Self-gravitating gaseous bars. I. Compressible analogs of Riemann ellipsoids with supersonic internal flows

We present two steady state models of compressible, self-gravitating three-dimensional fluid configurations with triaxial structures and supersonic internal motions. Both models have been constructed via dynamical simulations, starting from rapidly rotating, axisymmetric polytropic configurations that were dynamically unstable toward the development of a barlike or two-armed spiral structure. The two initial models differed mainly in their angular momentum distributions: one had the same specific angular momentum profile as a uniformly rotating, uniform-density sphere; the other had uniform vortensity. In both cases, the nonlinear development of the instability resulted in the formation of a triaxial configuration that was spinning with a well-defined pattern speed and exhibited strongly differential, internal motions. As viewed from a frame rotating with the pattern frequency of the system, the final configurations are in steady-state, in the sense that their structures are unchanging on a dynamical time scale, and appear to be dynamically stable. In both models, a "violin-shaped mach surface" and a pair of weak standing shock fronts appear to be integral components of the steady-state flow. By all accounts, these models are compressible analogs of Riemann S-type ellipsoids. Their steady state configurations are relevant to self-consistent models of galaxies, rapidly spinning compact stellar objects, and the structure and evolution of protostellar gas clouds.