# Local Stability of Galactic Discs in Modified Dynamics

## TL;DR

This paper investigates the local stability of galactic discs under a modified dynamical model, deriving a new stability criterion and showing it predicts greater stability than Newtonian gravity, with implications for galaxy types and star formation.

## Contribution

It introduces a modified Toomre stability criterion for galactic discs and demonstrates its implications for galaxy stability and star formation, extending beyond Newtonian models.

## Key findings

- Modified model predicts higher local stability than Newtonian gravity.
- LSB galaxies are more stable than HSB galaxies due to surface density effects.
- Growth rate of instabilities is lower in the modified model.

## Abstract

The local stability of stellar and fluid discs, under a new modified dynamical model, is surveyed by using WKB approximation. The exact form of the modified Toomre criterion is derived for both types of systems and it is shown that the new model is, in all situations, more locally stable than Newtonian model. In addition, it has been proved that the central surface density of the galaxies plays an important role in the local stability in the sense that LSB galaxies are more stable than HSBs. Furthermore, the growth rate in the new model is found to be lower than the Newtonian one. We found that, according to this model, the local instability is related to the ratio of surface density of the disc to a critical surface density $\Sigma^{crit}$. We provide observational evidence to support this result based on star formation rate in HSBs and LSBs.