62.0 1.5 Berkeley 81 50.0± 0.7 3 47.7 2.2 [43.3, 52.1] 69 48.2 0.3 NGC 2355 36.9± 0.7 3 36.2 0.9 [34.4, 37.0] 119 36.3 0.9 NGC 6802 11.8± 0.4 3 13.0 1.8 [9.6, 16.6] 77 12.0 0.7 NGC 6005 −25.6± 0.5 3 −25.5 3.2 [−31.9, −19.1] 174 −24.6 1.1 Pismis 18 −28.5± 0.6 3 −29.7 2.8 [−35.3, −24.1] 41 −28.2 0.8 Melotte 71 51.3± 0.4 3 51.6 0.7 [50.2, 53.0] 71 51.1 0.4 Pismis 15 36.3± 0.7 3 35.0 0.1 [32.6, 37.4] 93 35.2 0.8 Trumpler 20 −39.8± 0.2 3 −39.8 1.4 [−42.6, −37] 451 −40.0 1.2 Berkeley 44 −7.6± 0.4 3 −8.8 0.4 [−10.4, −7.2] 39 −8.8 0.7 NGC 2243 59.6± 0.5 3 59.5 0.6 [58.3, 60.7] 469 59.6 0.6 M67 34.1± 0.1 3 34.0 0.8 [32.4, 35.6] 110 33.9 0.8 a As stated earlier in the text, regarding the clusters γ Vel, NGC 2547 and NGC 2451 A and B, we directly used the selections obtained by several studies listed in Table 2.2; b References for the mean cluster RV s: (1) Conrad et al. (2017); (2) Rigliaco et al. (2016); (3) Soubiran et al. (2018); (4) López Martí, Belén and Jiménez-Esteban, Francisco and Bayo, Amelia and others; (5) Carrera et al. (2019); (6) Gaia Collaboration et al. (2018b); ; c Final selection only consists of two members, final fit is not possible; d We could not find any prior RV measurements from the literature for this cluster. 2.2.2 Proper motions and parallaxes In our earlier cluster calibration work using iDR4 data (Gutiérrez Albarrán et al., 2020), we made use of several GES membership studies using Gaia DR1 and DR2 to reinforce our final candidate selections. We thus made use in an indirect way of the precision and robustness that proper motions and parallaxes measured by Gaia can offer (as discussed in Sect. 1.3). One of the main improvements of the present analysis was to add the proper motions and parallaxes provided by Gaia EDR3 to identify robust astrometric candidates among the kinematic selec- tion. In order to do so, we first analysed the locus of probable members in pmra-versus-pmdec 2.2. Selection criteria and membership analysis 49 PMRA (mas/yr) PM D EC (m as /y r) Figure 2.10: pmra-versus-pmdec proper motions diagram showing the final candidate selection (red squares) for NGC 2516, a 100–150 Myr intermediate-age cluster. diagrams, reinforcing our kinematic selection. As the next step in our astrometric analysis, we then studied the parallax distributions of all clusters, applying Gaussian fits in a similar way to the RV distributions discussed in Sect. 2.2.1. In order to be able to use Gaia data for our cluster sample, we crossmatched the GES iDR6 files with Gaia EDR3 by making use of the CDS Upload X-Match window in TOPCAT6, an interactive graphical viewer and editor that we have used throughout all the analysis in this project. The X-Match window allows users to join a local table with any table provided by the VizieR database of astronomical tables7, or with SIMBAD8 (Wenger et al., 2000; Taylor, 2005). We chose a search radius of 5 arcsec for all clusters in our sample, and did not encounter any problems with duplicates. With all the crossmatched GES and Gaia data ready, we then constrained all the Gaia mea- surements according to a series of quality indicators in order to ensure that the proper motions, parallaxes and photometry we used throughout the membership analysis are of sufficient quality regarding their precision, reliability and consistency (Lindegren, 2018; Lindegren et al., 2018). We used the renormalized unit weight error (RUWE – Lindegren et al., 2018; Gaia Collaboration et al., 2021), only considering for the astrometric study of each cluster the stars with RUWE< 1.4 (Lindegren, 2018; de la Torre Rojo, 2020). Regarding the study of colour-magnitude diagrams us- ing photometry from Gaia (see Sect. 2.2.3), in addition to the criterion on RUWE, we also applied 6http://www.star.bris.ac.uk/~mbt/topcat/ 7https://vizier.cds.unistra.fr/viz-bin/VizieR 8http://simbad.u-strasbg.fr/simbad/ http://www.star.bris.ac.uk/~mbt/topcat/ https://vizier.cds.unistra.fr/viz-bin/VizieR http://simbad.u-strasbg.fr/simbad/ 50 Chapter 2. Cluster sample and membership selections the following filters on the relative magnitude errors on the G, GBP and GRP photometric bands: σG < 0.022 mag (equivalent to the relative flux error filter phot_g_mean_flux_over_error> 50), σRP < 0.054 mag (equivalent to phot_rp_mean_flux_over_error> 20), and σBP < 0.054 mag (equivalent to phot_bp_mean_flux_over_error> 20) (Gaia Collaboration et al., 2018a; Linde- gren et al., 2018; Duque Arribas, 2020; Gaia Collaboration et al., 2021). We refer to the following studies for more details on Gaia DR2 and EDR3 data processing and quality indicators (Cantat- Gaudin et al., 2018; Gaia Collaboration et al., 2018a,b; Lindegren, 2018; Lindegren et al., 2018; Randich et al., 2018; Gaia Collaboration et al., 2021; Riello et al., 2021; Torra et al., 2021). We studied the astrometric goodness of the kinematic members whose associated Gaia data fulfilled all these quality indicators by first plotting them in pmra-versus-pmdec diagrams and analysing the locus of probable members, as mentioned above. As reference in order to identify this location for each cluster, we made use of the estimated proper motions from the litera- ture listed in Table 2.5. As we can see in the example of Fig. 2.10 for intermediate-age cluster NGC 2516 (125–138 Myr), all astrometric members can be found clustered together in the ex- pected location in the pmra-versus-pmdec diagram as estimated by the literature. This is one of our most restrictive criteria, and so we discarded from our analysis all kinematic members that strayed significantly from the expected locus where most kinematic members converge. As a limit, we applied the criterion of studies such as Cantat-Gaudin et al. (2018) to select sources with proper motions within a maximum of 0.5 mas yr−1 of the centroid. This criterion, combining precise measurements (improved with the aforementioned quality indicators) and accurate literature estimates, allowed us to optimally reinforce our list of kine- matic members. We were also able to ascertain the astrometric membership of the marginal kinematic stars mentioned in Sect. 2.2.1 by studying their position in the proper motions dia- grams. We fully accepted them as potential candidates if they proved to be robust astrometric members, and discarded them if they presented appreciable dispersion in regards to the rest of the astrometric selection. On the other hand, we also count with a number of stars in each cluster to which we were not able to apply astrometric criteria, be it because there were no Gaia data available for those GES stars, or because the crossmatched Gaia data was filtered out with qual- ity indicators. In those cases, we analysed the stars with the same criteria we used in Gutiérrez Albarrán et al. (2020) (kinematics, gravity indicators, metallicity and lithium). See the individ- ual notes of Appendix B for more details on the individual decisions for each cluster in these cases. Similarly to the RV kinematic distributions, the next step in the astrometric analysis was to study the distributions of parallaxes (π) for each cluster. We note that we obtained astrometric candidates according to parallaxes only among the stars which fulfilled the proper motions cri- teria (the rest were fully discarded from our membership study, as we will summarize at the end of this subsection). As described in Sect. 2.2.1, we fitted the initial parallax distributions for all clusters in the sample, making use of Gaussian curves, applying a 2σ clipping procedure on the median, and adopting a 2σ limit about the cluster mean yielded by the Gaussian fit to obtain the most likely parallax members. As was the case with our RV selection, we also considered a series of marginal parallax members which fully fulfilled the kinematic and proper motions criteria and did not deviate appreciably from the set 2σ intervals resulting from the study of the parallax distributions. For these borderline stars, we chose to enlarge the obtained 2σ intervals up to a certain threshold to assess them, typically resulting in a slightly larger 3σ interval (the exact value depends on each cluster, as is detailed in Appendix B). In Table 2.5 we list all the mean parallax values, their associated dispersions and the resulting 2.2. Selection criteria and membership analysis 51 Parallax [mas] N 2.36 2.38 2.40 2.42 2.44 2.46 2.48 0 2 4 6 8 10 14 Parallax [mas] N 2.35 2.40 2.45 2.50 0 2 4 6 8 10 14 Figure 2.11: Distributions of parallaxes and Gaussian fits for the intermediate-age cluster NGC 2516 (125–138 Myr). We display the histogram both for sources resulting from the 2σ clipping procedure on all the GES sources in this field (top panel), and for likely cluster mem- bers after applying all of our membership criteria (bottom panel). 2σ intervals for all 38 clusters analysed, alongside the estimated parallax values from the litera- ture. As already discussed in Sect. 2.2.1, the candidate selections for clusters γ Vel, NGC 2547 and NGC 2451 A and B were taken from several prior membership studies from the literature. However, in this case we also made use of these astrometric criteria (as well as CMDs) to assess the goodness of the final selections, and improved the final selections by discarded several spu- rious stars that deviated appreciably in regards to our proper motions and parallax criteria. As in the case of kinematic distributions, we also fitted the parallax distributions of our final lists of candidate members for each cluster, and compared the central mean parallax and its dispersion with those available in the literature. We find all of our final estimates to be in agree- ment with the values given by the literature. Figure 2.11 additionally shows an example of the parallax distribution analysis for intermediate-age cluster NGC 2516, comparing the initial fit following the 2σ clipping procedure, from which we obtain a preliminary 2σ membership interval, with the final distribution of the parallaxes for the final candidates for the cluster. 52 Chapter 2. Cluster sample and membership selections As already mentioned, we consider astrometry to be one of the most restrictive criteria in our analysis due to its reliability and precision, and thus we fully discarded all stars which did not fulfil the criteria of first proper motions, and then parallax distributions. All non-members according to proper motions were discarded completely from our membership analysis, and all stars which fulfilled the proper motions criterion but proved to be non-members according to the distributions of parallaxes (either fulfilling the initial 2σ membership intervals, or the enlarged threshold of 3σ for the marginal stars mentioned above) were similarly discarded fully from the analysis. In contrast to this, we will see in Sects. 2.2.4 and 2.2.5 that other criteria such as gravity indicators and metallicity are less robust, and in consequence, we chose not to make them as restrictive in order to obtain the most probable lists of candidate members. Table 2.5: Fit parameters and parallax membership for the sample clusters. Clustera pmra b pmdec b Parallax (π)b 2σ clipping 2σ membership Final fit of member list (mas yr−1) (mas yr−1) (mas) ⟨π⟩ (mas) σ (mas) intervals ⟨π⟩ (mas) σ (mas) NGC 6530 1.32± 0.08 1 −2.07± 0.08 1 0.750 2 0.770 0.060 [0.65, 0.89] 0.769 0.062 ρ Oph −1.70± 0.07 1 0.20± 0.07 1 7.692 1 7.237 0.120 [7.001, 7.481] 7.250 0.116 Trumpler 14 −6.54± 0.07 1 2.06± 0.07 1 0.340 1 0.390 0.050 [0.290, 0.490] 0.395 0.066 Cha I −19.0± 5.00 3 2.00± 4.00 3 6.250 1 5.240 0.080 [5.080, 5.400] 5.247 0.087 NGC 2244 −1.70± 0.07 1 0.20± 0.07 1 0.590–0.710 1 0.670 0.060 [0.550, 0.790] 0.665 0.071 NGC 2264 −1.76± 0.08 1 −3.72± 0.07 1 1.250 1 1.380 0.040 [1.200, 1.600] 1.388 0.063 λ Ori 1.19± 0.51 4 −2.12± 0.39 4 2.462± 0.124 4 2.500 0.048 [2.404, 2.596] 2.492 0.060 Col 197 −5.81± 0.31 4 3.93± 0.39 4 1.135 1 1.020 0.050 [0.930, 1.130] 1.023 0.059 NGC 2232 −4.70 4 −1.80 4 3.067± 0.099 4 3.100 0.060 [2.980, 3.220] 3.111 0.058 IC 2391 −24.64± 0.88 4 23.32± 0.73 4 6.585 5 6.620 0.070 [6.490, 6.790] 6.613 0.086 IC 2602 −17.58± 0.83 4 10.70± 0.90 4 6.758 5 6.610 0.080 [6.460, 6.780] 6.629 0.084 IC 4665 −0.91± 0.28 4 −8.52± 0.28 4 2.872 5 2.900 0.060 [2.780, 3.020] 2.887 0.077 NGC 6405 1.31± 0.34 4 −5.85± 0.34 4 2.172 4 2.190 0.020 [2.150, 2.230] 2.185 0.022 Blanco 1 18.74± 0.43 4 2.60± 0.44 4 4.210± 0.120 4 4.200 0.070 [4.060, 4.340] 4.225 0.062 NGC 6067 −1.91± 0.12 4 −2.59± 0.12 4 0.443± 0.065 4 0.470 0.028 [0.416, 0.528] 0.472 0.024 NGC 6649 −0.01± 0.18 4 −0.06± 0.18 4 0.467± 0.087 4 0.491 0.060 [0.371, 0.611] . . . c . . . NGC 2516 −4.75± 0.44 4 11.22± 0.35 4 2.417± 0.045 4 2.429 0.031 [2.367, 2.491] 2.428 0.033 NGC 6709 −1.76± 0.08 1 −3.72± 0.07 1 1.250 1 1.380 0.040 [1.200, 1.600] 0.916 0.033 NGC 6259 −1.02± 0.13 4 −2.89± 0.12 4 0.408± 0.057 4 0.432 0.061 [0.310, 0.550] 0.463 0.034 NGC 6705 −1.57± 0.16 4 −4.14± 0.17 4 0.427± 0.083 4 0.411 0.039 [0.333, 0.489] 0.404 0.054 Berkeley 30 −0.25± 0.17 4 −0.33± 0.13 4 0.164 4 0.209 0.138 [−0.074, 0.478] 0.201 0.144 NGC 6281 −1.86± 0.30 4 −4.02± 0.24 4 1.873± 0.080 4 1.880 0.030 [1.820, 1.940] 1.889 0.056 NGC 3532 −10.39± 0.40 4 5.18± 0.40 4 2.066± 0.062 4 2.086 0.025 [2.035, 2.136] 2.085 0.024 NGC 4815 −5.76± 0.11 4 −0.96± 0.10 4 0.261± 0.062 4 0.294 0.076 [0.142, 0.446] 0.294 0.084 NGC 6633 1.20± 0.33 4 −1.81± 0.30 4 2.525± 0.073 4 2.533 0.045 [−0.448, 3.432] 2.545 0.051 NGC 2477 −2.45± 0.01 4 0.88± 0.01 4 0.665± 0.037 4 0.688 0.030 [0.628, 0.784] 0.694 0.029 Trumpler 23 −4.18± 0.12 4 −4.75± 0.11 4 0.352± 0.059 4 0.353 0.040 [0.273, 0.433] 0.347 0.043 Berkeley 81 −1.20± 0.16 4 −1.83± 0.16 4 0.254± 0.090 4 0.261 0.054 [0.153, 0.369] 0.263 0.048 NGC 2355 −3.80± 0.14 4 −1.09± 0.13 4 0.497± 0.056 4 0.530 0.022 [0.486, 0.574] 0.529 0.015 NGC 6802 −2.81± 0.11 4 −6.44± 0.13 4 0.309± 0.067 4 0.335 0.028 [0.279, 0.391] 0.349 0.053 NGC 6005 −4.01± 0.12 4 −3.81± 0.12 4 0.362± 0.060 4 0.390 0.051 [0.288, 0.492] 0.327 0.135 Pismis 18 5.66± 0.11 4 −2.29± 0.11 4 0.332± 0.052 4 0.349 0.022 [0.305, 0.393] 0.342 0.100 Melotte 71 −2.45± 0.12 4 4.21± 0.11 4 0.434± 0.056 4 0.443 0.026 [0.391, 0.495] 0.348 0.100 Pismis 15 −5.30± 0.10 4 3.33± 0.12 4 0.354± 0.049 4 0.387 0.061 [0.265, 0.509] 0.401 0.058 Trumpler 20 −7.09± 0.09 4 0.18± 0.09 4 0.251± 0.045 4 0.272 0.030 [0.212, 0.332] 0.285 0.048 Berkeley 44 0.01± 0.13 4 −2.83± 0.14 4 0.303± 0.060 4 0.322 0.042 [0.238, 0.406] 0.341 0.062 NGC 2243 −1.28± 0.13 4 5.49± 0.13 4 0.211± 0.060 4 0.225 0.052 [0.121, 0.329] 0.220 0.048 M67 −10.97± 0.24 4 −2.95± 0.24 4 1.135± 0.051 4 1.161 0.026 [1.110, 1.214] 1.162 0.026 a As stated earlier in the text, regarding the clusters γ Vel, NGC 2547 and NGC 2451 A and B, we directly used the selections obtained by several studies listed in Table 2.2; b References for the mean cluster proper motions (pmra and pmdec) and parallaxes: (1) Kuhn et al. (2019); (2) Wright et al. (2019); (3) López Martí, Belén and Jiménez-Esteban, Francisco and Bayo, Amelia and others; (4) Cantat-Gaudin et al. (2018); (5) Kounkel & Covey (2019); c d Final selection only consists of two members, final fit is not possible. 2.2. Selection criteria and membership analysis 53 2.2.3 Colour-magnitude diagrams (CMDs) Gbp-Grp M G Figure 2.12: CMD showing the final candidate selection (red squares) of IC 2602, a 35 Myr-old cluster. We overplot the PARSEC isochrones with Z=0.019 for 30 Myr (green curve) and 40 Gyr (grey curve). As a final criterion using data from Gaia EDR3, we made use of the photometry in the G, GBP and GRP bands to reinforce the selections of kinematic and astrometric candidates and dis- card field contaminants by means of MG-versus-GBP -GRP colour-magnitude diagrams (CMDs) (e.g., Duque Arribas, 2020; de la Torre Rojo, 2020; Riello et al., 2021) (see Chapter 1.1 for a brief overview on CMDs as a variant of the HR diagram and their application for open clusters). The absolute magnitudes MG were calculated using the apparent magnitudes G measured by Gaia, as well as the parallaxes (π) measured in milliarcseconds (mas), by means of the expression MG = G + 5 log10(π/100) (e.g., Duque Arribas, 2020). As already discussed in Sect. 2.2.2, we used a series of quality indicators to the Gaia data in order to ensure we were working with the most precise dataset possible, applying the following filters: RUWE< 1.4, σG < 0.022 mag, σRP < 0.054 mag, and σBP < 0.054 mag (Gaia Collaboration et al., 2018a; Lindegren et al., 2018; Duque Arribas, 2020; de la Torre Rojo, 2020; Gaia Collaboration et al., 2021). As we will also mention in Sect. 2.2.4, the use of Gaia photometry in CMDs offers a more precise and robust way to assess the membership of our astrometric candidates and discard field contaminants than criteria based on spectroscopic gravity indicators, such as the analysis of the potential candidate list in Kiel diagrams (the Teff -versus-log g plane). The reason why Kiel di- agrams proved to be less reliable is that log g values are generally less precise, and also scarcer in our sample (to the extent that the γ index is used instead for all the young clusters, see Sect. 2.2.4). Thus, we consider the analysis of CMDs to be a far more restrictive and reliable criterion than Kiel diagrams. We encountered several cases, to give an example, where a target star fully fulfilled the CMD criterion but appeared to deviate more appreciably in the Kiel dia- gram. In these cases, we relied more heavily on our CMD analysis due to its superior precision and reliability. Similarly to the astrometric criteria described above, we fully discarded any as- trometric candidates from the analysis when they deviated significantly from the expected trend in the CMD in a way that could not be explained by the existing inherent dispersion among 54 Chapter 2. Cluster sample and membership selections the cluster members. We note, however, that most of our astrometric selections already being quite robust, these spurious astrometric candidates were not particularly common in our analysis. For all clusters we made use of the PARSEC CMD isochrones (Bressan et al., 2012; de la Torre Rojo, 2020)9, choosing the Gaia EDR3 photometric system, with a metal fraction of Z=0.019 (except for the very low metallicity old cluster NGC 2243, where we used isochrones with Z=0.006), and ages ranging from 1 Myr to 5 Gyr. We also took the interstellar reddening and extinction into account when obtaining the isochrones for each cluster age by applying the corresponding AV (mag) extinction values. For each cluster, we calculated the AV extinction in the V band by means of the expression AV = 3.2E(B − V ), using the E(B − V ) reddening given by (Jackson et al., 2021) and listed in Tables 2.2 and 2.3. As an example, in Fig. 2.12 we present the CMD for the cluster IC 2602, a 35 Myr old young cluster, while the CMDs for all clusters in the sample are shown in Appendix C. 2.2.4 Gravity indicators: Kiel diagram and γ index lo gg Teff (K) Figure 2.13: Kiel diagram of the GES sources (open squares) in the field of the old cluster Trum- pler 20 (1.5 Gyr). Candidate members are indicated with red squares, while orange squares de- note Li-rich giant contaminants. We overplot the PARSEC isochrones with Z=0.019 for 600 Myr (turquoise curve), 1.5 Gyr (blue curve), and 3 Gyr (green curve). In addition to CMDs, we made use of the Teff and log g GES spectroscopic parameters to study the (Teff , log g) plane (also known as the Kiel diagrams) for each of the 26 intermediate-age and old clusters on our sample (for the young sample clusters we used the γ index, see below). 9http://stev.oapd.inaf.it/cgi-bin/cmd http://stev.oapd.inaf.it/cgi-bin/cmd 2.2. Selection criteria and membership analysis 55 Teff (K) γ i nd ex (d ex ) Figure 2.14: Gravity-sensitive spectral index γ as a function of Teff for the sources (open squares) in the field of the young cluster IC 2602 (35 Myr). The candidate members of the cluster are marked in red squares, while orange squares denote Li-rich giant contaminants. As indicated by the dashed lines, we classified any stars with Teff < 5200 K and γ > 1.01 as giants. This criterion, albeit considerably less robust than CMDs constructed with Gaia photometry, were also useful to further identify field giant stars among our potential candidates by studying their locus on the Kiel diagrams. CMDs and Kiel diagrams are thus helpful in order to exclude evolved field contaminants for which we were not able to establish a secure membership based on kinematics and astrometry alone. We consider all stars with log g < 3.5 to be likely giants, while Li-rich giants are giant stars with A(Li) > 1.5 (see Sect. 2.3 for more details on Li-rich giant contaminants). For all clusters we made use of the PARSEC isochrones (Bressan et al., 2012), with Z=0.019 (except for the very low metallicity old cluster NGC 2243, where we used isochrones with Z=0.006), and ages ranging from 50 Myr to 5 Gyr. As an example, in Fig. 2.13 we present the Kiel diagram for the cluster Trumpler 20, an 1.5 Gyr old cluster, while the Kiel diagrams for all intermediate-age and old clusters in our sample are shown in Appendix C. When observed with the GIRAFFE setups, few values of the recommended GES log g values are measured for the young stars in the field of clusters younger than 50 Myr. For this reason, for all young clusters in our sample we have made use of the γ index defined by Damiani et al. (2014) and provided by the Consortium. This index is another efficient gravity indicator for the GIRAFFE targets observed with the HR15N setup, allowing for a clear separation between low-gravity giants (γ ≥1), and higher gravity stars for spectral types later than G in the MS and PMS phases (γ ≤1), as shown by Spina et al. (2017). By plotting the γ index of the Li 56 Chapter 2. Cluster sample and membership selections candidate members as a function of the stellar effective temperature, we thus have an alternative method to identify giant background stars that we had to exclude before applying the other membership criteria (see Sect. 2.2.1). As in previous works (e.g., Damiani et al., 2014; Delgado Mena et al., 2016; Spina et al., 2017), we classify as Li-rich background giants all stars with effec- tive temperatures lower than 5200 K, A(Li)> 1.5, and γ > 1.01 (as further discussed in Sect. 2.3). In Fig. 2.14 we show as an example the γ-versus-Teff diagram for the young cluster IC 2602 (35 Myr), where the dashed lines (at Teff=5200 and γ=1.01) delimit the locus of the giant back- ground stars. This region is clearly separated from the main sequence and pre-main sequence member stars. The rest of γ-versus-Teff diagrams for all young clusters in our sample are dis- played in Appendix C. 2.2.5 Metallicity [Fe/H] Figure 2.15: Histogram of [Fe/H] values for all the GES stars (marked in red) in the field of the cluster NGC 6705, as well as the candidate members (marked in blue) resulting from our analysis. The histogram shows an increasing dispersion towards the tails, confirming that this initial distribution is dominated by field stars. We have also taken the metallicity of the clusters into account to identify additional non- members, using the spectroscopic index [Fe/H] derived from the GES analysis as a proxy of the metallicity. Similarly to the Kiel diagrams, this is not as robust a criterion as kinematics, as- trometry and CMDs, but still [Fe/H] histograms are effective as a reinforcement of our selections of probable candidates, and, given the homogeneity of cluster stars, the search for stars with metallicities too far away from the mean cluster value can signal these to be potential outliers that may have eluded the rest of criteria. As an example, we show a histogram of [Fe/H] metal- licity for cluster NGC 6705, plotted in Fig. 2.15. 2.2. Selection criteria and membership analysis 57 [Fe/H] [Fe/H] Figure 2.16: Distributions of [Fe/H] and Gaussian fits for the intermediate-age cluster NGC 6705 (300 Myr). We display the histogram both for sources resulting from the 2σ clipping procedure on all the GES sources in this field (top panel), and for likely cluster members after applying all of our membership criteria (bottom panel). Similarly to the selection of RV and parallax members (see Sects. 2.2.1 and 2.2.2), for the metallicity analysis we fitted the initial [Fe/H] distribution for each cluster, including all stars in the field before applying any other membership criteria, to obtain probable metallicity can- didates. As mentioned in earlier sections, for the young clusters we only took the non-giant stars into account to study the [Fe/H] distribution and obtain metallicity members, because of the high field contamination, while all stars were taken into account for intermediate-age and old clusters. We then fitted each of the distributions by applying a 2σ clipping procedure on the median and adopting a 2σ limit about the cluster mean [Fe/H] yielded by the Gaussian fit to identify the most likely metallicity members. Figure 2.16 shows an example of the [Fe/H] distribution analysis for cluster NGC 6705, comparing the initial fit following the 2σ clipping procedure, from which we obtain metallicity membership limits, with the final distribution of the metallicities of the final candidates for the cluster. In a similar manner to the cases of RV and parallax, we have also chosen to enlarge our 2σ intervals up to a certain threshold, typically a 3σ interval (the exact value depends on the cluster being studied, as detailed in the individual notes of Appendix B), for those stars which are marginal metallicity members and fulfil the rest of criteria. These stars do not deviate appre- ciably from the mean of the histogram, even if they are not included in our initially considered 58 Chapter 2. Cluster sample and membership selections 2σ interval, and so we considered them as additional candidates. Unlike UVES metallities, the [Fe/H] values derived from the GIRAFFE spectra are widely dispersed and subject to larger uncertainties that contribute to broadening the distributions, which is a result of the lower resolution spectroscopy of the setups selected during the Survey (e.g., Spina et al., 2014b). Even though this issue has been vastly improved in the latest GES releases, especially iDR6 (Gilmore et al., 2022, submitted; Randich et al., 2022, submitted), we can still consider metallicity and gravity criteria to be less reliable for GIRAFFE targets, and this is also a reason why we consider these criteria to be less robust, and, in consequence, less restrictive overall in our membership analysis (especially when compared to the precision of the Gaia data used in the analysis of astrometry and CMDs). Thus, we chose not to disregard potential cluster members which fulfil most criteria judging solely on either log g or metallicity. Thus, we note that in our analysis we have mainly used [Fe/H] metallicity to reinforce our candidate selections, and occasionally also to locate rogue outliers we might have missed with all prior criteria. Thanks to the precision of the data and measurements involved, we can use criteria such as Gaia astrometry to determine in a more restrictive way which stars are probable members, and which stars are to be accepted or discarded depending on whether they fulfil or not said criteria. In contrast to this, when studying the [Fe/H] metallicity as a criterion, there have been instances for a number of clusters in which we have accepted as members a number of stars which did not fulfil our metallicity criteria, presenting [Fe/H] values appreciably far from the mean of the distribution, even after considering a larger 3σ interval, as mentioned above. However, these stars did also fully fulfil the rest of criteria, including the more robust ones such as kinematics, astrometry and CMDs, and they were also often marked as members by relevant GES and Gaia studies from the literature, such as Jackson et al. (2021). Taking all this into account, in addition to the inherent higher uncertainties related to GIRAFFE metallicities, we have chosen to accept all these stars as probable cluster members in spite of their metallicity values. We analyse and list these individual instances in more detail in Appendix B and in the online tables described in Appendix D. We show the results of the analysis of the metallicity distributions for all clusters in Table 2.6, including the mean [Fe/H], dispersion and membership intervals rendered by each fit. As in the case of RV distributions, we then fitted the metallicity distributions of our final selections of candidate members for each cluster and compared the central mean [Fe/H] and its dispersion with those present in the literature. We find that our estimates mostly agree with the literature, with the exception of three clusters (namely, NGC 2244, Pismis 18, and Melotte 71). A possible explanation for this could be related to the inherent lower accuracy on the [Fe/H] values derived from GIRAFFE spectra. However, it is also worth noting that the literature values of [Fe/H] are obtained with different methods and from different datasets. Thus, we only conduct qualitative comparisons of these measures with those obtained from the homogeneously measured iDR6 sam- ple, which does not consist of a means of firmly assessing the membership of our final candidates. 2.2. Selection criteria and membership analysis 59 Table 2.6: Fit parameters and metallicity membership for the sample clusters. Clustera [Fe/H] References 2σ clipping 2σ membership Final fit of member list (dex) [Fe/H] ⟨[Fe/H]⟩ (dex) σ (dex) intervals ⟨[Fe/H]⟩ (dex) σ (dex) NGC 6530 −0.04± 0.01 1 0.00 0.08 [−0.16, 0.16] −0.01 0.09 ρ Oph −0.08± 0.02 2 0.02 0.09 [−0.16, 0.20] -0.03 0.20 Trumpler 14 −0.03± 0.02 1 0.00 0.06 [−0.12, 0.12] −0.02 0.07 Cha I −0.07± 0.04 2, 3 −0.02 0.04 [−0.10, 0.10] −0.04 0.05 NGC 2244 −0.23 4 −0.04 0.05 [0.14, 0.10] −0.05 b 0.05 NGC 2264 −0.06± 0.01 1, 2, 5 −0.03 0.06 [−0.21, 0.15] −0.03 0.06 λ Ori −0.01 4 −0.04 0.07 [−0.19, 0.09] −0.03 0.06 Col 197 . . . c . . . 0.02 0.06 [−0.10, 0.14] 0.01 0.06 NGC 2232 0.04± 0.01 4 0.02 0.04 [−0.15, 0.15] 0.00 0.05 IC 2391 −0.03± 0.02 1, 2, 6, 7, 8 −0.03 0.03 [−0.07, 0.05] −0.03 0.09 IC 2602 −0.02± 0.02 2, 7, 8 0.00 0.07 [−0.14, 0.14] 0.00 0.07 IC 4665 0.00± 0.02 2 −0.01 0.09 [−0.19, 0.17] 0.00 0.01 NGC 6405 0.07± 0.03 9, 10 0.03 0.12 [−0.21, 0.27] 0.00 0.06 Blanco 1 0.00 9, 12 0.01 0.02 [−0.03, 0.05] 0.01 0.02 NGC 6067 0.20± 0.08 9, 11 0.11 0.09 [−0.07, 0.29] 0.07 0.10 NGC 6649 . . . c . . . 0.03 0.19 [−0.35, 0.41] . . . d . . . NGC 2516 −0.02± 0.01 5, 13 0.02 0.05 [−0.08, 0.12] 0.00 0.06 NGC 6709 . . . c . . . 0.00 0.17 [−0.34, 0.34] −0.08 0.07 NGC 6259 0.21± 0.04 11, 14 0.18 0.09 [0.01, 0.37] 0.17 0.10 NGC 6705 0.16± 0.04 11, 13 0.06 0.08 [−0.10, 0.22] 0.06 0.08 Berkeley 30 0.10 15 −0.19 0.18 [−0.52, 0.20] −0.20 0.19 NGC 6281 0.06 9, 17 0.07 0.20 [−0.35, 0.45] 0.08 0.15 NGC 3532 −0.07± 0.10 16 0.02 0.06 [−0.10, 0.15] 0.02 0.07 NGC 4815 0.11± 0.01 11, 13, 18 0.07 0.20 [−0.34, 0.46] 0.01 0.08 NGC 6633 −0.01± 0.11 11, 13, 19 −0.01 0.19 [−0.39, 0.37] 0.03 0.15 NGC 2477 0.07± 0.03 9, 17, 20 0.10 0.04 [0.02, 0.18] 0.14 0.04 Trumpler 23 0.21± 0.04 11, 13, 21 0.16 0.10 [−0.04, 0.36] 0.19 0.07 Berkeley 81 0.22± 0.07 11, 13 0.18 0.11 [−0.04, 0.41] 0.18 0.10 NGC 2355 −0.11 4 −0.12 0.05 [−0.22, −0.02] −0.13 0.05 NGC 6802 0.10± 0.02 11, 13, 22 0.03 0.15 [−0.26, 0.34] 0.05 0.13 NGC 6005 0.19± 0.02 11, 13 0.14 0.10 [−0.06, 0.34] 0.19 0.08 Pismis 18 0.22± 0.04 11, 13 0.06 0.11 [−0.16, 0.28] 0.13 b 0.02 Melotte 71 −0.27 9, 12 −0.33 0.24 [−0.81, 0.15] −0.09 0.01 Pismis 15 0.01± 0.01 23 −0.10 0.22 [−0.54, 0.34] −0.07 0.11 Trumpler 20 0.10± 0.05 11, 13 0.06 0.10 [−0.15, 0.25] 0.08 0.10 Berkeley 44 0.27± 0.06 11, 13 0.12 0.09 [−0.06, 0.30] 0.12 0.09 NGC 2243 −0.38± 0.04 11, 13, 17 −0.57 0.13 [−0.84, −0.28] −0.61 0.13 M67 −0.01± 0.04 11, 17, 19 0.00 0.05 [−0.11, 0.09] 0.00 0.05 a For γ Vel, NGC 2547 and NGC 2451 A and B, we used the selections listed in Table 2.2; b For these clusters, the final mean [Fe/H] values deviate more appreciably from the literature values; c We could not find any prior measurements from the literature for these clusters; d Final selection only consists of two members, final fit is not possible. [Fe/H] References: Shown here are the most recent or robust estimates for each cluster, several studies are further cited in Appendix B: (1) Randich et al. (2018); (2) Spina et al. (2017); (3) Sacco et al. (2015); (4) Carrera et al. (2019); (5) Binks et al. (2022, in prep.); (6) De Silva et al. (2013); (7) Dumont et al. (2021b); (8) Smiljanic et al. (2011); (9) Netopil & Paunzen (2013); (10) Kılıçoğlu et al. (2016); (11) Magrini et al. (2018); (12) Bossini et al. (2019); (13) Jacobson et al. (2016); (14) Casali et al. (2019); (15) Paunzen et al. (2010); (16) Fritzewski et al. (2019); (17) Heiter et al. (2014); (18) Friel et al. (2014); (19) Sestito & Randich (2005); (20) Rain et al. (2021); (21) Overbeek et al. (2017); (22) Tang et al. (2017); (23) Carraro et al. (2005). 60 Chapter 2. Cluster sample and membership selections EW (L i) (m Å ) Teff (K) Figure 2.17: EW (Li)-versus-Teff diagram showing the final candidate selection (red squares) for IC 2602, a 35 Myr-old cluster. The upper envelope of EW (Li) for the cluster IC 2602 is shown in red; the upper and lower envelopes of the Pleiades cluster are shown in grey; and the turquoise line represents the upper envelope of the Hyades cluster. For completeness we also show here candidate members of the cluster from a couple of studies from the literature (Randich et al., 2001; Jeffries et al., 2009a). 2.2.6 Lithium content As discussed in the introduction (see Sect. 1.1, lithium is a powerful membership indicator and of great use in determining the age of clusters. Given that Li starts to be depleted during the PMS phase and that young FGKM stars seem to always show a strong lithium feature (e.g., Soderblom, 2010), the presence of lithium in stellar spectra is a relevant indicator of youth in late-type stars. However, a few G/K giants may also have large Li content, and contamination by Li-rich field giants therefore remains possible, were we to filter lithium members prior to other criteria (e.g., Smith et al., 1995). This is why we identified and discarded most of these field giants with the aid of gravity indicators and CMDs, before analysing the lithium content of the potential candidates (see Sects. 2.2.3 and 2.2.4). We obtained the Li members of each cluster by studying their position of the cluster candi- dates in EW (Li)-versus-Teff figures with a series of Li envelopes as a guide (see Chapter 4 for more details about empirical lithium envelopes). We use the upper lithium envelope of IC 2602 (35 Myr) (Montes et al., 2001; López-Santiago et al., 2003), the upper (Neuhaeuser et al., 1997) and lower (Soderblom et al., 1993) envelopes of the Pleiades (78–125 Myr), and the upper en- velope of the Hyades (750 Myr) (Soderblom et al., 1993). These envelopes delimit the region populated by member stars in well-known open clusters covering a large range of ages. Given that various studies have already obtained age estimates for the clusters we are studying, we can distinguish the bona-fide cluster members from the Li-rich contaminants and other field stars by studying their position in the EW (Li)-versus-Teff diagram with respect to the Li envelopes. 2.2. Selection criteria and membership analysis 61 Teff (K) EW (L i) (m Å ) Figure 2.18: EW (Li)-versus-Teff diagram showing the final candidate selection (red squares) for NGC 6633, a 575 Myr-old intermediate-age cluster. In green squares we mark a series of late-K and M stars with considerably higher values of EW (Li) than would be expected for this cluster, but still listed as final candidates of the cluster (see Appendix B). As an example, Fig. 2.17 shows the EW (Li)-versus-Teff diagram for the 35 Myr young cluster IC 2602. As described above, Li members would be in this case selected by studying the position of the selection with respect to the IC 2602 envelope. We disregard the stars lying above the IC 2602 envelope, which are younger than 35 Myr, and those at the bottom of the figure, which are older than the cluster members. In this specific case, we can also compare the position of the Li candidates and final selection for IC 2602 with the corresponding Li envelope for the same cluster (for the rest of clusters, the locus of the potential candidates would be compared with respect to the empirical envelopes closest to their age). We present the EW (Li)-versus-Teff diagrams for all clusters in our sample in Appendix C. We use the criterion of lithium to effectively reinforce our list of probable candidates, secur- ing the membership of the preliminary members according to the strength of their Li line and their position in the EW (Li)-versus-Teff diagram, as expected for each age range and spectral type (see Chapter 1). We have also discarded some individual stars in a number of the sample clusters in this way, considering them to be probable non-members on the basis of their posi- tion in the diagram, and their dispersion with respect to the rest of the candidates (for more details on the stars we discarded on the basis of lithium, see the individual notes in Appendix B). We note that in this updated version of the cluster membership analyses we have changed the order of criteria slightly with respect to our earlier work in Gutiérrez Albarrán et al. (2020), and have used lithium as one of the final criteria to be applied, after making use of kinematics, astrometry, CMDs, gravity indicators, and metallicity10. The reason for this is to avoid any 10In the earlier versions of our cluster calibration, we selected Li members directly after obtaining a preliminary list of kinematic candidates. Other field contaminants were then discarded afterwards using Kiel diagrams and [Fe/H] metallicity, and the final lists of candidates were reinforced using studies from the literature using Gaia 62 Chapter 2. Cluster sample and membership selections Teff (K) EW (L i) (m Å ) Figure 2.19: EW (Li)-versus-Teff diagram showing the final candidate selection (red squares) for NGC 2264, a 4 Myr-old SFR, displaying a considerable number of strong-accreting stars (green diamonds). Some of these present enhanced Li values of EW (Li) > 800 − 900 mÅ, well above the average levels of surface lithium for non-accreting cluster members in this age range. potential bias in our study, seeing as this work specifically revolves around the calibration of the lithium-age relation, and how the observable dispersion of the lithium content of cluster members depends on several parameters. Judging by our updated cluster member lists for those clusters which were already analysed in Gutiérrez Albarrán et al. (2020) with iDR4 data, we can conclude that having selected candidates on the basis of lithium earlier in our membership process did not appreciably bias the sample (all major differences and improvements can rather be explained by means of the improved iDR6, larger number of stars in the cluster sample, and added astrometry from Gaia). However, with our updated order of criteria, we already count with a robust list of probable candidate members, having already applied the other criteria, and it is then that we can use lithium, an effective age calibrator, to further reinforce the membership of our candidates without adding any unwanted bias to our analysis. The individual notes of Appendix B will discuss these specific cases in some more detail, but a case of the bias we could add to our selection by filtering candidates on the basis of lithium before considering the other criteria can be exemplified with intermediate-age clusters NGC 3532 and NGC 6633 (300 Myr and 575 Myr, respectively). The final selection for these clusters in- cluded a series of K-M stars with considerably higher values of EW (Li) than would be expected data 2.2. Selection criteria and membership analysis 63 for the age range and spectral types involved (see Fig. 2.18). However, all these stars showed no appreciable dispersion with respect to the rest, fulfilled all other criteria and were included in recent membership studies (such as Jackson et al. (2021)), and thus we concluded that these were indeed probable cluster candidates, and that the inherent difficulty of obtaining accurate lithium measurements for K-M stars in this age range could have resulted in defective EW (Li) data in the iDR6 file. In Chapter 3 we will be studying the dependence of the observable lithium dispersions in our cluster selections with parameters such as rotation and chromospheric activity, but for this cluster analysis process we generally did not take into account small Li variations and anomalies caused by various effects, such as the influence of the aforementioned parameters. There are some instances where these variations and effects did become more relevant for our analysis, however, as is the example of strong accreting stars in the case of the SFRs (age ≤ 5 Myr). EW (Li) values can be underestimated in stars with a strong mass accretion rate due to the veiling factor (Frasca et al., 2015; Lanzafame et al., 2015), and Li lines can also be enhanced due to the effects of strong accretion in PMS stars, resulting in appreciably overestimated values of surface lithium abundances (Stout-Batalha et al., 2000). Following the criterion applied by Sacco et al. (2017), for the SFRs in our sample we con- sidered as members all strong accretors with Hα10% > 270–300 km s−1 (White & Basri, 2003; Frasca et al., 2015; Sacco et al., 2017; Bonito et al., 2020)11, regardless of whether they seemed to be Li members or not (due to the aforementioned enhancement or underestimation of their Li content). We do require these strong accretor stars to be kinematic and astrometric can- didates in order to include them in the final member lists, however. A clear example of this NGC 2264 (see Fig. 2.19), a 4 Myr-old SFR whose final selection displays a number of stars with EW (Li) > 800 − 900 mÅ, well above the average levels of surface lithium for cluster members in this age range. The majority of these stars are strong accretors which fulfil all other criteria and are included in studies such as Jackson et al. (2021), and so we have explained their consid- erable Li content as being a result of accretion-induced enhancement. For more details, see the individual notes of Appendix B. All strong accretor stars for all SFRs are additionally listed in the long tables of Appendix D. Finally, we also note that the lithium criterion becomes steadily less applicable when analysing older clusters, as lower and fewer lithium measurements make it harder to ascertain the mem- bership of candidates based on their position in the EW (Li)-versus-Teff diagram. Therefore, for old clusters we relied more heavily on the rest of criteria, primarily astrometry and kinematics as usual, but also their metallicity distributions and surface gravity became more relevant in order to discard outliers. 2.2.7 Comparison with other Gaia studies As part of the preliminary work on the membership analysis of the 42 open clusters in the sam- ple, we did an extensive research on each cluster, and listed all available membership studies from the literature that included lists of candidates. In Appendix B we delve in detail on the comparisons between all these membership studies and our own final cluster selections. Some of 11A tracer of accretion and youth indicator in young PMS stars, Hα10% refers to the width of the Hα emission line at 10% peak intensity, and is a fast and efficient criterion for selecting accretor candidates. As already mentioned in Sect. 2.1 when discussing the cluster sample, Hα measurements are reliable only for clusters with no dominant nebular contribution to the emission. Accretion is also briefly discussed in Chapters 1 and 3. 64 Chapter 2. Cluster sample and membership selections these studies were more relevant than others for our work, and so this last subsection is focused on the discussion of a series of specific membership studies conducted from Gaia DR1 (Randich et al., 2018), DR2 (Cantat-Gaudin et al., 2018; Soubiran et al., 2018; Bossini et al., 2019) and EDR3 data (Jackson et al., 2021). We adopted the ages revised by Bossini et al. (2019) for nine of our sample clusters, and the RV s from Soubiran et al. (2018) for 28 of them, as reported in Tables 2.2 and 2.3 for the ages, and Table 2.4 for the radial velocities, respectively. We also observed that, judging by the measured Gaia ages by Bossini et al. (2019), as well as the empirical Li envelopes constructed by using our cluster candidates (see Chapter 4), it is possible that some of the former age estimates for the pre-selected intermediate-age and old clusters could be overestimates - NGC 6005, for example, had a former age estimate of 1.2 Gyr, while Bossini et al. (2019) gives a lower age of 973 ± 5 Myr, which is more in accordance with the Li envelope of our candidate selection. However, we note that we also decided not to use the age estimates by Bossini et al. (2019) for two clusters (NGC 2516 and NGC 6633). The reason for this is that we believe these ages to be overestimates as well, judging by both more recent age estimations, and once again our own candidate selections and obtained empirical lithium envelopes (see Chapter 4 and Appendix B for more details on the sample cluster ages). We have used the other three studies cited above (Cantat-Gaudin et al., 2018; Randich et al., 2018; Jackson et al., 2021) as an additional tool to assess our own selections after concluding all membership analyses and applying all the criteria discussed in this section. All these works were of great aid to confirm and reinforce the robustness of our final candidate selections, and were also markedly useful to aid in the confirmation of marginal members in those cases when the membership criteria were not sufficient to fully confirm their membership to the clusters. For the earlier work published in Gutiérrez Albarrán et al. (2020) we mainly made use of the first two studies, conducted from Gaia DR1 and DR2 (Cantat-Gaudin et al., 2018; Randich et al., 2018), and for the final version of this work extensive use has been made of the data in Jackson et al. (2021) in order to asses our final member selections (this is a publication using both GES iDR6 and Gaia EDR3 data, including 39 out of 42 of the clusters in our sample - all except for NGC 2477, Melotte 71 and M67 -, and a work in which I am also a coauthor, as listed in Appendix A). Randich et al. (2018) combined the parallaxes and proper motions in the Gaia DR1 TGAS catalogue and the spectroscopic information from the iDR4 GES data for eight open clusters to calibrate stellar evolution and ages. All eight of them are included in our data sample (namely, NGC 2547, IC 2391, IC 2602, IC 4665, NGC 2451 A and B, NGC 2516 and NGC 6633). As well as considering an astrometric membership selection, this work derived the cluster membership probabilities for the GES targets and used several spectroscopic tracers similar to ours: GES stars are required to have values of Teff , RV s (and vsini when possible), and log g or γ index, as well as EW (Li) measurements. Candidates were selected based on criteria such as lithium con- tent and RV membership probabilities, and contaminants were also discarded based on gravity, low metallicity, or slow rotation. Cantat-Gaudin et al. (2018) used the astrometry data provided by the Gaia DR2 release and applied an unsupervised membership assignment code (UPMASK) to list members and de- rived mean properties for 1229 clusters. Out of the 42 pre-selected clusters, 34 are included in Cantat-Gaudin et al. (2018) (all but Rho Oph, Cha I, NGC 6530, γ Vel, Blanco 1, Trum- pler 23, Pismis 18, and M67). In contrast to Randich et al. (2018), this study makes use of the 2.3. Identification of giant and non-giant contaminants 65 Gaia data alone and does not consider any spectroscopic criteria during the membership analysis. Finally, Jackson et al. (2021) combined GES iDR6 spectroscopic data with the astrometry provided by Gaia EDR3 to assign membership probabilities for a target sample of 63 open clus- ters, as well as 7 globular clusters. This work is solely based on the maximum likelihood modelling of the 3D kinematics of the targets, which separates them into cluster and field populations. Out of 43211 targets, Jackson et al. (2021) listed 13985 as highly probable cluster members, with P > 0.9, and an average membership probability of 0.993. Similarly to Cantat-Gaudin et al. (2018), the membership selection is purely kinematic and independent of photometry and chem- istry and the final selection catalogues from both studies can be successfully combined with other photometric and spectroscopic criteria from GES. For each of the clusters considered in these studies, see the individual notes in Appendix B for in-depth details regarding the comparison between the candidates listed in these Gaia studies and our final member selections. In the online tables described in Appendix D we also include for reference these Gaia membership selections alongside the columns listing the results of our membership analysis criteria. 2.3 Identification of giant and non-giant contaminants Teff (K) EW (L i) (m Å ) Figure 2.20: EW (Li)-versus-Teff diagram for the Li-rich giant outliers in the field of the young (red squares), intermediate-age (green squares) and old clusters (blue squares). As discussed in Sect. 2.2.4, gravity indicators help identify giant contaminants in the field of the clusters by plotting the sample stars in the Kiel diagram and the (γ, Teff) plane. Given their interest (e.g., Smiljanic et al., 2018; Magrini et al., 2021b), as a parallel result of the membership analysis we also listed some of these outliers for future study, specifically potential Li-rich giants with A(Li)> 1.5 (see Chapter 1 for more details on the interest of Li-rich giants). We consider as likely giants any source with log g < 3.5 (Spina et al., 2014a, 2017) and/or with γ > 1.01 (Damiani et al., 2014; Sacco et al., 2015; Casey et al., 2016; Spina et al., 2017). We also consider 66 Chapter 2. Cluster sample and membership selections γ i nd ex (d ex ) Teff (K) lo gg Teff (K) Figure 2.21: γ index and log g as a function of Teff for the Li-rich giant outliers (red squares) in the field of the young (top), and intermediate-age and old clusters (bottom). Li-rich giants to have Teff < 5200 K (Casey et al., 2016; Spina et al., 2017) and, in the case of stars in the field of young clusters, a lack of Hα emission, given that this is a youth indicator for PMS stars (Casey et al., 2016). In Figs. 2.20 and 2.21 we show all Li-rich giant outliers obtained in the field of each of the 42 clusters in our sample as a result of the membership analysis in diagrams of EW (Li), log g, and γ as a function of Teff , for both the young clusters and the intermediate-age and old clusters in the sample. All Li-rich giants are also listed in the following Sect. 2.4, in Tables 2.8 and 2.9, as well as in the long tables of Appendix C. We note that the classification of Li-rich giant stars in this work is only preliminary. We find 2.3. Identification of giant and non-giant contaminants 67 a large number of potential Li-rich giants in the field of some clusters (e.g., IC 2602) and, while these stars fulfil the adopted criteria (Teff < 5200 K and A(Li)> 1.5), given the rare nature of these objects, further confirmation would be required to accept them as bona fide Li-rich giants. It is also worth noting that we have selected all Li-rich giant outliers according to the filters on gravity criteria (γ index for young clusters, and log g for intermediate-age and old clusters) detailed in Table 2.7. In the case of several clusters, we do find some inconsistencies when plot- ting Li-rich giant outliers in CMDs, with the pre-selected Li-rich giants sometimes appearing to be non-giants according to photometric data. We detail these instances in the individual notes of Appendix B. For the moment, we have decided to limit our classification of Li-rich giant contaminants to gravity indicators, as has been done in all cited instances in the literature, but this issue does reinforce the necessity to further confirm the goodness of all selected Li-rich giant outliers in this study (see the future work in Chapter 5). Table 2.7: Criteria for giant and non-giant outliers. Outlier type Criteria Li-rich Gs log g < 3.5, γ > 1.01, A(Li)> 1.5, Teff < 5200 K Gs log g < 3.5, γ > 1.01, A(Li)< 1.5 NGs log g > 3.5, γ < 1.01, EW (Li) > 10 mÅ Possible NGs 1.01 > γ > 1.0, EW (Li) > 10 mÅ As part of our earlier analysis using GES iDR4 data presented in Gutiérrez Albarrán et al. (2020), in addition to Li-rich giants we also listed a series of giant contaminants which were not Li rich (A(Li)< 1.5), as well as a series of non-giant (NG) contaminants, all outliers which had not yet been studied in detail in previous GES works. We considered as NG outliers of interest all non-member stars with log g > 3.5 and a Li limit of EW (Li) > 10 mÅ (in order to exclude stars with very low values of Li). In the case of young clusters, we considered those non-member stars with γ < 1.01 to be definite NG contaminants, but decided to mark those stars in the 1.01 > γ > 1.0 range, as well as a small number of stars with γ < 1.0, as potential NG outliers only, as we found some log g < 3.5 measurements in the iDR4 sample for these young clusters in this γ range, which would have indicated that these stars were in fact giants. However, as already mentioned in earlier sections, given the lack of data log g is not the most reliable gravity indicator for young clusters, and thus we considered all these stars as potential NGs following our γ index criterion for giant contaminants. As an example of this earlier work, we display the locus of giant and NG outlier contaminants which we identified during the membership analysis of our then 20 cluster sample, in diagrams of EW (Li), log g, and γ as a function of Teff , for both the young clusters (Fig. 2.22) and the intermediate-age and old ones (Fig. 2.23). All these giant and NG contaminant stars were classified during this earlier membership analysis, as their Li content made them interesting targets, but we note that in the present updated version of our analysis with iDR6 and Gaia EDR3 we have decided to only list all potential Li-rich giants for the moment being. We consider Li-rich giants to be the most interesting field contaminants to study as future work, given their exceptional nature and their usefulness to further understand the workings of stellar lithium (see Chapter 5). 68 Chapter 2. Cluster sample and membership selections γ in de x Figure 2.22: Panels from top to bottom: EW (Li) and γ as a function of Teff for the Li-rich giant (blue squares), (non-Li-rich) giant (fuchsia squares), and NG (green squares) outliers in the field of the young clusters from the earlier iDR4 analysis in Gutiérrez Albarrán et al. (2020), in all cases without taking into account the rest of field stars. Turquoise squares indicate potential NGs in the 1.01 > γ > 1.0 range. 2.4 Cluster member selections In the final section of this chapter we present our results from the membership analysis of each cluster, as summarized in Table 2.8. For each cluster, we report i) the number of stars from the iDR6 sample observed with both UVES and GIRAFFE; ii) those with measured values of EW (Li); iii) the number of stars selected as candidate members; and iv) the number of Li-rich giant outliers. Readers are directed to the individual notes of Appendix B, where we offer a de- tailed and in-depth discussion of the membership analysis for each cluster, as well as commenting on features of interest regarding individual stars in the selection, and comparing our candidate 2.4. Cluster member selections 69 Figure 2.23: EW (Li)-versus-Teff and Kiel diagrams for the Li-rich giant (blue squares), (non-Li- rich) giant (fuchsia squares), and NG (green squares) outliers in the field of the intermediate-age and old clusters from the earlier iDR4 analysis in Gutiérrez Albarrán et al. (2020), in all cases without taking into account the rest of field stars. lists with former membership studies (also listed in Tables 2.2 and 2.3). The full tables resulting from our membership analysis, divided into young, intermediate-age and old age ranges, are provided in online form, and described in Appendix D. In these tables we list all membership criteria in our analysis, as well as relevant Gaia studies from the literature (see Sect.2.2.7), and the final selections of candidate members for each of the 42 open clusters 70 Chapter 2. Cluster sample and membership selections analysed. We also include the lists of Li-rich giants of interest catalogued in this work. We also show our final selections in the following figures: Figure 2.24 shows the EW (Li)- versus-Teff diagrams subdivided into young, intermediate-age, and old clusters; Fig. 2.25 shows the γ-versus-Teff diagram for the young clusters in our sample, as well as the Kiel diagram for all intermediate-age and old clusters in the sample. Additionally, Appendix C shows all the indi- vidual figures for the pre-selected clusters, including both candidate members as well as Li-rich contaminants of interest. In Figure 2.24 we also show the representative average errors in Teff and EW (Li) for all members of the young, intermediate-age and old clusters. These average errors amount to 68 K and 12 mÅ for the young clusters; 69 K and 7 mÅ for the intermediate-age clusters; and 65 K and 8 mÅ for the old clusters. 2.4.1 Discussion In Table 2.9 we show some further results of our membership analysis for the 42 clusters studied. As in Table 2.8, we show the number of stars in the field of each cluster from the initial iDR6 sample, and the number of candidate stars for all clusters, as well as the Li-rich giant outlier contaminants obtained as a parallel result during the membership analysis. With these results we derived percentages of the candidate members and contaminants, which we used to assess the number of members and outliers found for different age ranges and clusters. Regarding the candidate members, these percentages are considered firstly with respect to all stars in the field of each cluster, and also with respect to all stars that present Li in the initial sample. We present percentages for the Li-rich giant outliers with respect to all stars in the field only, however, given that these were selected taking A(Li) and not EW (Li) into account, as discussed in Sect. 2.3. These percentages allow us to to rank the clusters and age ranges in terms of the percentage of candidate members and contaminants identified, with respect to all GES iDR6 stars in the field of each cluster. First considering all clusters, old clusters NGC 2477 and M67 are the clusters with the highest percentage of candidate members (79.3%–90.0%), followed by NGC 2355 and NGC 2516 (53.8%–55.5%). Next we have Melotte 71, NGC 3532 and NGC 2243 (44.5–48.0%); and NGC 2264, NGC 2547 (the young cluster with the highest percentage), Berkeley 44 and NGC 6802 (31.3–39.0%). So far, we see that, apart from NGC 2547 and NGC 2264, the clusters that provide the highest candidate percentages are either in the old or intermediate range. In a 20.7–29.7% range we then list λ Ori, NGC 6705, Blanco 1, Trumpler 20, Col 197, NGC 6530, Trumpler 23, NGC 4815, and NGC 2244; followed by several clusters in the 10.2–19.7% range, namely NGC 6405, NGC 6281, NGC 6259, Pismis 18, Cha I, Berkeley 81, ρ Oph, Pismis 15, Trumpler 14, NGC 6005, Berkeley 30, NGC 6067, and γ Vel. Finally, the lowest percentages (3.2%–8.2%) we found for young and intermediate-age clusters: IC 2602 and NGC 6649 (the clusters with the lowest percentage of candidate members), NGC 2232, NGC 6633, IC 4665, NGC 2451 A and B, NGC 6709, and IC 2391. Regarding age ranges separately, the lowest percentages for young clusters are found for IC 2602, NGC 2232, IC 4665, NGC 2451 A and B, and IC 2391 (3.2%–8.3%), followed by the SFRs Cha I, ρ Oph and Trumpler 14 (13.2%–15.3%), then γ Vel and λ Ori (19.7%–20.7%), Col 197 and NGC 6530 (25.1%–25.8%), and finally NGC 2244 and NGC 2547, which present the highest percentages (29.7%–37.3%). For intermediate-age clusters, NGC 6649, NGC 6633 and NGC 6709 have the lowest member percentages (3.2%–8.2%), followed by NGC 6405, NGC 6281, NGC 6259 and Berkeley 30 (10.2%–15.3%), then NGC 6067, NGC 6705, Blanco 1 and NGC 4815 2.4. Cluster member selections 71 (16.3%–27.9%), and finally NGC 3532 and NGC 2516, for which we obtained the highest member percentages (44.7%–55.5%). In the case of the clusters in the old range, we note that NGC 2244 is the cluster with the highest percentage (90.0%), followed by M67 (79.3%), Melotte 71, NGC 2243, and NGC 2355 (44.5%–53.8%), and Trumpler 20, Trumpler 23, Berkeley 44 and NGC 6802 (24.2%–39.0%). On the other hand, the old clusters with the lowest candidate percentages are Pismis 18, Berkeley 81, Pismis 15, and NGC 6005 (12.2%–15.5%). Similarly, considering the outlier contaminants, we firstly note that we only obtained Li-rich contaminants in the field of 23 of the 42 clusters in our sample, with their presence becoming scarcer in the field of intermediate and old clusters, and all percentages are low (0.1%–1.7%) (as could be expected, considering that these stars only comprise 1–2% of FGKM giants, as discussed in Sect. 1.1). We found Li-rich giant outliers in 13 out of 16 young clusters, in five out of 13 intermediate-age clusters, and in four out of the 13 old clusters in the sample. We find the highest percentages of Li-rich giants mainly in the fields of young and intermediate- age clusters (as well as a couple of old clusters), with Col 197 having the highest percentage (1.7%), followed by IC 2391, NGC 6709, IC 2602, NGC 2243, NGC 3532, and NGC 6802 (1.0%– 1.4%). On the other hand, we find the lowest percentages (0.1%–0.8%) in the fields of Cha I, NGC 6530, ρ Oph, Trumpler 14, NGC 2451 A and B, NGC 2264, NGC 2232, NGC 6633, NGC 6005, λ Ori, NGC 6281, Pismis 15, NGC 2244, and NGC 6405 and γ Vel (the clusters with the lowest percentages of Li-rich giant outliers). If we consider individual age ranges for the contaminant stars, we see that for young clusters the highest percentages for Li-rich giants are found in the fields of Col 197, IC 2391 and IC 2602 (1.3%–1.7%), followed by Cha I (0.8%) and NGC 6530, ρ Oph, Trumpler 14, NGC 2451 A and B, and NGC 2264 (0.5%–0.6%). The clusters with the lowest Li-rich giant percentages (0.1%–0.4%) are λ Ori, NGC 2244 and γ Vel (incidentally some of the clusters which presented the highest member percentages), while we found no Li-rich giant contaminants in the fields of NGC 2547 and IC 4665. Regarding intermediate clusters, we found the highest percentage for Li-rich giants in the fields of NGC 6709 and NGC 3532 (1.0%–1.4%), followed by NGC 6633 (0.5%). The clusters with the lowest percentages of Li-rich giant outliers for intermediate-age clusters (0.1%– 0.3%) are found in the fields of NGC 6281, and NGC 6405. Finally, we only find Li-rich giants for four out of the 13 old clusters in the sample, with the clusters NGC 2243 and NGC 6802 presenting the highest percentages (1.0%–1.3%), while NGC 6005 and Pismis 15 have the lowest percentages (0.3%–0.5%). 72 Chapter 2. Cluster sample and membership selections Average error Teff (K) EW (L i) (m Å ) Average error EW (L i) (m Å ) Teff (K) Average error EW (L i) (m Å ) Figure 2.24: EW (Li)-versus-Teff diagrams for the final candidate members of the young clusters (1–50 Myr; top panel), as well as the intermediate-age (50–700 Myr; middle panel) and old clusters (> 700 Myr; bottom panel). Open squares indicate improbable EW (Li) values for some clusters members. Average errors in Teff (K) and EW (Li) (mÅ) are also shown, as well as the upper envelope of EW (Li) for IC 2602 (35 Myr, in red), the upper and lower envelopes of the Pleiades (78–125 Myr, in grey), and the upper envelope of the Hyades (750 Myr, turquoise). 2.4. Cluster member selections 73 Teff (K) γ i nd ex (d ex ) Figure 2.25: Gravity index γ as a function of Teff for the young members for all young clusters of the sample (top panel), and Kiel diagrams for all intermediate-age and old clusters for the candidate members of the intermediate-age (50–700 Myr; middle panel) and old clusters (> 700 Myr; bottom panel). We overplot the PARSEC isochrones in a similar age range, with a metallicity of Z=0.019. 74 Chapter 2. Cluster sample and membership selections Table 2.8: Main results for the 42 open clusters analysed, indicating, for each cluster, the number of stars from the sample detected in UVES and GIRAFFE; the number of stars with EW (Li) values; the number of stars selected as candidate members (including RV , astrometric and Li members, as well as the final members); and the number of Li-rich giant contaminants. Clustera UVES GIRAFFE Membership Li-rich G All stars With Li All stars With Li RV Gaia Li Final outliers NGC 6530 52 5 1931 1325 470 200 359 343 11 ρ Oph 23 20 288 277 48 29 37 44 2 Trumpler 14 43 11 1859 1045 228 55 165 159 11 Cha I 47 36 660 623 102 54 88 87 6 NGC 2244 8 6 444 385 143 79 123 116 1 NGC 2264 113 70 1740 1539 621 423 507 503 10 λ Ori 116 103 720 675 207 142 163 161 3 Col 197 8 3 401 363 123 86 104 92 7 γ Vel 79 50 1183 1140 . . . . . . . . . 234 1 NGC 2232 47 28 1822 1722 750 56 84 68 9 NGC 2547 54 33 423 372 . . . . . . . . . 151 0 IC 2391 48 26 386 374 56 27 37 35 6 IC 2602 131 89 1721 1651 309 43 59 55 24 IC 4665 34 30 533 514 233 29 51 33 0 NGC 2451 A/B 90 70 1566 1537 . . . . . . . . . 106 10 NGC 6405 21 12 680 486 251 80 53 51 1 Blanco 1 37 31 426 373 142 119 101 98 0 NGC 6067 27 16 753 327 209 126 60 56 0 NGC 6649 6 0 277 62 42 21 4 2 0 NGC 2516 51 32 708 645 460 378 379 376 0 NGC 6709 10 10 720 590 322 71 53 49 10 NGC 6259 16 14 478 264 125 71 39 35 0 NGC 6705 49 31 1017 579 391 313 142 139 0 Berkeley 30 14 13 318 144 78 44 24 24 0 NGC 6281 16 7 304 214 82 38 23 23 1 NGC 3532 67 51 1094 809 518 411 323 384 11 NGC 4815 14 12 204 92 68 50 30 29 0 NGC 6633 57 38 1605 1463 617 35 62 67 9 NGC 2477 11 10 114 0 86 71 9 9 0 Trumpler 23 16 15 165 70 51 41 25 23 0 Berkeley 81 14 14 265 159 69 42 25 24 0 NGC 2355 11 11 197 149 119 129 87 86 0 NGC 6802 13 13 184 69 77 51 36 32 2 NGC 6005 19 19 541 298 174 112 55 49 3 Pismis 18 10 10 134 72 41 24 12 10 0 Melotte 71 9 9 111 0 71 64 4 4 0 Pismis 15 11 11 322 201 91 66 33 31 1 Trumpler 20 29 26 1184 404 451 367 116 104 0 Berkeley 44 7 7 86 73 39 33 31 30 0 NGC 2243 27 27 634 576 469 446 289 289 8 M67 42 36 95 85 109 89 96 96 0 a Regarding the clusters γ Vel, NGC 2547 and NGC 2451 A and B, we directly used the selections obtained by several studies listed in Table 2.2. 2.4. Cluster member selections 75 Table 2.9: Results for the 42 open clusters in the sample, indicating, for each cluster: all stars (both UVES and GIRAFFE) from the GES sample and the number of stars detected with measured EW (Li) values, the number of stars selected as candidate members, and Li-rich giant field contaminants. Regarding member stars, we provide their percentages with respect to all GES stars and to those with a EW (Li) measurement in the field of each cluster. Cluster iDR6 stars Members Li-rich giants All With Li # %(All) %(with Li) # %(All) NGC 6530 1983 1330 343 17.3 25.8 11 0.6 ρ Oph 311 297 44 13.8 14.5 2 0.6 Trumpler 14 1902 1056 159 8.4 15.1 11 0.6 Cha I 707 659 87 12.3 13.2 6 0.8 NGC 2244 452 391 116 25.7 29.7 1 0.2 NGC 2264 1853 1609 503 27.1 31.3 10 0.5 λ Ori 836 778 161 19.3 20.7 3 0.4 Col 197 409 366 92 22.5 25.1 7 1.7 γ Vel 1262 1190 234 18.5 19.7 1 0.1 NGC 2232 1869 1750 68 3.6 3.9 9 0.5 NGC 2547 477 405 151 31.7 37.3 0 0.0 IC 2391 434 400 35 8.1 8.8 6 1.4 IC 2602 1852 1740 55 3.0 3.2 24 1.3 IC 4665 567 544 33 5.8 6.1 0 0.0 NGC 2451 A/B 1656 1607 106 6.4 6.6 10 0.6 NGC 6405 701 498 51 7.3 10.2 1 0.1 Blanco 1 463 404 96 20.7 23.8 0 0.0 NGC 6067 780 343 56 7.2 16.3 0 0.0 NGC 6649 283 62 2 0.7 3.2 0 0.0 NGC 2516 759 677 376 49.5 55.5 0 0.0 NGC 6709 730 600 49 6.7 8.2 10 1.4 NGC 6259 494 278 35 7.1 12.6 0 0.0 NGC 6705 1066 610 139 13.0 22.8 0 0.0 Berkeley 30 332 157 24 7.2 15.3 0 0.0 NGC 6281 320 221 23 7.2 10.4 1 0.3 NGC 3532 1145 860 384 33.5 44.7 11 1.0 NGC 4815 218 104 29 13.3 27.9 0 0.0 NGC 6633 1662 1501 67 4.0 4.5 9 0.5 NGC 2477 125 10 9 7.2 90.0 0 0.0 Trumpler 23 165 85 23 13.9 27.1 0 0.0 Berkeley 81 279 173 24 8.6 13.9 0 0.0 NGC 2355 208 160 86 41.4 53.8 0 0.0 NGC 6802 197 82 32 16.2 39.0 2 1.0 NGC 6005 560 317 49 8.8 15.5 3 0.5 Pismis 18 142 82 10 7.0 12.2 0 0.0 Melotte 71 120 9 4 3.4 44.5 0 0.0 Pismis 15 333 211 31 9.3 14.7 1 0.3 Trumpler 20 1213 430 104 8.6 24.2 0 0.0 Berkeley 44 93 80 30 32.3 37.5 0 0.0 NGC 2243 661 603 289 43.7 48.0 8 1.2 M67 131 121 96 73.3 79.3 0 0.0 Chapter 3 Dependence with rotation, activity and metallicity With final candidate selections obtained for the 42 clusters in the sample as a result of the membership analysis of Chapter 2, the next step towards the calibration of a Li-age relation was to conduct a comparative study that could allow us to quantify the observable lithium dispersion in the final member selection for each cluster. In order to do so, we chose three of the principal and most characteristic stellar parameters derived from the GES spectroscopic observations — namely, rotation, chromospheric activity Hα and [Fe/H] metallicity, and we also comment briefly on accretion (see Sect. 2.2.6) —, and analysed their effects on the EW (Li) values of all young, intermediate-age and old clusters, targeting both their observable Li dispersion (in the case of rotation and activity), as well as their effects on the overall Li depletion of the cluster (in the case of metallicity). With the use of these parameters, we characterized the properties of our cluster candidate members and confirmed the correlations and patterns observed in previous studies from the literature. We also direct the reader to the introduction in Sect. 1.2 for an overview of the literature findings on the correlations and effects of rotation, activity and metallicity on lithium depletion. 3.1 Rotation 3.1.1 vsini and Prot Table 3.1: Prot measurements from the literature for nine out of the 42 clusters of the sample. References for the cluster ages can be found in Tables 2.2 and 2.3. Cluster Age References name (Myr) Prot NGC 6530 1–2 Henderson & Stassun (2012) ρ Oph 1–3 Rebull et al. (2018) Cha I 2 Nardiello (2020) NGC 2264 4 Makidon et al. (2004); Lamm et al. (2005); Affer et al. (2013); Jackson et al. (2016) γ Vel 10–20 Nardiello (2020) NGC 2547 20–45 Irwin et al. (2008); Jackson et al. (2016) IC 2391 36± 2 Messina et al. (2011) NGC 2516 125–138 Irwin et al. (2007); Wright et al. (2011); Jackson et al. (2016); Fritzewski et al. (2020) NGC 3532 399± 5 Fritzewski et al. (2021) 77 78 Chapter 3. Dependence with rotation, activity and metallicity Stellar rotation is the first parameter we considered for the study of the dispersion of the observable EW (Li) in our final selections. In this section we describe the diagrams we used to characterize said dispersion, and confirm several correlations and patterns reported in the liter- ature regarding the Li-rotation relation (see Sect. 1.2.1). We mainly worked with the rotational velocities obtained by GES spectroscopy (vsini, where v is the rotational velocity at the equator, and i refers to the inclination with respect to the observer; see Sect. 2.1), and we were also able to crossmatch our final selections for nine out of our 42 clusters in the sample with studies from the literature which include photometric rotational periods (Prot, the length of time necessary for a star to make one complete revolution around its axis). Several of these studies make use of the rotational periods provided by photometric missions such as CoRoT, Kepler, K2, and TESS (as described in the overview of Sect. 1.3). All the aforementioned studies are listed in Table 3.1. Even though we only managed to obtain Prot measurements for nine clusters in our sample, these clusters include some of the largest member selections from our analysis, such as NGC 2264, NGC 2516 and NGC 3532 (as reported in Table 2.8), and we also counted with several studies for NGC 2264 and NGC 2516, which enlarged the available Prot data. In addition, we were able to work with rotational periods for several key ages in our sample, from SFRs such as NGC 2264, to young clusters in the 10–50 Myr range (like NGC 2547 or IC 2391), to intermediate-age clusters with an age similar to the Pleiades (NGC 2516), and clusters with an intermediate age between the Pleiades and the Hyades (NGC 3532). vsini (km/s) Pr ot (d ) Figure 3.1: Prot-versus-vsini for NGC 2264. Pr ot (d ) vsini (km/s) Figure 3.2: Prot-versus-vsini for NGC 2516. Due to the fact that vsini projected rotational velocities are defined in a way that depends on the often unknown inclination i, and they are also affected by the added uncertainties in de- termining stellar radii (see below), these measurements only give a minimum value for the actual rotational velocity of the star. Rotational period measurements, in contrast, are unaffected by these uncertainties, as they do not depend on the orientation of the star with respect to the observer. For this reason, rotational periods are generally preferred to those of vsini, and they provide more useful rotational information with an unambiguous measure of the angular velocity of a given star (e.g., Barnes et al., 1999; Irwin et al., 2007; Soderblom, 2010; Bouvier et al., 2016). Unfortunately, there is also the fact that greater effort is involved in determining Prot 3.1. Rotation 79 measurements than in obtaining vsini values, and this tends to limit the number of rotational periods obtained for stars, to the extent that typically only half to three quarters of the stars with measured vsini values yield rotational periods (Barnes et al., 1999). We encountered the same issue with our cluster sample, given that we counted with a far larger number of GES vsini rotational velocities than the smaller number of Prot we obtained from the literature for less than a quarter of the total number of clusters in our sample. Consequently, in this section we will study the Li-rotation relation by using both vsini and the available Prot values crossmatched for our sample, and in order to ensure that we can do this in a consistent way, we ran a consistency test to confirm that both Prot and vsini showed the expected correlation, in spite of the uncertainty added by the unknown inclinations in the case of vsini data. Because vsini and Prot are related by means of the expression vsini= 2πR∗sini/Prot (where R∗ is the radius of the star), we can plot the rotational periods obtained from the liter- ature against their corresponding vsini GES values, as exemplified in Figs. 3.1 and 3.2 for SFR NGC 2264 and intermediate-age cluster NGC 2516. These diagrams allowed us to check that the rotational periods fall within what would be expected from their vsini measurements (e.g., Barnes et al., 1999; López Skrzypinski, 2020). We were able to thus confirm that both parameters are correlated, following a clear trend of shortening period with increasing vsini, with no object located in the top right corner, as would be expected. The observed dispersions within the trend are well within the acceptable limits in all cases, and the stars showing higher or lower values of vsini for a similar Prot can be explained in a consistent way by taking into account i) the given star having a smaller or larger radius, and/or ii) smaller and larger angles of inclination. In the second case, for example, smaller and thus redder stars located in the upper envelope of the points in Figs. 3.1 and 3.2 would indicate a large angle of inclination, while larger and bluer stars located in the lower envelope of the points in the diagrams would indicate a smaller inclination angle (Barnes et al., 1999). 3.1.2 The Li-rotation relation Having confirmed that we can use both vsini and Prot values in a consistent way, we analysed the effects of rotation on the lithium dispersion of our final member selections by plotting EW (Li)- versus-Teff diagrams for all clusters in the sample, similarly to the analysis of Li content during the membership process of Chapter 2, but now colour-coding these diagrams by rotation, using both vsini, and Prot, when available. For all these diagrams, and following the style format of similar studies such as Popinchalk et al. (2021), the slowest rotators are marked in yellow and the fastest rotating stars are shown in dark purple. We note that open squares indicate vsini upper limits. For convenience of comparison with vsini, we also note that the colours in the auxiliary axis for Prot have been inverted in all EW (Li)-versus-Teff diagrams, with the longer rotational periods (corresponding to the slowest rotators) showing in yellow, and the shorter rotational periods (corresponding to the fastest rotating stars) in dark purple. In addition, cluster candidates with no reported values of either vsini or Prot are shown as grey diamonds. Even though the focus of these par- ticular diagrams is to analyse the Li-rotation relation, showing all candidate members for each cluster is also helpful in order to indicate the general spread and positions of the cluster members. In this section we will detail the trends and correlations observed in these diagrams for a number of clusters with key ages spanning the whole age range of our sample. For a more 80 Chapter 3. Dependence with rotation, activity and metallicity Figure 3.3: EW (Li)-versus-Teff diagram colour-coded by Prot for NGC 2264 (4 Myr). For reference, the upper Li envelope ob- tained in Chapter 4 for this cluster is plot- ted over the candidate selection. Figure 3.4: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2264. For reference, the upper Li envelope obtained in Chapter 4 for this cluster is plotted over the candidate selection. comprehensive analysis, we also selected here clusters with large candidate selections and/or available rotational periods: For the young age range we chose NGC 2264, a 4 Myr SFR, and young clusters IC 2391, IC 2602 and IC 4665 (35–38 Myr) and NGC 2547 (20–45 Myr). For the intermediate-age range, we have chosen NGC 2516 (125–138 Myr, with an age close to the Pleiades) as the main cluster to exemplify this age range, and NGC 3532 (300–399 Myr), with an intermediate age between the Pleiades and the Hyades, will also be discussed. Finally, to discuss the old cluster range we selected firstly NGC 2355 (900 Myr) and Trumpler 20 (1.4 Gyr), and, lastly, M67 and NGC 2243 (4–4.5 Gyr). Of these clusters, the final candidates of NGC 2264, NGC 2547, NGC 2516, and NGC 3532 have crossmatched Prot measurements available, as listed in Table 3.1. For the rest of the clusters in the sample we additionally refer the reader to the individual figures in Appendix E, as well as to the individual notes of Appendix B, where we also detail the general observed trends and individual cases of interest as regards to rotation. Starting with the SFR NGC 2264 (4 Myr), as displayed in Figs. 3.3 for Prot and 3.4 for vsini, we firstly observe for the EW (Li)-versus-Teff diagram colour-coded by vsini (Fig. 3.4) that the fastest rotating stars, shown in purple, tend to be lower-mass stars located in the upper envelope of the cluster (see Chapter 4), corresponding to stars with higher values of EW (Li). This is in agreement with the anti-correlation between rotation and Li depletion observed in several studies in the literature (described in Sect. 1.2.1). For this SFR, we also see that many candidates are slower rotating stars (shown in yellow), especially including a series of stars with very large EW (Li)s (800–1270 mÅ), many of which only show upper limits for vsini. This behaviour is also in agreement with what we know about very young PMS stars in SFRs, given that the presence of circumstellar discs in many of these stars can effectively affect their angular momentum, resulting in appreciably slower rotation (e.g., Barnes et al., 1999; Lamm et al., 2005; Frasca et al., 2015; Bouvier et al., 2016; Rebull et al., 2018; Fritzewski et al., 2020; Popinchalk et al., 2021). Many of the final candidates of NGC 2264 are strong accretors, particularly the aforementioned stars with measured EW (Li)s in the 800– 3.1. Rotation 81 EW (L i) (m Å ) vs in i ( km /s ) Myr Teff (K) Figure 3.5: EW (Li)-versus-Teff diagram colour-coded by vsini for IC 2391, IC 2602 and IC 4665 (35–38 Myr) 1270 mÅ range. As detailed in the individual notes of Appendix B, we believe these EW (Li)s to be overestimated due to the effect of strong accretion, and we can also explain the particularly low rotation of most of these stars taking into account the presence of strong accretion and the mechanism of disc-locking. We also comment here on the fact that SFRs show a notably higher dispersion in their candi- dates than in older clusters, and this is also due to all the different complex effects taking place for these very young T-Tauri stars in the PMS phase: from gravitational contraction resulting in fast rotation, to strong accretion and the interaction of circumstellar discs resulting in significant angular momentum loss, to chromospheric activity, and so on (e.g., Barnes et al., 1999; Lamm et al., 2005; Rebull et al., 2018) (also see Sect. 3.3). Regarding the EW (Li)-versus-Teff diagram colour-coded by Prot Fig. 3.3, we observe the same anti-correlation of rotation and Li depletion, locating the fastest rotating candidates (in the range of 1–5 d, shown in dark purple) tracing the upper envelope of the cluster and generally having higher EW (Li) values. We also find a large number of slower rotating stars (shown in lighter shades of purple, orange and yellow), scattered among the cluster candidates, but gener- ally showing EW (Li) values which are lower than the ones of their faster rotating counterparts. For this cluster we found candidates with slow periods in the 16–18 range. Such slow rotational periods were also observed in earlier studies for this cluster (Makidon et al., 2004; Lamm et al., 2005; Affer et al., 2013; Jackson et al., 2016), and are in agreement with the observed behaviour of very young SFRs, whose rotation rates are often affected by the interactions of circumstellar discs (studies such as Lamm et al. (2005) consider that stars with Prot >4 d are locked to their discs). Some of the aforementioned studies (Makidon et al., 2004; Lamm et al., 2005) also report Prot of 16–18 d (and even longer in the tails of the distributions) for some stars in NGC 2264 and several other SFRs. When decoupling from the discs, many of these very slow rotating stars are expected to spin up again down the Hayashi track towards the ZAMS (also see Sect 3.3), as we will see with the examples of clusters in the 10–45 Myr range below. 82 Chapter 3. Dependence with rotation, activity and metallicity We also note that it is important to take into account the different colour scales of Figs. 3.3 and 3.4 as regards to how the corresponding ranges of Prot and vsini are colour-coded. A swift comparative inspection of these figures could lead to the misleading conclusion that we find an appreciably larger number of fast rotating stars according to their rotational periods (shown in shades of purple) compared to the majority of yellow-shaded candidates (corresponding to the slower-rotating stars), according to their vsini measurements: If we observe the Prot-versus-vsini diagram of Fig. 3.1, however, we can see that the largest values of vsini corresponding to the fastest rotating stars (60–120 km s−1, colour-coded in dark purple) correspond to rotational periods of < 3 d (e.g., Fritzewski et al., 2021), while rotational periods in a range of 1–6 d, a typical intermediate range (e.g., Barnes et al., 1999; Fritzewski et al., 2020), would correspond to vsini values in a range of 20–50 km s−1 (also cited as an intermediate range for vsini by Irwin et al. (2007), while fast rotators are given as vsini > 55 km s−1 by Zapatero Osorio et al. (2002)), colour-coded as not only darker tones of purple, but also in lighter shades of purple and orange hues. In the Prot scale, on the other hand, lighter purple shades and orange and yellow tones already correspond to longer rotational periods up to 10 d, equivalent to slow vsini values of < 15 km s−1 (e.g., Irwin et al., 2007), while candidates are marked as yellow if they have very long Prot measurements up to 18 d. The mostly yellow-coded stars with vsini values up to 30 km s−1, including both slow rotators with < 15 km s−1 and more intermediate values in the lowest end of the 20–50 km s−1 range (Irwin et al., 2007), and would thus correspond to a rather ample range of longer Prot measurements (not just the longest rotational periods at the yellow end of the scale), as illustrated in Fig. 3.1, We can explain this observed dispersion by taking into account the i inclination of the vsini values, for example. The next clusters we will be discussing are young clusters IC 2391, IC 2602 and IC 4665 (see Fig. 3.5), which are often studied together due to having a very similar age, 35–38 Myr; as well as NGC 2547 (20–45 Myr, see Figs. 3.6 and 3.7), a slightly older cluster which we have also chosen as an example in order to analyse its dependence with Prot as well. Starting with the EW (Li)-versus-Teff diagram colour-coded by vsini for IC 2391, IC 2602 and IC 4665, plot- ted together in Fig. 3.5, we observe a trend where the fastest rotating stars (shown in purple) trace the upper envelope of the cluster (see Chapter 4), corresponding to stars which tend to show higher values of EW (Li) than the slower rotating stars at the same effective temperatures (shown in yellow). This pattern is similar to what we observed in NGC 2264 and the rest of SFRs (see Appendix B), but we note that for young clusters in the older age range considered here (30–45 Myr), the attested anti-correlation between Li depletion and rotation appears to be more clear and uniformly defined, and the cluster selections also show less dispersion. In addition, while we still observe a combination of both faster and slower rotating stars in these clusters, NGC 2264 and the rest of SFRs in the sample displayed an appreciably large number of slow rotators due to effects such as strong accretion and the interaction of many of the very young T-Tauri stars with circumstellar discs. In contrast, many of the stars in IC 2391, IC 2602 and IC 4665 are examples of PMS stars which have already decoupled from the discs — which generally happens for young stars after 5–7 Myr, and up to 8–10 Myr at most (e.g., Barnes et al., 1999; Frasca et al., 2015; Rebull et al., 2018) — and consequently spin up before experiencing the onset of renewed angular momentum loss on their arrival to the ZAMS, around an age of 30–40 Myr (e.g., Barnes et al., 1999; Irwin et al., 2007; Rebull et al., 2018; Llorente de Andrés et al., 2021). However, a dichotomy of rapid and slow rotators is still observed. Barnes et al. (1999) comments on the majority of the stars in clusters such as IC 2602 probably expe- riencing significant disc-locking in the past, which would explain the slower rotators at this age range, and the ample range of rotation values observed for the stars this cluster (also see, e.g., 3.1. Rotation 83 Figure 3.6: EW (Li)-versus-Teff diagram colour-coded by Prot for NGC 2547 (20– 45 Myr). Figure 3.7: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2547 (20– 45 Myr). Bouvier et al., 2016) (see also Subsect. 1.2.3 and Sect. 3.3). NGC 2547 (Fig. 3.7), for its part, shows a very similar trend, and in this case we can also see both fast and some slower rotators among the M-type stars of NGC 2547 B, which at 10– 20 Myr have not as yet completely depleted their Li content (see Chapter 1). Regarding the EW (Li)-versus-Teff diagram colour-coded by Prot for NGC 2547 (Fig. 3.6), we observe the same anti-correlation of rotation and Li depletion, with the fastest rotating candidates (< 3 d, shown in dark purple) also tracing the upper envelope of the cluster and generally having higher EW (Li) values. As in the case of NGC 2264, we note the difference between the colour scales of Figs. 3.6 and 3.7, as regards to how the corresponding ranges of Prot and vsini are colour-coded. For ex- ample, the M-type stars in Fig. 3.6 are coded as overwhelmingly dark purple, indicating shorter rotational periods in the range of 1–6 d. In contrast, this range of rotational periods seems to correspond to a larger range of vsini values marked in shades of not only dark purple, but also various shades of orange and red-purple. We also note that the literature studies which provided the Prot values for NGC 2547 (Irwin et al., 2008; Jackson et al., 2016) were mainly fo- cused on the study of M stars, which is why Fig. 3.6 shows only Prot values for that spectral type. Continuing our discussion on to the intermediate-age clusters, we have chosen NGC 2516 as the main example for this section, a ZAMS-age cluster with an age close to the Pleiades (125– 135 Myr). In the EW (Li)-versus-Teff diagram colour-coded by vsini for this cluster, displayed in Fig. 3.9, we observe a well-defined trend where the faster rotating stars (shown in shades of purple) clearly trace the Li envelopes of the cluster (see Chapter 4), particularly the upper envelope, corresponding to stars which tend to show higher values of EW (Li) than the slower rotating stars at the same temperatures (shown in yellow). In agreement with the studies from the literature discussed in Subsect. 1.2.1, we see that this Li-rotation connection is the strongest among early-K stars (Bouvier et al. (2018), for example, observed a tight Li-rotation relation in a restricted range of effective temperatures from 4400 K to 5300 K). Regarding the EW (Li)- versus-Teff diagram colour-coded by Prot for NGC 2516, as plotted in Fig. 3.8, we observe a similar trend — Making use of all the Prot values obtained from the literature (Irwin et al., 2007; Wright et al., 2011; Jackson et al., 2016; Fritzewski et al., 2020), we see how the faster rotators (< 3 d, 84 Chapter 3. Dependence with rotation, activity and metallicity Figure 3.8: EW (Li)-versus-Teff diagram colour- coded by Prot for NGC 2516 (125–138 Myr). Figure 3.9: EW (Li)-versus-Teff diagram colour- coded by vsini for NGC 2516 (125–138 Myr). shown in dark purple) tend to show higher EW (Li) values, particularly tracing the upper Li envelope, while the stars with longer rotational periods generally display less Li than their faster rotating counterparts, and many of these are GK stars tracing the lower envelope for this cluster. In addition, given that the arrival of the FGK stars at the ZAMS has caused the onset of angular momentum loss for many stars (e.g., Barnes et al., 1999; Rebull et al., 2018), for the clusters in this age range we observe a range of both fast rotators and an increasing number of slower rotating stars that have transitioned from fast to slow rotation (e.g., Irwin et al., 2007; Fritzewski et al., 2020, 2021). While faster rotators still appear (especially among the low-mass, later types) in many of the intermediate-age clusters in our sample well into the ZAMS phase until early MS (e.g., Rebull et al., 2018; Fritzewski et al., 2021), throughout the clusters in the intermediate-age range we also observe that the maximum values of rotation are significantly lower than for the young clusters in the sample, and this can be explained taking into account the loss of angular momentum and the spin-down of the stars upon reaching the ZAMS. We also note that even though the arrival at the ZAMS generally causes the stars to spin down due to angular momentum loss, we can also explain the dichotomy between the existing rapid and slow rotators in this age range by linking the faster rotators with stars with short-lived circumstellar discs in their PMS phase, whereas the stars with the longest-lived discs would al- ready arrive on the ZAMS with slower rotation values (e.g., Bouvier et al., 2016; Rebull et al., 2018; Arancibia-Silva et al., 2020). Another point of interest to explain the differing sequences of fast and slow rotators in this age range is also discussed by Rebull et al. (2018), who addi- tionally remark that in the age range between 10 Myr and Pleiades age (70–125 Myr) there is a competition for all FGKM stars between the spin-up caused by pre-ZAMS contraction and the loss of angular momentum caused by stellar winds. FGK stars tend to spin-down to slower rotations upon reaching the ZAMS, as discussed above, while for M-type stars pre-MS contrac- tion generally dominates, and so the predominant observable effect is that rotation rates actually increase with time (for a general overview of all these effects, also see Sect.. 3.3). M-type stars additionally arrive at the ZAMS later than FGK stars due to their lower masses, which is another factor to explain this dichotomy (e.g., Barnes et al., 1999; Irwin et al., 2008). 3.1. Rotation 85 Figure 3.10: EW (Li)-versus-Teff diagram colour- coded by Prot for NGC 3532 (300–399 Myr). For reference, the upper Li envelope obtained in Chapter 4 for this cluster is plotted over the candidate selection. Figure 3.11: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 3532 (300– 399 Myr). For reference, the upper Li en- velope obtained in Chapter 4 for this cluster is plotted over the candidate selection. Studies such as Irwin et al. (2007) additionally comment on the correlation between spectral type and Prot values, also noting the lack of slow rotators at very low masses for this cluster, something that we can also observe in Fig. 3.8, and proposing that these M-type stars may have experienced a particularly long spin-down timescale compared to solar-type stars. Fritzewski et al. (2020) also studied the rotational period distribution for NGC 2516, and observed a di- agonal slow rotator sequence preferentially occupied by warmer FGK stars, as well as a flat sequence of fast rotating stars among the cooler candidates, and a group of unusual slower- rotating M dwarfs (also see Figs. 3.8 and 3.9). The study concluded that the rotation and activity distributions for the cool stars of NGC 2516 are virtually indistinguishable from other clusters in this age range, such as Blanco 1, M 35 and the Pleiades (also see, e.g., Martín & Montes, 1997) (see also Sect. 3.3). Regarding the clusters in the early MS phase, we have chosen as an example the rich- populated NGC 3532 (Figs. 3.10 and 3.11), a 300–399 Myr cluster with an intermediate age between the Pleiades (78–125 Myr) and the Hyades (750 Myr). For this cluster we observe an appreciably large number of slow rotators (Fritzewski et al., 2021), as well as some faster ro- tating F-type stars. The Prot values provided by Fritzewski et al. (2021) showcase more clearly the remarkably well-populated and very prominent slow rotator sequence stretching diagonally from the late F-type candidates to the early M dwarfs, following a very linear trend with the faster rotators among F and early G stars showing higher EW (Li) values, while the late G and K stars display slowing rotation rates with decreasing values of EW (Li) (see also Sect. 3.3). These populations and sequences are more clearly defined when analysing the rotational periods than in Fig. 3.11, once again due to the differences in the colour-scales of the auxiliary axis for the vsini and Prot values (which we have also addressed above for NGC 2264 and NGC 2547). In the intermediate-age and old age ranges, the F-type cluster candidates begin to dominate among the faster rotators, due to them being inherently faster rotating stars than G-K stars be- cause of their larger mass and temperature (e.g., Wolff et al., 1986; Delgado Mena et al., 2015). 86 Chapter 3. Dependence with rotation, activity and metallicity Figure 3.12: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2355 (900 Myr). Figure 3.13: EW (Li)-versus-Teff diagram colour-coded by vsini for Trumpler 20 (1.4 Gyr). In addition, as a result of these stars being more massive and hotter, with a thinner convective region, F stars deplete Li more slowly than later spectral types, and thus we can see them in older clusters where K-M stars have already completely depleted their Li (see Subsect. 1.1.2). In addition to all this, we also remark that the GES selection process also favour brighter F-G stars before dimmer K-M stars as preferable targets for older clusters. On the other hand, for clusters in the early-MS phase we observe a general spin-down of rotation rates for FGK stars compared to their counterparts in younger clusters and earlier evolutionary phases. Studies such as Rebull et al. (2018) comment that for stars in this age range angular momentum loss from winds dominates throughout all spectral types, and the effects of pre-MS contraction (which causes stars to rotate faster) are still ongoing only for very low-mass stars. We finish the study of the rotation of NGC 3532 by noting, as also discussed in Appendix B, that we do not take into account the K-M candidate stars only classified as possible Li members (marked as open squares in Fig. 3.11, as well as in the individual figures of Appendix E), as we believe that, while these stars are probable candidates of the cluster, their EW (Li) values are not representative of the age of this cluster, and thus we have decided to forgo the study of the dispersion of their Li values with rotation or activity so as not to obtain misleading conclusions. Fritzewski et al. (2021) include a number of Prot values for late K and M-type stars for NGC 3532, as shown in Fig. 3.10, remarking on the wide distribution of rotation periods among the early M-dwarfs in their sample, and distinguishing both a fast rotator sequence, significantly evolved beyond ZAMS-age clusters, and a slow rotator sequence. To conclude our overview of the dependence of Li and rotation we study some examples among the old clusters in our sample (0.7–5 Gyr for our sample), beginning with an age range of 0.9–1.5 Gyr with NGC 2355 (900 Myr) and Trumpler 20 (1.4 Gyr). The EW (Li)-versus-Teff diagrams colour-coded by vsini for these clusters are displayed in Figs. 3.12 and 3.13. All the FGK stars in these clusters can be already found in the early MS phase at this age range, and one of the observable effects of this evolutionary stage is the continuing trend of angular momentum loss for many of these stars, resulting in significantly altered rotational velocities compared to 3.1. Rotation 87 Figure 3.14: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2243 (4 Gyr). Figure 3.15: EW (Li)-versus-Teff diagram colour-coded by vsini for M67 (4–4.5 Gyr). their rotation rates on the ZAMS, and thus in a larger number of slower rotating stars (e.g., Re- bull et al., 2018). Studies such as Fritzewski et al. (2020, 2021) study the rotational distributions of intermediate-age clusters (also see Sect. 3.3 below), and comment on how the candidates in ZAMS-age clusters tend to show a notably large spread regarding rotation, and how this spread mostly begins to converge onto a single sequence of period against colour for clusters reaching an age of 600 Myr. A series of F-type stars in our selections maintain higher vsini values than the rest of spectral types throughout the 0.7–5 Gyr age range of our old cluster sample, as can be expected given their larger mass and temperature. Even so, we observe that the rotation values for these F stars also continue to be lower than in the case of the young and intermediate-age cluster selections, with typical maximum values in a 70–90 km s−1 range for several old clusters, as well as a max- imum vsini of 30–40 km s−1 for others, and a maximum of 110 km s−1 in one of the youngest clusters of this age range, Trumpler 23 (800 Myr). From their part, the majority of GK stars in the old clusters of the sample also continue to show appreciably lower rotation values than their counterparts in young and intermediate-age clusters, displaying clear sequences of slow rotators in Figs. 3.12 and 3.13. As discussed above, in both of these figures we observe that the fastest rotators are F stars, and that the fastest rotating stars in this spectral type tend to have higher levels of EW (Li) as well, some of them tracing the upper envelope for the cluster (see Chapter 4). We also discern the Li-dip for these clusters (e.g., Delgado Mena et al., 2015), accounting for the higher levels of Li depletion in the 6400–6600 K range (see Subsect. 1.1.2). The slow rotator sequences formed by the GK candidates are relatively uniform in their vsini values, but we can also see that the faster rotators among these stars (shown in shades of orange) also tend to be stars with higher values of EW (Li), which once again is in agreement with the expected anti-correlation between rotation and Li-depletion observed throughout the cluster sample. These trends can also be observed in the last old clusters we have chosen as an example, namely M67 and NGC 2243, displayed in Figs. 3.14 and 3.15. With an age of 4–4.5 Gyr, the FG 88 Chapter 3. Dependence with rotation, activity and metallicity candidate stars for these clusters are firmly established in the MS phase, and the figures show the same trend of locating the faster rotating stars among the F stars and observing a slow rotator sequence among the late F and G stars. Barnes et al. (2016), who studied the distributions of rotational periods for the well-studied cluster M67, remark that the periods are observed to be a function of stellar mass, with the bluer and higher-mass stars having shorter periods (or higher vsini values), and the lower-mass redder stars having long periods (or lower vsini values). They continue to observe that the stars in their sample clearly follow a trend of increasing period (or lower vsini values) with redder colour (similarly to the one observed for the Hyades). Regarding our selections, this is a trend which we are also able to observe for both M67 and NGC 2243. The latter one, slightly younger than M67, contains a larger number of faster rotat- ing F stars in our final selection, and the fastest rotators (shown in darker purple shades) tend to also have higher values of EW (Li), with some of them tracing the upper Li envelope for this cluster (see Chapter 4). Although we encounter a lesser number of faster rotators among F and G stars in the selection for M67, we see that the fastest rotators among the late-F and early-G stars in M67 also trace the upper envelope for the cluster, showing higher values of EW (Li) than many of their slower rotating counterparts at similar Teff . Finally, the slow rotator sequences formed mainly by the G-type candidates are, as in the case of NGC 2355 and Trumpler 20, uniformly coloured (shown in shades of yellow and orange), although we can also say that some of the faster rotators among these stars (in darker hues of orange) can be once again seen tracing the upper Li envelope for these clusters. 3.2 Chromospheric activity The second stellar parameter we have considered in the study of the dispersion of the observable EW (Li) is stellar activity. We have limited our analysis to chromospheric activity (Hα). In this section we describe the diagrams to characterize the Li dispersion depending on activity, and confirm several correlations and patterns reported in the literature regarding the Li-activity relation (see Sect. 1.2.2). 3.2.1 The Li-activity relation Similarly to our study of rotation, in this section we analyse the effects of chromospheric ac- tivity (measured in this work by means of the Hα equivalent widths) on the lithium dispersion of our final member selections by plotting EW (Li)-versus-Teff diagrams for all clusters in the sample, colour-coded by Hα. These diagrams follow a similar style format to the equivalent figures colour-coded by rotation, with the most active stars marked in dark purple and the least active members shown in yellow. Once again, cluster candidates with no reported values of Hα are shown in grey diamonds, so as to display all candidate members in the figures to indicate the general spread of the member stars and facilitate the analysis. We will now detail the trends and correlations observed in these diagrams for a number of clusters with key ages spanning the young, intermediate-age and old ranges in our sample. Most of these clusters are the same ones we included in Section 3.1 to study rotation, but we note that we were not able to consider the same clusters in the old age range studied in the earlier section, as most clusters in this age range have very few reported Hα measurements in the iDR6 GES file, and so in this case we chose the one with the most values of chromospheric activity to better 3.2. Chromospheric activity 89 Figure 3.16: EW (Li)-versus-Teff diagram colour-coded by Hα for NGC 2264 (4 Myr). For reference, the upper Li envelope obtained in Chapter 4 for this cluster is plotted over the candidate selection. EW (L i) (m Å ) EW (H α) (Å ) Myr Teff (K) Figure 3.17: EW (Li)-versus-Teff diagram colour-coded by Hα for IC 2391, IC 2602 and IC 4665 (35–38 Myr). suit our purposes. We will consider the following clusters: For the young age range we have NGC 2264 (4 Myr) and IC 2391, IC 2602 and IC 4665 (32–38 Myr); NGC 2516 (125-138 Myr) is once again the main cluster we have chosen for the intermediate-age cluster; and among the old clusters we selected Trumpler 20 (1.4 Gyr) and NGC 2243 (4 Gyr). For the rest of the clusters in the sample we refer the reader to the individual figures in Appendix E, as well as to the individual notes of Appendix B, where we also detail the observed trends and individual cases of interest as regards to chromospheric activity. We start discussing the SFR NGC 2264 (4 Myr), displayed in Fig. 3.16. Similarly to the observed anti-correlation between rotation and Li depletion in Figs. 3.3 and 3.4, in the case of Hα we also observe a pattern where the stars with highest values of chromospheric activity (shown in dark purple) also tend to have some of the highest values of observable lithium, and the stars with more Hα emission similarly tend to be located in the upper envelope of the cluster candidates with more EW (Li), shown in purple and dark orange shades (see Chapter 1 and associated citations). We also note that the aforementioned strong accretors with appreciably high measured EW (Li)s in a 800–1270 mÅ range (see Sect. 3.1, as well as the individual notes of Appendix B) include two stars with the largest values of chromospheric activity for this cluster. And in fact, the Hα values for these stars are so large (250–300 Å) that the colour-coded marker consequently shows the rest of the candidates in shades that veer overwhelmingly towards the orange and yel- low hues (with, for example, high values of Hα up to 100–150 Å already colour-coded in dark yellow and various orange hues as a result). A swift inspection of this figure could thus give a misleading impression that this cluster is less chromospherically active than it actually is. The large number of candidates with large Hα values is also in agreement to what is known about SFRs, where strong Hα emission is a clear marker of the youth of its stars, as discussed in Chapter 1. Enhanced Hα emission is also one of the observable indicators of the presence of a 90 Chapter 3. Dependence with rotation, activity and metallicity Figure 3.18: EW (Li)-versus-Teff diagram colour-coded by Hα for NGC 2516 (125–138 Myr). circumstellar disc (e.g., Lamm et al., 2005). The next clusters discussed in this section are young clusters IC 2391, IC 2602 and IC 4665 (35–38 Myr, see Fig. 3.17). Similarly to the Li-rotation relation discussed in the earlier section (Fig. 3.5), we observe a trend in which the stars with higher values of Hα chromospheric activity (shown in shades of purple and darker orange) tend to be located in the upper envelope of the cluster, and generally show higher values of EW (Li) than the less active stars of the same spectral types. This pattern is similar to what we observed in NGC 2264 and the rest of SFRs, but we note that for young clusters in this 30–45 Myr range the observed correlation between higher values of EW (Li) and higher Hα activity appears to be more uniformly defined, and the cluster se- lections for this age range also show less observable dispersion compared to the very young SFRs. Similarly to the Li-rotation relation discussed in the earlier section (Figs. 3.8 and 3.9), for the intermediate-age cluster NGC 2516 (125–135 Myr) in Fig. 3.18 we also observe a clear and well-defined trend with the most active stars displaying higher values of EW (Li) and tracing the Li envelopes for the cluster, particularly the upper envelope. We also observe, however, that the most active stars in the lower envelope for this cluster (see Chapter 4) tend to have higher values of EW (Li) as well. The more active stars (shown in shades of purple and darker orange) are to be found among GKM types, with late K and M stars displaying the highest levels of Hα (shown in dark purple). We continue to see cluster selections which appear to be more defined and less dispersed than in the case of younger clusters, with NGC 2516 especially showing the expected Li-rotation and Li-activity correlations in a way that is particularly well-defined, following the expected trends observed in various studies from the literature (see Sect. 1.2.2). Finally, we note that the iDR6 file includes very few Hα measurements for the old cluster range, and none for four out of the 13 old clusters in our sample, and so it is often difficult to discern trends or correlations. We can note that all activity values for this age range are low, as can be expected of evolved clusters in a 0.7–5 Gyr age range, and in those cases where there is a sufficient number of stars, such as with NGC 2243 (see Fig. 3.20), we observe the expected 3.3. Colour-rotation and colour-activity diagrams 91 Figure 3.19: EW (Li)-versus-Teff diagram colour-coded by Hα for Trumpler 20 (1.4 Gyr). Figure 3.20: EW (Li)-versus-Teff diagram colour-coded by Hα for NGC 2243 (4–4.5 Gyr). correlation between Hα and Li, with the most active stars (shown in shades of purple and orange) having higher EW (Li) values and tracing the upper Li envelope of the cluster (see Chapter 4). We also note that for several clusters in the sample, such as the example of Trumpler 20 shown in Fig. 3.19, GES has only obtained Hα measurements for late-G and early-K UVES stars with very low EW (Li) values (as can be expected for late-type stars in this age range), and so it is difficult to discern any patterns as regards to the Li-activity relation for these clusters, beyond the fact that these stars have both low EW (Li) and Hα values, which is in agreement with the expected correlation between Li content and Hα emission. 3.3 Colour-rotation and colour-activity diagrams Although not the main focus of this project, gyrochronology is one of the most effective ways to study the evolution of FGKM stars through their changing rotation rates. This is often done by analysing age-rotation relationships across colour (e.g., Soderblom et al., 1983; Soderblom, 2010; Jeffries, 2014; Soderblom et al., 2014; Barrado et al., 2016; Popinchalk et al., 2021; Randich & Magrini, 2021). Given that magnetic activity is driven by rotation, chromospheric emission is also correlated with age as a result, with Hα emission (the standard indicator of chromospheric activity, as discussed in the former section) decaying as stars spin down with age (e.g., Popin- chalk et al., 2021). In this section we give a general overview of the evolution of rotation and chromospheric activity across age for the final selections of the clusters in our sample. While not directly targeting the dependence of the EW (Li) measurements with these parameters, or tracing the observable correlations between rotation, activity and Li depletion, a general analysis of how the distributions of rotation and activity evolve with age for different masses and spectral types is also of great use to reinforce the trends and correlations that we have observed in the former sections of this chapter in order to constrain the Li-age relation. We have done this by plotting a series of colour-rotation (using both Prot, when available, and vsini values) and colour-activity (using the available Hα measurements) diagrams, organized 92 Chapter 3. Dependence with rotation, activity and metallicity Figure 3.21: Rotation rates and rotational periods for solar-type stars in coeval clusters as a function of age from Jeffries (2014), adapted from Gallet & Bouvier (2013). The figure indicates the PMS, ZAMS and MS phases, and the dominant physical processes at work are also marked. by young, intermediate-age and old age ranges in Figs. 3.22, 3.23 and 3.24, respectively. These diagrams use colour as a proxy of spectral type and mass (e.g., Soderblom, 2010), and have been used frequently in the literature to study rotational and activity distributions for several clusters in various age ranges (e.g., Barnes et al., 1999; Lamm et al., 2005; Irwin et al., 2007, 2008; Barnes et al., 2016; Rebull et al., 2018; Fritzewski et al., 2020; Nardiello, 2020; Fritzewski et al., 2021; Popinchalk et al., 2021). For all diagrams we have used GBP -GRP Gaia EDR3 photometry, as in the case of the CMDs obtained during the membership analysis of the cluster sample (see Chapter 2.2.3), and similarly to some of the most recent studies from the literature mentioned above (e.g., Fritzewski et al., 2020, 2021). We note that Popinchalk et al. (2021) used G-GRP Gaia DR2 photometry rather than the GBP -GRP colour, given that their study is focused on a study of gyrochronology for M dwarfs, and they found that this colour was the one with the tightest relation to M-type stars, while the GBP magnitude is not as reliable for very low-mass stars (Fritzewski et al., 2020). Seeing as we are focusing this work mainly on FGK stars, however, we have continued to use the GBP -GRP colour in all cases and refer to Popinchalk et al. (2021) for an in-depth study of the rotational evolution of M-dwarfs across age. For each age range we have chosen a small number of representative clusters with key ages (six for the young age range, and five for both the intermediate-age and old clusters). This selection prioritized a larger number of final candidates to obtain sequences and trends that were as clear as possible, as well as clusters with Prot values available (see Sect. 3.1), and also clusters with as many reported Hα values as possible, especially in the old age range, where they become scarce (see Sect. 3.2). As well as the colour-rotation and colour-activity diagrams, in Figs. 3.22, 3.23 and 3.24 we also plot for each cluster its corresponding CMD for reference. Before discussing as a general overview these rotational and activity distributions across age, we also list here the cluster selections for each age-range: For the SFRs and young clusters (1– 50 Myr) we have selected NGC 6530 (1–3 Myr), NGC 2264 (4 Myr), γ Vel (10–20 Myr), IC 2391, IC 2602 and IC 4665 (in the same plot, with a general age of 35–38 Myr), NGC 2547 (20–45 Myr), and NGC 2451 A and B (39–44 Myr). As for intermediate-age clusters (80–700 Myr), we chose Blanco 1 (94 Myr), NGC 2516 (125 Myr), NGC 6709 (179 Myr), NGC 6705 (280 Myr), NGC 3532 3.3. Colour-rotation and colour-activity diagrams 93 (300 Myr), and NGC 6633 (574 Myr). Finally, for the old age range (0.7–5.0 Gyr), we selected Berkeley 81 (860 Myr), NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), Berkeley 44 (1.6 Gyr), and NGC 2243 (4 Gyr). For comparison purposes, we also note that each set of diagrams for the young, intermediate-age and old clusters is scaled according to the highest values of Prot, vsini and Hα present in each age range. 94 C h a pt er 3. D ependence w ith rotation,activity and m etallicity Figure 3.22: Colour-period diagram (upper panel, when available), colour-vsini diagram (second panel from the top), colour-activity diagram (third panel from the top), and CMD (bottom panel) for a selection of young clusters in our sample with key ages in the range 1–80 Myr. 3.3.C olour-rotation and colour-activity diagram s 95 Figure 3.23: Colour-period diagram (upper panel, when available), colour-vsini diagram (second panel from the top), colour-activity diagram (third panel from the top), and CMD (bottom panel) for a selection of intermediate-age clusters in our sample with key ages in the range 90–600 Myr. 96 C h a pt er 3. D ependence w ith rotation,activity and m etallicity Figure 3.24: Colour-vsini diagram (upper panel), colour-activity diagram (middle panel), and CMD (bottom panel) for a selection of old clusters in our sample with key ages in the range 0.8–4 Gyr. 3.3. Colour-rotation and colour-activity diagrams 97 We start this general overview of age-rotation and age-activity distributions across colour with the young age range (1–50 Myr) in Fig. 3.22. Considering the maximum observable levels for rotation and activity for this range, this merge is scaled with a maximum value of vsini=140– 150 km s−1, a Prot of 20 d, and a maximum Hα of 320 Å. We firstly observe that both the distributions of rotational periods and vsini for the SFRs (age ≤ 6 Myr, exemplified here by NGC 6530 and NGC 2264) show an appreciably wide range of rotation across all colours (e.g., Soderblom, 2010; Soderblom et al., 2014), although we do see a clear lack of slow rotators among the redder low-mass stars. Studies such as Lamm et al. (2005) also observe a large range of periods for a given colour in NGC 2264, and also conclude that lower-mass stars rotate on average much faster than the bluer, more massive stars in this age range. This wide range of rotation rates is related to the higher dispersion which is generally observed for SFRs due to all the different effects taking place for these very young stars (e.g., Rebull et al., 2018) (see Sect. 3.1). As discussed in the former sections of this chapter, we also see a high number of slower-rotating FGK stars (with Prot >4 d) in these distributions (e.g., Lamm et al., 2005), a direct consequence of the angular momentum loss caused by the interactions of the circumstellar discs for very young clusters (e.g., Barnes et al., 1999; Lamm et al., 2005; Rebull et al., 2018; Fritzewski et al., 2020; Popinchalk et al., 2021) (also see Sect. 3.1). At the same time, the youth of the stars in this age range, taking into account both SFRs and young stars with ages 10–50 Myr, also translates into a scale with higher rotation rates and activity levels than those seen in the intermediate-age and older clusters. Regarding chromospheric activity, for the SFRs selected we also observe a wider range of Hα emission across warmer and cooler stars than the distributions for older clusters, with an existing trend of more active stars towards redder colours (e.g., Lamm et al., 2005; Rebull et al., 2018). The activity-colour diagram for NGC 2264 also features the highest values of chromospheric activity observed in the whole age range, which is in agreement with the youth of the stars populating the SFRs. The decoupling of these very young stars from their circumstellar discs is expected to happen for most stars at an age of 8–10 Myr. This termination of the disc locking process causes the PMS stars to spin-up in various degrees (depending, for example, on whether they experienced significant disc-locking for a long period of time) before experiencing a renewed angular mo- mentum loss on their arrival to the ZAMS (e.g., Barnes et al., 1999; Lamm et al., 2005; Irwin et al., 2007; Frasca et al., 2015; Rebull et al., 2018; Dumont et al., 2021a) (also see Sect. 3.1). According to Rebull et al. (2018), the basic dependence of rotation on colour (and hence, on spectral type and, generally speaking, on mass) is already set in place by 8 Myr, with the scatter in rotation at a given mass decreasing with increasing age. In the figures for ages 10–50 Myr we can already observe this phenomenon as rotation-colour distributions which are becoming less wide and more defined. While also present in younger clusters to a lesser degree, such as NGC 2264 (Lamm et al., 2005), for these post-disc and pre-ZAMS PMS young clusters we also begin to observe clear peaks for bluer (more massive) and redder (less massive) stars, and a di- chotomy between rapid and slow rotators which will appear from this moment across the whole age ranges (e.g., Barnes et al., 1999; Irwin et al., 2007; Rebull et al., 2018; Popinchalk et al., 2021). These diagrams display a clear correlation between spectral type (and mass) and rotation for these young clusters, and we continue to see a lack of slow rotators at very low masses (e.g., Barnes et al., 1999; Irwin et al., 2007), something which is well exemplified, for example, by the period distribution of NGC 2547 (20–45 Myr) (Irwin et al., 2007). At this stage PMS stars are spinning up as a result of pre-ZAMS contraction, and also already beginning to experience some angular momentum loss caused by the interaction between the magnetic field of the stars 98 Chapter 3. Dependence with rotation, activity and metallicity and their stellar winds (e.g., Popinchalk et al., 2021). These two effects are competing with each other throughout the entire mass range, and the result is that contraction often dominates among the low-mass redder M stars (which consequently display higher rotation rates), while in the FGK range, angular momentum loss prioritizes and most of these stars spin down to slower rotations throughout this phase (Rebull et al., 2018). At the same time, we also begin to see a peak of fast rotators — which will become more evident in the intermediate-age range — for more massive, blue stars. In spite of angular momentum loss, as mentioned in Sect. 3.1, F-type stars rotate faster due to their higher mass and temperature, and so their rotation rates remain higher than for GK stars (e.g., Wolff et al., 1986; Delgado Mena et al., 2015). Regarding chromospheric activity, the distributions of Hα emission have also become less dispersed and more defined, with a continuing trend of more active stars towards redder colours (e.g., Lamm et al., 2005; Rebull et al., 2018). Young stars in the PMS phase also exhibit a broad and variable range of activity at a given age (e.g., Soderblom, 2010; Wright et al., 2011; Soderblom et al., 2014), which we can also observe in Fig. 3.22, and especially in the case of NGC 2264. To account for this broad range it is also helpful to comment on how activity is proportional to rotation, but also secondary to it, and a given rotation rate can result in a wider range of activity (Soderblom, 2010). Activity can also saturate at the notably high rotation rates observed in PMS stars, resulting in the fact, still not fully understood, that activity cannot remain proportional to rotation indefinitely (e.g., Soderblom, 2010; Soderblom et al., 2014). We also note that the trend of observing more active stars for low-mass redder stars is not as readily visible as in the case of the intermediate-age range, and this is a result of the scaling for this age range, which accounts for the very high chromospheric activity observable in SFRs such as NGC 2264. While still present as a tracer of the youth of these stars, the levels of Hα emission have also notably decreased in this later PMS stage of the young cluster range. Fig. 3.23 shows the rotation and activity distributions across colour for the intermediate-age range (50–700 Myr). Considering the maximum observable levels for rotation and activity for this range, this merge is scaled with a maximum value of vsini=150 km s−1, a Prot of 15 d, and a maximum Hα of 10 Å. With the arrival of FGK stars at the ZAMS (at an age similar to that of the Pleiades, 70– 100 Myr), angular momentum loss caused by stellar winds is already fully dominating and this results in lower rotation rates for the whole intermediate-age range and a notably higher number of slower rotators across these spectral types, as already discussed in some more detail in Sect. 3.1 (e.g., Rebull et al., 2018; Fritzewski et al., 2020; Popinchalk et al., 2021). This loss of angular momentum continues in the age range from the Pleiades to the Hyades (750 Myr) and the early MS phase. At the same time, pre-ZAMS contraction is still ongoing for the lowest-mass M stars for a considerable part of this intermediate-age range (as already mentioned in earlier sections, M-type stars have additionally not yet reached the ZAMS at an age range of the Pleiades) (e.g., Barnes et al., 1999; Rebull et al., 2018), while F-type stars continue to dominate among the faster-rotating stars, rotating faster than GK stars due to their mass and temperature. All this translates in a clear dichotomy of rapid and slow rotators that is increasingly defined in this age range, compared to the young cluster age, both for the colour-period and vsini-colour dis- tributions. To summarize the general trend for this range, FGK stars show a clear dependence of rotation on colour, corresponding to a monotonically increasing period rates to lower mass (that is to say, F stars rotate faster than GK stars, which rotate steadily more slowly), while the lower-mass M stars show an opposite trend of strongly decreasing period (faster rotation rates) as mass decreases (Rebull et al., 2018; Fritzewski et al., 2020, 2021; Popinchalk et al., 2021). 3.3. Colour-rotation and colour-activity diagrams 99 Regarding the vsini-colour plots, we can observe the aforementioned peaks of faster rotators first for the more massive F stars, and secondly for the low-mass redder late-K and M stars (Rebull et al., 2018; Fritzewski et al., 2020, 2021; Popinchalk et al., 2021). In the case of some clusters, like NGC 6705 (300 Myr), the peak for the bluer, more massive stars dominates in an appreciable way, while other clusters such as NGC 2516 (125 Myr) and NGC 3532 (280 Myr) show both peaks in a very clear way, and older clusters such as NGC 6633 (575 Myr) display low rotational rates consistently for all colours, with slighter faster rotators among the low-mass red stars. On the other hand, the structures in the rotational distributions of some of the selected clusters, such as NGC 6709 (173 Myr), are harder to analyse as a result of a smaller sample size. As for colour-period distributions for this range, Fritzewski et al. (2020) and Fritzewski et al. (2021) (among other studies) studied in detail the distributions for the Pleiades-age NGC 2516 cluster (125 Myr), and for the older NGC 3532 cluster (280 Myr), with an intermediate age be- tween the Pleiades and the Hyades. As already mentioned in Sect. 3.1, these studies describe the colour-period distributions for these clusters as displaying a triangular shape, which has been ob- served for a steadily increasing number of ZAMS and post-ZAMS clusters. This shape is formed by a diagonal slow rotator sequence delineating the upper boundary of the colour-period diagram and stretching from early G-type stars all the way to M dwarfs. The lower boundary is then defined by a less-populated flat sequence of fast rotating stars among the cooler, lower-mass M candidates, named as the ‘reservoir of rapid rotators’ by Popinchalk et al. (2021). The triangular shape with these two sequences of slow and fast rotators are clearly defined in the colour-period diagrams of Fig. 3.22 for NGC 2516 and NGC 3532. In the case of NGC 2516, we can also observe the region between these two sequences containing the stars which are undergoing the transition from fast to slow rotators, defined as the ‘gap’ (Fritzewski et al., 2020; Popinchalk et al., 2021). Popinchalk et al. (2021) further defines the region where these transitional stars begin to con- verge onto the slow rotator sequence as the ‘elbow’ (see Fig.3.25), which moves redwards with age, and becomes less defined and even absent in younger clusters (something which we can also confirm with an inspection of our period distributions). In the case of NGC 2516, Fritzewski et al. (2020) additionally noted on the unusual presence of a group of slower-rotating M dwarfs, which they defined as the ‘extended slow rotator sequence’, also visible in the period distribu- tion of NGC 2516 for our candidate selection. Rebull et al. (2018) also comments on the wide range of rotation rates at low masses for NGC 2516, something which we can also see in Fig. 3.22. As also discussed in Sect. 3.1, we can exemplify the rotational distribution of clusters with ages in between the Pleiades and the Hyades with the 280 Myr old cluster NGC 3532, studied in detail by Fritzewski et al. (2021). The period distribution for this cluster also presents the triangular shape described above, in this case showcasing a very structured and well-populated slow rotator sequence which stretches diagonally from the late-F stars to the early M dwarfs, as well as a reservoir of rapid rotators among the low-mass redder late-K and early-M candidates which are transitioning from fast to slow rotators. This study also commented on how the slow rotation sequence was remarkably linear, as we can also observe in Fig. 3.22, which seems to be an intrinsic feature of clusters with intermediate ages between the Pleiades and Hyades, such as NGC 3532. We also observe that the transitional stars in the ‘gap’ of the period distribution of NGC 2516 are not to be found in the period distribution for NGC 3532. Fritzewski et al. (2021) also observed this, among other characteristics, by comparing the distributions of NGC 2516 and NGC 3532 to observe the evolution from ZAMS-age clusters to clusters approaching the early MS. As for chromospheric activity for this intermediate-age range, the distributions of Hα emission 100 Chapter 3. Dependence with rotation, activity and metallicity Figure 3.25: Example of a rotation period distribution in Popinchalk et al. (2021) for Praesepe, a 600 Myr cluster, indicating the sequences of fast and slow rotators discussed in this section, and the labels used to describe them. have continued to become more defined with respect to the younger clusters, and we can observe a clear trend of more active stars towards redder colours in the case of Blanco 1, NGC 2516 and NGC 3532 (e.g., Fritzewski et al., 2020; Popinchalk et al., 2021). Younger stars in the ZAMS-age clusters can still exhibit a broader range of activity at a given age, however (e.g., Soderblom, 2010), which we can also observe in the case of Blanco 1 and NGC 2516. As expected, the levels of Hα emission have decreased considerably in the ZAMS phase in contrast to the PMS stars, and are minimal for massive blue stars. We note that three clusters in our selection for the intermediate-age range had very few Hα measurements in the iDR6 file, and so we are not able to analyse their activity distributions, and we note that we observe very low values in all cases. Finally, we discuss the rotation and activity distributions across colour for the old range (0.7–5.0 Myr), shown in Fig. 3.24. Considering the maximum observable levels for rotation and activity for this range, this merge is scaled with a maximum value of vsini=90 km s−1, a rota- tional period of 15 d, and a maximum Hα of 0.35 Å. We note that for the chosen selection in this old cluster range there are not available Prot values. As discussed in Sect. 3.1, the FGK stars in this age range are already in the MS phase, with a continuing trend of angular momentum loss with age (e.g., Rebull et al., 2018). This results in the observable lower rotation rates for the whole old range and a steadily higher number of slower rotators across all spectral types across age, as displayed in Fig. 3.24 (also see Sect. 3.1). In the rotation-colour diagrams we also continue to observe a clear dependence of rotation on colour and stellar mass, with the bluer, high-mass F-type stars having the highest rotation rates, and the redder, lower-mass stars rotating more slowly. Studies such as Barnes et al. (2016) remark that the stars in older clusters such as M67 (4.0–4.5 Gyr, with an age close to NGC 2243) follow the same trend of increasing period (lower rotation rates) with redder colour (decreasing mass) as the one observed in the Hyades (also see Sect. 3.1). In Figs. 3.22, 3.23 and 3.24 we have similarly observed that this correlation of rotation with colour and mass has been clearly visible since 10 Myr to 4 Gyr for the displayed selected clusters, with steadily lower rotation rates across all colours as age increases. In the old age range we additionally no longer see the peak of faster 3.4. [Fe/H] metallicity 101 rotators among the more evolved redder low-mass stars, and only observe the higher rotators among the higher-mass F-type stars. As for chromospheric activity, we note that the iDR6 file includes very few measurements of Hα for the old cluster range. We endeavoured to choose for the selection in Fig. 3.24 those clusters with as many available Hα values as possible, as well as with the most representative rotation-colour distributions, but even so there are two clusters with no available Hα measure- ments (NGC 2355 and Berkeley 44). The few values of chromospheric activity for the remaining three clusters also hinder the analysis in order to discern trends or correlations, but we can remark that the activity is very low for all clusters, as would be expected in the old age range for FGK stars in the MS, with a maximum value of 0.35 Å (incidentally, for the oldest 4 Gyr cluster NGC 2243). Apart from the observable decline of activity with age (e.g., Soderblom, 2010), among these very low values we also find that the most active stars in these clusters are redder, low-mass stars, continuing the same trend observable in younger clusters, where the most active objects in clusters are those with the latest spectral types (e.g., Popinchalk et al., 2021). 3.4 [Fe/H] metallicity Figure 3.26: EW (Li)-versus-Teff diagram com- paring the upper Li envelopes for NGC 2244 (4 Myr, [Fe/H]=−0.23 dex) and NGC 2264 (4 Myr, [Fe/H]=−0.08 dex). Figure 3.27: EW (Li)-versus-Teff diagram com- paring the upper Li envelopes for NGC 6705 (280–300 Myr, [Fe/H]=0.16 dex) and NGC 3532 (300–399 Myr, [Fe/H]=−0.08 dex). The last stellar parameter we have studied in this chapter is [Fe/H] metallicity. While rotation and Hα activity are useful parameters to quantify and explain the dispersion of the observable Li in each of the cluster selections, as we have seen in the former Sects. 3.1, 3.2 and 3.3, metallicity can also have an effect on the overall Li depletion of the clusters (see Sect. 1.2.4). In this section we have chosen a series of coeval clusters from our selection which present differing values of [Fe/H] metallicity, one of them typically being more metal-rich and the other one more metal- poor. Using the Li envelopes we have obtained in Chapter 4, we will assess the effects of these differing values of metallicity on the general level of Li depletion of each cluster, and thus on the 102 Chapter 3. Dependence with rotation, activity and metallicity Figure 3.28: EW (Li)-versus-Teff diagram com- paring the upper Li envelopes for NGC 6633 (575–773 Myr, [Fe/H]=−0.10 to −0.01 dex) and the Hyades (750 Myr, [Fe/H]=0.14 dex). Figure 3.29: EW (Li)-versus-Teff diagram com- paring the upper Li envelopes for NGC 2355 (900 Myr, [Fe/H]=−0.11 dex) and NGC 6802 (900 Myr, [Fe/H]=0.10 dex). relative position of the upper Li envelope of each selected pair of coeval clusters. We will consider the following clusters: For the young age range we have chosen the 4 Myr SFRs NGC 2244 ([Fe/H]=−0.23 dex) and NGC 2264 ([Fe/H]=−0.08 dex); for the intermediate- age range we firstly chose NGC 6705 (280–300 Myr, [Fe/H]=0.16 dex) and NGC 3532 (300– 399 Myr, [Fe/H]=−0.07 dex), as well as a comparison between NGC 6633 (575–773 Myr, [Fe/H]=−0.10 to −0.01 dex) and the Hyades (750 Myr, [Fe/H]=0.14 dex), as it is a cluster whose metallicity has been referenced and studied by several studies (Umezu & Saio, 2000; Jeffries et al., 2002). Finally, among the old clusters we selected firstly NGC 2355 (900 Myr, [Fe/H]=−0.11 dex) and NGC 6802 (900 Myr, [Fe/H]=0.10 dex), followed by Pismis 15 (1.3 Gyr, [Fe/H]=0.01 dex) and Trumpler 20 (1.4 Gyr, [Fe/H]=0.10 dex), and, finally, NGC 2243 (4.0 Gyr, [Fe/H]=−0.38 dex) and M67 (4.0–4.5 Gyr, [Fe/H]=−0.01 dex). We additionally refer to Ta- bles 2.2 and 2.3 for the ages we have considered in this study for each cluster, as well as Table 2.6 for the [Fe/H] values from the literature used here. We note that some of the selected clusters have very similar reported ages and can be considered coeval clusters, while others, which we have also decided to discuss in this section to further analyse the extent of the effects of metallicity on the Li envelopes, are in a close age range but do not share the same age. Before we discuss the observable results for the aforementioned clusters, we summarize a cou- ple of hypotheses from the literature regarding the effect of [Fe/H] metallicity on Li depletion, and we direct the reader to the introduction in Sect. 1.2.4 for a more detailed overview. The hy- pothesis we will be mainly considering here states that the most metal-rich clusters tend to show the higher Li abundances than their metal-poor counterparts (Randich et al., 2020; Randich & Magrini, 2021). According to this interpretation, when comparing two coeval clusters, one of them more metal-rich and the other more metal-poor, the upper Li envelope for the higher metallicity cluster should be located at least slightly above the one corresponding to the more subsolar cluster. On the other hand, several other studies have claimed the opposite of the former interpretation, stating that Li rather decreases at high metallicity (Umezu & Saio, 2000; Jeffries 3.4. [Fe/H] metallicity 103 Figure 3.30: EW (Li)-versus-Teff diagram com- paring the upper Li envelopes for Pismis 15 (1.3 Gyr, [Fe/H]=0.01 dex) and Trumpler 20 (1.4 Gyr, [Fe/H]=0.10 dex). Figure 3.31: EW (Li)-versus-Teff diagram com- paring the upper Li envelopes for NGC 2243 (4.0 Gyr, [Fe/H]=−0.38 dex) and M67 (4.0– 4.5 Gyr, [Fe/H]=−0.01 dex). et al., 2002; Dumont et al., 2021a). This hypothesis links high metallicity with more efficient convection zone, and in result more metal-rich clusters would be observed to deplete Li faster than more subsolar ones, and the upper Li envelopes of high metallicity clusters should rather be observed at least slightly below the ones corresponding to more metal-poor coeval clusters. However, Randich et al. (2020) do not find evidence of a Li decrease at high metallicity, and suggest that this observed decrease in Li for metal-rich stars does not seem to be real, and that the related findings could be enhanced by sample selection effects. The first clusters we have compared are the 4 Myr SFRs NGC 2244 ([Fe/H]=−0.23 dex) and NGC 2264 ([Fe/H]=−0.08 dex). The upper Li envelopes obtained in this work (see Chapter 4) are plotted together in Fig. 3.26. In all cases we will show the Li envelopes for both clusters on their own, without the cluster candidates, to further facilitate the comparison between the two (see Appendix C for the diagrams including the final candidates for each cluster). We observe that the Li envelope for NGC 2264, the most metal-rich cluster, is situated above the one corre- sponding to NGC 2244, which is a slightly subsolar cluster. This finding seems to support the hypothesis in Randich et al. (2020) and Randich & Magrini (2021). We found a similar result comparing the intermediate-age clusters NGC 6705 (280–300 Myr, [Fe/H]=0.16 dex) and NGC 3532 (300–399 Myr, [Fe/H]=−0.08 dex), whose obtained Li en- velopes are plotted in Fig. 3.27. In this case, we also observe that the Li envelopes for NGC 6705 (see Chapter 4), the more metal-rich cluster, are located slightly above the ones corresponding to the slightly subsolar cluster NGC 3532. However, we also have to bear in mind that these clusters are close in age, but not technically coeval (in this study we have considered 280 Myr for NGC 6705 and the older age of 399 Myr for NGC 3532). Thus, we can also expect to see the Li envelopes for NGC 6705 to be situated above those of NGC 3532 as a result of its younger age by 100 Myr, and it is more difficult to evaluate the effect of the differing metallicities in this case, or if [Fe/H] metallicity would have an observable effect on the Li envelopes for these two clusters. 104 Chapter 3. Dependence with rotation, activity and metallicity Although we have not analysed the Hyades cluster (750 Myr, [Fe/H]=0.14 dex) during our calibration for this work, we have also compared the upper envelope for this cluster (Soderblom et al., 1993) with NGC 6633 (575–773 Myr, [Fe/H]=−0.10 to −0.01 dex), given that the latter cluster has been considered by several of the literature studies mentioned above in the study of the dependence of metallicity on Li depletion (e.g., Umezu & Saio, 2000; Jeffries et al., 2002; Du- mont et al., 2021a). Both of the upper Li envelopes for these clusters are displayed in Fig. 3.28. In this case what we can observe is the the upper Li envelope for NGC 6633, a subsolar cluster, lies slightly above the Hyades. While this would seem to suggest the findings in the aforemen- tioned studies that the more metal-poor cluster NGC 6633 has consequently depleted less Li, it is worth noting that these studies considered both of these clusters as coeval, with an age very similar to the Hyades for NGC 6633 (see the individual notes in Appendix B). In this work, however, we do not consider these clusters as coeval, and have adopted an appreciably younger age of 575 Myr for NGC 6633, as reported by Bossini et al. (2019) making use of Gaia DR2 data. We believe that this younger age is in agreement with our final selection for this cluster, and explain the fact that its upper Li envelope lies slightly above the Hyades due to NGC 6633 being younger by at least 150 Myr, and not as a result of being more metal-poor. We thus suggest that the metallicity of NGC 6633 has no observable effect on the position of its Li envelope in comparison to the envelope for the Hyades cluster as these clusters do not seem to be coeval. Regarding the old age range, we firstly compared the 900 Myr old clusters NGC 2355 ([Fe/H]=−0.11 dex) and NGC 6802 ([Fe/H]=0.10 dex), whose Li envelopes are plotted together in Fig. 3.29. Similarly to the case of the comparison between NGC 2264 and NGC 2224, albeit less clearly defined, we see that the upper Li envelope for the most metal-rich cluster of these two, NGC 6802, tends to lie slightly above the envelope for NGC 2355, once again in apparent agreement of the hypothesis of lesser Li depletion at higher metallicity by Randich et al. (2020). We also note that the smaller candidate selection for NGC 6802 has somewhat hindered the construction of an optimum Li envelope for this cluster, in contrast to the better defined and smoother curves we have been able to obtain with larger cluster selections, and this might be a factor to explain the more ambiguous results for this comparison. The next clusters we considered are Pismis 15 (1.3 Gyr, [Fe/H]=0.01 dex) and Trumpler 20 (1.4 Gyr, [Fe/H]=0.10 dex), with their Li envelopes plotted in Fig. 3.30. Similarly to the case of NGC 6705 and NGC 3532, these clusters are not technically coeval, but rather have very close ages in the range of 1.3–1.8, with Trumpler 20 being older. The obtained upper Li envelopes for both clusters are practically in the same height and following the same curve, however, with the one corresponding to Trumpler 20, the more metal-rich cluster, being slightly lower in some areas. We consider that this slightly lower placement is a result of Trumpler 20 being somewhat older, however, and suggest that given that these clusters do not seem to be coeval, metallicity would have no significant observable effect on the Li envelopes in this case. Finally, we found a similar result comparing the obtained Li envelopes of the oldest clus- ters in our sample, namely NGC 2243 (4.0 Gyr, [Fe/H]=−0.38 dex) and M67 (4.0–4.5 Gyr, [Fe/H]=−0.01 dex), plotted in Fig. 3.31. These clusters are quite close in age, in a range of 4.0–4.5 Gyr, but are also not coeval, with NGC 2243 being younger than M67. Thus, we can expect to see the upper Li envelope for NGC 2243 to be located above that of M67 mainly as a result of its moderate younger age, and we once again suggest that this is not due to any observable effects of [Fe/H] metallicity on the Li depletion of these clusters. Chapter 4 The Li-age relation: Creating Li envelopes 4.1 Empirical lithium envelopes Having performed a thorough membership analysis and obtained lists of candidate members for the 42 open clusters in our sample in Chapter 2, and then having characterized the inherent Li dispersion of each of the cluster selections with the study of the dependence of Li on several stellar parameters, such as rotation and chromospheric activity (see Chapter 3), in this chapter we finally present our calibration of the Li-age relation, consisting of a series of empirical Li envelopes spanning the cluster age range from 1− 3 Myr to 4− 4.5 Gyr. Figure 4.1: EW (Li)-versus-Teff figure from Montes et al. (2001) showing the empirical Li en- velopes we have used throughout this work: the upper Li envelope for IC 2602 (Montes et al., 2001; López Santiago, 2005), the upper (Neuhaeuser et al., 1997) and lower (Soderblom et al., 1993) envelopes of the Pleiades, and the upper envelope of the Hyades (Soderblom et al., 1993). As already discussed in Sect. 2.2.6, in this work we have extensively worked with four empirical Li envelopes from the literature, namely IC 2602 (35 Myr) (Montes et al., 2001; López-Santiago et al., 2003; López Santiago, 2005), the upper (Neuhaeuser et al., 1997) and lower (Soderblom et al., 1993) envelopes of the Pleiades (78–125 Myr), and the upper envelope of the Hyades (750 Myr) (Soderblom et al., 1993) (see Fig. 4.1). Each of these Li envelopes trace the upper 105 106 Chapter 4. The Li-age relation: Creating Li envelopes and/or lower limit of EW (Li) for a given temperature for the candidates of representative clusters in the young, intermediate-age and old age ranges, respectively, and delimit the region popu- lated by the corresponding cluster member stars. In Chapter 2, this information enabled us to study the goodness of the cluster candidates according to their Li content in EW (Li)-versus-Teff diagrams. Using these Li envelopes as a guide, we could thus distinguish the bona-fide cluster members from Li-rich contaminants and other field stars, thus allowing us to fully obtain final selections of robust cluster candidates for each of the 42 clusters in the sample. In this project we aimed to use these cluster calibrations to characterize a Li-age relation and create such Li envelopes as we have been using in our analysis, for as many clusters in our sample as possible, and spanning a wider age range of empirical Li envelopes than was formerly available in the literature. We note the considerable utility of a larger set of Li envelopes for key age ranges for SFRs and young clusters, as well as intermediate-age clusters, and old clusters up to 5 Gyr, in order to calibrate age ranges of other open clusters or unknown field stars (see the future work in Chapter 5). Being able to have a larger number of Li envelopes also offers the possibility of more nuanced and precise estimations of age ranges, particularly by adding additional Li envelopes in the larger age range between Pleiades (78–125 Myr) and the Hyades (750 Myr), and also by obtaining more information on younger clusters than IC 2602 (35 Myr) and older clusters than the Hyades. 4.1.E m piricallithium envelopes 107 Figure 4.2: Empirical Li envelopes for the seven SFRs in our sample (age ≤ 6 Myr), plotted in EW (Li)-versus-Teff diagrams displaying the final selection of candidates for each cluster. These diagrams also include the Li envelopes used throughout this work, namely the upper envelope for the cluster IC 2602 (35 Myr, in red); the upper and lower envelopes of the Pleiades cluster (78–125 Myr, in grey); and the upper envelope of the Hyades cluster (750 Myr, in turquoise). 108 C h a pt er 4. T he Li-age relation: C reating Lienvelopes Figure 4.3: Empirical Li envelopes for seven out of the nine young clusters in our sample (age ≤ 50 Myr), plotted in EW (Li)-versus-Teff diagrams displaying the final candidates for each cluster. We also superimpose as dotted lines the Teff values delimiting the LDB region, given by Baraffe et al. (2015) (NGC 2547 is included twice, firstly indicating the lines for NGC 2547 B, and then for NGC 2547 A). These diagrams also include the Li envelopes used throughout this work (the upper envelope for IC 2602 (35 Myr, in red); the upper and lower envelopes of the Pleiades cluster (78–125 Myr, in grey); and the upper envelope of the Hyades cluster (750 Myr, in turquoise)). 4.1.E m piricallithium envelopes 109 Figure 4.4: Empirical Li envelopes for six out of the 13 intermediate-age clusters in our sample (age= 50–700 Myr), plotted in EW (Li)-versus- Teff diagrams displaying the final selection of candidates for each cluster. For all clusters we also superimpose as dotted lines the Teff values given by Baraffe et al. (2015), marking the point where Li depletion should be near complete for the lower-mass candidates. These diagrams also include the Li envelopes used throughout this work, namely the upper envelope for the cluster IC 2602 (35 Myr, in red); the upper and lower envelopes of the Pleiades cluster (78–125 Myr, in grey); and the upper envelope of the Hyades cluster (750 Myr, in turquoise). 110 C h a pt er 4. T he Li-age relation: C reating Lienvelopes Figure 4.5: Empirical Li envelopes for seven out of the 13 old clusters in our sample (age > 700 Myr), plotted in EW (Li)-versus-Teff diagrams displaying the final selection of candidates for each cluster. These diagrams also include the Li envelopes used throughout this work, namely the upper envelope for the cluster IC 2602 (35 Myr, in red); the upper and lower envelopes of the Pleiades cluster (78–125 Myr, in grey); and the upper envelope of the Hyades cluster (750 Myr, in turquoise). 4.1. Empirical lithium envelopes 111 We have created all empirical Li envelopes in a similar way to the aforementioned four en- velopes we have been using throughout the membership analysis. We made use of the final candidate selections for each cluster and created upper envelopes by selecting the members with the highest values of EW (Li) for each temperature range and spectral type, and, when possible, also lower Li envelopes by selecting the lower limit of EW (Li) values for each temperature range. As a result, we traced upper Li envelopes for the young clusters, upper and lower Li envelopes for the intermediate-age clusters, and upper Li envelopes for the old cluster range. We endeav- oured to obtain the most accurate and robust empirical envelopes as possible by making use of the analysis in Chapter 3, where we studied in detail the dependence of rotation, activity and metallicity on the inherent Li dispersion and overall Li content of all cluster selections. As a result of this project, we have obtained Li envelopes for 27 out of the 42 clusters in our sample, corresponding to approximately 64% of the cluster sample. We show all these Li envelopes, organized in age ranges from the SFRs to the older clusters, in Figs. 4.2 (SFRs, age ≤ 6 Myr), 4.3 (young clusters, age ≤ 50 Myr), 4.4 (intermediate-age clusters, age= 50– 700 Myr) and 4.5 (old clusters, age > 700 Myr). In all cases we also show the Li envelopes we have been using throughout this work for IC 2602, the Pleiades and the Hyades. Additionally, for all clusters in the age range of 1–600 Myr we superimpose as dotted lines the Teff values delimiting the LDB region given by Baraffe et al. (2015), which we will describe in more detail in Sect. 4.2. In Fig. 4.6 we also show the final Li envelopes sans cluster candidates, plotted together for the SFRs and young clusters, as well as the intermediate-age, and the old clusters. Fig. 4.7 additionally displays all 27 empirical Li envelopes in a single diagram. All these figures illustrate the potential of the obtained Li envelopes to serve as effective age calibrators for a wide range of ages. Finally, we refer the reader to Appendix F for the tables listing the Teff and EW (Li) values used to create the Li envelopes for each cluster. We note that given the empirical nature of these Li envelopes, their construction mainly depends on the goodness and sample size of the obtained cluster selections. Thus, we could not obtain Li envelopes for all the clusters in our sample, as several candidate selections did not include a sufficient number of stars that would allow for a complete envelope. For most of these clusters we were able to visually ascertain the potential height and shape of its upper and/or lower Li envelopes, but we were not able to fully create them by making use of the existing lists of cluster members because of a lack of GES candidates in key Teff ranges. However, given our large initial cluster sample, we are satisfied with these preliminary Li envelopes obtained in this work, insofar we were able to obtain at least one empirical Li envelope for all key ages spanning the whole age range of the sample, adding several upper envelopes corresponding to ages younger than IC 2602 (35 Myr), as well as a number of upper and lower Li envelopes with intermediate ages between the Pleiades (78–125 Myr) and the Hyades (750 Myr), and several upper envelopes for clusters older than the Hyades. ∗ Li envelopes: SFRs We will now provide a general overview in which we discuss how we obtained these empirical Li envelopes for all age ranges, offering additional details for some of the individual Li envelopes as well, starting with the seven SFRs (age 1–6 Myr, see Fig. 4.2), all of which had a sufficient number of candidates to create upper Li envelopes. We previously discussed in Chapter 3 how the candidate selections of SFRs show an appreciably higher Li dispersion than older clusters, due to the complex and diverse effects taking place for these very young stars, and we characterized said scattering by analysing the dependence of rotation, accretion and chromospheric activity on 112 Chapter 4. The Li-age relation: Creating Li envelopes Li content. It is because of this dispersion that some cluster candidates seem to deviate more from the rest, particularly those with notably high levels of EW (Li) due to their high accretion and activity (see Sects. 3.1 and 3.2, as well as the individual notes in Appendix B). Seeing as we can in this way explain the behaviour of these strong accreting and highly active stars with higher levels of Li, we have decided to not consider them when tracing the upper Li envelopes for these SFRs, choosing rather to follow the general trend for the majority of cluster candidates, as we believe that the EW (Li) values of these strong accretors are not representative of the cluster candidates as a whole, The most illustrative example of this is NGC 2264, although we have also seen it in NGC 6530, Trumpler 14, Cha I, NGC 2244 and λ Ori (see Appendix B). The higher inherent scattering of this cluster range, characterized in detail using the infor- mation on rotation and activity in Chapter 3, are visible when we plot the final Li envelopes for SFRs in the same age ranges (see Fig. 4.6, top panel). However, and especially when plotted in a scale that includes the complete cluster age range (see Fig. 4.7), the position of these Li envelopes are fully consistent with each other, and they give a helpful delimitation of the position and Li content of the very young stars in SFR. Moreover, given this very young age, the inherent dispersion of these cluster selections and the resulting upper Li envelopes does not hinder the role of the Li envelopes as effective age calibrators in any significant way, as their position in the EW (Li)-versus-Teff is unambiguous. By observing all Li envelopes for the SFRs plotted together in the top panel of Fig. 4.6, and how despite the aforementioned scattering all of them are located at very similar heights and follow practically the same angle of inclination, we can also reinforce our decision to exclude from the construction of the Li envelopes all strong accreting stars with measured EW (Li)s in the 800–1270 mÅ range. We can also observe that the Li envelopes for all SFRs in a 1–4 Myr range are superimposed over one another, while the older envelope for λ Ori (6 Myr) is located slightly below all of these. NGC 2244 and NGC 2264, at 4 Myr, are also coeval clusters whose slight difference between their Li envelopes we studied as potentially dependent on [Fe/H] metallicity (see Sect. 3.4). Finally, we note that for the SFRs with a larger number of cluster members (such as NGC 2264, NGC 6530 and Trumpler 14) we were able to create smoother and more detailed Li envelopes. ∗ Li envelopes: Young clusters The seven young clusters in our sample for which we obtained Li envelopes are shown in Fig. 4.3 and the top panel of Fig. 4.6. We see the progression of ages more clearly in this age range (10–45 Myr), with the upper Li envelope for γ Vel (10–20 Myr) situated below all the SFRs, followed by progressively lower Li envelopes for clusters in the 20–45 Myr age range (such as NGC 2232 and NGC 2547), reaching the existing upper Li envelope for the combination of IC 2391, IC 2602 and IC 4665 (35–38 Myr). We will now briefly discuss each of the young clusters with an obtained Li envelope: The envelope for Col 197 (13 Myr) is located above γ Vel in Fig. 4.6, being slightly younger, but it also appears to be superimposed on the younger SFRs in some places, suggesting an even younger age. This cluster proved to be one of the most unreliable ones during our membership analysis, being the only cluster in our sample whose estimated RV is not in agreement with the literature, and the obtained candidate selection for Col 197 also presented the most disagree- ments with the listed members in Jackson et al. (2021) as well (see Appendix B). Judging by all this, we consider that the upper Li envelope for this cluster is potentially not as reliable as 4.1. Empirical lithium envelopes 113 others and would need further analysis, unless its higher scatter could be explained by taking into account the inherent dispersion of all these young clusters, as well as the fact that the difference between the age range of the SFRs and Col 197 is quite small. The cluster candidates for γ Vel, on the other hand, yield Li envelopes which are clearly located below all the SFRs, tracing the Li content corresponding to an age range of 10–20 Myr. We decided to create a single upper envelope for both γ Vel A and B, as both populations are coeval and their candidates seem to trace the same Li envelopes. Seeing as the final selection for this cluster is particularly well defined in the EW (Li)-versus-Teff diagram, for this cluster we were able to obtain both an upper Li envelope and a tentative lower Li envelope (we note that we typically only obtained lower Li envelopes for the intermediate-age clusters). This is also the first cluster for which we delimited the LDB region with the aid of the values of Teff given by Baraffe et al. (2015) (see Sect. 4.2 for more details), and we were also able to fully trace the LDB for γ Vel as part of its upper Li envelope. Moreover, while we still see a level of inherent dispersion in the later young age range, we can also explain said scatter in the same way as with the SFRs — For example, the two stars with higher levels of EW (Li) above the upper Li envelope in Fig. 4.3 are fast rotating and active stars, respectively (see Chapter 3 and Appendix B). We also note that the upper Li envelope for the coeval NGC 2547 B is located close to the upper Li envelope for γ Vel, while NGC 2547 A is older. In Fig. 4.3, the dotted ‘Baraffe lines’ for NGC 2547 B are plotted first, and the figure is later repeated to show the corresponding lines for NGC 2547 A (see below). The upper Li envelopes for the remaining young clusters in an age range of 20–50 Myr (namely, NGC 2232, NGC 2547 A, and IC 2391, IC 2602 and IC 4665) begin to show the typical shape we will be encountering throughout the young and intermediate-age ranges, a reflection of how stars from different spectral types deplete Li in a different way and present different Li abundances, with low values for F-type stars, maximum around GK stars, and a decrease for M-dwarfs until complete Li depletion, depending on the age (see Subsect. 1.1.2). Similarly to the clusters discussed above, in Fig. 4.3 we also delimit the LDB region for all of these young clusters, although we only draw a complete Li envelope, including the LDB region, for IC 2391, IC 2602 and IC 4665 (as will be discussed in Sect. 4.2). The upper envelope for NGC 2232 is located above the one corresponding to IC 2602, which seems to reinforce the age estimations from the literature (18–32 Myr, making NGC 2232 slightly younger than IC 2602 at 35 Myr). On the other hand, the upper Li envelope we obtained for NGC 2547 A (20–45 Myr) can also be found slightly above IC 2602, albeit below NGC 2232. While several studies list the age of NGC 2547 A as 35–45 Myr, other age estimations give the aforementioned slightly more extended range of 20–45 Myr (e.g., Oliveira et al., 2003) (also see Table 2.2), and LDB measurements (see Sect. 1.1) have obtained an age of 35 Myr (e.g., Oliveira et al., 2003; Soderblom et al., 2014). Taking all these former age estimations into account, we could thus explain why the Li envelope for NGC 2547 A appears below NGC 2232, a somewhat younger cluster, but also slightly above IC 2602, which initially appeared to be the same age and even moderately older than IC 2602 according to the literature age estimations of 35–45 Myr. The height of the obtained upper Li envelope for NGC 2547 A does seem to indicate that this population is somewhat younger than was previously estimated in earlier studies, more in accor- dance with an age range of 20–35 Myr. Finally, for IC 2391, IC 2602 and IC 4665 (35–38 Myr) we have decided to continue using the upper Li envelope obtained by Montes et al. (2001), after confirming that we obtained a nearly identical upper Li envelope by making use of a combina- tion of the final candidate selections for all three of these clusters, as well as several additional members by Randich et al. (2001) and Jeffries et al. (2009a) (see Appendix B). We discuss our 114 Chapter 4. The Li-age relation: Creating Li envelopes completion of this envelope by fully delimiting the LDB region in Sect. 4.2. Finally, we note that NGC 2451 A and B (39–44 Myr) are the only young clusters for which we were not able to obtain complete Li envelopes, due to the smaller size of the final candidate selections. For example, the preliminary upper Li envelope we obtained for NGC 2451 B by making use of the existing candidate stars was located below the upper envelope of the Pleiades (78–125 Myr), and we believe this not to be a sign that the age of the cluster had been underes- timated, but rather a result of a clear lack of GK candidate stars with higher EW (Li) values for the 4500–5500 K range in the sample obtained from the literature. A reason for this conclusion is that we do observe F and early G candidate stars tracing the envelope for IC 2602, as well as late-K stars with higher levels of Li, indicating a probable higher Li envelope than the one we were able to obtain. Given that we already counted with more robust and reliable Li envelopes in this age range, we decided not to consider these two clusters. ∗ Li envelopes: Intermediate-age clusters We obtained upper and lower Li envelopes for six out of the 13 intermediate-age clusters in our sample, as shown in Fig. 4.4 and the middle panel of Fig. 4.6. All of these clusters have key ages spanning a range of 94–575 Myr, including clusters with a similar age to the Pleiades (78–125 Myr), such as Blanco 1 and NGC 2516, as well as slightly older clusters (NGC 6709, with 179 Myr), and clusters with intermediate ages between the Pleiades and the Hyades: namely, NGC 6705 and NGC 3532, with 280–399 Myr, and NGC 6633 (575 Myr). For all these clusters, in Fig. 4.4 we also superimpose as dotted lines the Teff values given by Baraffe et al. (2015), indicating the points where Li depletion is near complete for the lower-mass candidates (see Sect. 4.2 for more details). We did not create Li envelopes for the remaining seven intermediate-age sample clusters we have analysed in this work, even though we were generally able to visualize the probable height and shape of their corresponding Li envelopes. This is due to the smaller sample sizes of many of these clusters (such as NGC 6649, NGC 6259, Berkeley 30 and NGC 6281), and in several cases, also because of a lack of candidate members that hindered the construction of a full set of Li envelopes, especially for GK stars in a 4500–6000 K temperature range (as in the case of NGC 6405, NGC 6067 and NGC 4815). However, all of these remaining intermediate-age clusters have ages in the range already covered by the six clusters considered here (see Table 2.3), and so we note that we were able to obtain a set of robust and reliable Li envelopes for all key ages in this range. Similarly to the case of the young cluster range, for the intermediate-age clusters, in Fig. 4.6 we see that the upper and lower Li envelopes trace a clear progression of ages from 90 Myr to 600 Myr, with the clusters with similar ages to the Pleiades (Blanco 1 and NGC 2516) being located at a very similar height to the upper and lower envelopes for the Pleiades, and the ones with intermediate ages between the Pleiades and the Hyades being displayed progressively lower in the EW (Li)-versus-Teff diagram, until NGC 6633, which lies slightly above the upper enve- lope of the Hyades. The shape of these envelopes for all of these clusters up until NGC 6633 is also very similar to the upper and lower envelopes of the Pleiades, reflecting the Li depletion of different spectral types and masses at this age range, while the upper Li envelope for NGC 6633 is already more similar to the corresponding one for the Hyades. We will now discuss each of these six intermediate-age clusters and their obtained Li envelopes: 4.1. Empirical lithium envelopes 115 We have created the upper and lower envelopes for Blanco 1 (94 Myr) making use of both the final candidate selection from GES, and also a series of additional members with Li from Jeffries et al. (1998) (see Appendix B), providing useful candidates for temperature ranges where they were more lacking, particularly in the 5000–6000 K range (as discussed above, this lack of candidates for certain spectral types at certain temperature ranges is an issue which we have encountered for several intermediate-age clusters). The upper and lower envelopes for Blanco 1 trace the corresponding envelopes for the Pleiades, as expected due to their similar age, and they are also located practically at the same height, even taking into account the smaller sample size for the final selection of this cluster regarding GK stars. We suggest that had we counted with a larger number of GK candidates at higher levels of EW (Li), the upper Li envelope for this cluster would have traced the upper Li envelope of the Pleiades at the same height. The fact that the lower envelopes for both clusters are superimposed would seem to support this. NGC 2516 is another cluster with a similar age to the Pleiades, albeit a slightly older one (125–135 Myr versus the 70-125 Myr range typically estimated for the Pleiades). As such, the upper and lower Li envelopes trace the Li content of the candidate members at a height that is just slightly below the Pleiades. This cluster also contains one of the largest number of candidate members in this age range, and, as a result, the Li envelopes are also smoother and more detailed, following a shape that is also practically identical to that of the Pleiades, if a bit more rounded. For the construction of these envelopes we have not taken into account the four candidate stars with higher levels of EW (Li), marked as open squares in Fig. 4.4 (Appendix B). In Chapter 3 we characterized these candidate stars as exhibiting either higher values of rotation and/or higher values of chromospheric activity. The Li envelopes for NGC 6709 (179 Myr), for their part, lie below both the Pleiades and NGC 2516, in agreement with their slightly older age. Similarly to the case of NGC 2516, we also did not take into account the candidate star with the highest value of EW (Li) to create the upper Li envelope, and we explain this dispersion due to the fast rotation of this member (also see Sect. 3.1 and (Appendix B). For NGC 6705 and NGC 3532 (in an age range of 280–399 Myr) we obtained upper and lower Li envelopes below the Pleiades and all the former intermediate-age clusters (see Fig. 4.6). Due to the scarcer number of G and early-K candidate stars in a 4000–5500 K temperature range, however, the shape of the upper Li envelopes is notably less smooth and rounded for both of these clusters than for other intermediate-age clusters such as NGC 2516. This is particularly noticeable in the case of the otherwise well-populated selection for NGC 3532, for which we obtained an upper Li envelope which is appreciably pointed in its shape, compared to the rest of upper Li envelopes in this age range. We suggest that this resulting shape is due to a lack of a larger number of GK candidates in the aforementioned temperature range with higher values of EW (Li). The envelopes for both clusters, however, are located at similar heights in Fig. 4.6, with the somewhat older NGC 3532 lying slightly below NGC 6705, as would be expected. We also studied the dependence of metallicity on the Li depletion of these clusters in Sect. 3.4. There have been various age estimations for NGC 6633, as has been already discussed in Chapters 1 and 3 (also see the individual notes of Appendix B). Many studies considered an age close to the Hyades, but in this work we have used the age obtained by Bossini et al. (2019), estimating an appreciably younger age of 575 Myr for NGC 6633. We believe that this younger age is in the most agreement with our final selection for this cluster, and the obtained Li enve- lope thus lies moderately above the Hyades, in contrast to the old cluster sample, whose upper Li envelopes are always to be found first at the same level, and then progressively below the Hyades as the age increases. Finally, we also note that we have constructed the Li envelopes for 116 Chapter 4. The Li-age relation: Creating Li envelopes both NGC 3532 and NGC 6633 without taking into account the late-K and M candidates with improbably high values of EW (Li) at this age range. We discuss this issue in more detail in Sect. 2.2.6, Chapter 3, and the individual notes of Appendix B. ∗ Li envelopes: Old clusters Lastly, we obtained upper Li envelopes for seven out of the 13 old clusters in our sample, as shown in Fig. 4.5 and the bottom panel of Fig. 4.6. All of these seven clusters have key ages in a range of 0.9–4.5 Gyr, including three clusters with an age of 0.9–1.0 Gyr (namely, NGC 2355, NGC 6802 and NGC 6005), as well as two clusters in the 1.0–1.5 Gyr range (Pismis 15 and Trumpler 20), and, finally, the two oldest clusters in our sample, with an age of 4.0–4.5 Gyr (NGC 2243 and M67). While we see a progression of steadily lower upper Li envelopes as age increases (see Fig. 4.7), this progression is not as clear from a visual inspection as in the case of the young and intermediate-age ranges, due to the appreciably lower values of EW (Li) at these older ages, and also to the increasing difficulties to measure EW (Li) values at this age range. As a result of this, many envelopes in this range tend to be found clustered together below the Hyades, in a similar way to the corresponding Li envelopes for the very young SFRs (albeit with less inherent dispersion), and we only see noticeable differences when studying them in diagrams scaled for this age range (as shown in Fig. 4.6), and especially when comparing the younger clus- ters in this range with the oldest, which are located in the EW (Li)-versus-Teff diagram clearly below the rest of the clusters in this old age range. We also note that for those clusters with a smaller number of candidates in the final selections, the resulting Li envelopes will be less smooth than in the case of larger selections. In contrast, a larger number of candidates (such as in the case of NGC 2355, Trumpler 20, NGC 2243 and M67) enabled us to create Li envelopes that trace the Li content of the candidates in a way that better characterizes the cluster selection, similarly to the case of the young and intermediate-age ranges. Even so, we do see a definite trend of all these envelopes being located progressively lower in the EW (Li)-versus-Teff diagram as age increases. We did not create Li envelopes for six out of the 13 clusters in the old range, even though, similarly to the other age ranges, we were generally able to visualize the probable height and shape of their corresponding upper Li envelopes. This is due, once again, to the smaller sample size of several of these remaining clusters (such as Berkeley 81, NGC 2477 and Melotte 71), and also because of a lack of candidate members, generally for temperatures in the range of 5000– 6000 K, hindering the construction of complete upper Li envelopes (as in the case of Trumpler 23, Pismis 18 and Berkeley 44). Several of these old clusters, however, have ages in a range that is already covered by the seven clusters considered here (see Table 2.3), and so we note that we were able to obtain a set of reliable Li envelopes for all key ages in this range. To finish this section, we will now discuss each of these seven old clusters and their ob- tained Li envelopes: We firstly obtained upper Li envelopes for coeval clusters NGC 2355 and NGC 2608 (900 Myr), for which we also studied their dependence with metallicity in Sect. 3.4. Both envelopes are located at the level of the Hyades, or very slightly below it. For NGC 2355, which has a larger candidate selection, we created an envelope which traces the candidates more smoothly, NGC 6802 has a smaller selection size, and thus the resulting Li envelope is conse- quently somewhat less precise and more orientative in its shape. The envelopes for both clusters, however, are located at practically the same height in Fig. 4.6. For its part, NGC 6005 is only moderately older than NGC 2355 and NGC 6802, at an age of 973 Myr, and given the more 4.1. Empirical lithium envelopes 117 difficulty to distinguish between similar age ranges for the oldest clusters, as mentioned above, when plotted alongside NGC 2355 and NGC 6802, the Li envelope for NGC 6005 lies at a very similar height. The envelope for NGC 6005 was constructed with the guide of a larger candidate size than NGC 6802 but taking into account a fewer number of stars than NGC 2355. Overall, we can conclude that clusters in the range of 0.9–1.0 Gyr lie approximately at the same height, and slightly under the Hyades. Pismis 15 and Trumpler 20 are two clusters which have very similar ages in a 1.3–1.4 Gyr range, and we also compared them in regards to the influence of metallicity in Sect. 3.4. We find their corresponding upper Li envelopes below the ones for the clusters with ages in the 0.9–1.0 Gyr range, in agreement with their later age, but note that this is more appreciable for Trumpler 20 than Pismis 15, whose Li envelope is located only slightly below the one correspond- ing to NGC 6005 (973 Myr). We suggest that this may be a result of a less accurate upper Li envelope given that the final candidate selection for Pismis 15 does not contain a large number of members. The selection for Trumpler 20, however, is notably larger, and thus the resulting Li envelope reflects the cluster selection in a way that is smoother and more robust, and when plotting it in the EW (Li)-versus-Teff diagram, we see this envelope located more noticeably be- low the younger clusters of the old age range. Finally, we end this overview with the oldest clusters in our sample, NGC 2243 and M67, with ages in the range of 4.0–4.5 Gyr. Given their similar ages, we also studied their dependence with metallicity in Sect. 3.4. The upper Li envelopes for these last two clusters are located more noticeably below the rest of the old clusters, and given that we obtained a reasonably large selection size for both clusters, we consider these two Li envelopes to be among the most robust and reliable in this age range. 118 Chapter 4. The Li-age relation: Creating Li envelopes Figure 4.6: EW (Li)-versus-Teff diagrams displaying the empirical Li envelopes obtained for 27 out of the 42 clusters in the sample, including the young clusters (1–50 Myr; top panel), as well as the intermediate-age (50–700 Myr; middle panel) and old clusters (> 700 Myr; bottom panel). These diagrams also include the Li envelopes used throughout this work, namely the upper envelope of EW (Li) for the cluster IC 2602 (35 Myr), shown in red; the upper and lower envelopes of the Pleiades cluster (78–125 Myr), shown in grey; and the upper envelope of the Hyades cluster (750 Myr), in turquoise. 4.1. Empirical lithium envelopes 119 EW (L i) (m Å ) Teff (K) Figure 4.7: EW (Li)-versus-Teff diagrams displaying the empirical Li envelopes obtained for 27 out of the 42 clusters in the sample, including the young clusters (1–50 Myr), as well as the intermediate-age (50–700 Myr) and old clusters (> 700 Myr). These diagrams also include, in dashed lines, the Li envelopes used throughout this work, namely the upper envelope of EW (Li) for the cluster IC 2602 (35 Myr), shown in red; the upper and lower envelopes of the Pleiades cluster (78–125 Myr), shown in dark red; and the upper envelope of the Hyades cluster (750 Myr), in turquoise. 120 Chapter 4. The Li-age relation: Creating Li envelopes 4.2 Evolutionary models and the LDB A (L i)/ A (L i)0 Teff (K) Figure 4.8: Evolutionary tracks from Baraffe et al. (2015) for an age range of 5–625 Myr, where A(Li)/A(Li)0 is the ratio of surface Li abundance to initial abundance. We finish this chapter briefly discussing how we also made use of a series of evolutionary models to do a preliminary characterization of the lithium depletion boundary region (LDB, see Chapter 1) for those clusters with ages in the 10–600 Myr range, encompassing the young and intermediate-age clusters in our sample. In order to do so, we mainly used the models from Baraffe et al. (2015), which include evolutionary curves of growth for PMS and MS low-mass stars down to the hydrogen-burning limit, spanning a wide age range from 1 Myr to 10 Gyr. We also compared the models by Baraffe et al. (2015) with other evolutionary models, such as the ones by Somers et al. (2020), who obtained a number of theoretical evolutionary tracks and isochrones, also spanning a wide age range from PMS stars to red giant branch stars up to 15 Gyr. The models from Somers et al. (2020) are specifically constructed to analyse the effects of starspots on stellar structure and evolution (see the future work in Chapter 5 for the ways in which we could use these tracks to expand the analysis in this work), but we can also use the corresponding isochrones for a percentage of starspots of 0% to study and delimit the LDB, without taking into account the effect of starspots in this case. Although we have only used the models from Baraffe et al. (2015) in this work, we also compared the collection of spotless evo- lutionary tracks from Somers et al. (2020) with the ones by Baraffe et al. (2015), and concluded that they were generally consistent with each other. In Fig. 4.8 we show the evolutionary tracks from Baraffe et al. (2015) for an age range of 5–625 Myr, corresponding to the 10–600 Myr range of young and intermediate-age clusters for which we could at least partly identify the LDB. Each of these evolutionary tracks marks two key temperature values which we used to delimit the LDB region in Figs. 4.3, and 4.4, superimposed 4.2. Evolutionary models and the LDB 121 Table 4.1: Teff values from the evolutionary models of Baraffe et al. (2015) (see Fig. 4.8) indicated in the dotted lines of Figs. 4.3 and 4.4 to delimit the LDB region for clusters in an age range of 10–600 Myr. For the ages indicated in the table, Teff (1) refers to the temperature value corresponding to the point where Li levels are already expected to be negligible for the low-mass stars at that age, while Teff (2) marks the reemergence of stars with undepleted Li in the LDB. Age (Myr) Teff (1) (K) Teff (2) (K) 10–20 3900 3500 25 3900 3400 20–30 4000 3300 30–40 4000 3200 50–80 4300 3000 100–200 4400 2600–2900 300–400 4500 2500 500–625 4900–5000 1900–2100 on the cluster selections and obtained upper and lower Li envelopes as dotted lines. The first Teff value of interest indicates the end of the descending track, corresponding to the point where Li depletion is near complete for the low-mass stars. From this point until the emergence of the LDB, we should thus observe negligible Li levels for the late-K and M-dwarfs among the candidates for each cluster. The second and cooler Teff value we marked in Figs. 4.3 and 4.4 corresponds to the stars of the ascending part of the evolutionary track, indicating the point where we would start to observe cool, low-mass stars with undepleted Li in the LDB for each age. For the young clusters in Fig. 4.3 (10–50 Myr) we show the two dotted lines corresponding to the temperature values of these two points, fully delimiting the LDB, while for the intermediate- age clusters in Fig. 4.4 (100–600 Myr) we can only mark the Teff value corresponding to the descending point of the evolutionary track, seeing as the point marking the reemergence of mem- ber stars with undepleted Li, and thus the LDB, corresponds to increasingly cool Teff values which can no longer be displayed in the EW (Li)-versus-Teff diagrams, as the GES sample typi- cally does not include lower-mass stars with Teff < 3000. In Table 4.1 we show the values of Teff which we have used to draw the dotted lines in Figs. 4.4 and 4.5 for the young and intermediate- age clusters for which we obtained final Li envelopes. We note that we have chosen mean values for the listed age ranges, based on the curves of growth of Fig. 4.8, in a way that enabled us to do a helpful preliminary analysis of delimiting the LDB region for the clusters in our sample. Although in this work we have focused on FGK stars rather than M-dwarfs, as we will further discuss below, we also note that delimiting the region of the LDB with the aid of these evolution- ary models is helpful in order to further characterize our final Li envelopes, as well as evaluate the goodness of our cluster candidates. We observed that our cluster selections and resulting Li envelopes were typically consistent with the information from the evolutionary models from Baraffe et al. (2015). We mostly see apparent disagreements regarding the Li content of late-K and M-dwarfs in a small number of the intermediate-age clusters, most particularly in the case of NGC 3532 and NGC 6633, two clusters which include an appreciably large amount of late-K and M robust candidates with EW (Li) measurements which are too high. We commented on these cases as a general overview in Chapters 2 and 3, and we added a more detailed discussion in Appendix B, also citing the models of Baraffe et al. (2015) and the LDB for these cases. 122 Chapter 4. The Li-age relation: Creating Li envelopes Figure 4.9: EW (Li)-versus-Teff diagram showing the final candidate selection for IC 2602 (35 Myr, red squares), IC 2391 (36 Myr, green squares) and IC 4665 (38 Myr, turquoise squares). The upper Li envelope for the IC 2391, IC 2602 and IC 4665 is shown in red, including the LDB region, and we also superimpose as dotted lines the Teff values delimiting this LDB region, given by Baraffe et al. (2015). The upper and lower envelopes of the Pleiades cluster are shown in grey; and the turquoise line represents the upper envelope of the Hyades cluster. We suggested that these disagreements were probably due to the inherent difficulty in obtaining accurate Li measurements for the lower-mass KM stars in clusters older than 100–200 Myr, a conclusion which we can extrapolate to all the 100–600 Myr age range for the Li content of the lower-mass candidates. In this work we have decided to limit the use of the evolutionary models from Baraffe et al. (2015) to the information provided by the aforementioned Teff values, which enable us to delimit the LDB for the young cluster range, and to mark the point where Li depletion for low-mass members in complete for the intermediate-age cluster range. However, we have not included the LDB in the constructed empirical Li envelopes for all of the young clusters displayed in Fig. 4.3, mainly due to the fact that only M-type candidates are to be found in the LDB, and, as we mentioned above, this project is primarily focused on FGK stars. The reason for this is that M-dwarfs often require an individual study due to their inherent complexity, displaying more complex behaviour than FGK spectral types, and late M subtypes additionally tend to show different correlations with parameters (such as rotation and activity) that are not yet fully un- derstood (e.g., Kiman et al., 2019; Popinchalk et al., 2021). To this we can also add the increasing difficulty to obtain accurate and reliable EW (Li) measurements of M-dwarfs, as acutely illus- trated by the questionable EW (Li) GES iDR6 values for most of the late-K and M candidates in NGC 3532 and NGC 6633 discussed in the previous paragraph. Consequently, in most cases we have traced the final Li envelopes and calibrated a Li-age relation focusing primarily on the FGK candidates of the cluster sample. 4.2. Evolutionary models and the LDB 123 We have however decided to create a full Li envelope that includes the LDB region for four young clusters in our sample: Firstly for γ Vel, a 10–20 Myr-old cluster with a very narrow LDB delimited in a 3500–3900 K temperature range (see Sect. 4.1 and Fig. 4.3), and we also completed the upper Li envelope given by Montes et al. (2001) for the 35–38 clusters Myr-old IC 2391, IC 2602 and IC 4665 (see Fig. 4.9). We did this by extending the depth of the existing Li envelope in the late-K and M region and then using the information from Baraffe et al. (2015), delimiting the LDB region by means of the dotted lines in Fig. 4.9, to draw the completed enve- lope. We also reinforced the robustness of the placement of the envelope in the LDB by using the additional members from Randich et al. (2001) and Jeffries et al. (2009a) for IC 2602 as reference (see Appendix B). We confirmed that the ascending part of the curve in this region traced the un- depleted M stars in the LDB in a position that was not only consistent with the information from Baraffe et al. (2015), but also seemed to represent an average position for all available candidates. If we aimed to study the M candidate stars and the LDB in a more detailed way for the young clusters in an age range of 10–100 Myr (see future work in Chapter 5), we would sim- ilarly aim to complete the upper Li envelopes for the remaining clusters, such as NGC 2232 and NGC 2547. However, the process to do so is not straightforward. We would need to draw more information from evolutionary models such as Baraffe et al. (2015) in order to ascertain the depth of the Li envelopes in the LDB region for EW (Li)-versus-Teff diagrams. However, given that curves of growth such as the ones from Baraffe et al. (2015) and Somers et al. (2020) do not use EW (Li) measurements, but Li abundances (generally expressed as A(Li)/A(Li)0, the ratio of surface Li abundance to initial abundance), we would firstly need to convert the A(Li) abundances of these curves of growth to EW (Li) values in order to be able to use these evolutionary tracks to identify the depth of the Li envelopes at the LDB. This process would entail bilinear interpolation to convert the A(Li) values of the curves of growth to EW (Li)s by means of the interpolation tables in studies such as Zapatero Osorio et al. (2002) (for stars with Teff in a range of 2600–4000 K) and Soderblom et al. (1993) (for stars with Teff > 4200 K). The use of curves of growth using EW (Li) values rather than Li abundance is not common, but it has already been done in some studies from the literature (Jeffries et al., 2017; Dumont et al., 2021a). Finally, we end this section by addressing the reason why we have not directly used the GES iDR6 A(Li) values to work with the curves of growth of Baraffe et al. (2015). Firstly, we note that throughout this project we have worked extensively with EW (Li)-versus-Teff diagrams to select robust cluster candidate selections and create empirical Li envelopes. One of our main reasons for using EW (Li) measurements instead of Li abundances is that EW (Li) equivalent widths are the most direct GES measurements that we can use to characterize the Li content of open clusters. The A(Li) abundances available in the iDR6 GES file, on the other hand, were converted with the aid of theoretical curves of growth (see Sects. 1.3 and 2.1), and the process to obtain derived abundances consequently results in larger uncertainties than the ones for param- eters which are directly measured from the GES spectra (see Sect. 2.1). We have endeavoured to avoid any such added uncertainties for all the analysis in this work, and this is why we have limited the use of Li abundances to the selection of Li-rich giants as a side project during the membership analysis of Chapter 2, preferring to use EW (Li) measurements in every other step of our calibration of the Li-age relation. Another reason why we favour EW (Li) measurements before A(Li) values is due to the fact that the GES iDR6 file for our cluster sample provides a considerably larger number of EW (Li) equivalent widths than derived Li abundances, and thus we obtained larger cluster selections to characterize and calibrate the Li-age relation in this way. Chapter 5 Summary, conclusions and future work 5.1 Results and scientific prospects The present thesis is a large scale work during which we used the GES-derived data provided by in iDR6, as well as the available data from Gaia EDR3, with the objective of studying and calibrating Li as an age indicator for PMS, ZAMS and early MS FGKM late-type stars. We con- ducted a thorough analysis of membership and obtained lists of candidate members for a sample of 42 young, intermediate-age and old clusters, spanning a wide age range from 1–3 Myr-old SFRs to old clusters up to 5 Gyr, and characterized the Li content of the resulting candidate selections according to stellar parameters such as rotation, chromospheric activity and metallicity. All this work allowed us to derive an empirical Li-age relation and obtain a number of Li envelopes for key ages in our cluster sample. We now summarize the main results of this project as follows, drawing from the analysis from each chapter, and also discussing the various scientific prospects of this work: • Data and target sample: Throughout this project we have made use of the data provided by the sixth and last internal data release of the Gaia-ESO Survey (GES), iDR6, containing a large number of measurements for radial velocities, stellar atmospheric parameters and derived abundances for our cluster sample. In addition to GES iDR6 data, we have also used the precision astrometry and photometry measured from the latest release of Gaia, EDR3. Our cluster sample for this project consists of a total of 114, 325 UVES and GIRAFFE spectra for 42 clusters ranging in age from 1 Myr to 4.5 Gyr. The full sample included seven star-forming regions (SFRs, 1–6 Myr) and nine young clusters (10–50 Myr), as well as 13 intermediate-age clusters (90–575 Myr), and 13 old clusters (0.7–4.5 Gyr) (see Sect. 2.1). – This work has made use of the most recent and high precision data available from GES and Gaia. As discussed in Sects. 1.3 and 2.1, the combination of GES and Gaia data provides a rich dataset providing improved precision of 3D kinematics and spatial distributions, fundamental parameters and chemical abundances. The remarkable science potential of both the GES exploration and the Gaia mission allows for a full range of studies spanning numerous topics regarding the formation, evolution and dynamics of the Galaxy and its stars, among which we can list our aim to calibrate the Li-age relation. – As part of the UCM GES node, in the first stages of this PhD project I performed an extensive analysis to manually measure the EW (Li) equivalent widths for all of the iDR4 UVES spectra (see Sect. 2.1). Even though in this work we have updated all 125 126 Chapter 5. Summary, conclusions and future work analysis and presented all our results using the recommended parameters from iDR6, this initial process was also helpful to understand the inner workings of GES WGs, the homogenization of recommended parameters, and the release of data products to the GES consortium and the scientific community. – Our present sample of 42 young, intermediate-age and old clusters provided by GES iDR6 has been considerably improved and enlarged in regards to the sample of 20 clusters using data from GES iDR4 we worked with in Gutiérrez Albarrán et al. (2020) (see Sect. 2.1). – This is a large scale project, aiming to obtain candidate members and characterize the dependence of the Li content of the candidate stars with several parameters for a considerably high number of clusters. Such a large sample was markedly useful in order to better constrain the Li-age relation and obtain at least one robust empirical Li envelope for each key age range in the cluster sample. – We would also like to highlight this abundant number of stars and clusters in the context of the ample scientific scope of GES data, and note that in this thesis we have worked with one of the largest number of GES open clusters in the literature, alongside noteworthy studies such as Jackson et al. (2021) (in which I am also a coauthor), who presented membership probabilities for 63 open clusters using GES iDR6 and Gaia EDR3 data; Cantat-Gaudin et al. (2018), who analysed the membership of 1229 clusters using Gaia DR2 data; and Randich et al. (2018), who listed candidates for eight open clusters using GES iDR4 data; among others (see Sect. 2.2.7). – We also emphasize the large scope of this work and its potential usefulness for the scientific community, as we did not only aim to study the membership for the 42 clusters in our sample, but we also studied the dependence of the Li content of all cluster members with several stellar parameters, and calibrated a Li-age relation by constructing empirical Li envelopes to serve as effective age calibrators. • Bibliographical research: In this work we have done an extensive bibliographical re- search on each cluster as part of the preliminary work on the membership analysis of the cluster targets in Chapter 2 (see below). We highlight the vital part that this extensive compilation of literature data had in our study, and also note their usefulness for other studies focusing on open clusters and GES data. – For each cluster, we compiled as many previous data from the literature as possible regarding ages, distances and reddening (see Tables 2.2 and 2.3), as well as radial velocities (see Table 2.4), proper motions and parallaxes (listed in Table 2.5), and [Fe/H] metallicity values (see Table 2.6). In all these cases, we listed the most recent and/or the most robust estimates, while larger ranges were generally taken into ac- count in the individual notes of Appendix B. All these compiled values were notably useful throughout the project: we used the age estimations to list our cluster targets by age and perform our membership analyses, applied extinction values to the CMDs, and compared our distributions of RV , parallaxes and metallicity with the literature. – We also endeavoured to compile all previous data provided by other authors regard- ing Li abundances and previous measurements of EW (Li), in order to extend the age coverage, reinforce our membership selections and aid in the creation of empir- ical Li envelopes (see Chapter 4 and Appendix B). In addition, a vital part of this research work involved compiling all previous membership studies for all cluster tar- gets, and specifically membership analyses which used GES and/or Gaia data (see 5.1. Results and scientific prospects 127 Tables 2.2 and 2.3). We thoroughly used these previous membership studies to make comparisons with our final candidate selections (see Appendix B). • Membership analysis and candidate selections: We performed a thorough member- ship analysis to obtain selections of likely candidates for all target clusters, making use of all available GES iDR6 parameters, and based on several criteria, from radial velocity (RV ) distributions to astrometry provided by Gaia, to gravity indicators (log g and the γ index), colour−magnitude diagrams (CMDs) using photometry from Gaia, [Fe/H] metallicity, and lithium in EW (Li) vs Teff diagrams (see Sect. 2.2). We also made use of a number of studies from the literature conducted from Gaia DR1, DR2 and EDR3 data to assess our candidate selections after concluding our membership analysis (see Sect. 2.2.7). – For each cluster, we started the analysis by studying the RV distributions to obtain likely kinematic candidates, followed by a thorough study of the proper motions and parallaxes provided by Gaia. Gravity indicators such as log g and the γ index were helpful in order to discard field giant contaminants, and we also used photometry from Gaia in CMDs to confirm the membership of the astrometric selections. We complemented all these criteria with a study of the distribution of [Fe/H] metallicity, which helped to discard further contaminants, and, finally, we used lithium as a final criterion by plotting the candidates in EW (Li) vs Teff diagrams (see Sect. 2.2). – As a result of this membership study, we presented lists of robust members for all clus- ters in our sample and discussed which individual clusters and age ranges presented the highest percentages of members in our target sample (see Sect. 2.4 and Tables 2.8 and 2.9). In Appendix B we further offer an in-depth discussion covering different aspects about the membership analysis, candidate selections, individual cases of in- terest, and a comparison with existing studies from the literature for all 42 target clusters. Additionally, we display all individual figures in Appendix C, and include descriptions for the associated online long tables of results, described in Appendix D, in which we list the final candidates for all clusters and specify which membership criteria are fulfilled by each of the target stars for each cluster. – As is detailed in the individual notes of Appendix B, we found that our lists of cluster candidates were in general agreement with previous GES studies, and we particularly did an extensive comparison with the candidates of Jackson et al. (2021). We also fitted the distributions of RV , parallaxes and [Fe/H] metallicity values of all final cluster selections, as displayed in Tables 2.4 (for RV s), 2.5 (for parallaxes) and 2.6 (for metallicity). We found our resulting mean values to be consistent with the literature for the majority of clusters, with very few exceptions (see Sect. 2.2). – We would also like to note the various applications of our obtained selections of cluster candidates for the 42 target clusters. As well as being of notable use to study the dependence of Li depletion with stellar parameters and to calibrate a Li-age relation, these candidate selections can also be useful for a number of study areas. For example, they can serve as reference in similar membership studies targeting the same open clusters (as we have done in this work with multiple membership studies from the literature), or in order to perform a more in-depth study as regards to various areas, from the distribution of rotational velocities, to astrometry, metallicity, or gyrochronology, among others. – Given their interest for the understanding of stellar Li (see Chapter 1), as an addi- tional result of our membership analysis we also selected a series of preliminary Li-rich giant outliers for 23 out of the 43 of target clusters (see Sect. 2.3). As in the case 128 Chapter 5. Summary, conclusions and future work of the candidate selections, the number of Li-rich giants for each cluster is also given in Tables 2.8 and 2.9, and they are also listed in the online tables described in Ap- pendix D. Given the rare nature of these objects, we would need further confirmation to accept all stars listed as Li-rich giant contaminants in this study (see the future work below in Sect. 5.3). • Dependence with stellar parameters: Having obtained selections of final candidates for the cluster targets, in Chapter 3 we quantified their observable Li dispersion with a comparative study that analysed the dependence of three of the most characteristic stellar parameters derived from GES spectroscopy (namely, rotation, Hα chromospheric activity, and [Fe/H] metallicity) on Li depletion, for each cluster age and spectral type. We characterized the properties of the cluster members for all young, intermediate-age and old clusters, and confirmed the correlations and patterns observed in previous studies from the literature. – We firstly studied the effects of rotation, Hα activity and accretion on Li depletion (see Sects. 3.1 and 3.2). In the case of rotation, we used vsini data from GES for all clusters, as well as a series of rotation periods (Prot) for nine target clusters, several of them provided by missions such as Kepler, K2 and TESS (see Sect. 1.3). All individual figures from this chapter are listed in Appendix E. – We confirmed the Li-rotation and Li-activity anticorrelations previously reported in the literature, observing a general trend where the members with higher values of EW (Li) tended to be faster rotators and often also displayed high values of chromo- spheric activity (see Chapter 1). – We additionally studied the evolution of rotation and activity across age and their dependence with colour and stellar mass, making use of rotation-colour and activity- colour diagrams (see Sect. 3.3). This section offered a general overview of gyrochronol- ogy and the evolution of Hα with age which could be expanded in more detail for individual clusters, similarly to several studied from the literature (e.g., Barnes et al., 1999; Rebull et al., 2018; Fritzewski et al., 2020, 2021; Popinchalk et al., 2021). – While the analysis of rotation and activity characterized the inherent Li dispersion of each of the cluster candidate selections, the study of [Fe/H] metallicity targeted the effects on the overall Li depletion and corresponding Li envelopes of coeval clusters (see Sect. 3.4). To this effect, we compared several target clusters with the same or very similar ages which were appreciably metal-rich or metal-poor, and concluded that the Li envelopes for metal-rich clusters appeared to be located slightly above the corresponding ones for coeval metal-poor clusters. This seems to support the recent literature findings claiming that metal-rich clusters deplete less Li than their metal-poor counterparts (Randich et al., 2020; Randich & Magrini, 2021). We find this study to be of interest given the still standing disagreement on the correlation between metallicity and Li depletion (see Sect. 1.2.4). – As well as being key to characterize our cluster selections, we find these analyses to be of notable interest in order to continue the work to understand the behaviour of Li and its dependence with stellar parameters. The study presented in this chapter can also be expanded with additional parameters and models (such as the evolutionary tracks for several percentages of starspot covering from Somers et al. (2020), see the future work in Sect. 5.3)). • Calibrating the Li-age relation with empirical Li envelopes: Having obtained lists of candidate members for the 42 target clusters, and having analysed their dependence 5.1. Results and scientific prospects 129 on rotation, activity and metallicity, we finally calibrated a Li-age relation and created a number of empirical Li envelopes for several key age ranges in our sample, from 1− 3 Myr to 4− 4.5 Gyr (see Chapter 4 and Appendix F). – Each of these obtained Li envelopes trace the Li content of the candidates for represen- tative clusters in the young, intermediate-age and old age ranges in EW (Li)-versus-Teff diagrams. The Li envelopes were obtained in an empirical way from the characterized lists of cluster candidates, with the additional reference of the existing upper envelope for IC 2602 (35 Myr) (Montes et al., 2001), as well as the upper (Neuhaeuser et al., 1997) and lower (Soderblom et al., 1993) envelopes of the Pleiades (78–125 Myr), and the upper envelope of the Hyades (750 Myr) (Soderblom et al., 1993). – We have obtained Li envelopes for 27 out of the 42 clusters in our sample, correspond- ing to approximately 64% of the cluster sample. When it comes to the potential of these envelopes to estimate ages for clusters and stars, we note the considerable use- fulness of being able to use a larger number of upper and lower Li envelopes than was formerly available in the literature, including key age ranges from SFRs and young clusters, to intermediate-age clusters similar to the Pleiades, to clusters with ages between the Pleiades and the Hyades, to older clusters up to nearly 5 Gyr. All the obtained upper and lower envelopes can be found individually in Figs. 4.2 (SFRs), 4.3 (young clusters), 4.4 (intermediate-age clusters), and 4.5 (old clusters). In addition, Fig. 4.6 shows the final set of Li envelopes sans cluster candidates, organized by age ranges, and Fig. 4.7 displays all Li envelopes in a single diagram, showing their full potential as age calibrators. Appendix F further lists a number of tables with the Teff and EW (Li) values used to create the Li envelopes for each cluster. – We also made use of the evolutionary tracks from Baraffe et al. (2015) to do a pre- liminary characterization of the lithium depletion boundary (LDB) (see Sect. 4.2). We superimposed as dotted lines the Teff values values given by Baraffe et al. (2015) delimiting the LDB region for the young and intermediate-age clusters within an age range of 10–600 Myr (see Figs. 4.3 and 4.4). White this preliminary analysis of the LDB was of use to better constrain the Li envelopes for this age range, we note that this project was focused on FGK stars primarily, and so we refer the reader to the future work in Sect. 5.3 for a series of additional ways in which we could characterize the LDB and further study the M-dwarf candidates. – This large scale work has aimed to further understand the nature and behaviour of stellar Li. The dependence of Li depletion with stellar parameters (such as rotation, activity and metallicity) displays a complexity that is still not fully understood (see Chapter 1), and so the aim of this work to derive a Li-age relation by analysing and characterizing a large number of open clusters is an additional step towards a better understanding of this element. – Furthermore, the calibration of a Li-age relation allows for a powerful age indicator, especially for young clusters, and it is a method which includes a lesser number of systematic errors than other age calibrators. As something which has not been yet thoroughly studied in the literature, compared to other topics in stellar Astrophysics, we believe that the calibration of a Li-age is particularly useful to achieve a further understanding of the behaviour of stellar Li and the dependence of Li depletion with age and various stellar parameters. – Finally, we would like to highlight the large potential of using this large set of Li envelopes as effective age calibrators, be it to estimate ages for other open clusters 130 Chapter 5. Summary, conclusions and future work (similarly to our work in Chapter 2), or to derive age ranges for unknown field stars (see the future work below in Sect. 5.3). The combination of this larger number of obtained Li envelopes with the recent and high precision data from GES iDR6 and Gaia EDR3 would also result in more nuanced and reliable age estimations with this particular method. 5.2 Conclusions • This is a large scale work with a considerable sample of 42 open clusters spanning a wide age range from 1–3 Myr to 4–4.5 Gyr, making use of the most recent available data from GES iDR6, as well as high precision data provided by Gaia EDR3. • As part of this large scope project we have done an extensive bibliographical research on each of the 42 sample clusters, compiling a thorough selection of literature data on ages, distances, reddening, radial velocities (RVs), proper motions and parallaxes, [Fe/H] metallicity, previous Li measurements, and membership studies. We note the usefulness of such a detailed compilation of literature data, both in the context of this thesis, and also for its use in similar studies. • We have performed exhaustive and detailed membership analyses using all main available criteria, from kinematic and astrometric distributions to gravity indicators, CMDs, metal- licity and the analysis of Li content. We obtained selections of robust candidates for all 42 sample clusters, some of which had not been previously studied in detail by the GES con- sortium. We additionally did an in-depth work to study and compare previous selections of cluster candidates with our own to ensure coherent results. • The selections of cluster candidates obtained by means of recent GES and Gaia data can offer multiple applications for the scientific community, from the calibration of a Li-age relation (the aim of this particular work) to the further analysis of (the same or other) cluster members, or the characterization of a variety of stellar parameters and other areas of interest regarding open clusters and the formation and evolution of stars in the Galaxy. • We have characterized and quantified the observable dispersion in Li for all final cluster selections by performing a thorough comparative study to analyse the dependence of Li depletion on a series of stellar parameters. We have confirmed the Li-rotation and Li- activity connections previously reported in a large number of studies from the literature, observed the importance of accretion processes for PMS stars, did an in-depth study of gyrochronology for our sample clusters, and assessed the extent of the effects of [Fe/H] metallicity for coeval clusters. • We have calibrated a Li-age relation and obtained upper and/or lower empirical Li en- velopes for 64% of the cluster sample, including several key ages in a wide age range from 1–3 Myr to 4–4.5 Gyr. We note the considerable potential of using this Li-age calibration, derived by using recent and high-precision data from GES and Gaia, as a powerful age calibrator that includes less systematic errors than other age tracers. The larger number of Li envelopes would additionally allow for more nuanced and reliable estimations of age ranges for both open clusters and unknown field stars. • This work is of considerable use to continue to understand the ongoing compelling mystery that is the behaviour of stellar Li, particularly regarding the complex dependence of Li depletion on a wide variety of stellar parameters. As well as exploring the substantial uses 5.3. Future work 131 of open cluster calibrations and a Li-age relation as a reliable age tracer, we also note that the selection of preliminary Li-rich giant contaminants obtained as an additional result of this work is also of considerable interest to explore Li in stars. 5.3 Future work • Estimating the ages of field stars and their membership to kinematic groups and young associations: – The GES iDR6 file does not only include data on 86 open clusters, but it also provides astrophysical parameters (including EW (Li) values) and derived abundances for a large number of MW field stars. After performing a thorough analysis to derive a Li-age relation in this thesis and obtaining empirical Li envelopes for the young, intermediate-age and old clusters in our sample, our main aim regarding our future work is to explore the uses that this Li-age relation could have as an effective age calibrator by estimating age ranges for at least a sizeable part of these GES field stars, whose age is still unknown. – In a forthcoming paper, we also aim to study the potential membership of these field stars to young associations, stellar kinematic groups (SKGs) and moving groups (MGs) of different ages (see Fig. 5.1) (e.g., Montes et al., 2001; López Santiago, 2005). The confirmation and classification of new members of different kinematic groups and associations is incidentally a work that we started with GES data before this thesis was underway, during my final Master’s project (Gutiérrez Albarrán, 2014). Figure 5.1: Young associations and stellar kinematic groups in (U, V) Galactic velocity plane by Montes et al. (2001). • Li-rich giant outliers: As discussed in Sect. 2.3 and the individual notes of Appendix B, other main point of interest for our future work involves a more detailed study of the po- tential Li-rich giant outliers which we have obtained as a side result of our membership analysis in Chapter 2. We consider Li-rich giants to be of remarkable interest given their exceptional nature and their usefulness to further understand the behaviour of Li in stars (see Sect. 1.1). We intend to analyse in more detail all the contaminant stars that we have classified as Li-rich giants in this work, in order to confirm that they are in fact probable Li-rich contaminants (all Li-rich giants are listed in the online long tables described in 132 Chapter 5. Summary, conclusions and future work Appendix D. We would like to particularly focus both on a confirmation that their excep- tional Li content is real, and also to study the robustness of their position not only in Kiel diagrams, as we have mainly done in this work (see Sect. 2.3), but also in CMDs, where we have encountered the most apparent disagreements, with the pre-selected Li-rich giant in some cases appearing to be non-giants according to photometric data (see Appendix B). Figure 5.2: Effect of rotation and starspot coverage by Somers & Pinsonneault (2015b). • Study of the effect of starspot coverage on active stars: – A way in which we could expand the characterization of the dependence of the Li- rotation and Li-activity relations in Chapter 3 is by making use of the SPOTS evo- lutionary models by Somers et al. (2020), taking into account the effects of magnetic activity and different percentages of starspot coverage on the observable Li and the structure of active stars (see Fig. 5.2). Recent studies such as Franciosini et al. (2021) have used PMS models including radius inflation due to the presence or starspots and to magnetic inhibition to convection, and concluded that these models should be taken into account to better reproduce the Li depletion patterns observed for young star clusters. – While we believe that our overview of the effects of rotation and chromospheric ac- tivity on the stars in our cluster selections are reasonably reliable to do a preliminary characterization of the dependence of these parameters on Li depletion and obtain empirical Li envelopes that we can use to infer ages of cluster of field stars, adding the effects of different percentages of starspots on Li depletion (the available evolutionary tracks from Somers et al. (2020) range from spotless to a surface covering fraction of 85%) would also reinforce our results, as well as expand the characterization of the candidate stars in our sample. • Further applications of the evolutionary models: – Finally, as we discussed in Sect. 4.2, in this thesis we have primarily focused on the study and characterization of FGK stars. Due to the inherent added complexities 5.3. Future work 133 of the nature of M-dwarfs, as well as taking into account the additional difficulty to obtain reliable EW (Li) measurements for these lower-mass cool stars, we have consid- ered M-dwarfs in a secondary way throughout this project. While we believe that we fulfilled our aim to calibrate the Li-age relation and obtain Li envelopes which mainly trace the evolution of FGK cluster candidates, another point of interest for future work would be to study the M-type cluster members in more detail, and especially regarding a more detailed characterization of the LDB for young and intermediate-age clusters in an age range of 10–100 Myr. – Even though it was not our main objective, we did include the LDB region as part of the upper Li envelopes for four clusters in our sample, as discussed in Sect. 4.2. However, in order to perform an in depth study of the LDB for all the sample clusters in this age range, we would need to obtain additional information from evolutionary models, such as Baraffe et al. (2015), regarding the depth of the empirical Li envelopes in the LDB region for EW (Li)-versus-Teff diagrams. To do so we would use several interpolation tables from the literature (Soderblom et al., 1993; Zapatero Osorio et al., 2002) to transform the A(Li) values provided by the evolutionary models from Baraffe et al. (2015) into EW (Li) equivalent widths that we can use to characterize the LDB region (also see Sect. 4.2 for more details). This process of bilinear interpolation would also be useful to study the dependence of active candidates with the isochrones from (Somers et al., 2020), as mentioned above. Appendix A List of publications A.1 In this thesis A.1.1 Published in refereed journals 1."The Gaia-ESO Survey: Calibrating the lithium-age relation with open clusters and associa- tions. I. Cluster age range and initial membership selections", Gutiérrez Albarrán, M. L., Montes, D., Gómez Garrido, M., et al. (2020). A&A, 643, A71. DOI: 10.1051/0004-6361/202037620. arXiv:2009.00610. ORCID: 0000-0002-7569-3513 A.1.2 Conference proceedings 1."The Gaia-ESO Survey: calibrating the lithium-age relation with open clusters and associa- tions", Montes, D., Gutiérrez Albarrán, M. L., Gómez Garrido, M., et al. (2015), at GES 2015: Gaia-ESO Survey Third Science Meeting, held on December 1–4, 2015, in Vilnius, Lithuania. http://www.astrospectroscopy.tfai.vu.lt/ges2015/. 2."Calibrating the lithium-age relation with open clusters observed with GES (Gaia-ESO Survey)", Gutiérrez Albarrán, M. L., Montes, D., Gómez Garrido, M., et al. (2017). Highlights on Spanish Astrophysics IX, Proceedings of the XII Scientific Meeting of the Spanish Astronom- ical Society, held on July 18–22, 2016, in Bilbao, Spain. ADS:2017hsa9.conf..507G. 3."Membership, lithium and chromospheric activity of the young open clusters IC 2391, IC 2602 and IC 4665 from GES (Gaia-ESO Survey) observations", Gómez Garrido, M., Montes, D., Gutiérrez Albarrán, M. L., et al. (2017). Highlights on Spanish Astrophysics IX, Proceedings of the XII Scientific Meeting of the Spanish Astronomical Society, held on July 18–22, 2016, in Bilbao, Spain. ADS:2017hsa9.conf..506G. 4."The Gaia-ESO Survey: Calibrating the lithium-age relation with open clusters and associ- ations. I. Cluster age range and initial membership selections", Montes, D., Gutiérrez Albarrán, M. L., Gómez Garrido, M., et al. (2017), at GES 2017: Gaia-ESO Survey Fourth Science Meet- ing, held on September 4–8, 2017, Department of Physics and Astronomy University of Catania, Italy. https://www.gaia-eso.eu/events/archive/ges-2017-gaia-eso-survey-fourth-science-meeting. 5."The Gaia-ESO Survey: Calibrating the lithium-age relation with open clusters and associ- ations. I. Cluster age range and initial membership selections", Montes, D., Gutiérrez Albarrán, M. L., Gómez Garrido, M., et al. (2019), at GES 2019: Gaia-ESO Survey All-Hands meeting, 135 https://ui.adsabs.harvard.edu/abs/2020A&A...643A..71G https://www.aanda.org/articles/aa/full_html/2020/11/aa37620-20/aa37620-20.html https://arxiv.org/abs/2009.00610 https://orcid.org/my-orcid?orcid=0000-0002-7569-3513 http://www.astrospectroscopy.tfai.vu.lt/ges2015/ https://ui.adsabs.harvard.edu/abs/2017hsa9.conf..507G https://ui.adsabs.harvard.edu/abs/2017hsa9.conf..506G https://www.gaia-eso.eu/events/archive/ges-2017-gaia-eso-survey-fourth-science-meeting 136 Appendix A. List of publications held on September 27–29, 2019, in Firenze, Italy. https://sites.google.com/inaf.it/ges2019/home. 6."The Gaia-ESO Survey: Calibrating the lithium-age relation with open clusters and asso- ciations", Gutiérrez Albarrán, M.L., Montes, D., M. L., Gómez Garrido, M., et al. (2020), at Contributions to the XIV.0 Scientific Meeting (virtual) of the Spanish Astronomical Society, held online on 13–15 July 2020. ADS:2020sea..confE.145G. https://www.sea-astronomia.es/reunion- cientifica-2020. 7."Calibrating the lithium-age relation and its dependence with rotation, activity and metal- licity using open clusters and associations", Gutiérrez Albarrán, M.L., Montes, D., Tabernero, H. M., et al. (2020), at Star Clusters: The Gaia Revolution, held 5–7 October 2021, online at https://indico.icc.ub.edu/event/114/. Zenodo:10.5281/zenodo.5546589. A.2 Additional publications A.2.1 Published in refereed journals 2. "The Gaia-ESO Survey: Galactic evolution of lithium from iDR6", Romano, D., Ma- grini, L., Randich, S., et al. (including Gutiérrez Albarrán, M. L.) (2021). A&A, 653, A72. DOI:10.1051/0004-6361/202141340. 3. "The Gaia-ESO Survey: Membership probabilities for stars in 63 open and 7 globular clusters from 3D kinematics", Jackson, R. J., Jeffries, R. D., Wright, N. J, et al. (including Gutiérrez Albarrán, M. L.) (2021). Monthly Notices of the Royal Astronomical Society, 509, 1664-1680. DOI:10.1093/mnras/stab3032. 4. "The Gaia-ESO Survey: the role of magnetic activity and starspots on pre-main sequence lithium evolution", Franciosini, E., Tognelli, S., Degl’Innocenti, et al. (including Gutiérrez Al- barrán, M. L.) (2021). A&A, accepted. arXiv:2111.11196. 5. "The Gaia-ESO Public Spectroscopic Survey: motivation, implementation, GIRAFFE data processing, analysis, final data products", Gilmore, G., Randich, S., et al. (including Gutiérrez Albarrán, M. L.) (2022, submitted). A&A. 6. "The Gaia-ESO Survey: The Gaia-ESO Survey: Survey implementation, data products, open cluster survey, and legacy", Randich, S., Gilmore, G., et al. (including Gutiérrez Albarrán, M. L.) (2022, submitted). A&A. https://sites.google.com/inaf.it/ges2019/home https://ui.adsabs.harvard.edu/abs/2020sea..confE.145G https://www.sea-astronomia.es/reunion-cientifica-2020 https://www.sea-astronomia.es/reunion-cientifica-2020 https://indico.icc.ub.edu/event/114/ 10.5281/zenodo.5546589 https://ui.adsabs.harvard.edu/abs/2021A&A...653A..72R https://www.aanda.org/articles/aa/abs/2021/09/aa41340-21/aa41340-21.html https://ui.adsabs.harvard.edu/abs/2021MNRAS.tmp.2877J https://ui.adsabs.harvard.edu/abs/2021MNRAS.tmp.2877J https://ui.adsabs.harvard.edu/link_gateway/2021MNRAS.tmp.2877J/doi:10.1093/mnras/stab3032 https://arxiv.org/abs/2111.11196 Appendix B Cluster selections: Individual notes of Chapter 2 and 3 In this appendix we present an in depth account of each of the 42 clusters in the sample, including general information about the cluster, as well as a detailed discussion on membership analysis and final selections from Chapter 2, relevant particular cases, and a comparison of the final candidates with a series of studies from the literature. We also comment on particular cases in regards to the study of rotation, activity and metallicity in Chapter 3. We additionally refer to the individual figures of Chapter 2 in Appendix C, and to the individual figures of Chapter 4 in Appendix E. B.1 SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) ∗ NGC 6530 At a distance in a range of 1.25–1.33 kpc (Prisinzano et al., 2005; Wright et al., 2019; Damiani et al., 2019; Kuhn et al., 2019; Jackson et al., 2021), NGC 6530 is a 1–2 Myr SFR (Prisinzano et al., 2005; Damiani et al., 2019; Wright et al., 2019; Randich et al., 2020; Jackson et al., 2021) associated to the HII region M8 (Lagoon Nebula), with a complex morphology and star-formation history (Prisinzano et al., 2005; Damiani et al., 2019; Wright et al., 2019). Due to the very young age of this cluster, its low mass stars are still found in their pre-main sequence (PMS) phase, and therefore they often show Hα emission lines, UV excess emission due to accretion, near-IR emission from circumstellar discs, and they are also bright X-ray sources due to their active coronae (Prisinzano et al., 2005; Damiani et al., 2019). In our sample there are 1983 stars in the field of NGC 6530, of which 1330 have measured values of EW (Li). The membership analysis resulted in 470 RV candidates, 201 astrometric candidates, 359 Li candidates, and 343 final members (see Table 2.8). Of the final 359 Li candi- dates we discarded 16 stars according to the following criterion: We decided to discard all stars which we could not analyse using the astrometric and photometric Gaia data (be it because there were not Gaia data available for those stars, or because said data did not pass the quality indicators) if they were additionally listed as clear non-members by Jackson et al. (2021). All of these 16 stars are listed as clear non-members with a probability of 0.00–0.16, and one of them also has a metallicity value deviating appreciably from the mean of the cluster. As a result of the analysis of NGC 6530 we found 14 strong accreting stars, all of which are 137 138 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 Li members and classified as high-probability members (P> 0.90) by Jackson et al. (2021). We also note that five of the stars in our final selection present a [Fe/H] value which deviates appre- ciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed in Sect. 2.2.5, however, we have listed them as final candidates, given that they fully fulfil all the other criteria, including the more restrictive criteria, and they are all additionally listed as members by Jackson et al. (2021). Regarding kinematics, 44 stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 13.0–15.0 km s−1 from the mean of the cluster. Following the discussion in Sect 2.2.1, we accepted the stars which deviate from the limits es- tablished by the 2σ interval by ∼10 km s−1 given that they fulfil the rest of membership criteria (especially regarding available Gaia data, as well as gravity indicators and lithium). All of these stars are additionally listed as high-probability members by several studies (e.g, Damiani et al., 2019; Prisinzano et al., 2019; Wright et al., 2019; Jackson et al., 2021). On the other hand, we have also accepted as final candidates four stars with no measured RV values in iDR6, due to the fact that they fully fulfil the astrometry criteria (as well as the other criteria), and are also listed as members by these studies (e.g, Damiani et al., 2019; Prisinzano et al., 2019; Wright et al., 2019; Jackson et al., 2021). In regards to previous selections, we found the following number of common stars with our selection: 52 stars in Prisinzano et al. (2007) and Prisinzano et al. (2012), 148 in Spina et al. (2017), 255 in Damiani et al. (2019), 320 in Prisinzano et al. (2019), 286 in Wright et al. (2019), and one in Castro-Ginard et al. (2020). Finally, Jackson et al. (2021) includes 331 out of our 343 candidates. Of the remaining 12 stars, 10 of them were not included in their analysis, and two of them are listed with probabilities of 0.26–0.33 (Jackson et al. (2021) considers high-probability members to have P> 0.90 and definite non-members to have P< 0.10). We accepted these two stars given that they fulfilled all of our available membership criteria, and were furthermore included in several other studies (e.g, Damiani et al., 2019; Prisinzano et al., 2019; Wright et al., 2019). As already discussed in Sect. 2.3, we also note that we seem to find some inconsistencies when plotting the Li-rich giant outliers selected in the field of this cluster in the CMD diagram, with a couple of them appearing among the cluster candidates. However, when plotting them in the γ index-versus-Teff diagram the expected clear distinction is found between the non-giant cluster candidates and the Li-rich giant outliers. We plan on studying all Li-rich giant outliers in more detail in order to gain further confirmation on their nature as Li-rich giant contaminants (see the future work in Chapter 5). Regarding the study of rotation and activity, for a detailed discussion of this age range (SFR; 1–6 Myr) we refer the reader to the detailed discussion of the SFR NGC 2264 (4 Myr) in Chapter 3, and the individual figures for NGC 6530 can be found in Appendix E. We observed, similarly to the rest of SFRs, that the fastest rotating stars (including the analysis of both vsini and Prot values) tended to be located in the upper envelope of the cluster (see Chapter 4), corre- sponding to stars with higher values of EW (Li). We also found that a number of the candidates of this cluster are slower rotating stars (shown in orange and yellow shades), scattered among the cluster candidates, but generally showing less EW (Li) than their faster rotating counter- parts. For this cluster we observed candidates with both high vsini values up to 190 km s−1, and long Prot up to 16–18 d (Henderson & Stassun, 2012), as well as Hα activity up to 70–80 Å. Similarly to the observed anti-correlation between rotation and Li depletion, the analysis of the B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 139 dependence of EW (Li) with Hα also revealed a pattern where the stars with higher Hα emission tended to be located in the upper envelope of the cluster, with higher values of EW (Li) (shown in purple and dark orange shades). All these observed patterns are in agreement with the findings from the literature, taking into account firstly the anti-correlation between rotation and Li depletion; secondly, the fact that, apart from the young fast rotating stars in response to gravitational contraction, in SFRs the in- teraction with circumstellar discs also results in the presence of an appreciable number of slower rotating stars; and finally, the correlation between high values of EW (Li) and chromospheric Hα activity (see Chapter 1). ∗ Rho Oph Figure B.1: Rho Oph, a 1–3 Myr SFR. Credit: NASA/JPL-Caltech/UCLA. The ρ Ophiuchi (also referred to as ρ Oph) molecular cloud complex is one of the star forming regions closest to the Solar System, at an estimated distance of 120–140 pc (Rigliaco et al., 2016; Spina et al., 2017; Cánovas et al., 2019). Spina et al. (2017) gives a distance of 0.13± 0.01 kpc (see Table 2.2). ρ Oph consists of two major regions of dense gas and dust (L1688 and L1689), and is an interesting target due to its youth (1–3 Myr) (Barsony et al., 2012; Rigliaco et al., 2016; Spina et al., 2017; Cánovas et al., 2019; Randich et al., 2020; Kiman et al., 2021; Jackson et al., 2021), its large embedded young stellar population, and its active star formation (Wilking et al., 2015). There are 311 stars in the field of ρ Oph in our sample, of which 297 have measured EW (Li) values. The membership analysis resulted in 48 RV candidates, 29 astrometric candidates, 37 Li candidates, and 44 final members (see Table 2.8). In addition to the final 37 Li members, we have also considered for completeness seven strong accreting stars (see Sect 2.2.6) which pre- sented no values of EW (Li) in the iDR6 file. We also note that one of the stars in our final selection (16270456-2442140) presents a [Fe/H] value which deviates appreciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed in Sect. 2.2.5, however, we have listed it as a final candidate given that it fully fulfils all the other criteria, including the more restrictive criteria, and is additionally listed as a member by Cánovas et al. (2019) and Jackson et al. (2021). Of the final members in ρ Oph, 29 belong to the SFR L1688 (Rigliaco et al., 2016), and 15 of them are also strong accretors with Hα10% > 270–300 km s−1. Of these 15 accreting stars, 140 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 only one (16273311-2441152) does not pass our gravity criteria. This star, with γ=1.022 and A(Li)=3.2, could be listed as a potential Li-rich giant contaminant, but due to the fact that it is also a strong accretor (with Hα10% = 469.13 km s−1, we counted it as a likely member of ρ Oph, also in accordance with Rigliaco et al. (2016) and Jackson et al. (2021). Regarding other membership studies from the literature, Rigliaco et al. (2016) has 42 of our final candidates in their selection, while Ducourant et al. (2017) lists 10 common members, Spina et al. (2017) also lists 10 common stars for ρ Oph, and Cánovas et al. (2019) obtained 35 stars in common with our selection. Finally, we have 42 stars in common with Jackson et al. (2021). The remaining two stars in our selection for ρ Oph were not included in the analysis of Jackson et al. (2021), but are however listed as members by Rigliaco et al. (2016) and fulfil all our membership criteria. Regarding the study of rotation and activity, for a detailed discussion of this age range (SFR; 1–6 Myr) we refer the reader to the detailed discussion of NGC 2264 (4 Myr) in Chapter 3, and the individual figures for ρ Oph can be found in Appendix E. We observed, similarly to the rest of SFRs, that the fastest rotating stars (including the analysis of both vsini and Prot values) tended to be located in the upper envelope of the cluster (see Chapter 4), corresponding to stars with higher values of EW (Li). In this case we also found some of the fastest rotators among the M-type candidates. We also found that some of the candidates of this cluster are also slower rotating stars (shown in orange and yellow shades), scattered among the cluster candidates, but generally showing less EW (Li) than their faster rotating counterparts. For this cluster we observed candidates with both vsini values up to 84 km s−1, and long Prot up to 14 d (Rebull et al., 2018), as well as Hα activity up to 80 Å. Similarly to the observed anti-correlation between rotation and Li depletion, the analysis of the dependence of EW (Li) with Hα also revealed a pattern where the stars with higher Hα emission tended to be located in the upper envelope of the cluster, with higher values of EW (Li) (shown in purple and dark orange shades). ∗ Trumpler 14 Trumpler 14 is a 1–3 Myr SFR (Sampedro et al., 2017; Randich et al., 2020; Jackson et al., 2021) at a distance of 2.8–2.9 kpc (Mel’nik & Dambis, 2017; Sampedro et al., 2017), associated to the Carina Nebula, one of the most massive HII regions in the Galaxy, and one of the most active star-forming regions as well (Seo et al., 2019). Most of the stellar content of the Carina Nebula is concentrated in a few clusters, especially Trumpler 16 and Trumpler 14 (Damiani et al., 2017). In our sample there are 1902 stars in the field of Trumpler 14, of which 1046 have measured values of EW (Li). The membership analysis resulted in 228 RV candidates, 55 astrometric can- didates, 165 Li candidates, and 159 final members (see Table 2.8). Of the final 165 Li candidates we discarded six stars following the criterion mentioned above in the case of NGC 6530, namely that we could not analyse these stars using the astrometric and photometric Gaia data and they were additionally listed as non-members by Jackson et al. (2021) (most of them are clear non-members with a probability of 0.00, one of them is listed with P=0.27, but it is similarly discarded). One of these six stars also has a metallicity value deviating appreciably from the mean of the cluster. We also found five strong accreting stars among our final members, all of which are Li mem- bers and classified as high-probability members by Jackson et al. (2021). We also note that we B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 141 Figure B.2: Trumpler 14, a 1–3 Myr SFR. Credit: NASA, ESA, and J. Maíz Apellániz (Institute of Astrophysics of Andalucía, Spain), Acknowledgment: N. Smith (University of Arizona). discarded an F-type star with an EW (Li) that seemed to be higher than we would expect for a SFR (150 mÅ). This star had no recorded measurements of either accretion or Hα that could perhaps explain its EW (Li), and it was additionally listed as a non-member by Damiani et al. (2017). Regarding kinematics, five stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 13.0–15.0 km s−1 from the mean of the cluster. Following the discussion in Sect 2.2.1, we accepted the stars which deviate from the limits estab- lished by the 2σ interval by ∼10 km s−1, given that they fulfil the rest of membership criteria (especially regarding available Gaia data, as well as gravity indicators and lithium). All of these stars are additionally listed as high-probability members by Jackson et al. (2021). In addition, we have also accepted as final candidates 24 stars with no measured RV values in iDR6, due to the fact that they fully fulfil the astrometry criteria (as well as the other criteria), and are also listed as members by Jackson et al. (2021) with high probabilities in the range of 0.85–1.00. Regarding other membership selections from the literature, we found the following number of common stars with our selection: 63 stars in Spina et al. (2014b), as well as 65 in Damiani et al. (2017), 51 stars in Cantat-Gaudin et al. (2018), and one star in Castro-Ginard et al. (2020). Finally, Jackson et al. (2021) includes 153 out of our 159 candidates (the remaining six were not included in their analysis). We also note that Jackson et al. (2021) includes several stars which we initially discarded for not fulfilling our gravity criteria of γ < 1.01 for non-giants (see Sects. 2.2.4 and 2.3). The reason for this is that Jackson et al. (2021) considers a less restrictive criterion of γ < 1.33. As already discussed in Sect. 2.3, we also note that we seem to find some inconsistencies when plotting the Li-rich giant outliers selected in the field of this cluster in the CMD diagram, with eight of them appearing among the cluster candidates. However, when plotting them in the γ index-versus-Teff diagram the expected distinction is found between the non-giant cluster 142 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 candidates and the Li-rich giant outliers. We plan on studying all Li-rich giant outliers in more detail in order to gain further confirmation on their nature as Li-rich giant contaminants (see the future work in Chapter 5). Regarding the study of rotation and activity, for a detailed discussion of this age range (SFR; 1–6 Myr) we refer the reader to the detailed discussion of NGC 2264 (4 Myr) in Chapter 3, and the individual figures for Trumpler 14 can be found in Appendix E. We note that this cluster seems to show more dispersion than other SFRs (which is also expected in the case of this age range, due to the complex behaviour of these very young PMS stars). However, we were still able to observe a trend where the fastest rotating stars tended to be located in the upper envelope of the cluster (see Chapter 4), and generally showed higher values of EW (Li) than the slower rotating stars of the same spectral types. A number of the candidates for this cluster are also slower rotating stars (shown in orange and yellow shades), scattered among the cluster candi- dates, but generally showing less EW (Li) than their faster rotating counterparts. For this cluster there are no recorded values of Hα in the iDR6 file, and so we were only able to analyse its de- pendence with rotation. For this cluster we found candidates with vsini values up to 120 km s−1. ∗ Chamaeleon I Chamaeleon I (also referred to as Cha I) is a ∼2 Myr SFR (López Martí, Belén and Jiménez- Esteban, Francisco and Bayo, Amelia and others; Spina et al., 2014a; Sacco et al., 2015; Randich et al., 2020; Jackson et al., 2021). Cha I is relatively isolated from other SFRs and is part of a wider star-forming complex in the constellation of Chamaeleon, which contains two addi- tional smaller molecular clouds, Cha II and Cha III (Luhman et al., 2008; López Martí, Belén and Jiménez-Esteban, Francisco and Bayo, Amelia and others). Its proximity, at a distance of 0.16± 0.02 kpc (Spina et al., 2014a; Frasca et al., 2015; Sacco et al., 2017; Roccatagliata et al., 2018), as well as its compact size, rich stellar population, and its smaller extinction compared to other young clusters, makes it one of the most studied SFRs, and the target of multiple spec- troscopic and photometric surveys (Luhman et al., 2008; Luhman & Muench, 2008). Cha I was also one of the first young clusters observed by GES. The known stellar population of Cha I consists of ∼240 members (Sacco et al., 2017). Cha I is additionally composed of two subclusters (Luhman et al., 2008; Sacco et al., 2017; Roccatagliata et al., 2018), with a shift in velocity of ∼1 km s−1, and ages in the range of 5–6 Myr and 3–4 Myr, respectively. In our sample there are 707 stars in the field of Cha I, of which 659 have measured EW (Li) values. The membership analysis resulted in 102 RV candidates, 54 astrometric candidates, 88 Li candidates, and 87 final members (see Table 2.8). Of the final 88 Li candidates we discarded two stars: The first one (11080297-7738425) had no Gaia data available (thus, astrometry could not be analysed) and its [Fe/H] value deviated appreciably from the mean of the distribution, beyond the extended 3σ membership interval. The second star (11095340-7634255), also a non- member according to metallicity, we considered as a final non-member because we could not analyse this star using the astrometric and photometric Gaia data and it was additionally listed as a clear non-member with a probability of 0.00 by Jackson et al. (2021). As a result of the analysis of Cha I we found 35 strong accreting stars, of which only one (11104959-7717517) is not a Li member. This is probably due to possible veiling suppressing the absorption Li line, and so we classified this strong accretor as an additional likely member, and it is additionally considered as a member of Cha I by Jackson et al. (2021). Another effect of the activity and accretion of the stars in this SFR (e.g., Frasca et al., 2015) can be observed B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 143 in the case of four stars which present values of EW (Li) slightly larger than the rest of can- didates (841–948 mÅ). We consider them as members given that they exhibit little dispersion with respect to the rest of candidates, and explain their larger apparent values of Li given the fact that they are very young active stars, generally with high values of both accretion and Hα. Two of them, the ones with the largest EW (Li)s, are additionally strong accretors with Hα10% > 270–300 km s−1, and so their larger EW (Li)s could also be an effect of accretion- induced enhancement (see Sect 2.2.6, for example). We also note that three of the stars in our final selection were RV non-members accord- ing to the initial 2σ interval, with RV s deviating up to 3.7–10.2 km s−1 from the mean of the cluster. Following the discussion in Sect 2.2.1, we accepted the stars which deviate from the limits established by the 2σ interval by ∼10 km s−1 given that they fulfil the rest of membership criteria (especially regarding gravity indicators and lithium, as only one of them has available Gaia data), and all three of them are additionally listed as candidates by several studies (e.g, Esplin et al., 2017; Sacco et al., 2017; Galli et al., 2021; Jackson et al., 2021). Regarding previous selections, we found the following number of common stars with our se- lection: nine stars in Robrade & Schmitt (2007), 23 in Luhman & Muench (2008), and 47 in López Martí, Belén and Jiménez-Esteban, Francisco and Bayo, Amelia and others. We found 12 common stars in Spina et al. (2014a), all UVES members in their selection, except for 10555973- 7724399 and 11092378-7623207, for which several parameters are not released in the iDR6 cata- logue. We also found 88 of our candidate stars in the member list of Esplin et al. (2017), 75 in Sacco et al. (2017), and 66 in Galli et al. (2021). Finally, Jackson et al. (2021) includes 82 out of our 87 candidates (the remaining five were not included in their analysis). Regarding field contaminants, one Li-rich giant (11000515-7623259) is listed in Casey et al. (2016). Regarding the study of rotation and activity, for a detailed discussion of this age range (SFR; 1–6 Myr) we refer the reader to the detailed discussion of NGC 2264 (4 Myr) in Chapter 3, and the individual figures for Cha I can be found in Appendix E. We observed, similarly to the rest of SFRs, that the fastest rotating stars (including the analysis of both vsini and Prot values) tended to be located in the upper envelope of the cluster (see Chapter 4), and generally showed higher values of EW (Li) than the slower rotating stars of the same spectral types. A number of the candidates for this cluster are also slower rotating stars (shown in orange and yellow shades), scattered among the cluster candidates, but generally showing less EW (Li) than their faster rotating counterparts. We note, however, that for this cluster some of these slower rotating stars also show higher values of EW (Li), and some of them also have high chromospheric activity. The strong accreting stars mentioned above in this section also display slow rotation values, as could be expected: several of them show upper limits for vsini only, and the longest rotation period recorded by Nardiello (2020) for this selection also corresponds to an accreting star with Hα10% = 150 km s−1. For this cluster we observed candidates with both vsini values up to 90 km s−1, and long Prot up to 12 d (Nardiello, 2020), as well as Hα activity up to 110–120 Å. Finally, the analysis of the dependence of EW (Li) with Hα also revealed a pattern where the stars with higher Hα emission tended to be located in the upper envelope of the cluster, with higher values of EW (Li) (shown in purple and dark orange shades). Even though this general pattern can still be seen, given that SFRs also tend to show a larger dispersion than older clus- ters, in the case of this cluster we also found some of the most active members displaying lower values of EW (Li). 144 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 ∗ NGC 2244 Figure B.3: NGC 2244, a 4 Myr SFR. Credit: SST/NASA. NGC 2244 is a 2–4 Myr SFR (Michalska, 2019; Mužić et al., 2019; Jackson et al., 2021) at a distance of 1.4–1.7 kpc (Kharchenko et al., 2005; Kuhn et al., 2019; Michalska, 2019; Mužić et al., 2019). This very young cluster is associated with the Rosette Nebula in the Perseus Arm of the Galaxy. Embedded in an HII region, this cluster is rich in massive OB stars, as well as PMS stars showing Hα and X-ray emission (Michalska, 2019; Mužić et al., 2019). In our sample there are 452 stars in the field of NGC 2244, of which 391 have measured values of EW (Li). The membership analysis resulted in 143 RV candidates, 79 astrometric candidates, 123 Li candidates, and 116 final members (see Table 2.8). Of the final 123 Li candidates we discarded 11 stars which we could not analyse using the astrometric and photometric Gaia data, and which were additionally listed as non-members by Jackson et al. (2021) (all but one are definite non-members with a probability of 0.00, while the remaining one is listed with P=0.29, and is similarly discarded). We also found 10 strong accreting stars among our final members, and all but one are Li members and classified as high-probability members by Jackson et al. (2021) (the remaining one has no measured EW (Li) in DR6 and is not included in Jackson et al. (2021)). Regarding kinematics, one star in our final selection was a RV non-member according to the initial 2σ interval, with a RV deviating 6.0 km s−1 from the mean of the cluster. Following the discussion in Sect 2.2.1, we accepted it given that it fulfilled the rest of membership criteria, and it was also listed as a high-probability member by Jackson et al. (2021). On the other hand, we have also accepted as final candidates nine stars with no measured RV values in iDR6, due to the fact that they fully fulfil the astrometry criteria (as well as the other criteria), and are also listed as members by Jackson et al. (2021) with probabilities in the range of 0.53–0.99. Regarding other membership selections from the literature, we found the following number of common stars with our selection: 78 stars in Cantat-Gaudin et al. (2018), one star in Carrera et al. (2019), and 39 stars in Michalska (2019). Finally, Jackson et al. (2021) includes 114 out of our 116 candidates (the remaining two were not included in their analysis). We also note that B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 145 we included several stars with a marginal metallicity, deviating slightly from the 2σ interval, as they fulfilled the rest of criteria and were furthermore reinforced by high probabilities listed by Jackson et al. (2021). Regarding the study of rotation and activity, for a detailed discussion of this age range (SFR; 1–6 Myr) we refer the reader to the detailed discussion of NGC 2264 (4 Myr) in Chapter 3, and the individual figures for NGC 2244 can be found in Appendix E. Similarly to the rest of SFRs, we could observe a trend where the fastest rotating stars tended to be located in the upper envelope of the cluster (see Chapter 4), and generally showed higher values of EW (Li) than the slower rotating stars of the same spectral types. We also have to take into account, however, the larger dispersion found in SFRs due to their complex behaviour, which does not make the anti-correlation between rotation and Li depletion as clear as in the case of young and intermediate-age clusters, especially. A number of the candidates for this cluster are also once again slower rotating stars (shown in orange and yellow shades), scattered among the cluster candidates, but generally showing less EW (Li) than their faster rotating counterparts. For this cluster we observed candidates with high vsini values up to 140–150 km s−1, as well as Hα ac- tivity up to 110 Å. Meanwhile, the analysis of the dependence of EW (Li) with Hα also revealed a pattern where the stars with higher Hα emission tended to be located in the upper envelope of the cluster, and in the case of this cluster the stars with the highest EW (Li) values are also the ones with the highest values of Hα emission (shown in purple). ∗ NGC 2264 Figure B.4: NGC 2264, a 4 Myr SFR. Credit: ESO. At a distance of 0.70–0.80 kpc (Kharchenko et al., 2005; Spina et al., 2017; Cantat-Gaudin et al., 2018; Bonito et al., 2020; Gillen et al., 2020), NGC 2264 is a 4 Myr SFR (Jackson et al., 2021), the dominant component of the Mon OB1 association in the Monoceros constellation, situated in the local Orion-Cygnus spiral arm (Gillen et al., 2020). Several studies list ages in 146 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 the 1–5 Myr range (Spina et al., 2017; Cantat-Gaudin et al., 2018; Venuti et al., 2019; Arancibia- Silva et al., 2020; Bonito et al., 2020; Gillen et al., 2020; Randich et al., 2020). NGC 2264 is of great interest due to the Hα emission and accretion properties showcased by many of its young stars, and GES data is of great use to study these properties in detail Bonito et al. (2013). However, as we will also see when analysing the particularities of our candidate selection, this cluster also shows a strong level of nebular emission which, in combination with the Hα emission, can alter the stellar profiles and add difficulty to their physical interpretation (also see Sect 2.1). NGC 2264 is hierarchically structured, with multiple substructures and sub-populations, and multiple ongoing star formation events Gillen et al. (2020); Venuti et al. (2019). This SFR has been historically well-studied thanks to its large and well-defined membership, as well as its low-foreground extinction of E(B-V)=0.05–0.15 mag Gillen et al. (2020); Jackson et al. (2021). In our sample there are 1853 stars in the field of NGC 2264, of which 1609 have measured EW (Li) values. The membership analysis resulted in 621 RV candidates, 423 astrometric can- didates, 507 Li candidates (in addition to 28 stars which are final members but have EW (Li)s affected by accretion and activity), and 503 final members (see Table 2.8). Of the final 507(535) Li candidates we discarded 28 stars (not the same as the aforementioned 28 stars with EW (Li) values affected by accretion and activity), on the basis of not being able to analyse them using astrometric and photometric Gaia data, and all of these 28 stars were additionally listed as non-members by Jackson et al. (2021) (most are clear non-members with a probability of 0.00, while a few are listed with probabilities up to P=0.35, and are similarly discarded). In the analysis of NGC 2264 we found 144 strong accreting stars with Hα10% > 270– 300 km s−1 among our final members, and a high number of the remaining candidates show considerable values of accretion as well, albeit under that limit. Of these 144 strong accretors, all are Li members and classified as high-probability members by Jackson et al. (2021), except for 22 stars which show higher levels of EW (Li)s than expected (marked as ‘Y?’ in the table of Appendix D, more on this issue below), and two stars which do not appear to be Li members, but are similarly included as final members due to their strong accretion, as explained earlier in this section with the instance of Cha I. These two stars furthermore fulfil the rest of our criteria and are included as high probability members by Jackson et al. (2021). As in the case of Cha I, we explain their lower EW (Li) values as a probable result of veiling caused by accretion, suppressing the absorption Li line. As was also discussed earlier with Cha I, another effect of the chromospheric activity and the strong accretion of the very young stars in this SFR can be observed in the case of the 28 particular stars which present values of EW (Li) notably larger than the rest of candidates (800–1270 mÅ). Although they show a larger dispersion than the one observed in the simi- lar case of Cha I, we consider all the stars which fulfil the other criteria as final members of the cluster. Furthermore, 20 of them are listed as high probability members by Jackson et al. (2021) and several are also included in several others membership studies (e.g, Lim et al., 2016; Cantat-Gaudin et al., 2018; Maíz Apellániz, 2019; Venuti et al., 2019). We explain their quite larger apparent values of Li given the fact that these are very young active stars, with high values of both accretion and Hα (as we saw above, 22 of these 28 stars are strong accretors with Hα10% > 270–300 km s−1 (e.g., Bonito et al., 2020). Thus, their larger EW (Li)s seem to be an effect of accretion-induced enhancement and the additional effects of high chromospheric activity (also see Sect. 2.2.6 and Sects. 3.1 and 3.2 for this particular example). As for kinematics, three star in our final selection were RV non-members according to the B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 147 initial 2σ interval, with RV s deviating up to 9.0 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted them as final members, as they fulfilled the rest of membership criteria, and were also listed as high-probability members by Jackson et al. (2021). On the other hand, we have also accepted as final candidates 22 stars with no measured RV values in iDR6, due to the fact that they fully fulfilled all astrometric criteria (as well as the other criteria), and are also listed as members by Jackson et al. (2021) with probabilities in the range of 0.67–0.99. Regarding previous membership selections from the literature, we found the following number of common stars with our selection in several studies: 197 stars in Jackson et al. (2016), 69 stars in Lim et al. (2016), 130 stars in Spina et al. (2017), 116 stars in Cantat-Gaudin et al. (2018), 198 stars in Maíz Apellániz (2019), and 226 stars in Venuti et al. (2019). Finally, Jackson et al. (2021) includes 479 out of our 503 candidates. Of the remaining candidates in our selection, 21 were not included in their analysis, and the other four (which fully fulfil all our criteria) are listed with probabilities in the range of 0.29–0.38 by Jackson et al. (2021). As already discussed in Sect. 2.3, we also note that we seem to find some inconsistencies when plotting the Li-rich giant outliers selected in the field of this cluster in the CMD diagram, with one of them appearing among the cluster candidates. However, when plotting them in the γ index-versus-Teff diagram the expected distinction is found between the non-giant cluster candidates and the Li-rich giant outliers. We plan on studying all Li-rich giant outliers in more detail in order to gain further confirmation on their nature as Li-rich giant contaminants (see the future work in Chapter 5). Regarding the influence of rotation and activity on Li, we mainly refer to the discussion in Chapter 3 for a detailed account for this cluster. We will add a couple of comments here, however. Firstly, we note that the two stars (06403280+0951293 and 06405413+0948434) with the highest values of Hα (250–300 Å) for this cluster are among the high accreting stars with potentially over-estimated EW (Li) measurements in the 800–1270 mÅ range. As discussed above, we have confirmed that both of these stars are robust candidates of the cluster, fulfilling all criteria and being listed by Jackson et al. (2021) as high-probability members. We can additionally explain their appreciably high values of Hα to the youth of this SFR, and note that other young associ- ations with a similar age, such as Cha I, also display candidate stars with similarly high values of chromospheric activity. We also comment here on the presence of two candidate stars with Prot > 20 d (namely, 06393398+0949208 with Prot=26.5 d, and 06403432+0925172 with Prot=28.9 d). These stars are both strong accretors which fulfil all of our membership criteria, as well as being listed as high probability members by Jackson et al. (2021). However, although studies such as Makidon et al. (2004) and Lamm et al. (2005) report that SFRs routinely include stars with Prot values of 16–18 d, and even longer in the tails of the distributions, we are not certain whether these specific Prot values are reliable (we also reinforced this conclusion after comparing the Prot values of these stars with their corresponding vsini measurements). For this reason we have decided to omit these two stars from our study of the dependence of Prot. Another reason for this is that these overly long rotational periods would significantly affect the range in the colour-coded aux- iliary index of the EW (Li)-versus-Teff diagrams discussed in Chapter 3, hindering our analysis. ∗ λ Ori 148 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 λ Ori (also known as Collinder 69) is a 6 Myr young cluster (Jackson et al., 2021; Binks et al., 2022, in prep.), located at a distance of 0.41 kpc (Barrado et al., 2011; Dib et al., 2018), and the oldest of the associations included in the λ Ori star forming region, which includes several distinct zones at different evolutionary stages (Barrado et al., 2011). One of these is cluster Collinder 69, the oldest of the associations in the λ Ori region, with an age of 5–12 Myr. The stars in this region showcase a variety of effects and characteristics typical of very young stars, including the presence of circumstellar discs, accretion processes, rotation and chromospheric activity (Bayo et al., 2012). In our sample there are 836 stars in the field of λ Ori, of which 778 have measured values of EW (Li). The membership analysis resulted in 207 RV candidates, 142 astrometric candidates, 163 Li candidates (in addition to stars which are final members but have EW (Li)s affected by accretion and activity), and 161 final members (see Table 2.8). Of the final 163 Li candidates we discarded two stars because we were not able to analyse them using astrometric and photometric Gaia data, and they were listed as non-members with P=0.00–0.01 by Jackson et al. (2021). In the analysis we also found 34 strong accreting stars among our final candidates. Of these 34 strong accretors, all of them are Li members, and 17 are also listed as high-probability mem- bers by Jackson et al. (2021) (the rest are not included in their study). In addition, we list four stars with EW (Li) values slightly larger than the rest of candidates (870–950 mÅ). Similarly to the case of Cha I, we consider them as members given that they exhibit little dispersion with respect to the rest of candidates, and we explain their larger apparent values of Li for being young active stars, with high values of both accretion, and in some cases also chromospheric Hα. Two of them, the ones with the largest EW (Li) values, are additionally strong accretors with Hα10% > 270–300 km s−1, and so, once again, their larger EW (Li)s could also be an effect of accretion-induced enhancement. As for kinematics, 105 stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating 7–10 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted them as final members, as they fulfilled the rest of membership criteria, and all stars except for 14 (which are not included in their study) were also listed as high-probability members by Jackson et al. (2021). Regarding previous membership selections from the literature, we found the following number of common stars with our selection in several studies: 10 stars in Sacco et al. (2008), 70 stars in Hernández et al. (2010), 30 stars in Barrado et al. (2011), 16 stars in Franciosini & Sacco (2011), 51 stars in Bayo et al. (2012), and 94 stars in Cantat-Gaudin et al. (2018). Finally, Jackson et al. (2021) includes 116 out of our 161 candidates (the 45 remaining stars were not included in their study). Regarding the study of rotation and activity, for a detailed discussion of this age range (SFR; 1–6 Myr) we refer the reader to the detailed discussion of NGC 2264 (4 Myr) in Chapter 3, and the individual figures for λ Ori can be found in Appendix E. Similarly to the rest of SFRs, we observed a trend where the fastest rotating stars and the most active stars (shown in purple) tended to be located in the upper envelope of the cluster (see Chapter 4), and generally showed higher values of EW (Li) than the slower rotating and less active stars of the same spectral types. A number of the candidates for this cluster are also once again slower rotating stars (shown in yellow shades), and, similarly to the case of NGC 2264 and other SFRs in our sample, most of the strong accreting stars with the highest values of EW (Li) are also among the slowest rotators B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 149 (with many of them displaying only upper limits for vsini). For this cluster we found candidates with high vsini values up to 130 km s−1 and high Hα activity up to 180 Å. We note also that, similarly to the case of NGC 2264, the small number of stars displaying the highest values of vsini and Hα cause many of the rest of the cluster candidates to be colour-coded more uniformly in more orange and yellow tones due to the range of the auxiliary axis being enlarged. Although we can still observe the trends described (stars with higher rotation and activity values generally show higher values of EW (Li) as well), this fact makes it more difficult to distinguish between the values of the rest of the candidates. ∗ Col 197 Collinder 197 (abbreviated as as Col 197 or Cr 197) is a low-population young cluster with an age of 12–14 Myr (Bonatto & Bica, 2010; Vande Putte et al., 2010; Sampedro et al., 2017; Dias et al., 2019; Jackson et al., 2021; Romano et al., 2021), located at a distance of 0.80–0.90 kpc (Kharchenko et al., 2005; Bonatto & Bica, 2010; Vande Putte et al., 2010; Sampedro et al., 2017; Dias et al., 2019). One of the 471 clusters discovered by astronomer Per Collinder (Collinder, 1931), Col 197 is embedded in the HII region of Gum 15 (Bonatto & Bica, 2010). In our sample there are 409 stars in the field of Col 197, of which 366 have measured EW (Li) values. The membership analysis resulted in 123 RV candidates, 86 astrometric candidates, 104 Li candidates, and 92 final members (see Table 2.8). Similarly to other clusters, of the final 104 Li candidates we discarded 11 stars as we were not able to analyse them using astrometric and photometric Gaia data, and they were listed as non-members with P=0.00–0.01 by Jackson et al. (2021). We also decided to discard one star, in spite of fulfilling all our criteria, for being listed as a non-member by both Cantat-Gaudin et al. (2018) and Jackson et al. (2021). In addition, we have also accepted as final candidates six stars with no measured RV values in iDR6, due to the fact that they fully fulfil the astrometry criteria (as well as the other criteria), and are also listed as members by Jackson et al. (2021) with probabilities in the range of 0.70–1.00. In the analysis we also found 11 strong accreting stars among our final candidates. Of these 11 strong ac- cretors, all of them are Li members, and eight are also listed as members by Jackson et al. (2021). Regarding previous membership selections from the literature, we found 79 common stars in Cantat-Gaudin et al. (2018), and Jackson et al. (2021) includes 65 out of our 92 candidates. Of the remaining candidates in our selection, eight stars were not included in their study, and in an untypical way in all our membership comparisons with this work, we found the remaining 19 stars listed as non-members with P=0.00–0.02. All of these 19 stars seem to fulfil all of our criteria, including Gaia, so we have not discarded them from our final selection, but the disagree- ment is worth noting, even more so considering that this is the only cluster in our sample of 42 clusters whose final RV mean estimation additionally does not agree with the values given by the literature. Regarding the study of rotation and activity, for a detailed discussion of this age range (young clusters; 10–80 Myr) we refer the reader to the detailed discussion in Chapter 3 of IC 2391, IC 2602 and IC 4665 (35–38 Myr), and of NGC 2547 (20–45 Myr); and the individual figures for Col 197 can be also found in Appendix E. Similarly to the rest of young clusters, as discussed in Chapter 3, we observed a trend where the fastest rotating stars and the most active stars (shown in shades of purple and darker orange) tended to be located in the upper envelope of the cluster (see Chapter 4), and generally showed higher values of EW (Li) than the slower rotating and less active stars of the same spectral types. A number of the candidates for this cluster are also slower 150 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 rotating stars (shown in yellow shades), some of them being the aforementioned strong accreting stars. We note that some of the candidates displaying the highest values of EW (Li) also the ones with the highest values of Hα activity, but are slower rotating stars as well (which can be explained with the fact that several of these stars are strong accretors as well). For this clus- ter we found candidates with high vsini values up to 100 km s−1, as well as Hα activity up to 70 Å. ∗ Vela OB2 association: γ Velorum and NGC 2547 Figure B.5: NGC 2547, a 20–45 Myr young cluster. Credit: ESO. The Vela OB2 association is a dense cluster of stars consisting of some 100 early-type candi- date member stars in the constellation Vela, at a mean distance of 410 ± 12 pc (Jeffries et al., 2009b). The association is surrounded by a dust shell centered on its brighter and most massive component, spectroscopic binary system γ2 Vel (Jeffries et al., 2009b). The Vela complex has been subject to a highly dynamical evolution and is characterized by the presence of a number of PMS clusters (such as γ Vel, Trumpler 10 and NGC 2547), as well as two OB associations and two supernova remnants (Spina et al., 2014b). The nearby γ Velorum (also referred to as γ Vel) cluster is one of the dense PMS clusters around γ2 Vel that were observed by GES (e.g., Jeffries et al., 2014; Spina et al., 2014b; Mapelli et al., 2015; Sacco et al., 2015; Franciosini et al., 2018; Armstrong et al., 2020). Jeffries et al. (2014) studied the kinematic structure in the low mass stars surrounding γ2 Vel and found that the γ Vel cluster is composed of two populations (γ Vel A and B) that are kinematically distinct, with γ Vel A being 1–2 Myr older than γ Vel B. Franciosini et al. (2018) suggested γ Vel A and γ Vel B to be two kinematically separated independent clusters situated along the same line of sight. The age of both γ Vel A and B is generally listed in the literature as 10–20 Myr (e.g., Jeffries et al., 2014; Frasca et al., 2015; Sacco et al., 2017; Spina et al., 2017; Beccari et al., 2018; Franciosini et al., 2018; Armstrong et al., 2020; Jackson et al., 2021), and its distance is given in the range 0.35–0.40 kpc (Jeffries et al., 2014; Frasca et al., 2015; Sacco et al., 2017; Beccari et al., 2018; Franciosini et al., 2018). B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 151 Another young cluster around γ2 Vel is the open cluster NGC 2547. Sacco et al. (2015) also found a sample composed of two kinematically distinct populations (NGC 2547 A and B) with a RV distribution characterized by two peaks, the most prominent peak corresponding to NGC 2547 A. The study additionally found a kinematically distinct second population, NGC 2547 B, with a very similar RV to γ Vel B. The study concludes that NGC 2547 and γ Vel B share a common origin. Based on Gaia DR2 data, Beccari et al. (2018) found that the members of the populations B identified by Jeffries et al. (2014) and Sacco et al. (2015) belong to a set of overlapping clusters in space over an area of nearly 100 pc. The age of NGC 2547 is typically listed in the literature as either 35–45 Myr, or a slightly younger range of 20–35 Myr (e.g., Oliveira et al., 2003; Soderblom et al., 2014), with NGC 2547 B considered as younger than NGC 2547 A, with the same age as γ Vel, 10–20 Myr (e.g., Sacco et al., 2017; Spina et al., 2017; Beccari et al., 2018; Randich et al., 2018; Bossini et al., 2019; Jackson et al., 2021; Pang et al., 2021; Romano et al., 2021), and its distance is given in the range 0.36–0.39 kpc (Sacco et al., 2017; Spina et al., 2017; Beccari et al., 2018; Pang et al., 2021). In our sample there are 1262 and 477 stars in the field of γ Vel and NGC 2547, respectively, of which 1190 and 405 have measured EW (Li)s. The cluster membership selections for both γ Vel and NGC 2547 consist of 234 stars in γ Vel (99 in γ Vel A and 84 in γ Vel B, as well as 51 additional candidate stars that are not associated to a specific population), and 151 stars in NGC 2547 (138 in NGC 2547 A and 13 in NGC 2547 B). As mentioned in Sect. 2.2, for this study we used the membership selections obtained by a series of former studies in the literature: Regarding γ Vel, we first used Jeffries et al. (2014), the study specifying the members of γ Vel A and B, as well as a series of other GES studies (Damiani et al., 2014; Spina et al., 2014b; Frasca et al., 2015; Prisinzano et al., 2016; Cantat-Gaudin et al., 2019; Jackson et al., 2021). For NGC 2547 we similarly used several membership studies from the literature, some of which list the membership probabilities of each candidate to Pop. A/B Sacco et al. (2015); Randich et al. (2018); Cantat-Gaudin et al. (2018), while others do not Spina et al. (2017); Jackson et al. (2021). Gaia studies Randich et al. (2018), Cantat-Gaudin et al. (2018) and Jackson et al. (2021) offer updated membership probabilities for γ Vel A Jackson et al. (2021) and NGC 2547 (all three of them). Randich et al. (2018) listed a series of new members with respect to Sacco et al. (2015). Although their membership probabilities for each population are generally consistent with each other, a small number of stars were associated with different populations in Sacco et al. (2015) and Randich et al. (2018). In this case, we adopted the membership from Randich et al. (2018), as this is the most recent study of the two. For NGC 2547 we also compared the member stars in Sacco et al. (2015), Cantat-Gaudin et al. (2018) and Randich et al. (2018) with the candidate members in Bravi et al. (2018). For all our adopted candidates, Bravi et al. (2018) found high probabilities, namely ranging from 60 to 100%, of being RV members of the cluster. Finally, Jackson et al. (2021) offer updated probabilities for both clusters, and we have decided to also prioritize the membership probabilities of this work with respect to earlier studies, for those cases were they might appear to disagree. While we mainly used the membership lists offered by the aforementioned works, we also note that we did make use of the Gaia EDR3 data to analyse the proper motions, parallaxes and the position in the CMD for all stars marked as members for γ Vel and NGC 2547, in order to improve the final selections. We thus discarded a series of stars which deviated appreciably from the locus of the rest of members in the pmra-versus-pmdec diagram, as well as those stars which proved to be parallax non-members, and those which also deviated appreciably from the 152 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 rest in the CMDs. As to field contaminants, we also find two of the γ Vel Li-rich giants in our list (J08095783- 4701385 and J08102116-4740125), as well as one of the Li-rich giants from NGC 2547 (J08110403- 4852137), in Casey et al. (2016). Another one, (J08110403-4658057) in γ Vel, is listed in Smiljanic et al. (2018). Regarding the study of rotation and activity, for a detailed discussion of this age range (young clusters; 10–80 Myr) we refer the reader to the detailed discussion in Chapter 3 of IC 2391, IC 2602 and IC 4665 (35–38 Myr), and of NGC 2547 (one of the clusters discussed in this section); and the individual figures for both γ Vel and NGC 2547 can be also found in Appendix E. For both γ Vel and NGC 2547, we analysed the dependence of rotation and Hα activity with Li firstly taking into account both populations, and then studying each one separately. We note that we observed the same patterns and trends in both instances (Appendix E includes all of these figures, both for separate populations and both populations together). Similarly to the rest of young clusters, for both γ Vel and NGC 2547 we observed a trend where the fastest rotating stars (including the analysis of both vsini and Prot values) and the most active stars (shown in shades of purple and darker orange) tended to be located in the upper envelopes of the cluster (see Chapter 4), and generally showed higher values of EW (Li) than the slower rotating and less active stars of the same spectral types. This anti-correlation between Li depletion and high values of rotation and activity seems to be more clearly and uniformly defined in the clusters for this age range, compared to the greater dispersion observable in the younger SFRs. A number of the candidates for both clusters are also slower rotating stars (shown in yellow shades), generally displaying lower values of EW (Li) than the faster rotators. We also note that the most active stars are mainly found among late K and M-type stars for both clusters. For γ Vel we observed candidates with both high vsini values up to 110 km s−1 and longer Prot values up to 7–8 d (Nardiello, 2020), as well as Hα activity up to 16–17 Å. On the other hand, for NGC 2547 we observed candidates with both high vsini values up to 80 km s−1 and longer Prot values up to 11 d (Irwin et al., 2008; Jackson et al., 2016), as well as Hα activity up to 14–15 Å. Finally, we note that we have omitted a star from the study of activity for γ Vel A (08100280-4736372) which has an appreciably higher Hα value of 55 Å, compared to the aforementioned 14–15 Å maximum value for the cluster selection. This star is listed as a candidate of γ Vel A by several studies (Damiani et al., 2014; Jeffries et al., 2014; Frasca et al., 2015; Prisinzano et al., 2016), but is not included in (Jackson et al., 2021). While re- maining a candidate of the cluster, we have decided not to include it in the analysis of activity: partly because we were not certain about the reliability of the Hα value for this star, and also as it would significantly affect the range of the auxiliary colour-coded axis for the rest of candidates. ∗ NGC 2232 NGC 2232 is a young cluster with an age range of 18–38 Myr according to several studies (Liu & Pang, 2019; Jackson et al., 2021; Pang et al., 2021; Romano et al., 2021; Binks et al., 2022, in prep.), with the most recent veering towards younger ages in the 18–25 Myr range, which is in agreement with the obtained empirical Li envelope from our final selection (see Chapter 4). Located at a distance of 0.32–0.36 kpc in Monoceros (Kharchenko et al., 2005; Sampedro et al., 2017; Pang et al., 2021), NGC 2232 is a bright cluster that has not been studied very often. For example, very few previous studies have focused on Li-depletion in the lower mass stars of this B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 153 cluster (Monroe & Pilachowski, 2010; Binks et al., 2022, in prep.). In our sample there are 1869 stars in the field of NGC 2232, of which 1750 have measured values of EW (Li). The membership analysis resulted in 750 RV candidates, 56 astrometric can- didates, 84 Li candidates, and 68 final members (see Table 2.8). Of the final 68 Li candidates we discarded 16 stars because we were not able to analyse them using astrometric and photometric Gaia data, and they were listed as non-members with P=0.00–0.01 by Jackson et al. (2021). One of them additionally has [Fe/H] value deviating appreciably from the mean of the cluster, beyond the extended 3σ membership interval. In our final selection we note as a particular case a star with a EW (Li) value which is higher than the rest of candidates (841–948 mÅ), but without exhibiting a large dispersion with respect to the rest of the candidates. We consider it as a final member given that it fulfilled the other criteria as well as being listed in several studies as a candi- date of the cluster Cantat-Gaudin et al. (2018); Jackson et al. (2021); Binks et al. (2022, in prep.). Regarding previous membership selections from the literature, we found 46 stars in common with Cantat-Gaudin et al. (2018), as well as 49 stars in Pang et al. (2021), and 58 stars in Binks et al. (2022, in prep.). Finally, Jackson et al. (2021) includes 56 out of our 68 candidates (the remaining stars were not included in their study, except for one which was listed with P=0.30). Regarding the study of rotation and activity, for a detailed discussion of this age range (young clusters; 10–80 Myr) we refer the reader to the detailed discussion in Chapter 3 of IC 2391, IC 2602 and IC 4665 (35–38 Myr), and of NGC 2547 (20–45 Myr); and the individual figures for NGC 2232 can be also found in Appendix E. Similarly to the rest of young clusters, we observed a trend where the fastest rotating stars and the most active stars (shown in shades of purple and darker orange) tended to be located in the upper envelope of the cluster (see Chapter 4), and generally showed higher values of EW (Li) than the slower rotating and less active stars of the same spectral types. A smaller number of the candidates for this cluster are also slower rotating stars (shown in yellow shades), showing generally lower values of EW (Li) than their faster rotating counterparts. We also note that for this cluster the most active stars seem to be mainly late K and M-type stars. For this cluster we found candidates with vsini values up to 100 km s−1, as well as Hα activity up to 9–10 Å. ∗ IC 2391 Among the closest clusters to the Sun selected by GES, at a distance of 160± 10 pc (Spina et al., 2017) - other distance estimates are in the range of 100–175 pc (Platais et al., 2007; Smil- janic et al., 2011; De Silva et al., 2013; Pang et al., 2021) -, IC 2391 is an open cluster in the constellation Vela, with an age of 36±2 Myr (Bossini et al., 2019). Before the launch of Gaia its age was estimated in the 20–50 Myr range, and the lithium depletion boundary (LDB) method gives an age of 50–55 Myr (e.g., Stauffer et al., 1997; Randich et al., 2001; Barrado y Navascués, 2004; Platais et al., 2007; Smiljanic et al., 2011; De Silva et al., 2013). Even though it is located close to the Galactic plane, its proximity results in small reddening, and thus this cluster can be useful in order to study faint low-mass stars and brown dwarfs (Barrado y Navascués, 2004; Platais et al., 2007). Additionally, its proximity and youth (the age of this cluster implies that solar-mass stars have not yet arrived on, but are close to the ZAMS) make IC 2391 very inter- esting for the study of pre-main sequence evolutionary phases (Smiljanic et al., 2011). In our sample there are 434 stars in the field of IC 2391, of which 400 have measured EW (Li) values. The membership analysis resulted in 56 RV candidates, 27 astrometric candidates, 37 154 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 Li candidates, and 35 final members (see Table 2.8). Of the final 37 Li candidates we discarded two stars from the final member selection. These stars could not be analysed with any Gaia data (gravity, RV and Li were the only criteria available), and they were additionally classified as non-members with a probability of 0.00 by Jackson et al. (2021). We also note that we added one star as part of our final selection which initally was a RV non-member according to the initial 2σ interval, with a RV deviating 6.5 km s−1 from the mean of the cluster. We accepted it as it deviated by less than 10 km s−1 from the mean RV , fulfilled the rest of criteria and is listed as a member by Jackson et al. (2021). Regarding previous selections, we found the following number of common candidates in the membership lists of these non-GES studies: 19 stars in Barrado y Navascués et al. (2001b) and Barrado y Navascués (2004); three stars in Randich et al. (2001); four stars in Dodd (2004); six stars in Platais et al. (2007), Messina et al. (2011) and De Silva et al. (2013); and three stars in Elliott et al. (2016). We also refer to Gómez Garrido (2015) and Gómez Garrido et al. (2017) for a membership study of this cluster, alongside IC 2602 and IC 4665. Regarding GES studies, we firstly found four common stars in Spina et al. (2017) and 14 stars in Bravi et al. (2018). The latter study derived RV membership probabilities and lists of candidate members for this cluster (alongside IC 2602, IC 4665 and NGC 2547) using iDR4 data. Comparing our final selection of 35 members with the list of 53 candidate stars of Bravi et al. (2018), we find 30 kinematic candidates and 14 final members in common (all of the common members stars have high RV membership probabilities of at least 0.95, except for two stars in the 0.7–0.9 range). We note that, for many stars Bravi et al. (2018) used values of EW (Li) and/or Teff which were derived from one of the WG12 nodes and do not appear in our sample. As a result, we excluded these stars from our membership analysis and only consider those stars in Bravi et al. (2018) with EW (Li) values in our iDR6 sample. Our mean RV and σ for IC 2391 also agree with the estimates in Bravi et al. (2018) (see Table 2.4). Finally, a series of more recent studies using both GES and Gaia data also list updated membership probabilities for IC 2391 (Cantat-Gaudin et al., 2018; Randich et al., 2018; Jackson et al., 2021; Pang et al., 2021). We have 28 common stars as members with Randich et al. (2018), as well as 24 stars with Cantat-Gaudin et al. (2018), 29 with Jackson et al. (2021) (the remain- ing six were not included in their analysis), and 23 with Pang et al. (2021). As we mention in Sect. 2.2.7, in this study we relied more heavily on Jackson et al. (2021), the most extensive and one of the most recent studies using both GES and Gaia data. Thus, we decided to discard as a final member a marginal star according to our analysis given that Jackson et al. (2021) listed it as a non-member, even though Randich et al. (2018) considered it a candidate. To finish, for completeness we also mention here a series of recent studies that used Gaia-DR2 data to study the spacial-kinematic distribution and cluster membership of IC 2391 (Postnikova et al., 2019, 2020; Vereshchagin et al., 2019). Regarding the influence of rotation and activity on Li, we mainly refer to the discussion in Chapter 3 for a detailed account for this cluster, alongside IC 2602 and IC 4665. We observed candidates with vsini values up to 35 km s−1, as well as Hα activity up to 10–12 Å. We addi- tionally note that Messina et al. (2011) also provides five Prot values for this cluster (as shown in the individual figures of Appendix E). While not enough to be able to analyse any trends or patterns, they show short rotational periods up to 5 d. ∗ IC 2602 B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 155 At a distance of 150±10 pc (Spina et al., 2017), IC 2602 is an open cluster in the constellation Carina, close to the Galactic plane, with an age of 35 ± 1 Myr (Bossini et al., 2019). Previous studies found ages ranging from 30–67 Myr, a very similar age to IC 2391 (Randich et al., 1997; Stauffer et al., 1997; Randich et al., 2001; Smiljanic et al., 2011; Jackson et al., 2021; Pang et al., 2021; Romano et al., 2021). An age of about 46 Myr was also derived from the LDB method (Dobbie et al., 2012). IC 2602 (also referred to as the Southern Pleiades or Theta Carinae clus- ter) is the third brightest open cluster, following the Hyades. Alongside IC 2391, its proximity and youth –the solar-like stars belonging to this cluster are about to arrive on the ZAMS– make IC 2602 very interesting for the study of pre-main sequence evolutionary phases. In our sample there are 1852 stars in the field of IC 2602, of which 1740 have measured EW (Li) values. The membership analysis resulted in 309 RV candidates, 43 astrometric candi- dates, 59 Li candidates, and 55 final members (see Table 2.8). Of the final 59 Li candidates we discarded four stars from the final member selection. Two of them were also discarded via the criteria of RV and metallicity. In addition, similarly to other clusters, all four of these stars could not be analysed with any Gaia data (gravity, RV , Li, and sometimes metallicity were the only criteria available), and they were additionally classified as non-members with a probability of 0.00 by Jackson et al. (2021) (all four stars were also listed as non-members by Randich et al. (2018)). Comparing our selection with former studies, we found three stars in common with non-GES Randich et al. (2001), and we also reinforced our membership selection with 28 additional mem- bers of IC 2602 with measured EW (Li)s listed by this study. We also made use of 44 additional members with EW (Li) measurements from Jeffries et al. (2009a). All these member stars which were not measured by GES were of particular interest to construct the empirical lithium envelope for IC 2602 (with the envelope of Montes et al. (2001) as a base) as well, especially in the region of the LDB (see Chapter 4). We also refer to Gómez Garrido (2015) and Gómez Garrido et al. (2017) for a membership study of this cluster, alongside IC 2391 and IC 4665. Regarding GES studies, we firstly found 11 common stars in Spina et al. (2017), as well as 55 kinematic candidates and 27 final members in common with the list of 101 candidates in Bravi et al. (2018). As in the case of IC 2391, many of the stars in Bravi et al. (2018) have no EW (Li) values in the iDR6 sample, and therefore we excluded them in our own membership analysis.The mean RV and σ derived in Bravi et al. (2018) for IC 2602 are also in agreement with the ones obtained in this paper. As for GES studies that include Gaia data, we have 36 common stars listed as members with Randich et al. (2018), as well as 29 stars with Cantat-Gaudin et al. (2018), and 49 with Jackson et al. (2021) (the remaining six were not included in their analysis). Regarding the influence of rotation and activity on Li, we mainly refer to the discussion in Chapter 3 for a detailed account for this cluster, alongside IC 2391 and IC 4665. We observed candidates with vsini values up to 60 km s−1, as well as Hα activity up to 11 Å. ∗ IC 4665 At a distance of 360±10 pc (Spina et al., 2017), IC 4665 is an open cluster in the constellation Ophiuchus. Bossini et al. (2019) calculated an age of 38 ± 3 Myr for this cluster, in agreement with the 35–43 Myr range reported in several studies (Martín & Montes, 1997; Jeffries et al., 2001; Jackson et al., 2021; Pang et al., 2021; Romano et al., 2021). 156 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 In our sample there are 567 stars in the field of IC 4665, of which 544 have measured values of EW (Li). The membership analysis resulted in 233 RV candidates, 29 astrometric candidates, 51 Li candidates, and 33 final members (see Table 2.8). Of the final 51 Li candidates we discarded 18 stars from the final member selection. Similarly to the case of other clusters, all of these stars could not be analysed with any Gaia data (gravity, RV , Li, and, in some cases, metallicity were the only criteria available), and they were all classified as non-members by Jackson et al. (2021) (15 stars with a probability of 0.00, the remaining three in the potential but not definite non-member range of 0.17-0.49). Randich et al. (2018) also lists seven of these 18 stars as non- members (the rest were not considered in their analysis). Regarding previous selections, we found the following number of common candidates in the membership lists of these non-GES studies: six stars in de Wit et al. (2006) and Jeffries et al. (2009a); 11 stars in Manzi et al. (2008); and 17 stars in Lodieu et al. (2011). We also reinforced our membership selection with 23 additional members of IC 4665 with measured EW (Li)s listed by Manzi et al. (2008). We also refer to Gómez Garrido (2015) and Gómez Garrido et al. (2017) for a membership study of this cluster, alongside IC 2391 and IC 2602. As for GES studies, we found 15 common stars in Spina et al. (2017), as well as 30 kine- matic candidates and 19 final members in common with the list of 122 candidates in Bravi et al. (2018). Our mean RV and σ are also consistent with the previous estimates in this work. Finally, regarding GES studies that include Gaia data, we have 11 common stars listed as mem- bers with Randich et al. (2018), as well as 16 stars with Cantat-Gaudin et al. (2018), 23 stars with Pang et al. (2021), and 29 candidate stars in common with Jackson et al. (2021). In this latter comparison, three out of the remaining four stars were not included in the analysis of citejackson2021, and the other one was listed with a probability of 0.14, but seeing as it fully fulfilled all our criteria, including Gaia astrometry, we accepted it as a final member. In spite of using the same data sets and very similar membership criteria, it is probable that the reason for these individual deviations between our two analyses originated from the existing differences regarding, for example, criteria limits or the weight of the factors implicated in the decision to accept or discard stars (especially if they seem to be marginal stars according to the individual membership criteria) as final candidates. Regarding the influence of rotation and activity on Li, we mainly refer to the discussion in Chapter 3 for a detailed account for this cluster, alongside IC 2391 and IC 2602. We observed candidates with vsini values up to 60 km s−1, as well as Hα activity up to 6–7 Å. ∗ NGC 2451 A and B NGC 2451 A and NGC 2451 B are two open clusters projected along the same line of sight, and located at respective distances of 0.18–0.20 kpc and 0.36–0.37 kpc (Hünsch et al., 2004; Ba- log et al., 2009; Silaj & Landstreet, 2014; Pang et al., 2021). The age of both NGC 2547 A and B is generally listed in the literature in the 50–80 Myr range (e.g., Balog et al., 2009; Netopil & Paunzen, 2013; Silaj & Landstreet, 2014; Randich et al., 2018; Franciosini et al., 2021; Jackson et al., 2021; Pang et al., 2021), while individual ages are also listed, such as the estimations of Bossini et al. (2019), who calculated an age of 44 ± 2 Myr for NGC 2547 A and 39 ± 1 for NGC 2547 B. Thus, the nearer cluster NGC 2547 A seems to be slightly older than the more distant cluster NGC 2547 B Hünsch et al. (2004). While often studied together given their ac- cidental location along the same line of sight, several studies have endeavoured to separate the two clusters and determine the physical parameters of each of them (e.g., Hünsch et al., 2004; B.1. SFRs (age ≤ 6 Myr) and young open clusters (age ≤ 50 Myr) 157 Balog et al., 2009; Bossini et al., 2019; Jackson et al., 2021). In our sample there are 1656 in the field of NGC 2451 A/B, of which 1607 have measured values of EW (Li). The cluster membership selections for both NGC 2451 A and NGC 2451 B consist of 42 stars in NGC 2451 A and 64 stars in NGC 2451 B. As mentioned in Sect. 2.2, for this study we used the membership selections obtained by a series of former studies in the literature: Silaj & Landstreet (2014) only gives a candidate list for NGC 2451 A, while the rest include final member lists for both NGC 2451 A and NGC 2451 B (indicated as ’A’ and ’B’ in the table of Appendix D) (Spina et al., 2017; Randich et al., 2018; Cantat-Gaudin et al., 2018; Jackson et al., 2021). Gaia studies Randich et al. (2018), Cantat-Gaudin et al. (2018) and Jackson et al. (2021) offer updated membership probabilities for NGC 2451 A and NGC 2451 B. Although their mem- bership probabilities for each population are generally consistent with each other, a small number of stars were considered as members by Randich et al. (2018) and Cantat-Gaudin et al. (2018) but were listed as definite non-members in Jackson et al. (2021). In these cases, we adopted the membership from Jackson et al. (2021), as this is the most recent study. As seen with other clusters, we have decided to prioritize the membership probabilities of Jackson et al. (2021) with respect to earlier studies, for those cases were they might appear to disagree. While we mainly used the membership lists offered by the aforementioned works, we also note that we did make use of the Gaia EDR3 data to analyse the proper motions, parallaxes and the position in the CMD for all stars marked as members for NGC 2451 A/B, in order to improve the final selections. We thus discarded a series of stars which deviated appreciably from the locus of the rest of members in the pmra-versus-pmdec diagram, as well as those stars which proved to be parallax non-members, and those which also deviated appreciably from the rest in the CMDs. Most of these discarded stars were also listed as non-members by Jackson et al. (2021), in contrast to them being considered as members by earlier studies, which reinforced our decision to discard them on the basis of our astrometric criteria. Regarding the study of rotation and activity, for a detailed discussion of this age range (young clusters; 10–80 Myr) we refer the reader to the detailed discussion in Chapter 3 of IC 2391, IC 2602 and IC 4665 (35–38 Myr), and of NGC 2547 (10–45 Myr); and the individual figures for both NGC 2451 A and NGC 2451 B can be also found in Appendix E. For both NGC 2451 A and NGC 2451 B, we analysed the dependence of rotation and Hα activity with Li firstly taking into account both associated clusters, and then studying each one separately. We note that we observed the same patterns and trends in both instances (Appendix E includes all of these figures). Similarly to the rest of young clusters, for both NGC 2451 A and NGC 2451 B we observed a trend where the fastest rotating stars and the most active stars (shown in shades of purple and darker orange) tended to be located in the upper envelopes of the cluster (see Chapter 4), and generally showed higher values of EW (Li) than the slower rotating and less active stars of the same spectral types. A number of the candidates for both clusters are also slower rotating stars (shown in yellow shades), generally displaying lower values of EW (Li) than the faster rotators. We also note that the most active stars are mainly found among late K and M-type stars for both clusters. For NGC 2451 A we observed candidates with vsini values up to 60–70 km s−1, as well as Hα 158 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 activity up to 11–12 Å. On the other hand, for NGC 2451 B we observed candidates with vsini values also up to 60–70 km s−1, and Hα activity up to 9–10 Å. Finally, we note that we have omitted a star from the study of rotation for NGC 2451 A (07375005-3836495) which has an appreciably higher vsini value of 131.4 km s−1, compared to the aforementioned 60–70 km s−1 maximum value for the rest of the members of both NGC 2451 A and NGC 2451 B. This star is listed as a candidate of NGC 2451 A by all the studies listed above (Silaj & Landstreet, 2014; Spina et al., 2017; Cantat-Gaudin et al., 2018; Randich et al., 2018; Jackson et al., 2021). While remaining a candidate of the cluster, we have decided not to include in the analysis of rotation: partly because we were not certain about the reliability of the vsini value for this star, and also as it would significantly affect the range of the auxiliary colour-coded axis for the rest of candidates. B.2 Intermediate-age clusters (age= 50–700 Myr) ∗ NGC 6405 Figure B.6: NGC 6405, a 94 Myr intermediate-age cluster. Credit: AURA, NOAO, NSF. NGC 6405 (also known as M6) is a moderately-rich 80–100 Myr cluster (Kılıçoğlu et al., 2016; Netopil et al., 2016; Gao, 2018; Jackson et al., 2021), located between the local arm and the Sagit- tarius arm of the Galaxy at a distance of 0.40–0.48 kpc (Kharchenko et al., 2005; Kılıçoğlu et al., 2016; Mel’nik & Dambis, 2017; Gao, 2018). In our sample there are 701 stars in the field of NGC 6405, of which 498 have measured values of EW (Li). The membership analysis resulted in 251 RV candidates, 80 astrometric candidates, 53 Li candidates, and 51 final members (see Table 2.8). Of the final 53 Li candidates we discarded two stars: one of them we could not analyse using the astrometric and photometric Gaia data, and it was additionally listed as a clear non-member by Jackson et al. (2021). The remaining one was similarly listed as a non-member by both Cantat-Gaudin et al. (2018) and Jackson et al. (2021), and it was also a marginal non-member according to our parallax criterion. Regarding other membership selections from the literature, we found 46 stars in common with Cantat-Gaudin et al. (2018), and 45 star in Gao (2018). Jackson et al. (2021) includes 50 out of our 51 candidates. The remaining one is listed with P=0.28. Seeing as it fully fulfilled all our criteria, including Gaia astrometry, we accepted it as a final member. B.2. Intermediate-age clusters (age= 50–700 Myr) 159 As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for NGC 6405 can be found in Appendix E. Regarding rotation, we observed a clear trend where faster rotating stars tended to trace the upper Li envelope, showing higher values of EW (Li) than the slower rotating stars of the same spectral types. For this cluster we found candidates with vsini values up to only 40–50 km s−1. There are very few values of Hα activity measured for this cluster in the iDR6 file, not enough to discern a definite pattern, and all of them have low values up to 0.60 Å. ∗ Blanco 1 Blanco 1 is a nearby relatively young cluster with an age in the range 90–150 Myr (Gillen et al., 2020; Zhang et al., 2020; Jackson et al., 2021; Pang et al., 2021; Romano et al., 2021), lo- cated towards the South Galactic Pole at a distance of 0.23–0.24 kpc (Platais et al., 2011; Gillen et al., 2020; Zhang et al., 2020). Bossini et al. (2019) calculated an age estimation of 94±5 Myr, while studies based on the LDB method give slighter higher ages: 114 ± 10 Myr (Juarez et al., 2014) and 132 ± 24 Myr Cargile et al. (2010). Blanco 1 has been studied in a variety of ways, covering its photometric, spectroscopic and kinematic properties, as well as measuring the X-ray luminosities of its members. Due to its late discovery and location in the Southern Hemisphere, however, few studies were made of its proper motions (Platais et al., 2011). In addition, due to its low population, this cluster has not been as well studied as others nearby clusters, despite its proximity (Zhang et al., 2020). In our sample there are 463 stars in the field of Blanco I, of which 404 have measured values of EW (Li). The membership analysis resulted in 142 RV candidates, 119 astrometric candidates, 101 Li candidates, and 98 final members (see Table 2.8). Of the final 101 Li candidates we dis- carded three stars because we were not able to analyse them using astrometric and photometric Gaia data, and they were listed as non-members with P=0.00 by Jackson et al. (2021). As for kinematics, nine stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating 4–8 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted them as final members, as they fulfilled the rest of membership criteria, and all stars were also listed as high-probability members by Jackson et al. (2021). On the other hand, we have also accepted as final candidates two stars with no measured RV values in iDR6, due to the fact that they fully fulfil the astrometry criteria (as well as the other criteria), and are also listed as members by several studies (Platais et al., 2011; Zhang et al., 2020; Jackson et al., 2021). Regarding previous membership selections from the literature, we found 58 stars in com- mon with Platais et al. (2011), one star in Juarez et al. (2014), and 80 stars in Zhang et al. (2020). Finally, Jackson et al. (2021) includes 92 out of our 98 candidates. Four of the remaining ones were not included in their study, one is listed with P=0.37, and the last one is listed as a non-member with P=0.00. The latter two stars fully fulfil all our membership criteria, so we accepted them as final members. As in the case of IC 4665, it is probable that the reason for these individual deviations between our two analyses originated from the existing differences regard- ing criteria limits or the weight of the factors implicated in the decision to accept or discard stars. As to the influence of rotation and activity on Li, for a detailed discussion of this age range 160 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for Blanco 1 can be found in Appendix E. Like NGC 2516, Blanco 1 is a ZAMS-age cluster with an age similar to the Pleiades (e.g., Fritzewski et al., 2020, 2021). Regarding rotation, we observed a trend where faster ro- tating stars tended to trace the upper Li envelope, showing higher values of EW (Li) than the slower rotating stars of the same spectral types. The stars tracing the lower Li envelope of the cluster (see Chapter 4) show lower values of vsini as well. For this cluster we found candidates with vsini values up to only 50–60 km s−1. We could observe the same pattern in the case of Hα activity, with the most active stars mainly displaying higher values of EW (Li) and tracing the upper envelope for this cluster. The stars with the highest values of Hα are to be found among M-type stars, with the maximum value at 14–15 Å. ∗ NGC 6067 At a distance of 1.4–1.7 kpc (Kharchenko et al., 2005; Mel’nik & Dambis, 2017), NGC 6067 is a densely populated open cluster superimposed on the Norma star cloud, with an age in a 60–150 Myr range, with the most recent studies citing ages of 100–120 Myr (Frinchaboy & Ma- jewski, 2008; Netopil et al., 2016; Alonso-Santiago et al., 2017; Magrini et al., 2018; Rangwal et al., 2019; Randich et al., 2020; Jackson et al., 2021; Romano et al., 2021). In our sample there are 780 stars in the field of NGC 6067, of which 343 have measured values of EW (Li). The membership analysis resulted in 209 RV candidates, 126 astrometric candidates, 60 Li candidates, and 56 final members (see Table 2.8). Of the final 60 Li candidates we discarded four stars following the criterion we have applied in the case of all clusters in the sample: for these stars we were not able to analyse them using astrometric and photometric Gaia data, and they were further listed as non-members with P=0.00 (for two stars) and P=0.19–0.36 by Jackson et al. (2021). As for kinematics, two stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating 13–14 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted them as final members, as they fulfilled the rest of membership criteria, and all stars were also listed as high-probability members by Jackson et al. (2021). In addition, we have also accepted as a final candidate one star which fulfilled all criteria except for metallicity, having a [Fe/H] value deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed in Sect. 2.2.5, however, we have decided to list it as a final candidate, and it is additionally listed as a member by Cantat-Gaudin et al. (2018) and Jackson et al. (2021). Regarding previous membership selections from the literature, we found three stars in com- mon with Frinchaboy & Majewski (2008), eight stars in Alonso-Santiago et al. (2017), and 42 stars in Cantat-Gaudin et al. (2018). Jackson et al. (2021) includes all 56 of our final candidates. As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for NGC 6067 can be found in Appendix E. The faster rotating stars are mainly found among the F-type candidates, with vsini values up to 100 km s−1, and we also found that the faster rotators in a lesser range up to 60 km s−1 tended to have higher values of EW (Li). There are only two values of Hα measured for this cluster in the iDR6 file, with low values up to 0.24–0.25 Å. While we were not able to B.2. Intermediate-age clusters (age= 50–700 Myr) 161 discern a pattern, the most active stars out of the two also presented the highest value of EW (Li). ∗ NGC 6649 NGC 6649 is a compact and heavily-reddened (E(B-V)=1.43± 0.05 Myr) open cluster with an age in a 50–126 Myr range, close to the age of the Pleiades, with the most recent studies citing ages of 120 Myr (Kharchenko et al., 2005; Dib et al., 2018; Liu & Pang, 2019; Alonso- Santiago et al., 2020; Jackson et al., 2021), located in the first Galactic quadrant at a distance of 1.6–1.8 kpc (Dib et al., 2018; Alonso-Santiago et al., 2020). In our sample there are 283 stars in the field of NGC 6649, of which 62 have measured values of EW (Li). The membership analysis resulted in 34 RV candidates, 20 astrometric candidates, 3 Li candidates, and two final members (see Table 2.8). Of the final 3 Li candidates we discarded one star we were not able to analyse them using astrometric and photometric Gaia data, and which was listed as a non-member with P=0.00 by Jackson et al. (2021). As for kinematics, one star in our final selection was a RV non-member according to the initial 2σ interval, with a RV value deviating 10 km s−1 from the mean of the cluster. We accepted it as a final member, as it fulfilled the rest of membership criteria, and was also listed as a high-probability member by Jackson et al. (2021). Regarding previous membership selections from the literature, we found no stars in common with Cantat-Gaudin et al. (2018), and one star out of our two final candidates in common with Jackson et al. (2021) (the other one was not included in their study). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for NGC 6649 can be found in Appendix E. For this cluster we were not able to study any trends or correlations of EW (Li) with rotation and activity, due to the final selection only consisting of two stars, neither of them having Hα measurements, and only of one them having a vsini value reported in the iDR6 file. The aforementioned star, however, is a relatively fast rotating F star with 58.1 km s−1, which would fit the behaviour expected for the age of this cluster. ∗ NGC 2516 NGC 2516 is an open star cluster in the southern constellation of Carina, at a distance in the range of 0.39–0.41 kpc (Jeffries et al., 2001; Dias et al., 2002).The age of 251 ± 3 Myr in Bossini et al. (2019) is older than the previous age estimates ranging from 110 to 150 Myr (e.g., Jacobson et al., 2016; Magrini et al., 2017; Fritzewski et al., 2020; Randich et al., 2020; Dumont et al., 2021b; Franciosini et al., 2021; Jackson et al., 2021; Binks et al., 2022, in prep.). Although this name usually refers to IC 2602, this cluster has also been named the "Southern Pleiades" (Sung et al., 2002) given their similar ages and the presence of many bright stars in both clusters. NGC 2516 is of interest because of its richness, with a mass about twice that of the Pleiades (Terndrup et al., 2002), and also because of its slightly sub-solar metallicity of −0.06± 0.05 dex (Jacobson et al., 2016; Fritzewski et al., 2020). In the GES sample there are 759 stars in the field of NGC 2516, of which 677 have measured EW (Li) values. The membership analysis resulted in 460 RV candidates, 378 astrometric can- didates, 379 Li candidates (in addition to four possible Li members, see below), and 376 final 162 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 members (see Table 2.8). Of the final 379(383) Li candidates we discarded seven stars which we were not able to analyse using astrometric and photometric Gaia data, and all of them were further listed as non-members with P=0.00–0.10 by Jackson et al. (2021). The four stars we have classified as possible Li members (marked as ‘Y?’ in the table of Appendix D) present values of EW (Li) slightly larger than the rest of candidates (300–325 mÅ), especially regarding what we could expect from the age of the cluster. However, they do not exhibit appreciable dispersion with respect to the other members, all four stars fulfil the rest of membership criteria, and all of them are also listed as high probability members by Jackson et al. (2016), and so we have accepted them as final members of the cluster. Furthermore, we can also explain the higher observable values of EW (Li) of these stars considering the fact that they also exhibit either higher values of rotation and/or higher values of chromospheric activity (see more on rotation and activity in regards to this cluster at the end of this note, and in the individual figures of Appendix E). The effects of both rotation and activity could thus explain that these stars are members of NGC 2516 exhibiting a slower rate of Li depletion in result to the effects of rotation and activity. As for kinematics, 23 stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating 5–8 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted them as final members, as they fulfilled the rest of membership criteria, and all stars were also listed as high-probability members with P=0.99–1.00 by Jackson et al. (2021). In addition, we have also accepted as final candidates eight stars which fulfilled all criteria except for metallicity, having a [Fe/H] value deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed, however, we have decided to list them as members, and all of them are additionally listed as candidates of the cluster by both Randich et al. (2018) and Jackson et al. (2021). Regarding previous membership selections from the literature, we found the following num- ber of common stars with our selection in a series of both non-GES and GES studies: Firstly, we found 326 stars in Jeffries et al. (2001), 25 stars in Terndrup et al. (2002), 55 stars in Irwin et al. (2007), 44 stars in Jackson & Jeffries (2010), six stars in Wright et al. (2011), and two stars in Heiter et al. (2014). As for GES studies, we found 56 common stars in Jacobson et al. (2016), 15 stars in Jackson et al. (2016), 13 stars in Magrini et al. (2017), 49 stars in Bailey et al. (2018), 210 stars in Cantat-Gaudin et al. (2018), 332 stars in Randich et al. (2018), and 226 stars in Fritzewski et al. (2019). Finally, Jackson et al. (2021) includes 373 out of our 379 candidates (the remaining six stars were not included in their analysis). We also note that, in order to further reinforce the membership of the stars in the field of this cluster, we have also made use of the additional non-GES members with EW (Li) values of Jeffries et al. (1998). Regarding the influence of rotation and activity on Li, we mainly refer to the discussion in Chapter 3 for a detailed account for this cluster, and the individual figures are further shown in Appendix E. In our earlier work on this cluster (Gutiérrez Albarrán et al., 2020), we also briefly discussed a series of late K and M-type stars among our candidates in the 3500–4000 K tem- perature range with high values of Li, listed as members by a series of former studies (Jeffries et al., 1998; Irwin et al., 2007; Jackson & Jeffries, 2010; Jackson et al., 2016). We suggested that these stars, many of which appeared to be chromospherically active, might be lower mass, lower luminosity PMS stars which had not yet depleted most of their original Li content, and so could be used to study the LDB for this cluster (Pallavicini et al., 1997; Jackson & Jeffries, 2010). However, due to our more detailed study (see especially Chapter 4), we now discard B.2. Intermediate-age clusters (age= 50–700 Myr) 163 that possibility: according to evolutionary models such as Baraffe et al. (2015), at a Teff=4400– 4500 K, approximately, K-M stars are already expected to show negligible EW (Li) values until the emergence of stars with undepleted Li in the LDB, which for the age of this cluster would occur at about Teff=2900 K. Seeing as the coolest temperature in our sample for this cluster is Teff=3186 K, we cannot observe the LDB for NGC 2516 with the available data from GES iDR6, and thus we discard the possibility that these K-M stars with higher levels of EW (Li) may be PMS stars representative of the LDB for this cluster. For NGC 2516 we observed candidates with vsini values up to 100–110 km s−1 and Prot values as long as 12–13 d, as well as Hα activity up to 5 Å. We also note that we initially discarded a star (07571035-6101134) from our analysis of rotation due to its notably large value of vsini (280 km s−1, compared to the aforementioned 100–110 km s−1 maximum value for the rest of the members of the cluster. We now believe that The vsini value for this star seems to suffer from an accidental error in the iDR6 file, as other studies such as Jackson et al. (2016) cite the vsini value of this star as 26.2 km s−1, and thus we think it possible that the corresponding iDR6 measurement is actually 28.0 km s−1 instead of 280 km s−1. ∗ NGC 6709 At a distance of 1.1–1.2 kpc (Kharchenko et al., 2005; Vande Putte et al., 2010), NGC 6709 is a moderately rich open cluster situated towards the center of the Galaxy in the constellation Aquila, with an age in a 150–190 Myr range (Subramaniam & Sagar, 1999; Vande Putte et al., 2010; Jackson et al., 2021; Romano et al., 2021). Bossini et al. (2019) calculated an age estima- tion of 173± 34 Myr. In our sample there are 730 stars in the field of NGC 6709, of which 600 have measured values of EW (Li). The membership analysis resulted in 322 RV candidates, 71 astrometric candidates, 53 Li candidates, and 49 final members (see Table 2.8). Of the final 53 Li candidates we discarded four stars which we were not able to analyse using astrometric and photometric Gaia data, and all four of them were also listed as non-members with P=0.00 by Jackson et al. (2021).Regarding previous membership selections from the literature, we found 45 stars in com- mon with Cantat-Gaudin et al. (2018), and Jackson et al. (2021) includes 46 out of our 49 of final candidates. Of the remaining three, two stars were not included in their study, and the last one is listed with P=0.31. Given that said star fully fulfils our membership criteria, including astrometry, we included it in our final selection. As already discussed in Sect. 2.3, we also note that we seem to find some inconsistencies when plotting the Li-rich giant outliers selected in the field of this cluster in the CMD diagram, with two of them, for example, appearing very close among the non-giant cluster candidates. However, when plotting them in the Kiel diagram the expected distinction is found between the non-giant cluster candidates and the Li-rich giant outliers. We plan on studying all Li-rich giant outliers in more detail in order to gain further confirmation on their nature as Li-rich giant contaminants (see the future work in Chapter 5). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for NGC 6709 can be found in Appendix E. We observed a trend (albeit less distinct than in other clusters in this age range, due to the lack of a sufficient number of cluster candidates), where faster rotating stars tended 164 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 to trace the upper Li envelope (see Chapter 4). The fastest rotators can be found among F-type stars, as expected in this age range, while the G-K stars are mainly slower rotators. There are only two values of Hα activity measured for this cluster in the iDR6 file, but we do see that the most active star had a higher EW (Li) value, also tracing the upper Li envelope for the cluster. For this cluster we found candidates with vsini values up to only 80–90 km s−1, as well as Hα activity up to 0.45–0.50 Å. Finally, we also note that we have omitted a star (18505284+1020021) from the study of rotation for this cluster with an appreciably higher vsini value of 140 km s−1, compared to the aforementioned 80–90 km s−1 maximum value for the rest of the members of NGC 6709. This star fulfilled all membership criteria and is listed as a candidate of the cluster by all the studies listed above (Cantat-Gaudin et al., 2018; Jackson et al., 2021), including being marked as a high probability member by Jackson et al. (2021). While remaining a cluster candidate, we have decided not to include it in the analysis of rotation: partly because we were not certain about the reliability of the vsini value for this star, and also as it would significantly affect the range of the auxiliary colour-coded axis for the rest of candidates. ∗ NGC 6259 NGC 6259 is an open cluster with an age of 210 Myr (Sampedro et al., 2017; Magrini et al., 2018; Casali et al., 2019; Randich et al., 2020; Jackson et al., 2021), located at a distance of 1.9 kpc (Kharchenko et al., 2005; Vande Putte et al., 2010). In our sample there are 494 stars in the field of NGC 6259, of which 278 have measured values of EW (Li). The membership analysis resulted in 125 RV candidates, 71 astrometric can- didates, 39 Li candidates, and 35 final members (see Table 2.8). Of the final 39 Li candidates we discarded four stars which we were not able to analyse using astrometric and photometric Gaia data, and which were listed as non-members with P=0.00 by Jackson et al. (2021). Regarding previous membership selections from the literature, we found 20 stars in common with Cantat- Gaudin et al. (2018), and 34 out of our 35 members in Jackson et al. (2021). The remaining star in our final selection is listed in the latter study with P=0.32. Seeing as it fully fulfils all our membership criteria, we accepted it as a final member. As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for NGC 6259 can be found in Appendix E. We observed a trend (albeit less distinct than in other clusters in this age range, due to the lack of a sufficient number of cluster candidates), where faster rotating stars tended to trace the upper Li envelope (see Chapter 4). The fastest rotators can be found among F-type stars, as expected in this age range, while all G-K candidates are slow rotators. There is only one value of Hα activity measured for this cluster in the iDR6 file, and so we were not able to discern any trends or correlations for this cluster. For NGC 6259 we found candidates with vsini values up to only 90–100 km s−1, as well as Hα activity up to 1.2 Å. Finally, we also note that we have omitted a star (17003526-4439043) from the study of ro- tation for this cluster with an appreciably higher vsini value of 200 km s−1, compared to the aforementioned 90–100 km s−1 maximum value for the rest of the members of NGC 6259. This star fulfilled all membership criteria and is listed as a candidate of the cluster by all the studies listed above (Cantat-Gaudin et al., 2018; Jackson et al., 2021), including being marked as a high B.2. Intermediate-age clusters (age= 50–700 Myr) 165 probability member by Jackson et al. (2021). While remaining a cluster candidate, we have decided not to include it in the analysis of rotation: partly because we were not certain about the reliability of the vsini value for this star, and also as it would significantly affect the range of the auxiliary colour-coded axis for the rest of candidates. ∗ NGC 6705 Figure B.7: NGC 6705, a 280 Myr intermediate-age cluster. Credit: ESO. At a distance of 1.88 kpc (Dias et al., 2002; Kharchenko et al., 2005), NGC 6705 (also known as M11) is a massive and concentrated open cluster in the constellation Scutum, one of the richest and most compact of the known open clusters. NGC 6705 has an estimated age of 280–300 Myr (Jacobson et al., 2016; Magrini et al., 2017; Randich et al., 2020; Jackson et al., 2021; Romano et al., 2021), and was one of the three intermediate-age open clusters included in the first internal data release of GES (Cantat-Gaudin et al., 2014; Tautvaišienė et al., 2015). NGC 6705 is located in a clear area suffering from relatively little extinction. That and its location inside the solar circle makes it an important tracer of the inner disc abundance gradient (Cantat-Gaudin et al., 2014). In our sample there are 1066 stars in the field of NGC 6705, of which 610 have measured values of EW (Li). The membership analysis resulted in 391 RV candidates, 313 astrometric can- didates, 142 Li candidates, and 139 final members (see Table 2.8). Of the final 142 Li candidates we discarded three stars which we were not able to analyse using astrometric and photometric Gaia data, and which were further listed as non-members by Jackson et al. (2021). As for kinematics, eight stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 10–13 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted them as final members, as they fulfilled the rest of membership criteria, and all stars were also listed as high-probability members by Jackson et al. (2021). In addition, we have accepted as a final candidate one star which fulfilled all criteria except for metallicity and log g. As discussed in Sects. 2.2.4 and 2.2.5, however, we have decided to list it as a final candidate, and it is additionally listed as a member by Cantat-Gaudin et al. (2018) and Jackson et al. (2021). Comparing our final selection with existing membership studies from the literature for this cluster, we found the following number of common stars with a number of studies: Firstly, we 166 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 found 21 common stars in Magrini et al. (2014), as well as 27 stars in Tautvaišienė et al. (2015) and Jacobson et al. (2016), 15 stars in Sampedro et al. (2017) and Magrini et al. (2017), and 44 stars in Cantat-Gaudin et al. (2018) and 11 in Casamiquela et al. (2018). Finally, Jackson et al. (2021) includes 136 out of our final 139 candidates (the remaining three stars in our selection were not included in their study). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for NGC 6705 can be found in Appendix E. We observed a trend (albeit less distinct than in other clusters in this age range, due to the lack of a sufficient number of cluster candidates), where faster rotating stars tended to trace the upper Li envelope (see Chapter 4). Most of the fastest rotators are F-type stars for this cluster, as expected in this age range, while all G-K candidates are slow rotators. Several fast rotating F candidates have high vsini values up to 160 km s−1, comprising the largest values of vsini in the whole intermediate-age cluster range of our sample. There are only a small number of stars in our selection with Hα activity values in the iDR6 file (low values up to 0.30–0.40 Å), and so we were not able to discern any significant trends or correlations for this cluster. We can note, however, that of these stars the ones with the highest values of EW (Li) were also among the most active stars. ∗ Berkeley 30 Berkeley 30 is an open cluster with an age of 300–313 Myr (Kharchenko et al., 2005; Sampe- dro et al., 2017; Jackson et al., 2021; Romano et al., 2021), located at a distance of 4.7–4.9 kpc (Kharchenko et al., 2005; Sampedro et al., 2017). In our sample there are 332 stars in the field of NGC 6067, of which 157 have measured values of EW (Li). The membership analysis resulted in 78 RV candidates, 44 astrometric candidates, and 24 Li candidates, all of which are final members for the cluster (see Table 2.8). We also note that we have accepted as final candidates two stars which fulfilled all criteria except for metallicity, having [Fe/H] values deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed in Sect. 2.2.5, however, we have de- cided to list them as final members as they fulfil all other criteria (including the more restrictive criteria in our analysis), and both of them are additionally listed as members by Cantat-Gaudin et al. (2018), and by Jackson et al. (2021), with P=0.94–0.99. Regarding previous membership selections from the literature, we found five stars in common with Cantat-Gaudin et al. (2018), and Jackson et al. (2021) includes all 24 of our final candidates. As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for Berkeley 30 can be found in Appendix E. Due to the lack of a sufficient number of cluster candidates, it is difficult to discern a trend or pattern. The fastest rotators are F-type stars for this cluster, as expected in this age range, with vsini values up to 70 km s−1. There are no Hα activity values recorded in the iDR6 file for Berkeley 30. Finally, we also note that we have omitted a star (06575489+0314159) from the study of rotation for this cluster with a notably higher vsini value of 281.7 km s−1, compared to the aforementioned 70 km s−1 maximum value for the rest of the members of NGC 6259. This B.2. Intermediate-age clusters (age= 50–700 Myr) 167 star fulfilled all membership criteria and is listed as a candidate of the cluster by all the studies listed above (Cantat-Gaudin et al., 2018; Jackson et al., 2021), including being marked as a high probability member by Jackson et al. (2021). While remaining a cluster candidate, we have decided not to include it in the analysis of rotation: partly because we were not certain about the reliability of the vsini value for this star, and also as it would significantly affect the range of the auxiliary colour-coded axis for the rest of candidates. ∗ NGC 6281 At a distance of 0.47–0.51 kpc (Kharchenko et al., 2005; Joshi et al., 2016; Sampedro et al., 2017), NGC 6281 is an open cluster with an age of 314–316 Myr (Dias et al., 2002; Joshi et al., 2016; Sampedro et al., 2017; Jackson et al., 2021). In our sample there are 320 stars in the field of NGC 6281, of which 221 have measured values of EW (Li). The membership analysis resulted in 82 RV candidates, 38 astrometric candidates, and 23 Li candidates, all of which are final members for the cluster (see Table 2.8). We note that we have accepted as a final candidate a star which fulfilled all criteria except for metallicity, having a [Fe/H] value deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. Similarly to the case of many clusters, we have decided to list it as a final member as it fulfilled all other criteria, and it is additionally listed as a candi- date of NGC 6281 by Cantat-Gaudin et al. (2018), and by Jackson et al. (2021), with P=0.98. As for kinematics, another star in our final selection was a RV non-member according to the initial 2σ interval, with a RV value deviating 5 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we also accepted it as a final member, because it fulfilled the rest of membership criteria, and was also listed as a high-probability member by Jackson et al. (2021). Regarding previous membership selections from the literature, we found the following number of stars in common with several studies: Firstly, we found two stars in common with Frinchaboy & Majewski (2008) and Heiter et al. (2014), as well as 19 common stars in Cantat-Gaudin et al. (2018). Finally, Jackson et al. (2021) includes all 23 of our final candidates. As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for NGC 6281 can be found in Appendix E. Due to the lack of a sufficient number of cluster candidates, it is difficult to discern a trend or pattern, although we note that the selection for this cluster does not include any F-type stars, while all the G-type stars present upper limit values for vsini, and the fastest rotators in the selection were found among the K-type candidates, with low vsini values up to 9.5 km s−1. There are no Hα activity values recorded in the iDR6 file for NGC 6281. ∗ NGC 3532 Located in a crowded Galactic field in Carina, NGC 3532 is a very rich southern open cluster at a distance of 0.48–0.49 kpc (Kharchenko et al., 2005; Fritzewski et al., 2019). This cluster is intermediate in age between the Pleiades (78–125 Myr) and the Hyades (750 Myr), with an age estimation of 399± 5 Myr according to Bossini et al. (2019), while other studies give an age range of 300–399 Myr (Dobbie et al., 2012; Fritzewski et al., 2019; Jackson et al., 2021; Romano et al., 2021). Fritzewski et al. (2021) describe NGC 3532 as a cluster which is unique in age among the nearby open clusters, and further provides a very large stellar population, which en- 168 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 Figure B.8: NGC 3532, a 399 Myr young cluster. Credit: ESO/G. Beccari. ables detailed studies of several aspects, such as stellar rotation and the evolution of fast rotators. In our sample there are 1145 stars in the field of NGC 3532, of which 860 have measured values of EW (Li). The membership analysis resulted in 518 RV candidates, 411 astrometric candidates, 323 Li candidates, in addition to 72 stars presenting what we think are overesti- mated values of EW (Li) (see below for a more detailed discussion), and 384 final members (see Table 2.8). Of the final 323 Li candidates we discarded a small number of stars according to the following criteria: Firstly, we discarded seven stars which we were not able to analyse using as- trometric and photometric Gaia data, and which were further listed as non-members by Jackson et al. (2021). We also discarded one SB2 star, as well as another star we also could not analyse with astrometric criteria and deviated appreciably in the Kiel diagram. Lastly, we discarded two final stars with no Gaia data analysis available which was marked as a non-member by Fritzewski et al. (2019). As for kinematics, we note that 42 stars in our final selection were RV non-members ac- cording to the initial 2σ interval, with RV s deviating up to 8–11 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted all of them as final members, as they fulfilled the rest of membership criteria, and all 42 stars were also listed as high-probability members by Jackson et al. (2021). In addition, we have also accepted as final candidates two stars which fulfilled all criteria except for metallicity, having [Fe/H] values deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. Both stars are additionally listed as members by Jackson et al. (2021) with P=0.99. We will now discuss the 72 stars that we have classified as possible Li members (marked as ‘Y?’ in the table of Appendix D). We believe that all these stars show overestimated levels of EW (Li) on the iDR6 file, potentially caused by the inherent difficulty of obtaining accurate Li measurements for K-M type stars in this age range (also see Sect. 2.2.6). We however consider all these stars to be probable members of NGC 3532, given that i) They do not exhibit appreciable dispersion with respect to each other or the other members, and so we consider it improbable that all 93 stars are spurious outliers; ii) All of them consistently fulfil the rest of membership B.2. Intermediate-age clusters (age= 50–700 Myr) 169 criteria (including kinematics, astrometry, gravity and metallicity criteria); and iii) All of them are listed as high probability members by Jackson et al. (2016) with P=0.97–1.00, and several appear as candidates in other studies as well (Cantat-Gaudin et al., 2018; Fritzewski et al., 2019, 2021). We do consider that the EW (Li) values of these stars are not representative of the age of this cluster, as we will further summarize below, and thus they are marked as open squares in all EW (Li)-versus-Teff diagrams to differentiate them from the rest of the candidates (see Sect. 2.4 and Appendix C), and we have also decided not to take them into account when creating the empirical envelope for this cluster (see Chapter 4). These 72 stars are late-K and M type stars with Teff < 4100 K, and all of them consistently present values of EW (Li) which are considerably larger than we would expect for K-M stars in NGC 3532, a cluster with an age of 300–399 Myr. As discussed in Chapter 4 when creating the empirical envelope for this cluster with the aid of models such as Baraffe et al. (2015), at a Teff=4400–4500 K, K and M type stars are already expected to show negligible EW (Li) values until the emergence of stars with undepleted Li in the LDB, which for the age of this cluster would occur at about Teff=2500 K. Seeing as the coolest temperature in our sample for this clus- ter is Teff=3000 K, we can confidently discard the potential explanation that these K-M stars with higher levels of EW (Li) are representative of the LDB for this cluster. Another way with which we could potentially explain the higher EW (Li) values for these stars involves the study of their levels of rotation and activity (see Chapter 3 and the end of this individual note for more details in activity and rotation for this cluster). As we have al- ready seen in the case of clusters such as NGC 2516, we can explain higher observable values of EW (Li) considering the fact that they might exhibit either higher values of rotation and/or higher values of chromospheric activity. Due to the Li-rotation and Li-activity anti-correlations (see Chapter 1.1), these stars would consequently deplete lithium in a slower rate than their less active and/or slower rotating counterparts, and thus would exhibit higher values of EW (Li) as a result. Studies such as Pallavicini et al. (1990) concluded that, while less common, this effect can also be observed in K-type stars in older clusters with intermediate ages between the Pleiades (78–125 Myr) and the Hyades (750 Myr), such as both NGC 3532 (399 Myr) and NGC 6633 (575 Myr). As detailed at the end of this individual note and in Chapter 3, this cluster does indeed include a series of K-type stars exhibiting high rotation and chromospheric activity. Thus, these faster rotators and the more active stars could have consequently depleted Li more slowly, resulting in higher EW (Li)s than would be expected for late K-type stars at this age. However, we do not believe that we can explain the higher EW (Li) values of all 93 K-M stars in this way. Firstly, there is the fact that not all of them exhibit sufficiently high rotations and activity to be able to explain their observable Li as a consequence of these effects. Many of them are actually among the slowest rotating stars in the final selection for this cluster. And even so, we could confidently explain higher observable EW (Li) for certain stars in these spectral types at this age due to the influence of higher rotation and activity, but we would also find it highly improbable to observe these effects to such an extent for so many stars. We also note that we encounter a very similar problem with another intermediate age cluster with an age in-between the Pleiades and the Hyades, NGC 6633 (575 Myr), which could reinforce our conclusion that EW (Li)s in the case of these two clusters were accidentally overestimated during GES data processing. As another note of interest, many of these stars were not included in the iDR4 sample we used for the analysis in Gutiérrez Albarrán et al. (2020), potentially 170 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 because of the difficulty of measuring the EW (Li) of K-M stars with accuracy for clusters in this age range. Regarding previous membership selections from the literature, we found the following number of stars in common with these studies: Firstly, we found one star in common with Heiter et al. (2014), as well as 310 stars in Cantat-Gaudin et al. (2018), 216 stars in Fritzewski et al. (2019), 27 stars in Hetem & Gregorio-Hetem (2019), and 132 stars in Fritzewski et al. (2021). Finally, Jackson et al. (2021) includes 382 out of our 384 final candidates (the remaining two stars in our final selection were not included in their study). As to the influence of rotation and activity on Li, we mainly refer to the discussion in Chap- ter 3 for a detailed account for the rotation of this cluster. Regarding Hα activity (as shown in the individual figures of Appendix E), we observe a similar trend to the one discussed in Sect. 3.2 for NGC 2516, albeit somewhat less defined, with the most active stars mainly displaying higher values of EW (Li) and tracing the upper envelope for this cluster. As in the case of rotation, we note that we have not taken into account the K-M stars classified as possible Li members (marked as open squares in the individual figures of Appendix E), as we believe that the EW (Li) values of these stars are not representative of the age of this cluster. In the case of the study of activity, we have additionally seen that adding the possible lithium members significantly affected the range of the auxiliary colour-coded axis for the rest of candidates. ∗ NGC 4815 NGC 4815 is a heavily populated open cluster with an age of 500–570 Myr (Friel et al., 2014; Jacobson et al., 2016; Magrini et al., 2017, 2018; Jackson et al., 2021) in the southern constel- lation of Musca, at a distance in the range of 2.4–2.9 kpc (Dias et al., 2002; Friel et al., 2014). NGC 4815 was one of the intermediate-age open clusters which were observed during the first six months of GES, and had not been observed spectroscopically before then (Friel et al., 2014; Tautvaišienė et al., 2015). Its location inside the solar circle makes it an important tracer of the abundance gradient in the inner regions of the Galaxy, where few intermediate-age clusters are found (Friel et al., 2014). This crowded cluster, however, suffers from a significant field star con- tamination and high and variable reddening (Friel et al., 2014), factors which complicate its study. In our sample there are 218 stars in the field of NGC 4815, of which 104 have measured values of EW (Li). The membership analysis resulted in 68 RV candidates, 50 astrometric candidates, 30 Li candidates, and 29 final members (see Table 2.8). Similarly to our analysis of others clusters in the sample, of the final 30 Li candidates we discarded one star for not being able to analyse it using astrometric and photometric Gaia data, and because it was additionally listed as a non-member by Jackson et al. (2021). As for kinematics, five stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 14 km s−1 from the mean of the cluster. We accepted all of them as final members as they fulfilled the rest of membership criteria, and all stars were also listed as high-probability members by Jackson et al. (2021). Regarding previous membership selections from the literature, we found the following num- ber of stars in common with several studies: Firstly, we found five stars in common with Friel et al. (2014), Magrini et al. (2014), Tautvaišienė et al. (2015) and Jacobson et al. (2016), as well as three common stars in Magrini et al. (2017), and seven stars in Cantat-Gaudin et al. (2018). Finally, Jackson et al. (2021) includes all 29 of our final candidates. We also note that B.2. Intermediate-age clusters (age= 50–700 Myr) 171 two of the final candidates in our sample (12572442-6455173 and 12575818-6459323) show higher values of EW (Li) compared to the other candidates, showing more dispersion with respect to the rest of the cluster members as well. Fulfilling the rest of criteria, these stars seem to be Li-rich (non-giant) members, and are included as candidates of the cluster by a series of previous studies (Magrini et al., 2014; Tautvaišienė et al., 2015; Jacobson et al., 2016; Jackson et al., 2021). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for NGC 4815 can be found in Appendix E. Due to the lack of a sufficient number of cluster candidates, it is difficult to discern a trend or pattern for this cluster, although we note that the fastest rotators are F-type stars for this cluster, as expected in this age range, with vsini values up to 80 km s−1. There are no Hα activity values recorded in the iDR6 file for Berkeley 30. Finally, we also note that we have omitted four stars from the study of rotation for this cluster. These stars display appreciably higher vsini values up to 181 km s−1, compared to the aforementioned 80 km s−1 maximum value for the rest of the members of NGC 4815. These stars fulfilled all membership criteria and are listed as candidates of the cluster by all the studies listed above (Cantat-Gaudin et al., 2018; Jackson et al., 2021), including being marked as high probability members by Jackson et al. (2021). While remaining cluster candidates, we have de- cided not to include in the analysis of rotation: partly because we were not certain about the reliability of these vsini measurements for these stars (also judging by the range of vsini values for other clusters from the sample which are close in age), and also because adding them to the figure significantly affected the range of the auxiliary colour-coded axis for the rest of candidates. ∗ NGC 6633 At a distance of 0.39 kpc (Dias et al., 2002; Kharchenko et al., 2005), NGC 6633 is an open cluster in the constellation Ophiuchus. The age estimations for this cluster vary depending on the study, spanning an age range of 575–773 Myr: from 600–630 Myr (Sestito & Randich, 2005; Jacobson et al., 2016; Magrini et al., 2017), to the estimation of 773+50 −10 Myr by Bossini et al. (2019) (older than the age of the Hyades, 750 Myr), to 575 Myr in the recently published paper by Jackson et al. (2021) (younger than the age of the Hyades). On the other hand, Umezu & Saio (2000) and Jeffries et al. (2002) considered a very similar age to the Hyades for NGC 6633, and concluded that the lower metallicity of this cluster, −0.10–−0.01 dex (Jeffries et al., 2002; Jacobson et al., 2016; Magrini et al., 2018), was a factor that could explain why the EW (Li) envelope for NGC 6633 lied above the Hyades, and thus, the fact that, according to the study, Li was being depleted at a slower pace in the case of NGC 6633. We personally have interpreted the dependence of Li depletion with cluster metallicity differently, as discussed in Sect. 3.4. In our sample there are 1662 stars in the field of NGC 6633, of which 1501 have measured values of EW (Li). The membership analysis resulted in 617 RV candidates, 35 astrometric candidates, 62 Li candidates (in addition to 19 stars presenting what we think are overestimated values of EW (Li), see below for a more detailed discussion), and 67 final members (see Ta- ble 2.8). Of the final 62 Li candidates we discarded 14 stars which we were not able to analyse using astrometric and photometric Gaia data, and which were further listed as non-members by Jackson et al. (2021). Regarding kinematics and astrometry, we note that both the RV and parallax distributions 172 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 for NGC 6633 revealed a large contaminant population in the middle of the distribution, which could not be discarded with the aid of the 2σ clipping procedure (as we have done in the case of the remaining 41 clusters in the sample to identify contaminants in the tails of the distri- bution). The presence of this contaminant population significantly affected the mean RV and mean parallax rendered by the Gaussian fits, and also gave very high final dispersions even after the final convergence of the clipping procedure was reached. When comparing the final fits with the literature values (see Tables 2.4 and 2.5), we saw that taking all the contaminant RV s and parallaxes in the middle of the distributions into consideration caused the mean RV and parallax to deviate considerably from the reference estimates for this cluster and effectively affected the final cluster candidate selection well. For this reason, we decided to manually filter out this contaminant population before re-analysing the RV and parallax distributions. In this way, we obtained mean values fully consistent with the literature estimations. This step was vital in or- der to obtain a probable final list of candidate members for this cluster, seeing as we found that some of the stars in the contaminant population even seemed to fulfil the rest of criteria in spite of clearly not being part of NGC 6633 according to the kinematic and astrometric distributions (which is why kinematics and astrometry are the first criteria applied and the most restrictive in our analysis). Regarding the 19 stars which we have classified as possible Li members (marked as ‘Y?’ in the table of Appendix D), we refer to the detailed discussion in the individual note of NGC 3532, another intermediate-age cluster that showed the same issue with a larger number of stars. As in the case of this other cluster, for NGC 6633 we similarly believe that all these stars show overestimated levels of EW (Li) on the iDR6 file, potentially caused by the inherent difficulty of obtaining accurate Li measurements for K-M type stars in this age range (also see Sect. 2.2.6). We consider all these stars to be probable members of NGC 6633 for the same reasons we ac- cepted them in the case of NGC 3532, namely that i) They do not exhibit appreciable dispersion with respect to each other or the other members, and so we consider it improbable that all 19 stars would be spurious outliers; ii) All of them consistently fulfil the rest of membership criteria (including kinematics, astrometry, gravity and metallicity criteria); and iii) Six of these stars are listed as high probability members by Jackson et al. (2016) with P=0.87–1.00 (the rest of them were not included in their study), and several appear as candidates in other studies as well (Cantat-Gaudin et al., 2018; Randich et al., 2018). While the EW (Li) values of these stars are not representative of the age of this cluster, they are marked as open squares in all EW (Li)-versus-Teff diagrams to differentiate them from the rest of the candidates (see Sect. 2.4 and Appendix C), and we have also decided not to take them into account when creating the empirical envelope for this cluster (see Chapter 4). These 19 stars are late K and M type stars with Teff < 4800–5000 K, and all of them con- sistently present values of EW (Li) which are considerably larger than we would expect for K-M stars in NGC 6633 (575–630 Myr). As discussed in Chapter 4 when creating the empirical enve- lope for this cluster with the aid of models such as Baraffe et al. (2015), at a Teff=5000–5200 K KM stars are already expected to show negligible EW (Li) values until the emergence of stars with undepleted Li in the LDB, which for the age of this cluster would occur at a much cooler temperatures than 3315 K, which is the lowest Teff present in the iDR6 sample for this cluster. Thus, once again we can confidently discard the potential explanation that these K-M stars with higher levels of EW (Li) might be representative of the LDB for this cluster, as we tentatively proposed in Gutiérrez Albarrán et al. (2020). As to the influence of rotation and activity on Li, as detailed at the end of this individual B.2. Intermediate-age clusters (age= 50–700 Myr) 173 note and in Chapter 3, some of the K-M stars discussed here also exhibit high rotation (the iDR6 sample for this cluster does not offer any values of Hα). These faster rotators certainly could have consequently depleted Li more slowly, resulting in higher EW (Li)s than would be expected for K-M stars at this age. As in the case of NGC 3532, however, we do not believe that we can explain the higher EW (Li) values of all these 19 stars in this way, and in addition, there is the fact that not all of them exhibit sufficiently high rotation values in order to be able to explain their observable Li as a consequence of these effects. Regarding previous membership selections from the literature, we found the following num- ber of stars in common with these studies: Firstly, we found seven stars in common with Heiter et al. (2014), as well as eight stars in Jacobson et al. (2016), six stars in Magrini et al. (2017), 24 stars in Sampedro et al. (2017), 22 stars in Cantat-Gaudin et al. (2018), and 32 stars in Randich et al. (2018). Finally, Jackson et al. (2021) includes only 19 out of our 67 final can- didates, and all the remaining stars in our final selection were not included in their study. We also note that we reinforced the membership of our final selection by making use of the addi- tional members with EW (Li) in Jeffries (1997), Heiter et al. (2014), Magrini et al. (2017), and Sampedro et al. (2017). Finally, regarding non-members, one of the Li-rich giants in our list (J18265248+0627259) is listed in Smiljanic et al. (2018). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (90–700 Myr) we refer the reader to the detailed discussion of NGC 2516 (125–138 Myr) and NGC 3532 (300–399 Myr) in Chapter 3, and the individual figures for NGC 6633 can be found in Appendix E. We can observe a trend, albeit less distinct than in other clusters in this age range, where faster rotating stars tend to trace the upper Li envelope, and we also see the fastest rotators among F-type stars, as expected. There are very few values of Hα activity measured for this cluster in the iDR6 file, but we do see that the most active star has one of the highest values of EW (Li) among the cluster candidates for NGC 6633. As in the case of NGC 3532, we note that we have not taken into account the K-M stars classified as possible Li members only (marked as open squares in the individual figures of Appendix E), as we believe that the EW (Li) values of these stars are not representative of the age of this cluster. Thus, we have decided to forgo the study of the dispersion of their Li values with rotation or activity so as not to obtain misleading conclusions. We note that adding them to our study of rotation and activity, however, did not significantly affect the range of the colour-coded axis for the rest of the candidates. For this cluster we found candidates with vsini values up to only 24 km s−1 (appreciably lower than the rest of the intermediate-age clusters, and some of the old clusters as well), and we found low Hα activity up to 0.14 Å. Finally, we also note that we have omitted a star (18283294+0649160) from the study of rotation for this cluster with an appreciably higher vsini value of 78 km s−1, compared to the aforementioned 24 km s−1 maximum value for the rest of the members of NGC 6633. This star fulfilled all membership criteria and is listed as a candi- date of the cluster by all the studies listed earlier for this cluster (Cantat-Gaudin et al., 2018; Randich et al., 2018; Jackson et al., 2021), including being marked as a high probability member by Jackson et al. (2021). While remaining a cluster candidate, we have decided not to include it in the analysis of rotation: partly because we were not certain about the reliability of the vsini value for this star, and also as it would significantly affect the range of the auxiliary colour-coded axis for the rest of candidates. 174 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 B.3 Old clusters (age > 700 Myr) ∗ NGC 2477 Figure B.9: NGC 2477, a 700 Myr old cluster. Credit: ESO/J. Pérez. At a distance of 1.4–1.5 kpc (Kharchenko et al., 2005; Cantat-Gaudin et al., 2018; Dib et al., 2018; Gao, 2018; Rain et al., 2021), NGC 2477 is an open cluster with an age of 0.7–1.0 Gyr (Gao, 2018; Rain et al., 2021), one of the richest open clusters in the Southern sky. As such, it provides a very good statistical basis for studies of stellar and dynamical evolution in open clusters (Eigenbrod et al., 2004). In our sample there are 125 stars in the field of NGC 2477, of which only 10 have measured values of EW (Li). The membership analysis resulted in 86 RV candidates, 71 astrometric can- didates, and nine Li candidates, all of which we considered as final members (see Table 2.8). We note that we have accepted as a final candidate one star with no measured RV in iDR6, due to the fact that it fully fulfilled the astrometry criteria (as well as the other criteria), and was also listed as a member by Cantat-Gaudin et al. (2018). We have also accepted as a final candidate another star which fulfilled all criteria except for metallicity, having a [Fe/H] value deviating ap- preciably from the rest of candidates even while considering the larger 3σ membership interval. This star is additionally listed as a member by Cantat-Gaudin et al. (2018) and Jadhav et al. (2021). Regarding previous membership selections from the literature, we found three stars in com- mon with Eigenbrod et al. (2004), 10 stars in Cantat-Gaudin et al. (2018), and seven stars in Jadhav et al. (2021). We note that this is one of the three clusters out of our sample of 42 clusters which is not included in Jackson et al. (2021). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (0.7–4.5 Gyr) we refer the reader to the detailed discussion of NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), NGC 2243 (4 Gyr) and M67 (4–4.5 Myr) in Chapter 3, and the individual figures for NGC 2477 can be found in Appendix E. The fastest rotators for this cluster are late-F and G stars, as expected in this age range, albeit with low vsini values up to 10 km s−1. In spite of the small number of candidates for this cluster, we could also observe a trend in which the faster ro- tators also displayed the highest EW (Li) values. There are only four G stars with low Hα values B.3. Old clusters (age > 700 Myr) 175 up to 0.12–0.14 Å for this cluster, and so it is difficult to analyse any trends and correlations, al- though we note that the most active star out of the four is also the one with the highest EW (Li). ∗ Trumpler 23 At a distance in the range of 1.9–2.2 kpc (Dias et al., 2002; Overbeek et al., 2017), Trum- pler 23 is a well-populated open cluster with an age of about 800 Myr (Jacobson et al., 2016; Magrini et al., 2017, 2018; Overbeek et al., 2017; Jackson et al., 2021). Given its position in a crowded field close to the Galactic plane, and therefore a heavy level of field star contamination, Trumpler 23 is a relatively understudied cluster (Carraro et al., 2005; Bonatto & Bica, 2010). Given its location and super-solar metallicity, however, this cluster can be a useful key in order to probe the inner Galactic disc and determine Galactic abundance distributions (Overbeek et al., 2017). In our sample there are 165 stars in the field of Trumpler 23, of which 85 have measured values of EW (Li). The membership analysis resulted in 51 RV candidates, 41 astrometric can- didates, 25 Li candidates, and 23 final members (see Table 2.8). Of the final 25 Li candidates we discarded two stars which we were not able to analyse using astrometric and photometric Gaia data, and which were further listed as non-members with P=0.00 by Jackson et al. (2021). As for kinematics, two stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 6 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted them as final members, as they fulfilled the rest of member- ship criteria, and both stars were also listed as high-probability members by Jackson et al. (2021). Regarding previous membership selections from the literature, we firstly found nine stars in common with Jacobson et al. (2016), as well as 10 stars in Magrini et al. (2017) and Overbeek et al. (2017), and 14 stars in Sampedro et al. (2017). Finally, Jackson et al. (2021) includes all 23 of our final candidates. We note that, in spite of being listed as a non-member by Overbeek et al. (2017), we considered the UVES star 16004025-5329439 as a candidate of Trumpler 23, as op- posed to a Li-rich giant non-member, given that this star fulfilled all our membership criteria, and was listed as a member by several studies, such as Magrini et al. (2017) and Jackson et al. (2021). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (0.7–4.5 Gyr) we refer the reader to the detailed discussion of NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), NGC 2243 (4 Gyr) and M67 (4–4.5 Myr) in Chapter 3, and the individual figures for Trumpler 23 can be found in Appendix E. Due to the lack of a sufficient number of cluster candidates, it is difficult to discern a trend or pattern for this cluster, although we note that the fastest rotators are F-type stars, as expected in this age range, with vsini values up to 110 km s−1 (the highest vsini in the whole old cluster range), and we found the slowest rotating stars among the early-K candidates. There are no Hα activity values recorded in the iDR6 file for Trumpler 23. Finally, we also note that we have additionally omitted two stars from the study of rota- tion for this cluster. These stars display appreciably higher vsini values up to 180 km s−1, compared to the aforementioned 110 km s−1 maximum value, as well as the typical range up to 40–50 km s−1 for most of the fastest rotators in Trumpler 23. These stars fulfilled all membership criteria and are listed as high probability members by Jackson et al. (2021). While remaining cluster candidates, we have decided not to include in the analysis of rotation: partly because we were not certain about the reliability of the vsini measurements for these stars, and also because adding them to the figure significantly affected the range of the auxiliary colour-coded axis for 176 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 the rest of candidates. ∗ Berkeley 81 Berkeley 81 (also known as Br 81 or Be 81), located at a distance of 3 kpc (Dias et al., 2002; Donati et al., 2014a), has an age of 0.75–1 Gyr (Donati et al., 2014a; Jacobson et al., 2016; Magrini et al., 2017, 2018; Jackson et al., 2021; Romano et al., 2021). In our sample there are 279 stars in the field of Berkeley 81, of which 173 have measured values of EW (Li). The membership analysis resulted in 69 RV candidates, 42 astrometric can- didates, 25 Li candidates, and 24 final members (see Table 2.8). Of the final 25 Li candidates we discarded one star which we were not able to analyse using astrometric and photometric Gaia data, and because it was further listed as a non-member by Jackson et al. (2021). We also con- sidered one UVES Li-rich giant star (19014498-0027496) as an additional candidate instead of a giant contaminant, not only because it fulfilled all of our membership criteria, but also because other studies (Jacobson et al., 2016; Magrini et al., 2017) considered it to be a member of this cluster. As for kinematics, two stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating 11 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted them as final members, as they fulfilled the rest of membership criteria, and all stars were also listed as high-probability members by Jackson et al. (2021). In addition, we have also accepted as a final candidate one star which fulfilled all criteria except for metallicity, having a [Fe/H] value deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. This star is also listed as a member with P=0.99 by Jackson et al. (2021). On the other hand, another star we have discarded for deviating appreciably from the [Fe/H] of the cluster, as it was not included in any study, and we also could not analyse this star using astrometry. Regarding previous membership selections from the literature, we firstly found seven stars in common with Magrini et al. (2015), as well as 13 stars in Jacobson et al. (2016) and Magrini et al. (2017), 10 stars in Sampedro et al. (2017), and three stars in Cantat-Gaudin et al. (2018). Finally, Jackson et al. (2021) includes all 24 of our final candidates. As to the influence of rotation and activity on Li, for a detailed discussion of this age range (0.7–4.5 Gyr) we refer the reader to the detailed discussion of NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), NGC 2243 (4 Gyr) and M67 (4–4.5 Myr) in Chapter 3, and the individual figures for Berkeley 81 can be found in Appendix E. The fastest rotators for this cluster are F stars, as expected in this age range, with vsini values up to 70 km s−1. In spite of the small number of candidates for this cluster, we can observe a trend in which the faster rotators also have higher EW (Li) values, and several of them trace the upper Li envelope for the cluster. The G and early-K stars in the selection all show low vsini values with low EW (Li), in agreement with the expected correlation. We also note that for this cluster GES has only obtained Hα measurements for the early-K UVES stars in the selection, and so it is difficult to discern any patterns as regards to the Li-activity relation for this cluster, beyond the fact that these stars have both low EW (Li) and Hα values (with values up to 0.20 Å), in agreement with the expected correlation between Li content and Hα emission. The Li-rich member of Berkeley 81, however, also presents low activity. ∗ NGC 2355 B.3. Old clusters (age > 700 Myr) 177 At a distance of 1.8–1.9 kpc (Jacobson et al., 2011; Buckner & Froebrich, 2014), NGC 2355 is an open cluster with an age of 0.8–1 Gyr (Kharchenko et al., 2005; Sampedro et al., 2017; Jackson et al., 2021; Romano et al., 2021). This cluster is targeted because of its location in the outer part of the Galactic disc, where only a few open clusters have been studied, and it is also of interest because its stars are bright enough to be easily observed with high-resolution spectroscopy (Soubiran et al., 2000; Donati et al., 2015). In our sample there are 208 stars in the field of NGC 2355, of which 160 have measured values of EW (Li). The membership analysis resulted in 119 RV candidates, 129 astrometric candidates, 87 Li candidates, and 86 final members (see Table 2.8). Of the final 87 Li candidates we discarded one star which we were not able to analyse using astrometric and photometric Gaia data, and was further listed as a non-member by Jackson et al. (2021), as well as not fulfilling the gravity criteria. As for kinematics, 23 stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 6–8 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted all of them as final members, as they fulfilled the rest of membership criteria, and all stars were also listed as high-probability members by Jackson et al. (2021) with P=0.99–1.00. In addition, we have also accepted as a final candidate two stars which fulfilled all criteria except for metallicity, having a [Fe/H] value deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. Both stars are also listed as members with P=1.00 by Jackson et al. (2021). Regarding previous membership selections from the literature, we found 64 stars in common with Cantat-Gaudin et al. (2018), and Jackson et al. (2021) includes 84 of our 86 final candidates (the remaining two stars in our selection were not included in their study). Regarding the influence of rotation and activity on Li, we mainly refer to the discussion in Chapter 3 for a detailed account for this cluster, and the individual figures are further shown in Appendix E. For this cluster we found candidates with vsini values up to 70 km s−1. There are no Hα activity values recorded in the iDR6 file for Trumpler 23. Finally, we also note that we have additionally omitted one star (07165551+1343191) from the study of rotation for this cluster, displaying a higher vsini value of 109 km s−1, compared to the aforementioned 70 km s−1 maximum value for the rest of the candidates of the cluster. This star fulfilled all membership criteria and is listed as a member with P=0.81 by Jackson et al. (2021). While remaining a cluster candidate, we have decided not to include it in the analysis of rotation: partly because we were not certain about the reliability of the vsini measurements for this star, and also because adding it to the figure significantly affected the range of the auxiliary colour-coded axis for the rest of candidates. ∗ NGC 6802 NGC 6802 is an inner disc open cluster in the constellation Fuchs, with an age of 0.9–1.0 Gyr (Jacobson et al., 2016; Magrini et al., 2017; Tang et al., 2017; Magrini et al., 2018; Jackson et al., 2021; Romano et al., 2021), and located at a distance of 1.8 kpc (Dias et al., 2002). NGC 6802 has been considered of interest in past studies (e.g., Tang et al., 2017) in order to calibrate the survey-derived abundances, given the chemical and kinematic homogeneity of the members of 178 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 these open clusters. In our sample there are 197 stars in the field of NGC 6802, of which 82 have measured values of EW (Li).The membership analysis resulted in 77 RV candidates, 51 astrometric candidates, 36 Li candidates, and 32 final members (see Table 2.8). Of the final 36 Li candidates we discarded four stars which we were not able to analyse using astrometric and photometric Gaia data, and were further listed as non-members by Jackson et al. (2021). As for kinematics, six stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 4–17 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted all of them as final members, as they fulfilled the rest of membership criteria, and all stars were also listed as high-probability members by Jackson et al. (2021) with P=0.94–0.99. We also note that the final selection of this cluster includes a couple of stars which present values of EW (Li) slightly larger than the rest of candidates (112–113 mÅ). Given that these stars do not exhibit appreciable dispersion with respect to the other members, however, we have not classified them as possible Li members (which we generally mark as ‘Y?’ in the table of Appendix D). These two stars fulfil the rest of membership criteria, and one of them is also listed as a high probability member by Jackson et al. (2016) (the other one is not included in their study), and so we have accepted them as final members of the cluster. Furthermore, we can also explain the higher observable values of EW (Li) of these stars considering the fact that they also exhibit values of rotation that are in the middle of the scale for this cluster (see the individual figures of Appendix E). The effects of rotation could thus explain that these stars are members of NGC 6802 exhibiting a slightly slower rate of Li depletion as a result. Regarding previous membership selections from the literature, we found the following stars in common with several studies: Firstly, we found eight common stars with Jacobson et al. (2016) and Magrini et al. (2017), as well as 10 stars in Sampedro et al. (2017), 18 stars in Tang et al. (2017), and five common stars in Cantat-Gaudin et al. (2018). Jackson et al. (2021) includes 31 of our 32 final candidates (the remaining star in our selection was not included in their study). Finally, one of the Li-rich giants in our list (J19304281+2016107) is also listed in Casey et al. (2016). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (0.7–4.5 Gyr) we refer the reader to the detailed discussion of NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), NGC 2243 (4 Gyr) and M67 (4–4.5 Myr) in Chapter 3, and the individual figures for NGC 6802 can be found in Appendix E. The fastest rotators for this cluster (shown in dark purple) are F stars, as expected in this age range, with vsini values up to 70 km s−1. We could observe a trend in which the faster rotators among the FG stars (shown in shades of purple and dark orange) tended to have higher EW (Li) values, with several of them tracing the upper Li envelope for the cluster. The late-G and early-K stars in the selection all show vsini values with very low values of EW (Li) (shown in yellow). We also note that for this cluster GES has only reported Hα measurements for one late-G star in our selection (a very low value of 0.03 Å), and so it is not possible to discern any patterns as regards to the Li-activity relation for this cluster (apart from the fact that this star combines both very low Hα and EW (Li) values). Finally, we also note that we have additionally omitted one star (19304209+2015581) from the study of rotation for the selection of NGC 6802, displaying a higher vsini value of 160 km s−1, B.3. Old clusters (age > 700 Myr) 179 compared to the aforementioned 70 km s−1 maximum value for the rest of the candidates of the cluster. This star fulfilled all membership criteria and is listed as a high probability member by Jackson et al. (2021). While remaining a cluster candidate, we have decided not to include it in the analysis of rotation: partly because we were not certain about the reliability of the vsini measurements for this star, and also because adding it to the figure significantly affected the range of the auxiliary colour-coded axis for the rest of candidates. ∗ NGC 6005 At a distance of 2.7 kpc (Dias et al., 2002; Kharchenko et al., 2005), NGC 6005 is a Southern open cluster in the constellation Norma with an age of 0.97–1.20 Gyr (Jacobson et al., 2016; Magrini et al., 2017; Bossini et al., 2019; Jackson et al., 2021). Bossini et al. (2019) calculated an age of 973± 4 Myr for this cluster. In our sample there are 560 stars in the field of NGC 6005, of which 317 have measured values of EW (Li).The membership analysis resulted in 174 RV candidates, 112 astrometric can- didates, 55 Li candidates, and 49 final members (see Table 2.8). Of the final 55 Li candidates, we discarded five stars which we were not able to analyse using astrometric and photometric Gaia data, and were further listed as non-members by Jackson et al. (2021). We have also discarded another star which fulfilled all criteria except for metallicity, having a [Fe/H] value deviating ap- preciably from the rest of candidates even while considering the larger 3σ membership interval. In contrast to our decision to accept stars as final candidates if they fulfil the rest of criteria apart from metallicity or log g, especially the more restrictive astrometric criteria, in this case we have discarded it from the final selection on the basis of not being able to analyse it with Gaia data, and additionally for not being included by Jackson et al. (2021). As for kinematics, two stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 7–11 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted both of them as final members, as they fulfilled the rest of membership criteria, and both stars were also listed as members of the cluster by Jackson et al. (2021) with P=0.90–0.91. We also note that the final selection of this cluster includes three stars which present values of EW (Li) slightly larger than the rest of candidates (102–118 mÅ). Given that these stars do not exhibit appreciable dispersion with respect to the other members, however, we have not classified them as possible Li members (which we generally mark as ‘Y?’ in the table of Ap- pendix D). These two stars fulfil the rest of membership criteria, and they are also listed as high probability members by Jackson et al. (2016), and so we have accepted them as final members of the cluster. Furthermore, we can also explain the higher observable values of EW (Li) of these stars considering the fact that they also exhibit values of rotation that are in the middle of the scale for this cluster (see the individual figures of Appendix E). The effects of rotation could thus explain that these stars are members of NGC 6005 exhibiting a slightly slower rate of Li depletion as a result. Regarding previous membership selections from the literature, we found the following stars in common with several studies: Firstly, we found 12 common stars with Jacobson et al. (2016), as well as seven stars in Magrini et al. (2017), 11 stars in Sampedro et al. (2017), and 12 common stars in Cantat-Gaudin et al. (2018). Jackson et al. (2021) includes all 49 of our final candidates. 180 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 As already discussed in Sect. 2.3, we also note that we seem to find some inconsistencies when plotting the Li-rich giant outliers selected in the field of this cluster in the CMD diagram, with all three of them appearing among the non-giant cluster candidates. However, when plotting them in the Kiel diagram the expected distinction is found between the non-giant cluster candidates and the Li-rich giant outliers. We plan on studying all Li-rich giant outliers in more detail in order to gain further confirmation on their nature as Li-rich giant contaminants (see the future work in Chapter 5). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (0.7–4.5 Gyr) we refer the reader to the detailed discussion of NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), NGC 2243 (4 Gyr) and M67 (4–4.5 Myr) in Chapter 3, and the individual figures for NGC 6005 can be found in Appendix E. The fastest rotators for this cluster (shown in purple and dark orange hues) are F and G stars, with vsini values up to 30–40 km s−1, while the late-G and early-K stars all show vsini values with very low values of EW (Li) (shown in yellow). The distribution of rotation for this cluster is somewhat more dispersed than in the case of other clusters, but even so we could discern a certain trend where several faster rotators had higher EW (Li) values as well, and the late-G/early-K stars of the cluster selection all show both low rotation and EW (Li) values. We also note that for this cluster GES has only reported Hα measurements for one late-G star in our selection (a very low value of 0.06 Å), and so it is not possible to discern any patterns as regards to the Li-activity relation for this cluster (apart from the fact that this star combines both very low Hα and EW (Li) values). Finally, we also note that we have additionally omitted one star (15555645-5725340) from the study of rotation for this cluster, displaying an appreciably higher vsini value of 150 km s−1, compared to the aforementioned 30–40 km s−1 maximum range for the rest of the candidates of the cluster. This star fulfilled all membership criteria and is listed as a high probability member by Jackson et al. (2021). While remaining a cluster candidate, we have decided not to include it in the analysis of rotation: partly because we were not certain about the reliability of the vsini measurements for this star, and also because adding it to the figure significantly affected the range of the auxiliary colour-coded axis for the rest of candidates. ∗ Pismis 18 At a distance of 2.2 kpc (Dias et al., 2002), Pismis 18 is a Southern open cluster with an age of 1.2 Gyr (Jacobson et al., 2016; Magrini et al., 2017, 2018; Jackson et al., 2021). In our sample there are 142 stars in the field of Pismis 18, of which 82 have measured values of EW (Li).The membership analysis resulted in 41 RV candidates, 24 astrometric candidates, 12 Li candidates, and 10 final members (see Table 2.8). Of the final 12 Li candidates, we discarded two stars which we were not able to analyse using astrometric and photometric Gaia data, and were further listed as non-members by Jackson et al. (2021). As for kinematics, one star in our final selection was a RV non-member according to the initial 2σ interval, with a RV deviating up to 6 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted it as a final member as it fulfilled the rest of membership criteria, and was also listed as a member of the cluster by Jackson et al. (2021) with P=0.98. Regarding previous membership selections from the literature, we found the following stars in common with several studies: Firstly, we found five common stars with Jacobson et al. (2016), as well as three stars in Magrini et al. (2017), and all of our 10 stars are listed in Hatzidimitriou B.3. Old clusters (age > 700 Myr) 181 et al. (2019). Jackson et al. (2021) also includes all 10 of our final candidates. As to the influence of rotation and activity on Li, for a detailed discussion of this age range (0.7–4.5 Gyr) we refer the reader to the detailed discussion of NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), NGC 2243 (4 Gyr) and M67 (4–4.5 Myr) in Chapter 3, and the individual figures for Pismis 18 can be found in Appendix E. Due to the lack of a sufficient number of cluster candi- dates, it is difficult to discern a trend or pattern for this cluster, although we note that the fastest rotators are F-type stars, as expected in this age range, with vsini values up to 56.7 km s−1. We found the slowest rotating stars among the late-G/early-K candidates. We also note that for this cluster GES has only reported Hα measurements for one late-G star in our selection (a very low value of 0.03 Å), and so it is not possible to discern any patterns as regards to the Li-activity relation for this cluster (apart from the fact that this star combines both very low Hα and EW (Li) values). Finally, we also note that we have additionally omitted one star (13365304-6204298) from the study of rotation for the selection of NGC 6802, displaying an appreciably higher vsini value of 102 km s−1, compared to the aforementioned 56.7 km s−1 maximum value for the rest of the candidates of the cluster. This star fulfilled all membership criteria and is listed as a high probability member by Jackson et al. (2021). While remaining a cluster candidate, we have decided not to include it in the analysis of rotation: partly because we were not certain about the reliability of the vsini measurements for this star, and also because adding it to the figure significantly affected the range of the auxiliary colour-coded axis for the rest of candidates. ∗ Melotte 71 At a distance of 2.2–3.2 kpc (Kharchenko et al., 2005; Buckner & Froebrich, 2014), Melotte 71 (also known as Mel 71) is an anticentre open cluster, lying within the potentially critical transi- tion zone between the inner and outer disc Twarog et al. (2006). Bossini et al. (2019) calculated an age of 1294± 89 Myr for this cluster, while Netopil et al. (2016) listed an age of 0.7 Gyr. In our sample there are 120 stars in the field of Melotte 71, of which nine have measured values of EW (Li).The membership analysis resulted in 71 RV candidates, 64 astrometric candidates, and 4 Li candidates, all of which we considered as final members (see Table 2.8). Regarding pre- vious membership selections from the literature, we found three stars in common with Sampedro et al. (2017), and four common stars in Cantat-Gaudin et al. (2018). We note that this is one of the three clusters out of our sample of 42 clusters which is not included in Jackson et al. (2021). As to the influence of rotation and activity on Li, for a detailed discussion of this age range (0.7–4.5 Gyr) we refer the reader to the detailed discussion of NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), NGC 2243 (4 Gyr) and M67 (4–4.5 Myr) in Chapter 3, and the individual figures for Melotte 71 can be found in Appendix E. Due to the lack of a sufficient number of cluster candi- dates, it is not possible to discern a trend or pattern for this cluster, apart from the fact that the late G stars with vsini values available combine both very low rotation and EW (Li) values. We can also say that of these stars, the one with the highest EW (Li) values is also the one with the highest vsini value, of about 8 km s−1. There are no Hα activity values recorded in the iDR6 file for Melotte 71. ∗ Pismis 15 182 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 At a distance of 2.6–2.9 kpc (Kharchenko et al., 2005; Sampedro et al., 2017), Pismis 15 is an open cluster with an age of 1.3 Gyr (Carraro et al., 2005; Kharchenko et al., 2005; Sampedro et al., 2017; Liu & Pang, 2019; Jackson et al., 2021). In our sample there are 333 stars in the field of Pismis 15, of which 211 have measured values of EW (Li). The membership analysis resulted in 91 RV candidates, 66 astrometric candidates, 33 Li candidates, and 31 final members (see Table 2.8). Of the final 33 Li candidates, we dis- carded two stars which we were not able to analyse using astrometric and photometric Gaia data, and were further listed as non-members by Jackson et al. (2021). We have also accepted as final candidates two stars which fulfilled all criteria except for metallicity, having a [Fe/H] value devi- ating appreciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed in Sect. 2.2.5, however, we have decided to list them as final candidates, and they are both additionally listed as members by Jackson et al. (2021) with P=0.99. We also note that the final selection of this cluster includes a small number of stars which present values of EW (Li) slightly larger than the rest of candidates (92–147 mÅ). Given that these stars do not exhibit appreciable dispersion with respect to the other members, however, we have not classified them as possible Li members (which we generally mark as ‘Y?’ in the table of Appendix D). These eight stars fulfil the rest of membership criteria, and they are also listed as high probability members by Jackson et al. (2016) with P=0.98–0.99, and so we have accepted them as final members of the cluster. Furthermore, a couple of these stars also exhibit high values of rotation according to the range observed for this cluster (see the individual figures of Appendix E). The effects of rotation could thus also explain the higher values of EW (Li) of these stars, as we could explain them as members of Pismis 15 exhibiting a slightly slower rate of Li depletion as a result of being faster rotators. Regarding previous membership selections from the literature, we found five common stars with Sampedro et al. (2017), as well as 15 stars in Cantat-Gaudin et al. (2018). Jackson et al. (2021) includes all 31 of our final candidates. As to the influence of rotation and activity on Li, for a detailed discussion of this age range (0.7–4.5 Gyr) we refer the reader to the detailed discussion of NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), NGC 2243 (4 Gyr) and M67 (4–4.5 Myr) in Chapter 3, and the individual figures for Pismis 15 can be found in Appendix E. The fastest rotators for this cluster are F and early G stars, with vsini values up to 30–40 km s−1, while the late-G stars tend to show low vsini values with very lower values of EW (Li). The distribution of rotation for this cluster is somewhat more dispersed than in the case of other clusters, but even so we could discern a certain trend where several faster rotators had higher EW (Li) values as well, and the late-G/early-K stars of the cluster selection generally show both low rotation and EW (Li) values. We also note that for this cluster GES has only reported Hα measurements for one late-G star in our selection (a very low value of 0.06 Å), and so it is not possible to discern any patterns as regards to the Li-activity relation for this cluster (apart from the fact that this star combines both very low Hα and EW (Li) values). ∗ Trumpler 20 At a distance of 3.0–3.3 kpc (Dias et al., 2002; Donati et al., 2014b), Trumpler 20 is an open cluster located towards the Galactic centre, with an age of 1.4–1.8 Gyr (Donati et al., 2014b; Jacobson et al., 2016; Magrini et al., 2017; Jackson et al., 2021; Romano et al., 2021). Its position B.3. Old clusters (age > 700 Myr) 183 Figure B.10: Trumpler 20, a 1.4 Gyr old cluster. Credit: ESO/T. Preibisch. in the inner part of the disc and its age (few OC with an age > 1 Gyr located in the inner disc are known) make Trumpler 20 particularly interesting regarding the study of the chemical properties and structure of the Galactic disc (Donati et al., 2014b). In our sample there are 1213 stars in the field of Trumpler 20, of which 430 have measured values of EW (Li). The membership analysis resulted in 451 RV candidates, 367 astrometric can- didates, 116 Li candidates, and 104 final members (see Table 2.8). Of the final 116 Li candidates, we discarded 12 stars which we were not able to analyse using astrometric and photometric Gaia data, and were further listed as non-members by Jackson et al. (2021). We have also discarded another star which fulfilled all criteria except for metallicity, having a [Fe/H] value deviating ap- preciably from the rest of candidates even while considering the larger 3σ membership interval. In contrast to our decision to accept stars as final candidates if they fulfil the rest of criteria apart from metallicity or log g (see below), especially regarding the more restrictive astrometric criteria, in this case we have discarded it from the final selection on the basis of not being able to analyse it with Gaia data, and additionally for being listed as a definite non-member by Jackson et al. (2021). As for kinematics, five stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 10 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted all of them as final members, as they fulfilled the rest of membership criteria, and all stars were also listed as members of the cluster by Jackson et al. (2021) with P=0.87–0.98. We have also accepted as final candidates 10 stars which fulfilled all criteria except for metallicity, having a [Fe/H] value deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed in Sect. 2.2.5, however, we have decided to list them as final candidates, and they are additionally listed as members by Jackson et al. (2021) with P=0.94–0.99. We also note that the final selection of this cluster includes a number of stars which present values of EW (Li) slightly larger than the rest of candidates (90–120 mÅ). Given that these stars do not exhibit appreciable dispersion with respect to the other members, however, we have not classified them as possible Li members (which we generally mark as ‘Y?’ in the table of Appendix D). These stars fulfil the rest of membership criteria, and they are also listed as high 184 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 probability members by Jackson et al. (2016) with P=0.89–.99, and so we have accepted them as final members of the cluster. Furthermore, we may also explain the higher observable values of EW (Li) of several of these stars considering the fact that they also exhibit values of rotation that are in the middle and high end of the scale for this cluster (see the individual figures of Appendix E). The effects of rotation could thus explain that these stars are members of Trum- pler 20 exhibiting a slightly slower rate of Li depletion as a result. Finally, we also find one star (12400449-6036566) which also exhibits a high EW (Li) (137 mÅ) and stands apart from the rest of the candidates. We listed this star as a Li-rich candidate of the cluster. This star fulfilled the rest of our criteria, and it is also listed as a Li-rich member by Smiljanic et al. (2016). Regarding previous membership selections from the literature, we found the following stars in common with several studies: Firstly, we found 97 common stars with Donati et al. (2014b), as well as 23 stars in Tautvaišienė et al. (2015), 23 stars in Jacobson et al. (2016), 23 stars in Smiljanic et al. (2016), 17 stars in Magrini et al. (2017), 31 stars in Sampedro et al. (2017), and 42 stars in Cantat-Gaudin et al. (2018). Finally, Jackson et al. (2021) includes all but one of our 104 final candidates. The remaining star in our selection fulfils all of our criteria in spite of being listed as a non-member in Jackson et al. (2021). Once again, the reason for these individual deviations between our two analyses probably originates from the existing differences regarding criteria limits or the weight of the factors implicated in the decision to accept or discard stars as final candidates. Regarding the influence of rotation and activity on Li, we mainly refer to the discussion in Chapter 3 for a detailed account for this cluster, and the individual figures are further shown in Appendix E. For this cluster we found candidates with vsini values up to 70–80 km s−1 and Hα activity up to 1.0 Å. Finally, we also note that we have additionally omitted three stars (12391248-6035506, 12392657-6035049 and 12394776-6040044) from the study of rotation for this cluster, displaying appreciably higher vsini values of 110–117 km s−1, compared to the aforementioned 70–80 km s−1 maximum range for the rest of the candidates of the cluster. These stars fulfilled all membership criteria and are listed as high probability members by Jackson et al. (2021). While remaining cluster candidates, we have decided not to include them in the analysis of rotation: partly be- cause we were not certain about the reliability of the vsini measurements for these stars, and also because adding them to the figure significantly affected the range of the auxiliary colour-coded axis for the rest of candidates. ∗ Berkeley 44 At a distance of 1.8–3.1 kpc (Dias et al., 2002; Hayes & Friel, 2014), Berkeley 44 (also known as Br 44) is an open cluster with a dense background field and an age of 1.4–1.6 Gyr (Hayes & Friel, 2014; Jacobson et al., 2016; Magrini et al., 2017, 2018; Jackson et al., 2021; Romano et al., 2021). In our sample there are 93 stars in the field of Berkeley 44, of which 80 have measured values of EW (Li).The membership analysis resulted in 39 RV candidates, 33 astrometric candidates, 31 Li candidates, and 30 final members (see Table 2.8). Of the final 31 Li candidates, we discarded one star which we were not able to analyse using astrometric and photometric Gaia data, and was further listed as a non-member by Jackson et al. (2021). As for kinematics, five stars in our final selection were RV non-members according to the B.3. Old clusters (age > 700 Myr) 185 initial 2σ interval, with RV s deviating up to 3–4 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted both of them as final members, as they fulfilled the rest of membership criteria, and both stars were also listed as members of the cluster by Jackson et al. (2021) with P=0.86–0.99. We have also accepted an additional star as a final candidate, fulfilling all criteria except for metallicity, with a [Fe/H] value deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed in the case of other clusters, however, we have decided to list it as a final candidate, and it is also listed as a high probability member by Jackson et al. (2021) with P=1.00. Regarding previous membership selections from the literature, we found the following stars in common with several studies: Firstly, we found three common stars with Jacobson et al. (2016) and Magrini et al. (2017), as well as eight stars in Sampedro et al. (2017), and 20 stars in Cantat-Gaudin et al. (2018). Finally, Jackson et al. (2021) includes all 30 of our final candidates. As to the influence of rotation and activity on Li, for a detailed discussion of this age range (0.7–4.5 Gyr) we refer the reader to the detailed discussion of NGC 2355 (900 Myr), Trumpler 20 (1.4 Gyr), NGC 2243 (4 Gyr) and M67 (4–4.5 Myr) in Chapter 3, and the individual figures for Berkeley 44 can be found in Appendix E. The fastest rotators for this cluster are F stars, as expected in this age range, with vsini values up to 90 km s−1. In spite of the small number of candidates for this cluster, we can observe a trend in which the faster rotators generally have higher EW (Li) values, while the late-G/early-K stars in the selection all show low vsini values with low EW (Li), in agreement with the expected correlation. There are no Hα activity values recorded in the iDR6 file for Berkeley 44. Finally, we also note that we have additionally omitted one star (19171454+1937098) from the study of rotation for this cluster, displaying an appreciably higher vsini value of 200 km s−1, compared to the aforementioned 90 km s−1 maximum value for the rest of the candidates of the cluster. This star fulfilled all membership criteria and is listed as candidates of the cluster by all the studies listed above (Cantat-Gaudin et al., 2018; Jackson et al., 2021), including being marked as a high probability member by Jackson et al. (2021). While remaining a cluster candidate, we have decided not to include it in the analysis of rotation: partly because we were not certain about the reliability of the vsini measurement for this star, and also because adding it to the figure significantly affected the range of the auxiliary colour-coded axis for the rest of candidates. ∗ NGC 2243 At a distance of 4.5 kpc (Dias et al., 2002; Jacobson et al., 2011; Magrini et al., 2014), NGC 2243 is a rich open cluster in the constellation of Canis Major. This old cluster has an age in the range of 3.8–4.4 Gyr (Richer et al., 1998; Jacobson et al., 2011; Heiter et al., 2014; Magrini et al., 2017, 2018; Jackson et al., 2021; Romano et al., 2021). NGC 2243 is one of the most metal-poor clusters known (Carraro et al., 1994; Jacobson et al., 2011), with a [Fe/H] value of −0.38±0.04 dex (Magrini et al., 2017, 2018). Earlier estimates give metallicities ranging from −0.60 to −0.48 dex (Jacobson et al., 2011; Heiter et al., 2014). We note that for the individual figures of this cluster (see Appendix C), due to the low metallicity of this cluster we considered PARSEC isochrones with Z=0.006 instead of the usual near-solar metallicity of Z=0.019 we have used for the rest of the clusters in our sample. In our sample there are 661 stars in the field of NGC 2243, of which 603 have measured values of EW (Li). The membership analysis resulted in 469 RV candidates, 446 astrometric 186 Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 candidates, and 289 Li candidates, all of which we listed as final members of the cluster (see Table 2.8). Regarding kinematics, 36 stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 8 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted both of them as final members, as they fulfilled the rest of membership criteria, and both stars were also listed as members of the cluster by Jackson et al. (2021) with P=0.93–1.00. We have also accepted three additional stars as final candidates. These three stars fulfilled all criteria except for metallicity, with a [Fe/H] value de- viating appreciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed in the case of other clusters, however, we have decided to list them as members of the cluster, and they are also listed as high probability members by Jackson et al. (2021) with P=0.99–1.00. Regarding previous membership selections from the literature, we found the following stars in common with several studies: Firstly, we found nine common stars with Jacobson et al. (2011), as well as one star in Heiter et al. (2014), 13 stars in Magrini et al. (2017), 42 stars in Sampedro et al. (2017), and 178 stars in Cantat-Gaudin et al. (2018). Finally, Jackson et al. (2021) includes all but one of our 289 of our final candidates (the remaining star in our selection was not included in their study). Given that NGC 2243 and M67 are very close age-wise, we also note that we have additionally made use of the Li envelope created by our candidate selection for M67 (see Chapter 4), as well as former M67 attested members, to help confirm the membership of our selection for NGC 2243. As already discussed in Sect. 2.3, we also note that we seem to find some inconsistencies when plotting the Li-rich giant outliers selected in the field of this cluster in the CMD diagram, with five of them appearing among the non-giant cluster candidates. However, when plotting them in the Kiel diagram the expected distinction is found between the non-giant cluster candidates and the Li-rich giant outliers. We plan on studying all Li-rich giant outliers in more detail in order to gain further confirmation on their nature as Li-rich giant contaminants (see the future work in Chapter 5). Regarding the influence of rotation and activity on Li, we mainly refer to the discussion in Chapter 3 for a detailed account for this cluster, and the individual figures are further shown in Appendix E. For this cluster we found candidates with vsini values up to 40 km s−1 and low Hα activity up to 0.3–0.4 Å. Finally, we also note that we have additionally omitted two stars (06292306-3122164 and 06291358-3116426) from the study of rotation for this cluster, displaying appreciably higher vsini values of 339–345 km s−1, compared to the aforementioned 40 km s−1 maximum value for the rest of the candidates of the cluster. These two stars fulfilled all membership criteria and are listed as candidates of the cluster by all the studies listed above (Cantat-Gaudin et al., 2018; Jackson et al., 2021), including being marked as high probability members by Jackson et al. (2021). While remaining cluster candidates, we have decided not to include them in the analysis of rotation: partly because we were not certain about the reliability of the vsini measurements for these stars, and also because adding them to the figure significantly affected the range of the auxiliary colour-coded axis for the rest of candidates. ∗ M67 At a distance of 800–900 pc (Dias et al., 2002; Kharchenko et al., 2005), M67 (also known as B.3. Old clusters (age > 700 Myr) 187 Messier 67 or NGC 2682) is a solar-age, solar-metallicity open cluster in the constellation of Can- cer, with an age in the range of 3.6–4.5 Gyr, an age close to that of the Sun (Balachandran, 1995; Richer et al., 1998; Pallavicini et al., 2005; Sestito & Randich, 2005). M67 is of importance and has been extensively observed because it is well-populated, and also for being one of the closest old open clusters, which allows for precise photometric observations of its main sequence (García López et al., 1988). All of this makes it an important laboratory for the study of stellar evolution. In our sample there are 131 stars in the field of M67, of which 121 have measured values of EW (Li).The membership analysis resulted in 109 RV candidates, 89 astrometric candidates, and 96 Li candidates, all of which we listed as final members of the cluster (see Table 2.8). As for kinematics, eight stars in our final selection were RV non-members according to the initial 2σ interval, with RV s deviating up to 4–9 km s−1 from the mean of the cluster. As in the case of other cluster analyses, we accepted both of them as final members, as they fulfilled the rest of membership criteria, and both stars were also listed as members of the cluster by Jackson et al. (2021) with P=0.99. We have also accepted as a final candidate of the cluster a star which fulfilled all criteria except for metallicity, with a [Fe/H] value deviating appreciably from the rest of candidates even while considering the larger 3σ membership interval. As discussed in the case of other clusters, however, we have decided to list it as a final candidate, and it is also listed as a high probability member by Jackson et al. (2021) with P=0.99. Regarding previous membership selections from the literature, we found the following stars in common with several studies: Firstly, we found 65 common stars with Pace et al. (2012), as well as 50 stars in Pasquini et al. (2012), two stars in Carlberg (2014), 65 stars in Geller et al. (2015), 55 stars in Brucalassi et al. (2017), 74 stars in Sampedro et al. (2017), 29 stars in Jadhav et al. (2021), and seven stars in Ilin et al. (2021). Finally, Jackson et al. (2021) includes all 96 of our final candidates. We also note that in order to reinforce the membership of our GES selection we made use of several lists of M67 candidates from a series of non-GES studies (Hobbs & Pilachowski, 1986; Balachandran, 1995; Pallavicini et al., 1997; Pasquini et al., 1997; Jones et al., 1999; Randich et al., 2002). Regarding the influence of rotation and activity on Li, we mainly refer to the discussion in Chapter 3 for a detailed account for this cluster, and the individual figures are further shown in Appendix E. For this cluster we found candidates with vsini values up to 30 km s−1 and low Hα activity up to 0.1 Å. Appendix C Individual figures of Chapter 2 This appendix includes individual figures for several membership criteria discussed in Chap- ter 2.2, for all 42 clusters in the sample. For the final selection of candidate members in each cluster, we show the final RV distribution and parallax distributions, the pmra-versus-pmdec proper motions diagram, the CMD, the γ-versus-Teff and/or Kiel diagrams, and the EW (Li)- versus-Teff diagram. When available, strong accretor members and Li-rich giant contaminants are further plotted alongside the candidate members. C.1 Young clusters 189 190 Appendix C. Individual figures of Chapter 2 RV [km/s] N −6 −4 −2 0 2 4 6 0. 00 0. 05 0. 10 0. 15 0. 20 Figure C.1: RV distribution for NGC 6530. Parallax (mas) Figure C.2: Parallax distribution for NGC 6530. PMRA (mas/yr) PM D EC (m as /y r) Figure C.3: PMs diagram for NGC 6530. Gbp-Grp M G Figure C.4: CMD for NGC 6530. Teff (K) γ i nd ex (d ex ) Figure C.5: γ index-versus-Teff dia- gram for NGC 6530. Teff (K) EW (L i) (m Å ) Figure C.6: EW (Li)-versus-Teff diagram for NGC 6530. C.1. Young clusters 191 RV [km/s] N −9 −8 −7 −6 −5 −4 0. 0 0. 1 0. 2 0. 3 0. 4 Figure C.7: RV distribution for ρ Oph Parallax (mas) Figure C.8: Parallax distribution for ρ Oph PM D EC (m as /y r) PMRA (mas/yr) Figure C.9: PMs diagram for ρ Oph. Gbp-Grp M G Figure C.10: CMD for ρ Oph. γ i nd ex (d ex ) Teff (K) Figure C.11: γ index-versus-Teff dia- gram for ρ Oph. Teff (K) EW (L i) (m Å ) Figure C.12: EW (Li)-versus-Teff diagram for ρ Oph. 192 Appendix C. Individual figures of Chapter 2 RV [km/s] N −15 −10 −5 0 0. 00 0. 05 0. 10 0. 15 Figure C.13: RV distribution for Trumpler 14. Parallax (mas) Figure C.14: Parallax distribution for Trumpler 14. PMRA (mas/yr) PM D EC (m as /y r) Figure C.15: PMs diagram for Trum- pler 14. Gbp-Grp M G Figure C.16: CMD for Trumpler 14. γ i nd ex (d ex ) Teff (K) Figure C.17: γ index-versus-Teff dia- gram for Trumpler 14. Teff (K) EW (L i) (m Å ) Figure C.18: EW (Li)-versus-Teff diagram for Trumpler 14. C.1. Young clusters 193 RV [km/s] N 13 14 15 16 17 18 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 Figure C.19: RV distribution for Cha I. Parallax (mas) Figure C.20: Parallax distribution for Cha I. PMRA (mas/yr) PM D EC (m as /y r) Figure C.21: PMs diagram for Cha I. Gbp-Grp M G Figure C.22: CMD for Cha I. γ i nd ex (d ex ) Teff (K) Figure C.23: γ index-versus-Teff diagram for Cha I. Teff (K) EW (L i) (m Å ) Figure C.24: EW (Li)-versus-Teff diagram for Cha I. 194 Appendix C. Individual figures of Chapter 2 RV [km/s] N 24 26 28 30 32 34 36 38 0. 00 0. 05 0. 10 0. 15 0. 20 Figure C.25: RV distribution for NGC 2244. Parallax [mas] N 0.5 0.6 0.7 0.8 0 1 2 3 4 5 6 Figure C.26: Parallax distribution for NGC 2244. PMRA (mas/yr) PM D EC (m as /y r) Figure C.27: PMs diagram for NGC 2244. Gbp-Grp M G Figure C.28: CMD for NGC 2244. Teff (K) γ i nd ex (d ex ) Figure C.29: γ index-versus-Teff diagram for NGC 2244. Teff (K) EW (L i) (m Å ) Figure C.30: EW (Li)-versus-Teff diagram for NGC 2244. C.1. Young clusters 195 RV [km/s] N 14 16 18 20 22 24 0. 00 0. 05 0. 10 0. 15 0. 20 Figure C.31: RV distribution for NGC 2264. Parallax [mas] N 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 0 1 2 3 4 5 6 7 Figure C.32: Parallax distribution for NGC 2264. PMRA (mas/yr) PM D EC (m as /y r) Figure C.33: PMs diagram for NGC 2264. Gbp-Grp M G 2264 Figure C.34: CMD for NGC 2264. γ i nd ex (d ex ) Teff (K) Figure C.35: γ index-versus-Teff diagram for NGC 2264. Teff (K) EW (L i) (m Å ) Figure C.36: EW (Li)-versus-Teff diagram for NGC 2264. 196 Appendix C. Individual figures of Chapter 2 RV [km/s] N 24 25 26 27 28 29 30 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 Figure C.37: RV distribution for λ Ori. Parallax [mas] N 2.30 2.35 2.40 2.45 2.50 2.55 2.60 0 1 2 3 4 5 6 Figure C.38: Parallax distribution for λ Ori. PMRA (mas/yr) PM D EC (m as /y r) Figure C.39: PMs diagram for λ Ori. Gbp-Grp M G Figure C.40: CMD for λ Ori. γ i nd ex (d ex ) Teff (K) Figure C.41: γ index-versus-Teff diagram for λ Ori. Teff (K) EW (L i) (m Å ) Figure C.42: EW (Li)-versus-Teff diagram for λ Ori. C.1. Young clusters 197 RV [km/s] N 18 19 20 21 22 23 24 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 Figure C.43: RV distribution for Col 197. Figure C.44: Parallax distribution for Col 197. PM D EC (m as /y r) PMRA (mas/yr) Figure C.45: PMs diagram for Col 197. M G Gbp-Grp Figure C.46: CMD for Col 197. Teff (K) γ i nd ex (d ex ) Figure C.47: γ index-versus-Teff dia- gram for Col 197. Teff (K) EW (L i) (m Å ) Figure C.48: EW (Li)-versus-Teff diagram for Col 197. 198 Appendix C. Individual figures of Chapter 2 PM D EC (m as /y r) PMRA (mas/yr) Figure C.49: PMs diagram for γ Vel. Gbp-Grp M G Figure C.50: CMD for γ Vel. γ i nd ex (d ex ) Teff (K) Figure C.51: γ index-versus-Teff diagram for γ Vel. Teff (K) EW (L i) (m Å ) Figure C.52: EW (Li)-versus-Teff diagram for γ Vel. C.1. Young clusters 199 RV [km/s] N 24.0 24.5 25.0 25.5 26.0 26.5 0. 0 0. 2 0. 4 0. 6 0. 8 Figure C.53: RV distribution for NGC 2232. Parallax [mas] N 2.95 3.00 3.05 3.10 3.15 3.20 3.25 0 2 4 6 8 Figure C.54: Parallax distribution for NGC 2232. PMRA (mas/yr) PM D EC (m as /y r) Figure C.55: PMs diagram for NGC 2232. Gbp-Grp M G Figure C.56: CMD for NGC 2232. Teff (K) γ i nd ex (d ex ) Figure C.57: γ index-versus-Teff diagram for NGC 2232. Teff (K) EW (L i) (m Å ) Figure C.58: EW (Li)-versus-Teff diagram for NGC 2232. 200 Appendix C. Individual figures of Chapter 2 PM D EC (m as /y r) PMRA (mas/yr) Figure C.59: PMs diagram for NGC 2547. Gbp-Grp M G Figure C.60: CMD for NGC 2547. γ i nd ex (d ex ) Teff (K) Figure C.61: γ index-versus-Teff diagram for NGC 2547. Teff (K) EW (L i) (m Å ) Figure C.62: EW (Li)-versus-Teff diagram for NGC 2547. RV [km/s] N 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 0. 0 0. 2 0. 4 0. 6 0. 8 Figure C.63: RV distribution for IC 2391. Parallax [mas] N 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 0 1 2 3 4 5 Figure C.64: Parallax distribution for IC 2391. C.1. Young clusters 201 PMRA (mas/yr) PM D EC (m as /y r) Figure C.65: PMs diagram for IC 2391. Gbp-Grp M G Figure C.66: CMD for IC 2391. γ i nd ex (d ex ) Teff (K) Figure C.67: γ index-versus-Teff diagram for IC 2391. Teff (K) EW (L i) (m Å ) Figure C.68: EW (Li)-versus-Teff diagram for IC 2391. RV [km/s] N 16.0 16.5 17.0 17.5 18.0 18.5 19.0 0. 0 0. 2 0. 4 0. 6 0. 8 Figure C.69: RV distribution for IC 2602. Parallax [mas] N 6.4 6.5 6.6 6.7 6.8 0 1 2 3 4 5 Figure C.70: Parallax distribution for IC 2602. 202 Appendix C. Individual figures of Chapter 2 PMRA (mas/yr) PM D EC (m as /y r) Figure C.71: PMs diagram for IC 2602. Gbp-Grp M G Figure C.72: CMD for IC 2602. γ i nd ex (d ex ) Teff (K) Figure C.73: γ index-versus-Teff diagram for IC 2602. Teff (K) EW (L i) (m Å ) Figure C.74: EW (Li)-versus-Teff diagram for IC 2602. RV [km/s] N −16.0 −15.5 −15.0 −14.5 −14.0 −13.5 −13.0 −12.5 0. 0 0. 2 0. 4 0. 6 0. 8 Figure C.75: RV distribution for IC 4665. Parallax [mas] N 2.7 2.8 2.9 3.0 3.1 0 1 2 3 4 5 6 7 Figure C.76: Parallax distribution for IC 4665. C.1. Young clusters 203 PM D EC (m as /y r) PMRA (mas/yr) Figure C.77: PMs diagram for IC 4665. Gbp-Grp M G Figure C.78: CMD for IC 4665. γ i nd ex (d ex ) Teff (K) Figure C.79: γ index-versus-Teff diagram for IC 4665. Teff (K) EW (L i) (m Å ) Figure C.80: EW (Li)-versus-Teff diagram for IC 4665. 204 Appendix C. Individual figures of Chapter 2 PMRA (mas/yr) PM D EC (m as /y r) Figure C.81: PMs diagram for NGC 2451 A and B. Gbp-Grp M G Figure C.82: CMD for NGC 2451 A and B. γ i nd ex (d ex ) Teff (K) Figure C.83: γ index-versus-Teff diagram for NGC 2451 A and B. Teff (K) EW (L i) (m Å ) Figure C.84: EW (Li)-versus-Teff diagram for NGC 2451 A and B. C.2. Intermediate-age clusters 205 C.2 Intermediate-age clusters 206 Appendix C. Individual figures of Chapter 2 RV [km/s] N −10.5 −10.0 −9.5 −9.0 −8.5 −8.0 −7.5 −7.0 0. 0 0. 2 0. 4 0. 6 Figure C.85: RV distribution for NGC 6405. Parallax [mas] N 2.14 2.16 2.18 2.20 2.22 2.24 0 5 10 15 20 Figure C.86: Parallax distribution for NGC 6405. PM D EC (m as /y r) Figure C.87: PMs diagram for NGC 6405. M G Gbp-Grp Figure C.88: CMD for NGC 6405. Figure C.89: Kiel diagram for NGC 6405. EW (L i) (m Å ) Figure C.90: EW (Li)-versus-Teff diagram for NGC 6405. C.2. Intermediate-age clusters 207 RV [km/s] N 4.5 5.0 5.5 6.0 6.5 7.0 7.5 0. 0 0. 2 0. 4 0. 6 0. 8 Figure C.91: RV distribution for Blanco 1. Parallax [mas] N 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 0 1 2 3 4 5 6 7 Figure C.92: Parallax distribution for Blanco 1. PMRA (mas/yr) PM D EC (m as /y r) Figure C.93: PMs diagram for Blanco 1. Gbp-Grp M G Figure C.94: CMD for Blanco 1. Figure C.95: Kiel diagram for Blanco 1. EW (L i) (m Å ) Figure C.96: EW (Li)-versus-Teff diagram for Blanco 1. 208 Appendix C. Individual figures of Chapter 2 RV [km/s] N −44 −42 −40 −38 −36 −34 −32 0. 00 0. 05 0. 10 0. 15 0. 20 Figure C.97: RV distribution for NGC 6067. Parallax [mas] N 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0 5 10 15 20 Figure C.98: Parallax distribution for NGC 6067. PMRA (mas/yr) PM D EC (m as /y r) Figure C.99: PMs diagram for NGC 6067. M G Figure C.100: CMD for NGC 6067. Figure C.101: Kiel diagram for NGC 6067. EW (L i) (m Å ) Figure C.102: EW (Li)-versus-Teff diagram for NGC 6067. C.2. Intermediate-age clusters 209 PMRA (mas/yr) PM D EC (m as /y r) Figure C.103: PMs diagram for NGC 6649. Gbp-Grp M G Figure C.104: CMD for NGC 6649. Figure C.105: Kiel diagram for NGC 6649. EW (L i) (m Å ) Figure C.106: EW (Li)-versus-Teff diagram for NGC 6649. 210 Appendix C. Individual figures of Chapter 2 RV [km/s] N 22 23 24 25 26 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 Figure C.107: RV distribution for NGC 2516. Parallax [mas] N 2.30 2.35 2.40 2.45 2.50 2.55 0 2 4 6 8 10 12 Figure C.108: Parallax distribution for NGC 2516. PMRA (mas/yr) PM D EC (m as /y r) Figure C.109: PMs diagram for NGC 2516. Gbp-Grp M G Figure C.110: CMD for NGC 2516. Figure C.111: Kiel diagram for NGC 2516. EW (L i) (m Å ) Figure C.112: EW (Li)-versus-Teff diagram for NGC 2516. C.2. Intermediate-age clusters 211 RV [km/s] N −11.0 −10.5 −10.0 −9.5 −9.0 −8.5 −8.0 −7.5 0. 0 0. 2 0. 4 0. 6 0. 8 Figure C.113: RV distribution for NGC 6709. Parallax [mas] N 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0 5 10 15 Figure C.114: Parallax distribution for NGC 6709. PMRA (mas/yr) PM D EC (m as /y r) Figure C.115: PMs diagram for NGC 6709. Gbp-Grp M G Figure C.116: CMD for NGC 6709. Figure C.117: Kiel diagram for NGC 6709. EW (L i) (m Å ) Figure C.118: EW (Li)-versus-Teff diagram for NGC 6709. 212 Appendix C. Individual figures of Chapter 2 RV [km/s] N −38 −36 −34 −32 −30 −28 −26 0. 00 0. 05 0. 10 0. 15 0. 20 Figure C.119: RV distribution for NGC 6259. Parallax [mas] N 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0 5 10 15 Figure C.120: Parallax distribution for NGC 6259. PMRA (mas/yr) PM D EC (m as /y r) Figure C.121: PMs diagram for NGC 6259. Gbp-Grp M G Figure C.122: CMD for NGC 6259. Figure C.123: Kiel diagram for NGC 6259. EW (L i) (m Å ) Figure C.124: EW (Li)-versus-Teff diagram for NGC 6259. C.2. Intermediate-age clusters 213 Parallax [mas] N 32 34 36 38 40 0. 00 0. 10 0. 20 0. 30 Figure C.125: RV distribution for NGC 6705. Parallax [mas] N 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0 2 4 6 8 10 Figure C.126: Parallax distribution for NGC 6705. PMRA (mas/yr) PM D EC (m as /y r) Figure C.127: PMs diagram for NGC 6705. Gbp-Grp M G Figure C.128: CMD for NGC 6705. Figure C.129: Kiel diagram for NGC 6705. EW (L i) (m Å ) Figure C.130: EW (Li)-versus-Teff diagram for NGC 6705. 214 Appendix C. Individual figures of Chapter 2 RV [km/s] N 42 44 46 48 50 52 54 56 0. 00 0. 05 0. 10 0. 15 Figure C.131: RV distribution for Berkeley 30. Parallax [mas] N −0.1 0.0 0.1 0.2 0.3 0.4 0.5 0. 0 1. 0 2. 0 3. 0 Figure C.132: Parallax distribution for Berkeley 30. PM D EC (m as /y r) Figure C.133: PMs diagram for Berke- ley 30. Gbp-Grp M G Figure C.134: CMD for Berkeley 30. Figure C.135: Kiel diagram for Berke- ley 30. EW (L i) (m Å ) Figure C.136: EW (Li)-versus-Teff diagram for Berkeley 30. C.2. Intermediate-age clusters 215 RV [km/s] N −6.5 −6.0 −5.5 −5.0 −4.5 −4.0 −3.5 0. 0 0. 2 0. 4 0. 6 Figure C.137: RV distribution for NGC 6281. Parallax [mas] N 1.75 1.80 1.85 1.90 1.95 2.00 0 1 2 3 4 5 6 7 Figure C.138: Parallax distribution for NGC 6281. PMRA (mas/yr) PM D EC (m as /y r) Figure C.139: PMs diagram for NGC 6281. Gbp-Grp M G Figure C.140: CMD for NGC 6281. Figure C.141: Kiel diagram for NGC 6281. EW (L i) (m Å ) Figure C.142: EW (Li)-versus-Teff diagram for NGC 6281. 216 Appendix C. Individual figures of Chapter 2 RV [km/s] N 3 4 5 6 7 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 Figure C.143: RV distribution for NGC 3532. Parallax [mas] N 2.02 2.04 2.06 2.08 2.10 2.12 2.14 0 5 10 15 Figure C.144: Parallax distribution for NGC 3532. PMRA (mas/yr) PM D EC (m as /y r) Figure C.145: PMs diagram for NGC 3532. Gbp-Grp M G Figure C.146: CMD for NGC 3532. Figure C.147: Kiel diagram for NGC 3532. Figure C.148: EW (Li)-versus-Teff diagram for NGC 3532. C.2. Intermediate-age clusters 217 RV [km/s] N −40 −35 −30 −25 −20 −15 0. 00 0. 04 0. 08 Figure C.149: RV distribution for NGC 4815. Parallax [mas] N 0.1 0.2 0.3 0.4 0 1 2 3 4 5 6 Figure C.150: Parallax distribution for NGC 4815. PMRA (mas/yr) PM D EC (m as /y r) Figure C.151: PMs diagram for NGC 4815. M G Gbp-Grp Figure C.152: CMD for NGC 4815. Figure C.153: Kiel diagram for NGC 4815. EW (L i) (m Å ) Figure C.154: EW (Li)-versus-Teff diagram for NGC 4815. 218 Appendix C. Individual figures of Chapter 2 RV [km/s] N −31 −30 −29 −28 −27 −26 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 Figure C.155: RV distribution for NGC 6633. Parallax [mas] N 2.40 2.45 2.50 2.55 2.60 2.65 0 2 4 6 8 10 Figure C.156: Parallax distribution for NGC 6633. PM D EC (m as /y r) PMRA (mas/yr) Figure C.157: PMs diagram for NGC 6633. Gbp-Grp M G Figure C.158: CMD for NGC 6633. Figure C.159: Kiel diagram for NGC 6633. EW (L i) (m Å ) Teff (K) Figure C.160: EW (Li)-versus-Teff diagram for NGC 6633. C.3. Old clusters 219 C.3 Old clusters 220 Appendix C. Individual figures of Chapter 2 RV [km/s] N 2 4 6 8 10 0. 00 0. 10 0. 20 Figure C.161: RV distribution for NGC 2477. Parallax [mas] N 0.66 0.68 0.70 0.72 0.74 0 5 10 15 20 Figure C.162: Parallax distribution for NGC 2477. PMRA (mas/yr) PM D EC (m as /y r) Figure C.163: PMs diagram for NGC 2477. Gbp-Grp M G Figure C.164: CMD for NGC 2477. Figure C.165: Kiel diagram for NGC 2477. EW (L i) (m Å ) Figure C.166: EW (Li)-versus-Teff dia- gram for NGC 2477. C.3. Old clusters 221 RV [km/s] N −66 −65 −64 −63 −62 −61 −60 −59 0. 00 0. 10 0. 20 0. 30 Figure C.167: RV distribution for Trumpler 23. Parallax [mas] N 0.25 0.30 0.35 0.40 0 5 10 15 Figure C.168: Parallax distribution for Trumpler 23. PMRA (mas/yr) PM D EC (m as /y r) Figure C.169: PMs diagram for Trum- pler 23. Gbp-Grp M G Figure C.170: CMD for Trumpler 23. Figure C.171: Kiel diagram for Trum- pler 23. EW (L i) (m Å ) Figure C.172: EW (Li)-versus-Teff diagram for Trumpler 23. 222 Appendix C. Individual figures of Chapter 2 RV [km/s] N 47.6 47.8 48.0 48.2 48.4 48.6 0. 0 0. 5 1. 0 1. 5 2. 0 Figure C.173: RV distribution for Berkeley 81. Parallax [mas] N 0.15 0.20 0.25 0.30 0.35 0 2 4 6 8 Figure C.174: Parallax distribution for Berkeley 81. PMRA (mas/yr) PM D EC (m as /y r) Figure C.175: PMs diagram for Berke- ley 81. Gbp-Grp M G Figure C.176: CMD for Berkeley 81. Figure C.177: Kiel diagram for Berkeley 81. EW (L i) (m Å ) Figure C.178: EW (Li)-versus-Teff diagram for Berkeley 81. C.3. Old clusters 223 RV [km/s] N 34 35 36 37 38 0. 0 0. 2 0. 4 0. 6 Figure C.179: RV distribution for NGC 2355. Parallax [mas] N 0.50 0.52 0.54 0.56 0 5 10 15 20 25 30 Figure C.180: Parallax distribution for NGC 2355. PMRA (mas/yr) PM D EC (m as /y r) Figure C.181: PMs diagram for NGC 2355. Gbp-Grp M G Figure C.182: CMD for NGC 2355. Figure C.183: Kiel diagram for NGC 2355. EW (L i) (m Å ) Figure C.184: EW (Li)-versus-Teff diagram for NGC 2355. 224 Appendix C. Individual figures of Chapter 2 RV [km/s] N 10.5 11.0 11.5 12.0 12.5 13.0 13.5 0. 0 0. 2 0. 4 0. 6 Figure C.185: RV distribution for NGC 6802. Parallax [mas] N 0.25 0.30 0.35 0.40 0.45 0.50 0 2 4 6 8 10 Figure C.186: Parallax distribution for NGC 6802. PMRA (mas/yr) PM D EC (m as /y r) Figure C.187: PMs diagram for NGC 6802. Gbp-Grp M G Figure C.188: CMD for NGC 6802. Figure C.189: Kiel diagram for NGC 6802. EW (L i) (m Å ) Figure C.190: EW (Li)-versus-Teff diagram for NGC 6802. C.3. Old clusters 225 RV [km/s] N −27 −26 −25 −24 −23 0. 0 0. 1 0. 2 0. 3 0. 4 Figure C.191: RV distribution for NGC 6005. Parallax [mas] N 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 1 2 3 4 Figure C.192: Parallax distribution for NGC 6005. PMRA (mas/yr) PM D EC (m as /y r) Figure C.193: PMs diagram for NGC 6005. Gbp-Grp M G Figure C.194: CMD for NGC 6005. Figure C.195: Kiel diagram for NGC 6005. EW (L i) (m Å ) Figure C.196: EW (Li)-versus-Teff diagram for NGC 6005. 226 Appendix C. Individual figures of Chapter 2 RV [km/s] N −29.5 −29.0 −28.5 −28.0 −27.5 −27.0 0. 0 0. 2 0. 4 0. 6 0. 8 Figure C.197: RV distribution for Pis- mis 18. Parallax [mas] N 0.330 0.335 0.340 0.345 0.350 0.355 0.360 0.365 0 10 20 30 40 50 Figure C.198: Parallax distribution for Pismis 18. PMRA (mas/yr) PM D EC (m as /y r) Figure C.199: PMs diagram for Pismis 18. Gbp-Grp M G Figure C.200: CMD for Pismis 18. Figure C.201: Kiel diagram for Pismis 18. EW (L i) (m Å ) Figure C.202: EW (Li)-versus-Teff diagram for Pismis 18. C.3. Old clusters 227 RV [km/s] N 50.5 51.0 51.5 52.0 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 Figure C.203: RV distribution for Melotte 71. Parallax [mas] N 0.330 0.335 0.340 0.345 0.350 0.355 0.360 0.365 0 10 20 30 40 50 Figure C.204: Parallax distribution for Melotte 71. PMRA (mas/yr) PM D EC (m as /y r) Figure C.205: PMs diagram for Melotte 71. Gbp-Grp M G Figure C.206: CMD for Melotte 71. Figure C.207: Kiel diagram for Melotte 71. EW (L i) (m Å ) Figure C.208: EW (Li)-versus-Teff diagram for Melotte 71. 228 Appendix C. Individual figures of Chapter 2 RV [km/s] N 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 0. 0 0. 2 0. 4 0. 6 Figure C.209: RV distribution for Pis- mis 15. Parallax [mas] N 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0 2 4 6 8 Figure C.210: Parallax distribution for Pismis 15. PMRA (mas/yr) PM D EC (m as /y r) Figure C.211: PMs diagram for Pismis 15. Gbp-Grp M G Figure C.212: CMD for Pismis 15. Figure C.213: Kiel diagram for Pismis 15. EW (L i) (m Å ) Figure C.214: EW (Li)-versus-Teff diagram for Pismis 15. C.3. Old clusters 229 RV [km/s] N −43 −42 −41 −40 −39 −38 −37 −36 0. 0 0. 1 0. 2 0. 3 0. 4 Figure C.215: RV distribution for Trumpler 20. Parallax [mas] N 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0 2 4 6 8 10 Figure C.216: Parallax distribution for Trumpler 20. PMRA (mas/yr) PM D EC (m as /y r) Figure C.217: PMs diagram for Trum- pler 20. Gbp-Grp M G Figure C.218: CMD for Trumpler 20. lo gg Teff (K) Figure C.219: Kiel diagram for Trum- pler 20. EW (L i) (m Å ) Figure C.220: EW (Li)-versus-Teff diagram for Trumpler 20. 230 Appendix C. Individual figures of Chapter 2 RV [km/s] N −10.0 −9.5 −9.0 −8.5 −8.0 −7.5 −7.0 0. 0 0. 2 0. 4 0. 6 Figure C.221: RV distribution for Berkeley 44. Parallax [mas] N 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0 2 4 6 8 Figure C.222: Parallax distribution for Berkeley 44. PMRA (mas/yr) PM D EC (m as /y r) Figure C.223: PMs diagram for Berke- ley 44. M G Gbp-Grp Figure C.224: CMD for Berkeley 44. Figure C.225: Kiel diagram for Berkeley 44. EW (L i) (m Å ) Figure C.226: EW (Li)-versus-Teff diagram for Berkeley 44. C.3. Old clusters 231 RV [km/s] N 58.0 58.5 59.0 59.5 60.0 60.5 61.0 61.5 0. 0 0. 2 0. 4 0. 6 Figure C.227: RV distribution for NGC 2243. Parallax [mas] N 0.10 0.15 0.20 0.25 0.30 0.35 0 2 4 6 8 10 Figure C.228: Parallax distribution for NGC 2243. PMRA (mas/yr) PM D EC (m as /y r) Figure C.229: PMs diagram for NGC 2243. Gbp-Grp M G Figure C.230: CMD for NGC 2243. Figure C.231: Kiel diagram for NGC 2243. EW (L i) (m Å ) Figure C.232: EW (Li)-versus-Teff diagram for NGC 2243. 232 Appendix C. Individual figures of Chapter 2 RV [km/s] N 32 33 34 35 36 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 Figure C.233: RV distribution for M67. Parallax [mas] N 1.10 1.12 1.14 1.16 1.18 1.20 1.22 0 5 10 15 20 Figure C.234: Parallax distribution for M67. PMRA (mas/yr) PM D EC (m as /y r) Figure C.235: PMs diagram for M67. Gbp-Grp M G Figure C.236: CMD for M67. Figure C.237: Kiel diagram for M67. EW (L i) (m Å ) Figure C.238: EW (Li)-versus-Teff diagram for M67. Appendix D Long tables of Chapter 2 This appendix describes the long tables containing all the parameters from GES and Gaia which we have used throughout this work, as well as the tables summarizing the membership analysis of Chapter 2 and the final cluster selections for each of the 42 clusters in the sample. The full tables are available in both FITS and Excel format via this Google Drive link. We will now detail the format and columns of these tables, displayed below as truncated tables showing the first 20 rows for intermediate-age cluster NGC 2516 (the same format applies to all clusters in the sample): Firstly, Tables D.4 and D.5 contain the GES parameters (shown in a single file in the link above as ‘NGC2516_GES’, here separated into two tables for con- venience). Tables D.6 and D.7 show all the Gaia EDR3 data, as well the Prot measurements (when available) used in the analysis of Chapter 3. Due to space limitations, these two tables have been similarly separated in the examples of this appendix, and are provided in a single file in the link above (named ‘NGC2516_Gaia_Prot’). Finally, Table D.8 displays the results of the membership analyses of Chapter 2 (shown in the file as ‘NGC2516_selection’). The columns for each table are described as follows: 233 https://drive.google.com/drive/folders/1abgQjkENdapOFf5BvsJ0-OdfSbv6h-s7?usp=sharing 234 Appendix D. Long tables of Chapter 2 Table D.1: GES parameters (see the exemplified Tables D.4 and D.5). Column name Description CNAME GES object name from coordinates RA Right ascension in J2000 (hrs) DEC Declination in J2000 (deg) VRAD Radial velocity (km s−1) E_VRAD Error in radial velocity (km s−1) VSINI vsini rotational velocity (km s−1) E_VSINI Error in vsini (km s−1) TEFF Effective temperature Teff (K) E_TEFF Error in Teff (K) TEFF_IRFM Infrared photometric temperature (K)a E_TEFF_IRFM Error in infrared photometric temperature (K) LOGG logg surface gravity (dex)b E_LOGG Error in logg (dex) GAMMA γ indexc (dex) E_GAMMA Error in γ index (dex) FEH [Fe/H] metallicity (dex) E_FEH Error in [Fe/H] metallicity (dex) EWC_LI Blends-corrected values of EW (Li) (mÅ) E_EWC_LI Error in EW (Li) (mÅ) LIM_EWC_LI Flag for blends-corrected EW (Li) errord EW_LI_UNVEIL The primarily-used veiling-corrected values of EW (Li) (mÅ) E_EW_LI_UNVEIL Error in EW (Li) (mÅ) LIM_EW_LI_UNVEIL Flag for veiling-corrected EW (Li) errorsd LI1 A(Li) neutral Li abundances in logϵ(X) (dex) E_LI1 Error in A(Li) (dex) EW_HA_ACC Hα EW: accretion (Å) E_EW_HA_ACC Error in Hα EW: accretion (Å) HA10 Hα10%, width of the Hα emission line at 10% peak intensity (km s−1) E_HA10 Error in Hα10% (km s−1) EW_HA_CHR Hα chromospheric activity (Å) E_EW_HA_CHR Error in Hα chromospheric activity (Å) a Not shown in Table D.4, primarily measured for young clusters; b Used in this work for intermediate-age and old clusters; c The empirical gravity indicator defined by Damiani et al. (2014) and used in the case of the young clusters; d 0=no flag necessary; 1=EW (Li) corrected by blends contribution using models; 2=EW (Li) measured separately — Li line resolved, UVES only; and 3=Upper limit — no error for EW (Li) is given; 235 Table D.2: Gaia parameters and Prot measurements (see the exemplified Tables D.6 and D.7). Column name Description CNAME GES object name from coordinates parallax π parallax (mas) parallax_error Error in parallax (mas) pmra pmra, PM in RA (mas yr−1) pmra_error Error in pmra (mas yr−1) pmdec pmdec, PM in DEC (mas yr−1) pmdec_error Error in pmdec (mas yr−1) ruwe RUWE renormalized unit weight error phot_g_mean_mag G photometric band (mag) phot_bp_mean_mag GBP photometric band (mag) phot_rp_mean_mag GRP photometric band (mag) phot_g_mean_mag_error Error in G photometric band (mag) phot_bp_mean_mag_error Error in GBP photometric band (mag) phot_rp_mean_mag_error Error in GRP photometric band (mag) bp_rp Obtained Gaia Gbp−rp colour index (mag) Mg Obtained absolute magnitude MG (mag) Prot Prot measurements, when available (d) Table D.3: Membership analysis and candidate selections (see the exemplified Table D.8). Column name Description CNAME GES object name from coordinates RV_mem Membership: RV PM_mem Membership: Proper motions Parallax_mem Membership: Parallax CMD_mem Membership: CMD logg_mem Membership: logg (intermediate-age and old clusters) gamma_mem Membership: γ index (young clusters) Met_mem Membership: [Fe/H] metallicity Li_mem Membership: EW (Li) Cantat_Gaudin_2018 Members from Cantat-Gaudin et al. (2018)a Randich_2018 Members from Randich et al. (2018)a Jackson_2021_MEM3D Members from Jackson et al. (2021)a, b Jackson_2021_MEMQG Members from Jackson et al. (2021)a, c Final Final candidate membersd (Particular_cases Final column listing particular casese a Additional columns, whenever possible, listing candidates according to relevant Gaia studies from the literature; b Jackson et al. (2021) — MEM3D refers to the membership using the full data set; c Jackson et al. (2021) — MEMQC refers to the probability computed using data set filtered to remove targets with suspect Gaia data; d ‘Y’=members; ‘n’=Non-members; e particular cases include the Li-rich giant outliers (listed as ‘Li-rich G’), strong accretors (‘Strong accretor’), and the SB1 and SB2 binary stars (‘SB1’ and ‘SB2’) listed by GES iDR6 and Merle et al. (2017, 2020). 236 A ppen d ix D . Long tables of C hapter 2 Table D.4: NGC 2516 GES parameters (I)a. CNAME RA DEC RV vsini Teff log g γ [Fe/H] (hrs) (deg) (km s−1) (km s−1) (K) (dex) (dex) 07515457-6047568 117.98 -60.80 6.8 ± 0.4 11.1 ± 1.2 4369 ± 76 4.90 ± 0.18 0.920 ± 0.009 0.00 ± 0.09 07515966-6047220 118.00 -60.79 25.8 ± 0.3 < 7.0 4233 ± 78 4.69 ± 0.18 0.907 ± 0.005 0.06 ± 0.10 07520129-6043233 118.01 -60.72 14.5 ± 0.8 . . . . . . . . . 0.830 ± 0.023 . . . 07520389-6050116 118.02 -60.84 25.5 ± 0.3 < 7.0 4256 ± 76 4.90 ± 0.18 0.892 ± 0.005 0.05 ± 0.09 07521002-6044245 118.04 -60.74 25.5 ± 0.3 < 7.0 4153 ± 76 4.74 ± 0.18 0.893 ± 0.005 0.00 ± 0.09 07521382-6047151 118.06 -60.79 24.2 ± 0.3 < 7.0 3993 ± 77 4.75 ± 0.18 0.861 ± 0.007 -0.02 ± 0.10 07521911-6039241 118.08 -60.66 -7.4 ± 0.5 14.6 ± 2.5 3189 ± 96 4.95 ± 0.23 0.824 ± 0.015 -0.38 ± 0.09 07522464-6043006 118.10 -60.72 -4.1 ± 0.6 15.5 ± 2.6 3845 ± 77 4.56 ± 0.18 0.876 ± 0.014 -0.14 ± 0.09 07523060-6049134 118.13 -60.82 23.4 ± 0.4 < 7.0 3444 ± 108 4.88 ± 0.24 0.812 ± 0.012 -0.29 ± 0.09 07523629-6046405 118.15 -60.78 31.2 ± 0.5 < 7.0 3883 ± 107 4.85 ± 0.24 0.815 ± 0.013 -0.08 ± 0.08 07524604-6039537 118.19 -60.66 23.7 ± 0.3 < 7.0 4141 ± 76 4.76 ± 0.18 0.888 ± 0.005 0.00 ± 0.09 07525994-6053288 118.25 -60.89 23.4 ± 0.3 10.0 ± 1.1 4053 ± 76 4.92 ± 0.18 0.844 ± 0.008 -0.03 ± 0.10 07530001-6042137 118.25 -60.70 5.7 ± 0.4 9.0 ± 1.2 3921 ± 77 4.69 ± 0.18 0.856 ± 0.009 -0.01 ± 0.10 07530057-6048094 118.25 -60.80 24.1 ± 0.3 9.0 ± 1.0 3913 ± 75 4.80 ± 0.18 0.838 ± 0.007 -0.08 ± 0.09 07530259-6050259 118.26 -60.84 28.4 ± 1.0 84.3 ± 1.3 . . . . . . 0.962 ± 0.004 . . . 07531031-6046400 118.29 -60.78 23.3 ± 0.4 13.3 ± 1.2 3623 ± 110 4.87 ± 0.23 0.830 ± 0.012 -0.27 ± 0.09 07531177-6041390 118.30 -60.69 23.4 ± 0.4 8.4 ± 1.3 3841 ± 108 4.84 ± 0.23 0.836 ± 0.010 -0.11 ± 0.09 07531326-6043422 118.31 -60.73 3.6 ± 0.3 < 7.0 3972 ± 77 4.79 ± 0.18 0.858 ± 0.007 0.01 ± 0.09 07532107-6058131 118.34 -60.97 22.4 ± 0.5 10.5 ± 1.1 3879 ± 108 4.85 ± 0.23 0.838 ± 0.014 -0.08 ± 0.09 07532163-6102129 118.34 -61.04 23.5 ± 0.4 9.3 ± 1.6 3620 ± 108 4.84 ± 0.23 0.826 ± 0.011 -0.22 ± 0.09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a This is a truncated table showing the first 20 rows. Full tables available via this Google Drive link. https://drive.google.com/drive/folders/1abgQjkENdapOFf5BvsJ0-OdfSbv6h-s7?usp=sharing 237 Table D.5: NGC 2516 GES parameters (II)a. CNAME EW (Li) EW (Li) EW (Li) EW (Li) A(Li) Hα Hα10% Hα (blends-corrected) (mÅ) error flag (veiling-corrected) (mÅ) error flag c (dex) (accretion) (Å) (km s−1) (activity) (Å) 07515457-6047568 < 22 3 < 22 3 < 0.2 . . . . . . . . . 07515966-6047220 . . . . . . 75 ± 5 0 0.6 ± 0.1 0.82 ± 0.07 94.81 ± 1.79 1.78 ± 0.14 07520129-6043233 . . . . . . 108 ± 24 0 . . . . . . . . . . . . 07520389-6050116 < 13 3 13 ± 6 0 < -0.4 . . . . . . 0.78 ± 0.09 07521002-6044245 . . . . . . 39 ± 6 0 -0.1 ± 0.3 0.16 ± 0.07 106.61 ± 6.58 0.92 ± 0.09 07521382-6047151 . . . . . . 86 ± 7 0 0.4 ± 0.2 0.19 ± 0.11 119.19 ± 9.95 1.08 ± 0.14 07521911-6039241 . . . . . . 127 ± 15 0 < -1.0 . . . . . . . . . 07522464-6043006 . . . . . . 84 ± 15 0 0.0 ± 0.3 0.42 ± 0.32 . . . 1.71 ± 0.35 07523060-6049134 . . . . . . 128 ± 13 0 -0.7 ± 0.5 0.76 ± 0.14 . . . 1.61 ± 0.16 07523629-6046405 . . . . . . 117 ± 14 0 0.4 ± 0.3 . . . . . . 0.18 ± 0.16 07524604-6039537 . . . . . . 35 ± 6 0 -0.3 ± 0.4 0.25 ± 0.07 96.33 ± 2.59 1.22 ± 0.12 07525994-6053288 . . . . . . 70 ± 8 0 0.4 ± 0.2 0.26 ± 0.09 114.25 ± 33.15 1.12 ± 0.16 07530001-6042137 . . . . . . 80 ± 9 0 0.2 ± 0.2 . . . . . . 0.09 ± 0.07 07530057-6048094 . . . . . . 57 ± 8 0 -0.2 ± 0.3 . . . . . . 0.49 ± 0.08 07530259-6050259 . . . . . . < 9 3 . . . 0.45 ± 0.11 241.81 ± 37.44 1.51 ± 0.13 07531031-6046400 . . . . . . 98 ± 13 0 -0.3 ± 0.5 1.47 ± 0.19 97.84 ± 3.38 2.59 ± 0.21 07531177-6041390 . . . . . . 126 ± 10 0 0.5 ± 0.2 0.22 ± 0.11 92.52 ± 2.90 1.13 ± 0.16 07531326-6043422 . . . . . . 74 ± 7 0 0.2 ± 0.2 . . . . . . 0.08 ± 0.07 07532107-6058131 . . . . . . 129 ± 14 0 0.6 ± 0.2 1.99 ± 0.27 132.89 ± 10.14 3.46 ± 0.35 07532163-6102129 . . . . . . 101 ± 12 0 -0.5 ± 0.6 2.14 ± 0.19 119.94 ± 6.70 3.28 ± 0.36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a This is a truncated table showing the first 20 rows. Full tables available via this Google Drive link. https://drive.google.com/drive/folders/1abgQjkENdapOFf5BvsJ0-OdfSbv6h-s7?usp=sharing 238 A ppen d ix D . Long tables of C hapter 2 Table D.6: NGC 2516 Gaia parametersa. CNAME π pmra pmdec RUWE G GBP GRP GBP−RP MG (mas) (mas yr−1) (mas yr−1) error (mag) (mag) (mag) (mag) (mag) 07515457-6047568 2.560 ± 0.027 -5.73 ± 0.04 10.74 ± 0.03 1.0 15.752 ± 0.003 16.573 ± 0.004 14.868 ± 0.004 1.71 7.79 07515966-6047220 2.435 ± 0.032 -3.93 ± 0.04 11.10 ± 0.04 1.0 15.965 ± 0.003 16.848 ± 0.006 15.037 ± 0.004 1.81 7.90 07520129-6043233 2.111 ± 0.061 -24.60 ± 0.09 28.61 ± 0.08 1.0 17.420 ± 0.003 18.653 ± 0.017 16.347 ± 0.006 2.31 9.04 07520389-6050116 2.462 ± 0.028 -4.19 ± 0.04 11.49 ± 0.03 1.0 15.928 ± 0.003 16.807 ± 0.005 15.012 ± 0.004 1.79 7.88 07521002-6044245 2.403 ± 0.032 -4.83 ± 0.04 11.49 ± 0.04 1.1 16.087 ± 0.003 16.998 ± 0.006 15.149 ± 0.004 1.85 7.99 07521382-6047151 2.457 ± 0.042 -4.62 ± 0.06 10.61 ± 0.05 1.0 16.604 ± 0.003 17.642 ± 0.008 15.599 ± 0.005 2.04 8.56 07521911-6039241 3.613 ± 0.073 -16.21 ± 0.11 2.75 ± 0.09 1.0 17.731 ± 0.003 19.182 ± 0.020 16.564 ± 0.006 2.62 10.52 07522464-6043006 3.367 ± 0.357 -1.59 ± 0.50 0.76 ± 0.45 6.0 17.814 ± 0.003 18.607 ± 0.016 16.330 ± 0.006 2.28 10.45 07523060-6049134 2.401 ± 0.068 -4.60 ± 0.10 11.72 ± 0.08 1.0 17.514 ± 0.003 18.877 ± 0.024 16.376 ± 0.006 2.50 9.42 07523629-6046405 1.731 ± 0.063 -3.34 ± 0.09 -0.66 ± 0.10 0.9 17.441 ± 0.003 18.664 ± 0.022 16.370 ± 0.006 2.29 8.63 07524604-6039537 2.443 ± 0.030 -3.98 ± 0.04 10.94 ± 0.04 1.0 16.127 ± 0.003 17.047 ± 0.007 15.183 ± 0.005 1.86 8.07 07525994-6053288 2.500 ± 0.045 -4.32 ± 0.06 11.44 ± 0.06 1.0 16.696 ± 0.003 17.794 ± 0.009 15.666 ± 0.005 2.13 8.69 07530001-6042137 2.030 ± 0.043 -14.78 ± 0.06 13.56 ± 0.06 1.1 16.685 ± 0.003 17.722 ± 0.009 15.687 ± 0.004 2.03 8.22 07530057-6048094 2.441 ± 0.048 -4.25 ± 0.07 10.88 ± 0.07 1.1 16.779 ± 0.003 17.899 ± 0.008 15.711 ± 0.005 2.19 8.72 07530259-6050259 2.435 ± 0.028 -4.12 ± 0.04 10.96 ± 0.04 1.0 15.852 ± 0.003 16.709 ± 0.006 14.935 ± 0.006 1.77 7.78 07531031-6046400 2.531 ± 0.060 -3.41 ± 0.09 12.14 ± 0.09 0.9 17.420 ± 0.003 18.765 ± 0.022 16.297 ± 0.006 2.47 9.44 07531177-6041390 2.328 ± 0.049 -4.75 ± 0.07 12.04 ± 0.07 1.0 17.006 ± 0.003 18.124 ± 0.012 15.956 ± 0.006 2.17 8.84 07531326-6043422 2.142 ± 0.037 -2.38 ± 0.05 7.98 ± 0.06 1.0 16.508 ± 0.003 17.506 ± 0.008 15.521 ± 0.004 1.99 8.16 07532107-6058131 2.412 ± 0.048 -4.36 ± 0.07 11.44 ± 0.06 1.0 16.858 ± 0.003 18.016 ± 0.014 15.795 ± 0.005 2.22 8.77 07532163-6102129 2.392 ± 0.053 -4.02 ± 0.07 11.32 ± 0.08 1.0 17.175 ± 0.003 18.430 ± 0.017 16.080 ± 0.006 2.35 9.07 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a This is a truncated table showing the first 20 rows. Full tables available via this Google Drive link. https://drive.google.com/drive/folders/1abgQjkENdapOFf5BvsJ0-OdfSbv6h-s7?usp=sharing 239 Table D.7: NGC 2516 Prot measurementsa. CNAME Prot (d) Prot (d) Prot (d) Prot (d) Irwin et al. (2007) Wright et al. (2011) Jackson et al. (2016) Fritzewski et al. (2020) 07515457-6047568 . . . . . . . . . . . . 07515966-6047220 . . . . . . . . . . . . 07520129-6043233 . . . . . . . . . . . . 07520389-6050116 . . . . . . . . . . . . 07521002-6044245 . . . . . . . . . . . . 07521382-6047151 . . . . . . . . . . . . 07521911-6039241 . . . . . . . . . . . . 07522464-6043006 . . . . . . . . . . . . 07523060-6049134 . . . . . . . . . . . . 07523629-6046405 . . . . . . . . . . . . 07524604-6039537 . . . . . . . . . . . . 07525994-6053288 5.66 . . . 5.66 5.66 07530001-6042137 . . . . . . . . . . . . 07530057-6048094 11.61 . . . 11.61 11.61 07530259-6050259 . . . . . . 4.58 . . . 07531031-6046400 . . . . . . 2.52 . . . 07531177-6041390 4.58 . . . 4.58 4.58 07531326-6043422 . . . . . . . . . . . . 07532107-6058131 2.52 . . . 2.52 2.52 07532163-6102129 2.34 . . . 2.34 2.34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a This is a truncated table showing the first 20 rows. Full tables available via this Google Drive link. https://drive.google.com/drive/folders/1abgQjkENdapOFf5BvsJ0-OdfSbv6h-s7?usp=sharing 240 A ppen d ix D . Long tables of C hapter 2 Table D.8: NGC 2516 membership analysis and selectiona. CNAME Membership Cantat-Gaudin Randich Jackson et al (2021) Final Particular γ RV PMs π CMD [Fe/H] EW (Li) et al (2018) et al (2018) MEM3D MEMQG members cases 07515457-6047568 N . . . . . . . . . . . . . . . . . . . . . N 0.5901 0.5542 n . . . 07515966-6047220 Y Y Y Y Y Y Y Y Y 0.9991 0.9991 Y . . . 07520129-6043233 N . . . . . . . . . . . . . . . . . . . . . Y 0 0 . . . . . . 07520389-6050116 Y Y Y Y Y Y Y Y Y 0.9997 0.9997 Y . . . 07521002-6044245 Y Y Y Y Y Y Y Y Y 0.9998 0.9998 Y . . . 07521382-6047151 Y Y Y Y Y Y Y N Y 0.9999 0.9999 Y . . . 07521911-6039241 N . . . . . . . . . . . . . . . . . . . . . N 0 0 n . . . 07522464-6043006 N . . . . . . . . . . . . . . . . . . . . . N 0 -1 n . . . 07523060-6049134 Y Y Y Y Y Y Y . . . Y 0.9999 0.9999 Y . . . 07523629-6046405 N . . . . . . . . . . . . . . . . . . . . . Y 0 0 n . . . 07524604-6039537 Y Y Y Y Y Y Y Y Y 0.9999 0.9999 Y . . . 07525994-6053288 Y Y Y Y Y Y Y . . . Y 1 1 Y . . . 07530001-6042137 N . . . . . . . . . . . . . . . . . . . . . N 0 0 n . . . 07530057-6048094 Y Y Y Y Y Y Y . . . Y 0.9999 1 Y . . . 07530259-6050259 N . . . . . . . . . . . . . . . . . . Y Y 0.9967 0.9971 . . . . . . 07531031-6046400 Y N . . . . . . . . . . . . . . . . . . Y 0.99 0.9854 n . . . 07531177-6041390 Y Y Y Y Y Y Y . . . Y 0.9998 0.9999 Y . . . 07531326-6043422 N . . . . . . . . . . . . . . . . . . . . . N 0 0 n . . . 07532107-6058131 Y Y Y Y Y Y Y . . . Y 0.9999 0.9999 Y . . . 07532163-6102129 Y Y Y Y Y Y Y Y Y 0.9999 0.9999 Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a This is a truncated table showing the first 20 rows. Full tables available via this Google Drive link. https://drive.google.com/drive/folders/1abgQjkENdapOFf5BvsJ0-OdfSbv6h-s7?usp=sharing Appendix E Individual figures of Chapter 3 This appendix includes all the individual figures corresponding to the analysis of Chapter 3, For each of the 42 clusters in the sample, we firstly show EW (Li)-versus-Teff diagrams colour-coded by both rotation (both vsini and Prot, when available) and Hα activity. For a description of these figures, we refer to the individual notes of Appendix B. In addition, in this appendix we also show all the figures displaying Prot (when available), vsini and Hα activity opposite the G-Grp colour-index. These figures are organized by age ranges from the SFRs to the oldest clusters, with Prot-versus-G-Grp situated at the top, vsini-versus-G-Grp as the middle panel, and Hα-versus-G-Grp as the bottom panel. E.1 Young clusters 241 242 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) Pr ot (d ) Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.1: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for NGC 6530. E.1. Young clusters 243 Teff (K) EW (L i) (m Å ) Pr ot (d ) Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.2: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for ρ Oph. 244 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Figure E.3: EW (Li)-versus-Teff diagram colour-coded by vsini for Trumpler 14. No values of Hα are reported in the iDR6 GES file for the candidate selection of this cluster. E.1. Young clusters 245 Teff (K) EW (L i) (m Å ) Pr ot (d ) Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.4: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for Cha I. 246 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.5: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 2244. E.1. Young clusters 247 Teff (K) EW (L i) (m Å ) Pr ot (d ) Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.6: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for NGC 2264. 248 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.7: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for λ Ori. E.1. Young clusters 249 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.8: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for Col 197. 250 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) Pr ot (d ) Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.9: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for γ Vel, without differentiating between γ Vel A and γ Vel B. E.1. Young clusters 251 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Figure E.10: EW (Li)-versus-Teff diagram colour-coded by vsini for γ Vel A. Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.11: EW (Li)-versus-Teff diagram colour-coded by Hα for γ Vel A. Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Figure E.12: EW (Li)-versus-Teff diagram colour-coded by vsini for γ Vel B. Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.13: EW (Li)-versus-Teff diagram colour-coded by Hα for γ Vel B. 252 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.14: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 2232. E.1. Young clusters 253 Teff (K) EW (L i) (m Å ) Pr ot (d ) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) 10 EW (L i) (m Å ) EW (H α) (Å ) 10 Teff (K) Figure E.15: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for NGC 2547, without differentiating between NGC 2547 A and NGC 2547 B. 254 Appendix E. Individual figures of Chapter 3 20 Teff (K) EW (L i) (m Å ) Pr ot (d ) 20 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) 20 Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.16: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for NGC 2547 A. E.1. Young clusters 255 Teff (K) EW (L i) (m Å ) Pr ot (d ) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) 2451 B 10-20 Figure E.17: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for NGC 2547 B. 256 Appendix E. Individual figures of Chapter 3 EW (L i) (m Å ) Pr ot (d ) Teff (K) Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.18: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for IC 2391. E.1. Young clusters 257 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) EW (L i) (m Å ) EW (H α) (Å ) Teff (K) 35 Figure E.19: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for IC 2602. 258 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) EW (L i) (m Å ) EW (H α) (Å ) Teff (K) Figure E.20: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for IC 4665. E.1. Young clusters 259 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.21: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel) and Hα (bottom panel) for NGC 2451, without differentiating between NGC 2451 A and NGC 2451 B. 260 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Figure E.22: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2451 A. Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.23: EW (Li)-versus-Teff diagram colour-coded by Hα for NGC 2451 A. Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Figure E.24: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2451 B. Teff (K) EW (L i) (m Å ) EW (H α) (Å ) 39 Figure E.25: EW (Li)-versus-Teff diagram colour-coded by Hα for NGC 2451 B. E.2. Intermediate-age clusters 261 E.2 Intermediate-age clusters Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.26: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 6405. 262 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.27: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for Blanco 1. E.2. Intermediate-age clusters 263 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.28: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 6067. 264 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Figure E.29: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 6649. No values of Hα are reported in the iDR6 GES file for the candidate selection of this cluster. E.2. Intermediate-age clusters 265 Teff (K) EW (L i) (m Å ) Pr ot (d ) Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.30: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for NGC 2516. 266 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.31: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 6709. E.2. Intermediate-age clusters 267 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.32: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 6259. 268 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Teff (K) EW (L i) (m Å ) EW (H α) (Å ) Figure E.33: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 6705. E.2. Intermediate-age clusters 269 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Figure E.34: EW (Li)-versus-Teff diagram colour-coded by vsini for Berkeley 30. No values of Hα are reported in the iDR6 GES file for the candidate selection of this cluster. Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Figure E.35: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 6281. No values of Hα are reported in the iDR6 GES file for the candidate selection of this cluster. 270 Appendix E. Individual figures of Chapter 3 Teff (K) EW (L i) (m Å ) Pr ot (d ) Figure E.36: EW (Li)-versus-Teff diagram colour-coded by Prot (top panel), vsini (middle panel), and Hα (bottom panel) for NGC 3532. E.2. Intermediate-age clusters 271 Teff (K) EW (L i) (m Å ) vs in i ( km /s ) Figure E.37: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 4815. No values of Hα are reported in the iDR6 GES file for the candidate selection of this cluster. 272 Appendix E. Individual figures of Chapter 3 Figure E.38: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 6633. E.3. Old clusters 273 E.3 Old clusters 274 Appendix E. Individual figures of Chapter 3 Figure E.39: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 2477. E.3. Old clusters 275 Figure E.40: EW (Li)-versus-Teff diagram colour-coded by vsini for Trumpler 23. No values of Hα are reported in the iDR6 GES file for the candidate selection of this cluster. 276 Appendix E. Individual figures of Chapter 3 Figure E.41: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for Berkeley 81. E.3. Old clusters 277 Figure E.42: EW (Li)-versus-Teff diagram colour-coded by vsini for NGC 2355. No values of Hα are reported in the iDR6 GES file for the candidate selection of this cluster. 278 Appendix E. Individual figures of Chapter 3 Figure E.43: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 6802. E.3. Old clusters 279 Figure E.44: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 6005. 280 Appendix E. Individual figures of Chapter 3 Figure E.45: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for Pismis 18. E.3. Old clusters 281 Figure E.46: EW (Li)-versus-Teff diagram colour-coded by vsini for Melotte 71. No values of Hα are reported in the iDR6 GES file for the candidate selection of this cluster. 282 Appendix E. Individual figures of Chapter 3 Figure E.47: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for Pismis 15. E.3. Old clusters 283 Figure E.48: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for Trumpler 20. 284 Appendix E. Individual figures of Chapter 3 Figure E.49: EW (Li)-versus-Teff diagram colour-coded by vsini for Berkeley 44. No values of Hα are reported in the iDR6 GES file for the candidate selection of this cluster. E.3. Old clusters 285 Figure E.50: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for NGC 2243. 286 Appendix E. Individual figures of Chapter 3 Figure E.51: EW (Li)-versus-Teff diagram colour-coded by vsini (top panel), and Hα (bottom panel) for M67. Appendix F Tables for the empirical Li envelopes of Chapter 4 This final appendix lists a series of short tables including the Teff and EW (Li) values which were used to create the empirical Li envelopes for each of the 27 out of 42 clusters in our sample. These Li envelopes are discussed in Chapter 4. Similarly to the tables in Appendixes D, ?? and ??, the values of EW (Li) used to create all Li envelopes are corrected (subtracted adja- cent Fe (6707.43 Å line), and we have also used the veiling-corrected EW (Li)s whenever available. Table F.1: Upper Li envelope for NGC 6530 Teff (K) EW (Li) (mÅ) 6867 39 5850 241 5099 397 4736 440 4595 475 4452 546 4286 590 4202 631 3742 721 Table F.2: Upper Li envelope for Rho Oph Teff (K) EW (Li) (mÅ) 3231 844 3837 713 4058 661 4476 531 287 288 Appendix F. Tables for the empirical Li envelopes of Chapter 4 Table F.3: Upper Li envelope for Trumpler 14 Teff (K) EW (Li) (mÅ) 6941 50 6801 91 6421 187 5982 243 5760 257 5360 334 5165 368 4992 406 4854 446 4582 505 4461 540 4301 597 Table F.4: Upper Li envelope for Cha I Teff (K) EW (Li) (mÅ) 5084 404.1 4307.36 541.5 3988.39 660.9 3273.17 799.5 Table F.5: Upper Li envelope for NGC 2244 Teff (K) EW (Li) (mÅ) 3735 693 3973 661 4242 616 4409 582 4545 508 4577 474 4766 416 5035 384 5074 360 5382 292 6796 74 289 Table F.6: Upper Li envelope for NGC 2264 Teff (K) EW (Li) (mÅ) 6275 168 6127 218 5843 242 5428 327 4993 400 4795 442 4768 498 4466 559 4129 624 3796 685 3618 717 3466 736 Table F.7: Upper Li envelope for λ Ori Teff (K) EW (Li) (mÅ) 3101 771 3534 708 3865 653 3968 623 4441 542 4898 437 5181 365 5218 306 6113 191 6200 153 Table F.8: Upper Li envelope for Col 197 Teff (K) EW (Li) (mÅ) 6818 84 6033 206 5120 353 5026 434 4826 469 4546 519 4108 634 3852 679 290 Appendix F. Tables for the empirical Li envelopes of Chapter 4 Table F.9: Upper Li envelope for γ Vel Teff (K) EW (Li) (mÅ) 6010 195 5357 312 4971 380 4558 450 4287 527 3958 562 3765 552 3668 538 3470 562 3356 601 3172 671 3056 718 Table F.10: Lower Li envelope for γ Vel Teff (K) EW (Li) (mÅ) 3968 416 3812 387 3531 346 3423 251 3381 199 3305 126 3232 103 Table F.11: Upper Li envelope for NGC 2232 Teff (K) EW (Li) (mÅ) 6836 52 6330 117 5927 193 5420 263 4506 387 3799 360 3709 118 291 Table F.12: Upper Li envelope for NGC 2547 A Teff (K) EW (Li) (mÅ) 6984 59 6662 114 5650 262 4469 369 4024 347 3866 204 3744 119 3726 114 Table F.13: Upper Li envelope for NGC 2547 B Teff (K) EW (Li) (mÅ) 3506 170 3615 391 3565 451 3086 669 Table F.14: Upper Li envelope for IC 2391, IC 2602 and IC 4665 Teff (K) EW (Li) (mÅ) 6890 60 6515 113 6051 225 4923 340 4151 320 3945 150 3850 112 3370 100 3280 95 3236 112 3075 364 3026 432 Table F.15: Upper Li envelope for Blanco 1 Teff (K) EW (Li) (mÅ) 6538 78 5766 192 5303 269 4459 268 4136 199 3926 103 292 Appendix F. Tables for the empirical Li envelopes of Chapter 4 Table F.16: Lower Li envelope for Blanco 1 Teff (K) EW (Li) (mÅ) 6317 91 6038 134 5960 146 5677 158 5446 152 5017 130 4875 116 4520 38 Table F.17: Upper Li envelope for NGC 2516 Teff (K) EW (Li) (mÅ) 6839 65 6531 109 5453 214 5069 267 4740 281 4453 275 4058 110 Table F.18: Lower Li envelope for NGC 2516 Teff (K) EW (Li) (mÅ) 6789 32 6335 91 5996 122 5745 130 5557 131 5234 120 4795 72 4668 46 4256 13 293 Table F.19: Upper Li envelope for NGC 6709 Teff (K) EW (Li) (mÅ) 7411 34 6628 94 5601 199 5293 223 5015 222 4558 182 4412 114 4366 73 4200 51 Table F.20: Lower Li envelope for NGC 6709 Teff (K) EW (Li) (mÅ) 6641 31 6086 93 5743 121 5216 117 4743 43 Table F.21: Upper Li envelope for NGC 6705 Teff (K) EW (Li) (mÅ) 6969 56 6554 113 6098 153 5605 195 4424 159 4335 82 Table F.22: Lower Li envelope for NGC 6705 Teff (K) EW (Li) (mÅ) 7000 14 6587 56 6234 92 5700 91 5395 91 4798 72 4613 43 4339 18 294 Appendix F. Tables for the empirical Li envelopes of Chapter 4 Table F.23: Upper Li envelope for NGC 3532 Teff (K) EW (Li) (mÅ) 6837 57 6254 116 5995 130 4989 165 4734 169 4441 113 4340 81 4178 49 4062 38 Table F.24: Lower Li envelope for NGC 3532 Teff (K) EW (Li) (mÅ) 6888 3 6662 42 6330 80 6183 96 5909 95 5557 78 5318 55 5005 22 4594 8 Table F.25: Upper Li envelope for NGC 6633 Teff (K) EW (Li) (mÅ) 5879 96 5716 64 5420 39 5211 19 4946 12 4878 11 295 Table F.26: Upper Li envelope for NGC 2355 Teff (K) EW (Li) (mÅ) 6975 55 6716 68 6248 81 5773 69 5655 60 5304 32 5157 18 4976 9 Table F.27: Upper Li envelope for NGC 6802 Teff (K) EW (Li) (mÅ) 6914 57 6341 80 6097 78 5074 31 4920 15 Table F.28: Upper Li envelope for NGC 6005 Teff (K) EW (Li) (mÅ) 6651 87 6156 83 5433 46 5290 28 4785 9 Table F.29: Upper Li envelope for Pismis 15 Teff (K) EW (Li) (mÅ) 6223 80 5600 53 5183 16 296 Appendix F. 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Introduction Lithium as an age indicator Stellar nucleosynthesis and Li production Lithium depletion for FGKM stars The lithium depletion boundary (LDB) Open clusters Li-rich giants Calibrating the Li-age relation Lithium and rotation Lithium and activity Lithium and accretion processes Lithium and metallicity Data surveys and missions The Gaia-ESO Survey (GES) Gaia CoRoT, Kepler, K2, and TESS Description of the work Chapter 2. Cluster sample and membership selections Data GES spectra and data reduction Cluster sample Selection criteria and membership analysis Kinematic selection Proper motions and parallaxes Colour-magnitude diagrams (CMDs) Gravity indicators: Kiel diagram and index Metallicity Lithium content Comparison with other Gaia studies Identification of giant and non-giant contaminants Cluster member selections Discussion Chapter 3. Dependence with rotation, activity and metallicity Rotation vsini and Prot The Li-rotation relation Chromospheric activity The Li-activity relation Colour-rotation and colour-activity diagrams [Fe/H] metallicity Chapter 4. The Li-age relation: Creating Li envelopes Empirical lithium envelopes Evolutionary models and the LDB Chapter 5. Summary, conclusions and future work Results and scientific prospects Conclusions Future work Appendix A. List of publications In this thesis Published in refereed journals Conference proceedings Additional publications Published in refereed journals Appendix B. Cluster selections: Individual notes of Chapter 2 and 3 SFRs (age 6 Myr) and young open clusters (age 50 Myr) Intermediate-age clusters (age=50–700 Myr) Old clusters (age >700 Myr) Appendix C. Individual figures of Chapter 2 Young clusters Intermediate-age clusters Old clusters Appendix D. Long tables of Chapter 2 Appendix E. Individual figures of Chapter 3 Young clusters Intermediate-age clusters Old clusters Appendix F. Tables for the empirical Li envelopes of Chapter 4 Bibliography