A method for evaluating models that use galaxy rotation curves to derive the density profiles

TL;DR

This paper reviews and evaluates methods using galaxy rotation curves to infer matter density profiles, testing two approaches based on General Relativity, and finds neither can fit data without dark matter.

Contribution

It introduces a new evaluation method for galaxy rotation curve models and applies it to test GR-based approaches, revealing their limitations without dark matter.

Findings

Neither approach fits data without dark matter

CT approach improves with dark matter inclusion

BG approach cannot be improved with dark matter halos

Abstract

There are some approaches, either based on General Relativity (GR) or modified gravity, that use galaxy rotation curves to derive the matter density of the corresponding galaxy, and this procedure would either indicate a partial or a complete elimination of dark matter in galaxies. Here we review these approaches, clarify the difficulties on this inverted procedure, present a method for evaluating them, and use it to test two specific approaches that are based on GR: the Cooperstock-Tieu (CT) and the Balasin-Grumiller (BG) approaches. Using this new method, we find that neither of the tested approaches can satisfactorily fit the observational data without dark matter. The CT approach results can be significantly improved if some dark matter is considered, while for the BG approach no usual dark matter halo can improve its results.