Elongated Gravity Sources as an Analytical Limit for Flat Galaxy Rotation Curves

TL;DR

This paper proposes that elongated, filament-like gravitational sources could explain flat galaxy rotation curves, offering an alternative to dark matter and suggesting that prolate halo models may better fit galactic data.

Contribution

It introduces the idea that elongated gravitational structures can produce flat rotation curves, providing an analytical limit and a new perspective on galaxy dynamics.

Findings

Rotation curves are natural with cylindrical gravitational potentials.

Scaling exponent of the Tully-Fisher relation is approximately 4.

Prolate halo models may better fit small-scale galaxy data.

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.