On the stability of a galactic disk in modified gravity

Abstract

We find the dispersion relation for tightly wound spiral density waves in the surface of rotating, self-gravitating disks in the framework of Modified Gravity (MOG). Also, the Toomre-like stability criterion for differentially rotating disks has been derived for both fluid and stellar disks. More specifically, the stability criterion can be expressed in terms of a matter density threshold over which the instability occurs. In other words the local stability criterion can be written as ∑0crit(vs, k, a, μ0 ), where ∑crit is a function of vs (sound speed), ? (epicycle frequency) and ? and μ0 are the free parameters of the theory. In the case of a stellar disk the radial velocity dispersion sr appears in crit instead of vs. We find the exact form of the function ∑crit for both stellar and fluid selfgravitating disks. Also, we use a sub-sample of THING∑ catalog of spiral galaxies in order to compare the local stability criteria. In this perspective, we have compared MOG with Newtonian gravity and investigated the possible and detectable differences between these theories.