Global spiral modes in multi - component disks

We performed two-dimensional non-linear hydrodynamical simulations of two-component gravitating disks aimed at studying stability properties of these systems. In agreement with previous analytical and numerical simulations, we find that the cold gas component strongly affects the growth rates of the unstable global spiral modes in the disk. Already a five percent admixture of cold gas increases approximately twofold the growth rate of the most unstable global mode while a twenty percent gas admixture enhances the modal growth rate by a factor of four. The local stability properties of a two-component disk coupled by self-gravity are governed by a stability criterion similar to Toomre's Q-parameter derived for one-component systems. Using numerical simulations, we analyse the applicability of a two-component local stability criterion for the analysis of the stability properties of global modes. The comparison of non-linear simulations with the analytical stability criterion shows that the two-component disks can be globally unstable while being stable to the local perturbations. The minimum value of the local stability criterion provides, however, a rough estimate of the global stability properties of two-component systems. We find that two-component systems with a content of cold gas of ten percent or less are globally stable if the minimum value of the stability parameter exceeds ∼ 2.5.