# Comparing the dark matter models, modified Newtonian dynamics and modified gravity in accounting for the galaxy rotation curves

## TL;DR

This study compares six different models, including dark matter, modified Newtonian dynamics, and modified gravity, to explain galaxy rotation curves, revealing none fit all cases well and highlighting the limitations of simplified profiles.

## Contribution

It provides a comprehensive comparison of six models using Bayesian and AIC criteria across diverse galaxy types, highlighting their respective strengths and limitations.

## Key findings

- MOND fits the most galaxies among the models.
- No single model fits all galaxy rotation curves well.
- Simplified dark matter profiles may be insufficient.

## Abstract

We compare six models (including the baryonic model, two dark matter models, two modified Newtonian dynamics models and one modified gravity model) in accounting for the galaxy rotation curves. For the dark matter models, we assume NFW profile and core-modified profile for the dark halo, respectively. For the modified Newtonian dynamics models, we discuss Milgrom's MOND theory with two different interpolation functions, i.e. the standard and the simple interpolation functions. As for the modified gravity, we focus on Moffat's MSTG theory. We fit these models to the observed rotation curves of 9 high-surface brightness and 9 low-surface brightness galaxies. We apply the Bayesian Information Criterion and the Akaike Information Criterion to test the goodness-of-fit of each model. It is found that non of the six models can well fit all the galaxy rotation curves. Two galaxies can be best fitted by the baryonic model without involving the nonluminous dark matter. MOND can fit the largest number of galaxies, and only one galaxy can be best fitted by MSTG model. Core-modified model can well fit about one half LSB galaxies but no HSB galaxy, while NFW model can fit only a small fraction of HSB galaxies but no LSB galaxy. This may imply that the oversimplified NFW and Core-modified profiles couldn't well mimic the postulated dark matter halo.