On the gravitational stability of the Maclaurin disk
  We study the global gravitational stability of a gaseous self-gravitating
Maclaurin disk in the absence of a halo. Further, we replace Newtonian gravity
with the specific Modified gravity theory known as MOG in the relevant
literature. MOG is an alternative theory for addressing the dark matter problem
without invoking exotic dark matter particles, and possesses two free
parameters $\alpha$ and $\mu_0$ in the weak field limit. We derive the
equilibrium gravitational potential of the Maclaurin disk in MOG and develop a
semi-analytic method for studying the response of the disk to linear
non-axysymmetric perturbations. The eigenvalue spectrum of the normal modes of
the disk is obtained and its physical meaning has been explored. We show that
Maclaurin disks are less stable in MOG than in Newtonian gravity. In fact both
parameters $(\alpha,\mu_0)$ have destabilizing effects on the disk.
Interestingly $\mu_0$ excites only the bar mode $m=2$ while $\alpha$ affects
all the modes. More specifically, when $\alpha>1$, the bar mode is strongly
unstable and unlike in Newtonian gravity can not be avoided, at least in the
weak field limit, with increasing the pressure support of the disk.
