Galactic Disc Rotation: Analytic models and asymptotic results

TL;DR

This paper presents an exact analytic model demonstrating that thin disc galaxies can support flat rotation curves solely through Newtonian gravity, revealing insights into galaxy mass distribution and the missing mass problem.

Contribution

It introduces a novel analytic approach to model self-gravitating thin disc galaxies with flat rotation curves, linking disc density to rotation profiles and highlighting the presence of extensive outer mass regions.

Findings

Thin discs alone can produce flat rotation curves under Newtonian gravity.

Reconstructed discs have large outer regions containing most of their mass.

The model connects exponential discs with flat rotation curves.

Abstract

This paper outlines an exact analytic model for self-gravitating thin disc galaxies with flat rotation curves. It is shown that thin discs of matter alone can support perfectly flat rotation curves under Newtonian gravity, without needing extended halos or modified gravity. The method allows disc density to be inferred from polynomial approximations to the rotation curve. Several expository models are presented. The model also shows the link between flat rotation curves and "exponential" discs. It is also shown that reconstructed discs inherently posses vast mass "hinterlands" in their outer regions, that can contain the majority of their total mass. Some implications for the problem of missing mass are discussed.