Abstract
The flattening of spiral-galaxy rotation curves is unnatural in view of the expectations from Kepler’s third law and a central mass. It is interesting, however, that the radius-independence velocity is what one expects in one less dimension. In our three-dimensional space, the rotation curve is natural if, outside the galaxy’s center, the gravitational potential corresponds to that of a very prolate ellipsoid, filament, string, or otherwise cylindrical structure perpendicular to the galactic plane. While there is observational evidence (and numerical simulations) for filamentary structure at large scales, this has not been discussed at scales commensurable with galactic sizes. If, nevertheless, the hypothesis is tentatively adopted, the scaling exponent of the baryonic Tully–Fisher relation due to accretion of visible matter by the halo comes out to reasonably be 4. At a minimum, this analytical limit would suggest that simulations yielding prolate haloes would provide a better overall fit to small-scale galaxy data.
Highlights
With decades of effort [1], it has been established that the rotation speed of spiral galaxies is largely independent of the distance to their center, v ∼ constant, even well beyond the end of the luminous matter distribution, wh√ereas Kepler’s third law applied to a point-like mass or spherical source yields v ∼ 1/ r
Much evidence of dark matter in present-day cosmology seems consistent with it having filamentary structure at large scales
A linear rise out to a radius R given by Equation (21), followed by a flat v∞ = 2Gλ, is a reasonable first approximation to numerous spiral galaxy rotation curves, and follows from a finite-sized cylinder of uniform density
Summary
With decades of effort [1], it has been established that the rotation speed of spiral galaxies is largely independent of the distance to their center, v ∼ constant, even well beyond the end of the luminous matter distribution, wh√ereas Kepler’s third law applied to a point-like mass or spherical source yields v ∼ 1/ r. Under the hypothesis that the dark matter halo has reached a uniform temperature (and it is not known how this happens, as it depends on the dark matter interactions, but requires some sort of heat conduction between different spherical shells), one finds that the equation admits the power-law solution ρ (8) This behavior is exactly what is needed to produce the observed flat rotation curves. An exception that is still standing is the possibility of O(100M ) black holes [10]
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