Galaxy rotation favors prolate dark matter haloes

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.