JEANS INSTABILITY IN A ROTATING MEDIUM IN THE PRESENCE OF INHOMOGENEOUS COMPRESSIBILITY

The Jeans instability in a rotating medium is studied in a model in wh ich the spatial distributions of the angular rotation velocity, pressu re, and density are constant but the compressibility changes on accoun t of some thermodynamic inhomogeneity of the medium. It is shown that the linearized equations are conjugate to a certain variational princi ple. Cylindrical or plane approximations are used to relate the densit y and potential perturbations. The critical radius of a circular regio n with finite compressibility is determined, assuming that this region is surrounded by an incompressible medium and that the angular rotati on velocity of the system is inadequate to stabilize the compressible gas in a model with an infinite medium. On the contrary, under similar conditions in a cylindrically symmetric geometry, long, narrow gaps f illed by the compressible gas are always unstable. Applications to the dynamics of planetary rings and galaxies are discussed.