Local stability criterion for a self-gravitating gaseous disk of spiral galaxies

An improved linear stability theory of small-amplitude oscillations of a self-gravitating, infinitesimally thin gaseous disk of spiral galaxies has been developed by Bertin, Lau, Lin, Mark, Morozov, Polyachenko, and others in the approximation of moderately tightly wound gravity perturbations. In this regime, the generalized Lin-Shu type dispersion relation was also found by including higher order terms in the small parameter 1/kr for wavenumber k and radius r. It was shown that in the differentially rotating disks for nonaxisymmetric (spiral) perturbations Toomre's modified critical Q-parameter is larger than the standard one: the fact that the spiral perturbations in the nonuniformly rotating system are more unstable than the axisymmetric ones is taken into account in this modified local stability criterion. We use hydrodynamical simulations to test the validity of the modified local criterion.