Sausage and kink oscillations in astrophysical disk configurations

The development of hydrodynamic oscillations in various rotating astrophysical disks ranging from planetary rings to galaxies is studied analytically. The dispersion relation of wave propagation is derived. Modes of oscillation are examined from this dispersion relation that are suitable for obtaining information not just on oscillations but also on some instability properties of the disk-shaped structure. It is shown that unstable oscillations of different types, sausage compression and kink bending, may be excited effectively due to the Jeans gravitational instability and the kink transverse instability, respectively. The obtained results for the sausage oscillations may be applicable for such phenomena as the appearance of the in-plane spiral and circular structures, while the case for the kink mode is more relevant for the systematic vertical corrugations of astrophysical disks.