ar X iv :1 11 1. 24 72 v1 [ as tr o- ph .H E ] 10 N ov 2 01 1 Search for signatures of magnetically-induced alignment in the arrival directions measured by the Pierre Auger Observatory The Pierre Auger Collaboration P. Abreu74, M. Aglietta57, E.J. Ahn93, I.F.M. Albuquerque19, D. Allard33, I. Allekotte1, J. Allen96, P. Allison98, J. Alvarez Castillo67, J. Alvarez-Muñiz84, M. Ambrosio50, A. Aminaei68, L. Anchordoqui109, S. Andringa74, T. Antičić27, A. Anzalone56, C. Aramo50, E. Arganda81, F. Arqueros81, H. Asorey1, P. Assis74, J. Aublin35, M. Ave41, M. Avenier36, G. Avila12, T. Bäcker45, M. Balzer40, K.B. Barber13, A.F. Barbosa16, R. Bardenet34, S.L.C. Barroso22, B. Baughman98, J. Bäuml39, J.J. Beatty98, B.R. Becker106, K.H. Becker38, A. Bellétoile37, J.A. Bellido13, S. BenZvi108, C. Berat36, X. Bertou1, P.L. Biermann42, P. Billoir35, F. Blanco81, M. Blanco82, C. Bleve38, H. Blümer41, 39, M. Bohá̌cová29, D. Boncioli51, C. Bonifazi25, 35, R. Bonino57, N. Borodai72, J. Brack91, P. 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Ziolkowski45 1 Centro Atómico Bariloche and Instituto Balseiro (CNEA- UNCuyo-CONICET), San Carlos de Bariloche, Argentina 2 Centro Atómico Constituyentes (Comisión Nacional de Energía Atómica/CONICET/UTN-FRBA), Buenos Aires, Argentina 3 Centro de Investigaciones en Láseres y Aplicaciones, CITEFA and CONICET, Argentina 4 Departamento de Física, FCEyN, Universidad de Buenos Airesy CONICET, Argentina 2 7 IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 8 Instituto de Astronomía y Física del Espacio (CONICET- UBA), Buenos Aires, Argentina 9 Instituto de Física de Rosario (IFIR) - CONICET/U.N.R. and Facultad de Ciencias Bioquímicas y Farmacéuticas U.N.R., Rosario, Argentina 10 National Technological University, Faculty Mendoza (CONICET/CNEA), Mendoza, Argentina 11 Pierre Auger Southern Observatory, Malargüe, Argentina 12 Pierre Auger Southern Observatory and Comisión Nacional deEnergía Atómica, Malargüe, Argentina 13 University of Adelaide, Adelaide, S.A., Australia 16 Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ,Brazil 17 Pontifícia Universidade Católica, Rio de Janeiro, RJ, Brazil 18 Universidade de São Paulo, Instituto de Física, São Carlos,SP, Brazil 19 Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil 20 Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil 21 Universidade Estadual de Feira de Santana, Brazil 22 Universidade Estadual do Sudoeste da Bahia, Vitoria da Conquista, BA, Brazil 23 Universidade Federal da Bahia, Salvador, BA, Brazil 24 Universidade Federal do ABC, Santo André, SP, Brazil 25 Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro, RJ, Brazil 26 Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil 27 Rudjer Bošković Institute, 10000 Zagreb, Croatia 28 Charles University, Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics, Prague, Czech Republic 29 Institute of Physics of the Academy of Sciences of the Czech Republic, Prague, Czech Republic 30 Palacky University, RCATM, Olomouc, Czech Republic 32 Institut de Physique Nucléaire d’Orsay (IPNO), UniversitéParis 11, CNRS-IN2P3, Orsay, France 33 Laboratoire AstroParticule et Cosmologie (APC), Université Paris 7, CNRS-IN2P3, Paris, France 34 Laboratoire de l’Accélérateur Linéaire (LAL), UniversitéParis 11, CNRS-IN2P3, Orsay, France 35 Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Universités Paris 6 et Paris 7, CNRS-IN2P3, Paris, France 36 Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Université Joseph Fourier, INPG, CNRS-IN2P3, Grenoble, France 37 SUBATECH, École des Mines de Nantes, CNRS-IN2P3, Université de Nantes, Nantes, France 38 Bergische Universität Wuppertal, Wuppertal, Germany 39 Karlsruhe Institute of Technology - Campus North - Institutfür Kernphysik, Karlsruhe, Germany 40 Karlsruhe Institute of Technology - Campus North - Institutfür Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany 41 Karlsruhe Institute of Technology - Campus South - Institutfür Experimentelle Kernphysik (IEKP), Karlsruhe, Germany 42 Max-Planck-Institut für Radioastronomie, Bonn, Germany 43 RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany 44 Universität Hamburg, Hamburg, Germany 45 Universität Siegen, Siegen, Germany 46 Dipartimento di Fisica dell’Università and INFN, Genova, Italy 47 Università dell’Aquila and INFN, L’Aquila, Italy 48 Università di Milano and Sezione INFN, Milan, Italy 49 Dipartimento di Fisica dell’Università del Salento and Sezione INFN, Lecce, Italy 50 Università di Napoli "Federico II" and Sezione INFN, Napoli, Italy 51 Università di Roma II "Tor Vergata" and Sezione INFN, Roma, Italy 52 Università di Catania and Sezione INFN, Catania, Italy 53 Università di Torino and Sezione INFN, Torino, Italy 54 Dipartimento di Ingegneria dell’Innovazione dell’Università del Salento and Sezione INFN, Lecce, Italy 56 Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo(INAF), Palermo, Italy 57 Istituto di Fisica dello Spazio Interplanetario (INAF), Università di Torino and Sezione INFN, Torino, Italy 58 INFN, Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy 61 Università di Palermo and Sezione INFN, Catania, Italy 63 Benemérita Universidad Autónoma de Puebla, Puebla, Mexico 64 Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV), México, D.F., Mexico 66 Universidad Michoacana de San Nicolas de Hidalgo, Morelia,Michoacan, Mexico 67 Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexico 3 68 IMAPP, Radboud University Nijmegen, Netherlands 69 Kernfysisch Versneller Instituut, University of Groningen, Groningen, Netherlands 70 Nikhef, Science Park, Amsterdam, Netherlands 71 ASTRON, Dwingeloo, Netherlands 72 Institute of Nuclear Physics PAN, Krakow, Poland 73 University of Łódź, Łódź, Poland 74 LIP and Instituto Superior Técnico, Technical University of Lisbon, Portugal 78 J. Stefan Institute, Ljubljana, Slovenia 79 Laboratory for Astroparticle Physics, University of Nova Gorica, Slovenia 80 Instituto de Física Corpuscular, CSIC-Universitat de València, Valencia, Spain 81 Universidad Complutense de Madrid, Madrid, Spain 82 Universidad de Alcalá, Alcalá de Henares (Madrid), Spain 83 Universidad de Granada & C.A.F.P.E., Granada, Spain 84 Universidad de Santiago de Compostela, Spain 85 Rudolf Peierls Centre for Theoretical Physics, Universityof Oxford, Oxford, United Kingdom 87 School of Physics and Astronomy, University of Leeds, United Kingdom 88 Argonne National Laboratory, Argonne, IL, USA 89 Case Western Reserve University, Cleveland, OH, USA 90 Colorado School of Mines, Golden, CO, USA 91 Colorado State University, Fort Collins, CO, USA 92 Colorado State University, Pueblo, CO, USA 93 Fermilab, Batavia, IL, USA 94 Louisiana State University, Baton Rouge, LA, USA 95 Michigan Technological University, Houghton, MI, USA 96 New York University, New York, NY, USA 97 Northeastern University, Boston, MA, USA 98 Ohio State University, Columbus, OH, USA 99 Pennsylvania State University, University Park, PA, USA 100 Southern University, Baton Rouge, LA, USA 101 University of Chicago, Enrico Fermi Institute, Chicago, IL, USA 105 University of Nebraska, Lincoln, NE, USA 106 University of New Mexico, Albuquerque, NM, USA 108 University of Wisconsin, Madison, WI, USA 109 University of Wisconsin, Milwaukee, WI, USA 110 Institute for Nuclear Science and Technology (INST), Hanoi, Vietnam (†) Deceased (a) at Konan University, Kobe, Japan Abstract We present the results of an analysis of data recorded at the Pierre Auger Observatory in which we search for groups of directionally-aligned events (or ‘multiplets’) which exhibit a correlation between arrival direction and the inverse of the energy. These signatures are expected from sets of events coming from the same source after having been deflected by intervening coherent mag- netic fields. The observation of several events from the samesource would open the possibility to accurately reconstruct the position of the source and also measure the integral of the component of the magnetic field orthogonal to the trajectory of the cosmic rays. We describe the largest multiplets found and compute the probability that they appeared by chance from an isotropic distribution. We find no statistically significant evidencefor the presence of multiplets arising from magnetic deflections in the present data. Key words: Ultra-High Energy Cosmic Rays, Pierre Auger Observatory, Arrival Directions 4 PACS:98.70.Sa 1. Introduction The origin of ultra-high energy cosmic rays is a long-standing open question, and the iden- tification of their sources is one of the primary motivationsfor the research conducted at the Pierre Auger Observatory. If the density of cosmic rays sources is not too large, it is expected that there could be indications of the presence of multiplets, i.e. sets of events with different energy that come from a single point-like source. Due to the magnetic fields that cosmic rays traverse on their paths from their sources to the Earth, theywill be deflected and this deflection is proportional to the inverse of their energy if the deflections are small. Therefore, to identify sets of cosmic rays that come from a single source, a search for events that show a correlation between their arrival direction and the inverse of their energy has been performed using the data recorded at the Pierre Auger Observatory. The observation of cosmic ray multiplets could allow for the accurate location of the direction of the source and could also provide a new means to probe the galactic magnetic field, as it should be possible toinfer the value of the integral of the component of the magnetic field orthogonal to the trajectoryof the cosmic rays. Note that to observe a correlated multiplet the source should be steady,in the sense that its lifetime is larger than the difference in the time delays due to the propagationin the intervening magnetic fields for the energies considered. Moreover, magnetic fields should also be steady in the same sense so that cosmic rays traverse approximately the same fields. This study relies on the acceleration at the source of a proton component (or intermediate mass nuclei being accelerated and photo-disintegrated during extragalactic propagation with the deflections due to extragalactic magnetic fields being smallcompared to those in the Galaxy). Due to the magnitude of the known magnetic fields involved, heavy nuclei at these energies would appear spread over a very large region of the sky, probing regions with different ampli- tudes and directions of the magnetic field, and hence losing their alignment and correlation with the inverse of energy. The galactic magnetic field is poorly constrained by the available data, even though there has been considerable effort to improve this knowledge using different observational techniques, see e.g. [1, 2, 3]. This field is usually described as the superposition of a large-scale regular component and a turbulent one. The regular component has a few µG strength and is coherent on scales of a few kpc with a structure related to the spiral armsof the galactic disk, and eventually also a more extended halo component (see e.g. [4]). The deflection of cosmic rays with energy E and chargeZ by the regular component of the magnetic field~B after traversing a distanceL is given by δ ≃ 16◦ 20 EeV E/Z ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∫ L 0 d~l 3 kpc × ~B 2 µG ∣ ∣ ∣ ∣ ∣ ∣ ∣ , (1) where 1 EeV≡ 1018 eV. This is the predominant deflection because, although theturbulent component has a root mean square amplitude ofBrms ≃ (1 − 2)Breg, it has a much smaller coherence length (typicallyLc ≃ 50-100 pc) [5, 6], leading to a smaller deflection, with a typical Preprint accepted for publication in Astroparticle Physics November 11, 2011 root mean square value δrms ≃ 1.5◦ 20 EeV E/Z Brms 3 µG √ L 1 kpc √ Lc 50 pc . (2) After traveling a distanceL through the turbulent field, the trajectories of cosmic rayswould be displaced a distance∼ δrmsL with respect to the one they would have had if only the regular field were present. If this displacement is smaller than the coherence lengthLc, this means that all the particles with that energy have experienced nearly the same values of the turbulent field along their trajectories. Thus, the effect is that the arrival direction of cosmic rays will coherently wiggle with an amplitudeδrms(E) around the direction determined by the deflection due to the regular magnetic field as a function of the energy. Conversely, whenδrms(E)L > Lc, particles of the same energy that have probed uncorrelated values of the turbulent field are able to reach the observer from the source and several images appear, scattered byδrms(E) around the image that would be produced by the regular field alone. Which of thetwo regimes actually takes place depends on the energy considered and on the distance traveled in the turbulent field. For instance, for L ≃ 2 kpc and energy about 20 EeV, the second situation applies, while at much higher ener- gies the first one holds. Extragalactic magnetic fields could also deflect the trajectories of cosmic rays, but their strength is yet unknown and the relevance of their effect is amatter of debate, see e.g. [7, 8, 9]. 2. The Pierre Auger Observatory and the data set The Pierre Auger Observatory, located in Malargüe, Argentina (35.2◦S, 69.5◦W) at 1400 m a.s.l. [10], was designed to measure ultra-high energy cosmic rays (energyE > 1018) with unprecedented statistics. It consists of a surface array of1660 water-Cherenkov stations. The surface array is arranged in an equilateral triangular gridwith 1500 m spacing, covering an area of approximately 3000 km2 [11]. The array is overlooked by 27 fluorescence telescopes located on hills at four sites on its periphery [12]. The surface and air fluorescence detectors are designed to perform complementary measurements of air showers created by cosmic rays. The surface ar- ray is used to observe the lateral distribution of the air shower particles at ground level, while the fluorescence telescopes are used to record the longitudinal development of the shower as it moves through the atmosphere. In this work we analyze events with zenith angles smaller than 60◦ recorded by the surface de- tector from 1st January 2004 to 31st December 2010. The events are required to have at least five active stations surrounding the station with the highest signal, and the reconstructed core must be inside an active equilateral triangle of stations [13]. Thecorresponding exposure is 25806 km2 sr yr. The angular resolution, defined as the 68th percentile of the distribution of opening angles between the true and reconstructed directions of simulatedevents, is better than 0.9◦ for events that trigger at least six surface stations (E > 10 EeV) [14]. The energy resolution is about 15% and the absolute energy scale, given by the fluorescence calibration, has a systematic uncertainty of 22% [15]. 6 3. Method adopted for the multiplets search In the limit of large energy, and hence small deflections, it is a good approximation to con- sider the following simplified relation between the cosmic ray observed arrival directions, de- scribed by the unit vector~θ, and the actual source direction~θs ~θ = ~θs + Ze E ∫ L 0 d~l × ~B ≃ ~θs + ~D(~θs) E , (3) whereZe is the electric charge of the cosmic ray andD ≡ |~D(~θs)| will be called the deflection power and will be given in units of 1◦ 100 EeV, which is≈ 1.9eµG kpc. In the case of proton sources, departures from the linear approximation are relevant for en- ergies below 20 EeV for typical galactic magnetic field models [16], as the deflections of the trajectories are large and the integral of the magnetic fieldcomponent orthogonal to the path can- not be approximated as a constant for a fixed source direction. This fact motivates the restriction of the present analysis to events with energies above 20 EeV. In order to identify sets of events coming from the same source, the main requirement will be that they appear aligned in the sky and have a high value of thecorrelation coefficient between the arrival direction and the inverse of the energy. To compute the correlation coefficient for a given subset ofN nearby event directions, we first identify the axis along which the correlation is maximal. For this we initially use an arbitrary coordinate system (x, y) in the tangent plane to the celestial sphere (centered in the average direction to the events) and compute the covariance Cov(x, 1/E) = 1 N N ∑ i=1 (xi − 〈x〉)(1/Ei − 〈1/E〉) (4) and similarly for Cov(y, 1/E). We then rotate the coordinates to a system (u,w) in which Cov(w, 1/E) = 0, and hence Cov(u, 1/E) is maximal. This corresponds to a rotation angle between theu andx axes given by α = arctan ( Cov(y, 1/E) Cov(x, 1/E) ) . (5) The correlation betweenu and 1/E is measured through the correlation coefficient C(u, 1/E) = Cov(u, 1/E) √ Var(u)Var(1/E) , (6) where the variances are given by Var(x) = 〈 (x− 〈x〉)2 〉 . We demonstrate this procedure in Figure 1. In the left panel we show the selection of coordinatesu andw for a set of events of a simulated source superimposed on a background of isotropically distributed events. In the right panel the correlation betweenu and 1/E for the same source events is plotted. 7 (a) (b) Figure 1: Selection of coordinatesu andw for a set of events of a simulated source (black thick asterisks) superimposed on a background of isotropically-distributed events (blueasterisks) (a). The size of the circles is proportional to the energy of the events. Correlation betweenu and 1/E for the same source events (b). A given set of events will be identified as a correlated multiplet whenC(u, 1/E) > Cmin and, when the spread in the transverse directionw is small,W = max(|wi −〈w〉 |) 20 EeV from a source with spectral indexs = 2.5 is larger than 45 EeV with a probability of 97% (for a spectral indexs = 3 this probability is∼ 90% and for s = 2 it is ∼ 99.7% ). Hence, requiring one high energy event above 45 EeV is not restrictive, 9 (a) (b) Figure 3: Chance probabilityPch for finding in isotropic simulations one large multiplet of agiven multiplicity as a function ofWmax (adoptingCmin = 0.9) (a) and as a function ofCmin (adoptingWmax = 1.5◦) (b) (see text). and it simplifies the strategy to start the search for multiplets, which proceeds by looking at all possible sets of events contained in windows of 20◦ around those high energy events. Since we are ultimately interested in multiplicities larger than 8 (see Fig. 3 in which it is apparent that for the present statistics above 20 EeV correlated sets of smaller multiplicity are very likely to appear by chance in isotropic simulations), it is possible to make this search more efficient by first identifying the high energy end of the candidate multiplets. We hence consider for every event above 45 EeV the quadruplets that it forms with the events within a circle of 15◦ having energies above 25 EeV and with a correlation coefficientC(u, 1/E) ≥ 0.8. The precise values of these cuts are not crucial as long as they allow one to safely include the larger multiplets of interest. For each of these candidates we then extend the search including all the events above 20 EeV with an angular distance to the highest energy one smaller than 20◦ and at a distance smaller than 3Wmax from the quadruplet axis. This allows us to find the correlated multiplets satisfying the cuts inWmax andCmin in a very efficient way, as it is desirable to be able to perform a large number of simulations. The multiplets search procedure has been designed for sources having a light composition. For sources having instead a heavy composition above 20 EeV,multiplets will be much more difficult to identify since they would typically spread through a larger region in the sky and also the linearity of their directional distribution will be lost. Once a correlated multiplet is identified, from the linear fitto the relation u = us+ D E , (7) the position of the source (us, 0) (in theu-w coordinate system) and the deflection powerD can be obtained. A true correlated multiplet arising from magnetic field deflections of events from a single source can also include by chance some events from the background that appear aligned and cor- 10 related in energy with the events from the source. We have estimated the fraction of events that is expected to be due to chance background alignments by simulating an isotropic background distribution of events with the energy of the observed events above 20 EeV and superimposing multiplets of 12 events from simulated sources. We found that 29% of the reconstructed multi- plets do not pick additional background events, while 46% just pick one additional background event and 25% pick two or more. Thus, the fraction of events added from the background is typically very small. 4. Results We applied the method discussed in Section 3 to 1509 events above 20 EeV recorded at the Pierre Auger Observatory from 1st January 2004 to 31st December 2010. We implemented a search for all possible multiplets which extend up to 20◦ in the sky and contain at least one event with energy above 45 EeV, and that have a half-width smaller thanWmax = 1.5◦ and a correlation coefficient larger thanCmin = 0.9. The largest multiplet found in this data set is one 12-plet and there are also two independent decuplets. They are displayed in Figure 4. Their deflection power, position of the potential source location and correlation coefficient are listed in Table 1. Decuplet II in Table 1 consists of three dependent sets of tenevents (a-c) that are formed by the combination of a set of twelve events. These three decupletsare not independent of each other since they have most events in common. The uncertainties in the reconstruction of the position of the potential sources have been calculated propagating the uncertainties in energy and arrival direction to an uncertainty in the rotation angle (Eq. 5) andin the linear fit performed to the deflection vs. 1/E (Eq. 7). The probability that the observed number (or more) of correlated multiplets appears by chance can be computed by applying a similar analysis to simulations of randomly distributed events weighted by the geometric exposure of the experiment[19] and with the energies of the observed events. The fraction of simulations with at least one multiplet with 12 or more events is 6%, and the fraction having at least three multiplets with10 or more events is 20%. Therefore, there is no statistically significant evidence for the presence of multiplets from actual sources in the data. We note that with the present statistics, an individual multiplet passing the required selection cuts should have at least 14 correlated events in order that its chance probability be 10−3. Measurements by the Pierre Auger Observatory [20] of the depth of shower maximum and its fluctuations indicate a trend towards heavy nuclei with increasing energy. This interpreta- tion of the shower depths is not certain, however. It relies on shower simulations that use hadronic interaction models to extrapolate particle interaction properties two orders of magni- tude in centre-of-mass energy beyond the regime where they have been tested experimentally. Magnetic alignment and correlation with the inverse of the energy as searched here are not ex- pected for heavy nuclei. Assuming there are sources which accelerate an appreciable proton component, the non-observation of significant multiplets could be the consequence of having a large density of sources. Given the present statistics, the maximum source density which would allow to observe a multiplet containing 12 events above 20 EeV from the nearest source to the Earth can be roughly estimated by considering that this source should produce a fraction 12/1509 ≈ 1/125 of the total flux observed in the field of view of the Auger Observatory in this energy range. Assuming that the sources have equal intrinsic luminosity and are uniformly 11 distributed and that cosmic rays in this energy range can arrive from distances up to about 1 Gpc, the above mentioned constraints imply that the nearest source should be within∼ 10 Mpc. Thus, the mean local density of sources should not be larger than a few 10−4 Mpc−3. The fact that we have not seen a larger multiplet is an indication that the density of sources is probably larger. This very rough estimation is subject to large fluctuations but it is indicative that densities within the current lower limits may lead to the kind of signals searched for here. We note, however, that this bound would be relaxed if contributions of heavy cosmicray primaries become significant, or if very strong turbulent magnetic fields were present. Figure 4: Observed multiplets with 10 or more events in galactic coordinates. The size of the circles is proportional to the energy of the event. Plus signs indicate the positionsof the potential sources for each multiplet. One decuplet is in fact three dependent decuplets that are formed by the combination of twelve events and the three corresponding reconstructions of the potential sources are shown. The solid line represents the border of the field of view of the Southern Observatory for zenith angles smaller than 60◦ and the grey shaded area is the region outside the field of view. 5. Conclusions A search for ultra-high energy cosmic ray multiplets was performed in the data gathered be- tween 1st January 2004 and 31st December 2010 by the Pierre Auger Observatory with energy above 20 EeV. The largest multiplet found was one 12-plet. The probability that it appears by chance from an isotropic distribution of events is 6%. Thus,there is no significant evidence for the existence of correlated multiplets in the present data set. Future data will be analyzed to check if some of the observed multiplets grow significantly or if some new large multiplets appear. 12 multiplet D[◦100 EeV] (l, b)S[◦] ∆uS[◦] ∆wS[◦] C 12− plet 4.3± 0.7 (−46.7, 13.2) 2.4 0.9 0.903 10− plet I 5.1± 0.9 (−39.9, 23.4) 2.7 0.9 0.901 10− plet IIa 8.2± 1.3 (−85.6,−80.4) 4.3 1.9 0.920 10− plet IIb 7.6± 1.2 (−79.6,−77.9) 4.0 1.6 0.919 10− plet IIc 6.5± 1.1 (−91.5,−75.7) 3.9 1.6 0.908 Table 1: Deflection power,D; reconstructed position of the potential source in galactic coordinates, (l, b)S; uncertainty in the reconstructed position of the potential source alongthe direction of deflection,∆uS, and orthogonal to it,∆wS; and linear correlation coefficient,C, for the largest correlated multiplets found. The data correspond to events with energy above 20 EeV from 1st January 2004 to 31st December 2010. 6. Acknowledgments The successful installation, commissioning and operationof the Pierre Auger Observatory would not have been possible without the strong commitment and effort from the technical and administrative staff in Malargüe. We are very grateful to the following agencies and organizations for financial support: Co- misión Nacional de Energía Atómica, Fundación Antorchas, Gobierno De La Provincia de Men- doza, Municipalidad de Malargüe, NDM Holdings and Valle LasLeñas, in gratitude for their continuing cooperation over land access, Argentina; the Australian Research Council; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Pro- jetos (FINEP), Fundação de Amparo à Pesquisa do Estado de Riode Janeiro (FAPERJ), Fun- dação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Ministério de Ciência e Tec- nologia (MCT), Brazil; AVCR AV0Z10100502 and AV0Z10100522, GAAV KJB100100904, MSMT-CR LA08016, LC527, 1M06002, and MSM0021620859, CzechRepublic; Centre de Calcul IN2P3/CNRS, Centre National de la Recherche Scientifique (CNRS), Conseil Régional Ile-de-France, Département Physique Nucléaire et Corpusculaire (PNC-IN2P3/CNRS), Départe- ment Sciences de l’Univers (SDU-INSU/CNRS), France; Bundesministerium für Bildung und Forschung (BMBF), Deutsche Forschungsgemeinschaft (DFG), Finanzministerium Baden-Würt- temberg, Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF), Ministerium für Wis- senschaft und Forschung, Nordrhein-Westfalen, Ministerium für Wissenschaft, Forschung und Kunst, Baden-Württemberg, Germany; Istituto Nazionale diFisica Nucleare (INFN), Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR),Italy; Consejo Nacional de Ciencia y Tecnología (CONACYT), Mexico; Ministerie van Onderwijs, Cultuur en Wetenschap, Neder- landse Organisatie voor Wetenschappelijk Onderzoek (NWO), Stichting voor Fundamenteel On- derzoek der Materie (FOM), Netherlands; Ministry of Science and Higher Education, Grant Nos. 1 P03 D 014 30, N202 090 31/0623, and PAP/218/2006, Poland; Fundação para a Ciência e a Tec- nologia, Portugal; Ministry for Higher Education, Science, and Technology, Slovenian Research Agency, Slovenia; Comunidad de Madrid, Consejería de Educación de la Comunidad de Castilla La Mancha, FEDER funds, Ministerio de Ciencia e Innovación and Consolider-Ingenio 2010 (CPAN), Xunta de Galicia, Spain; Science and Technology Facilities Council, United Kingdom; Department of Energy, Contract Nos. 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Sommers, Astropart. Phys. 14 (2001) 271 [astro-ph/0004016]. [20] J. Abraham et al [The Pierre Auger Collaboration], Phys. Rev. Lett. 104 (2010) 091101. 14 http://arxiv.org/abs/astro-ph/0302388 http://arxiv.org/abs/astro-ph/0410419 http://arxiv.org/abs/astro-ph/9607086 http://arxiv.org/abs/astro-ph/9906309 http://arxiv.org/abs/astro-ph/0004016 1 Introduction 2 The Pierre Auger Observatory and the data set 3 Method adopted for the multiplets search 4 Results 5 Conclusions 6 Acknowledgments