RT Journal Article T1 Galaxy rotation favors prolate dark matter haloes A1 Bariego Quintana, Adriana A1 Llanes Estrada, Felipe José A1 Manzanilla Carretero, Oliver AB The flattening rotation velocity v(r) -> constant found by Vera Rubin and collaborators and very apparent in the SPARC (Spitzer photometry & accurate rotation curves) galaxy-rotation data coincides with Kepler's law in one less dimension. Thus, it is naturally reproduced by elongated dark matter distributions with the axis of prolateness perpendicular to the galactic plane. This theoretical understanding is borne out by the detailed fits to the rotation data that we here report: for equal dark matter profile, elongated distributions provide smaller chi 2 than purely spherical ones. We also propose to use the geometric mean of the individual halo ellipticities, as opposed to their arithmetic average, because the ratio of the ellipsoid's minor to major half-axes s = c/a E (0; oo) corresponds to spherical haloes for s = 1, so that the usually reported average is skewed toward oblateness and fails to reveal the large majority of prolate haloes. Several independently coded fitting exercises concur in yielding s <1 for most of the database entries and the oblate exceptions are understood and classified. This likely prolateness is of consequence for the estimated dark matter density near Earth. PB American Physical Society SN 2470-0010 YR 2023 FD 2023-04-23 LK https://hdl.handle.net/20.500.14352/87539 UL https://hdl.handle.net/20.500.14352/87539 LA eng NO © 2023 American Physical SocietyWe thank our engineer David Fernandez Sanz for maintaining an adequate computing environment suited to our needs at the theoretical physics departmental cluster, and C. Pieterse and N. Loizeau for useful conversations. Financially supported by spanish Grant No. MICINN: PID2019-108655 GB-I00 (Spain) , and Universidad Complutense de Madrid under research group 910309 and the IPARCOS, Institute for Particle and Cosmos physics institute. NO Ministerio de Ciencia e Innovación (MICINN) NO Universidad Complutense de Madrid DS Docta Complutense RD 27 abr 2025