# Modified Gravity (MOG) fits to observed radial acceleration of SPARC galaxies

## TL;DR

This paper demonstrates that Modified Gravity (MOG) can accurately fit the observed radial acceleration data of SPARC galaxies, aligning with the radial acceleration relation and providing an alternative to dark matter explanations.

## Contribution

The study shows that MOG parameters can be adjusted within observational bounds to fit galaxy rotation curves and the radial acceleration relation simultaneously.

## Key findings

- MOG fits the rotation curves of SPARC galaxies.
- MOG reproduces the radial acceleration relation with a specific acceleration scale.
- Adjusted MOG parameters are consistent with observational data.

## Abstract

The equation of motion in the generally covariant modified gravity (MOG) theory leads, for weak gravitational fields and non-relativistic motion, to a modification of Newton's gravitational acceleration law. In addition to the metric $g_{\mu\nu}$, MOG has a vector field $\phi_\mu$ that couples with gravitational strength to all baryonic matter. The gravitational coupling strength is determined by the MOG parameter $\alpha$, while parameter $\mu$ is the small effective mass of $\phi_\mu$. The MOG acceleration law has been demonstrated to fit a wide range of galaxies, galaxy clusters and the Bullet Cluster and Train Wreck Cluster mergers. For the SPARC sample of rotationally supported spiral and irregular galaxies, McGaugh et al. [24] (MLS) have found a radial acceleration relation (RAR) that relates accelerations derived from galaxy rotation curves to Newtonian accelerations derived from galaxy mass models. Using the same SPARC galaxy data, mass models independently derived from that data, and MOG parameters $\alpha$ and $\mu$ that run with galaxy mass, we demonstrate that adjusting galaxy parameters within $\pm 1$-sigma bounds can yield MOG predictions consistent with the given rotational velocity data. Moreover, the same adjusted parameters yield a good fit to the RAR of MLS, with the RAR parameter $a_0=(5.4\pm .3)\times 10^{-11}\,{\rm m/s^2}$.