# Global stability of self-gravitating disks in modified gravity

## TL;DR

This study uses N-body simulations to compare the stability of self-gravitating disks in Modified Gravity (MOG) versus Newtonian gravity, finding MOG disks are more stable and that certain parameters further enhance this stability.

## Contribution

It provides the first detailed comparison of disk stability in MOG versus Newtonian gravity, highlighting the stabilizing effects of MOG parameters on bar formation.

## Key findings

- MOG disks are more stable against bar instability than Newtonian disks.
- Increasing MOG parameters $\alpha$ and $\mu_0$ reduces bar growth rate.
- Both exponential and Mestel-like density profiles show similar stability trends.

## Abstract

We study the global stability of a self-gravitating disk in the context of Modified Gravity (MOG) using N-body simulations. This theory is a relativistic scalar-tensor-vector theory of gravity and presented to address the dark matter problem. In the weak field limit MOG possesses two free parameters $\alpha$ and $\mu_0$ which have been already determined using rotation curve data of spiral galaxies. The evolution of a stellar self-gravitating disk and more specifically the bar instability in MOG is investigated and compared to a Newtonian case. Our models have exponential and Mestel-like surface densities as $\Sigma\propto \exp(-r/h)$ and $\Sigma\propto 1/r$. It is found out that, surprisingly, the disks are more stable against the bar mode in MOG than in Newtonian gravity. In other words, the bar growth rate is effectively slower than the Newtonian disks. Also we show that both free parameters, i.e. $\alpha$ and $\mu_0$, have stabilizing effects. In other words, increase in these parameters will decrease the bar growth rate.