Galaxy rotation favors prolate dark matter haloes

Abstract

The flattening rotation velocity $v(r)\to \mathrm{constant}$ found by Vera Rubin and collaborators and very apparent in the SPARC 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 $s=c/a\in (0,\infty )$ corresponds to spherical haloes for $s=1$, so that the usually reported average is skewed towards 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.

26 pages, original primary work, about 40 plots, 1.4 Mbytes. v2: small latex and edition fixes (repeated label, overlapping paragraphs, shortened a table to 1-column format, etc.)

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• The Science of the Einstein Telescope
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• Probing the black holes in a dark matter halo of M87 using gravitational wave echoes
• The Gravito-Electromagnetic Approximation to the Gravimagnetic Dipole and its Velocity Rotation Curve
• The torsion of stellar streams and the overall shape of galactic gravity's source
• Newtonian Gravity and Galaxy Rotation Curves: An Axisymmetric Green's Function Perspective
• No evidence for Keplerian taper of far-out galactic rotation