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 in ternal motions. Both models have been constructed via dynamical simulations , starting from rapidly rotating, axisymmetric polytropic configurations th at were dynamically unstable toward the development of a barlike or two-arm ed spiral structure. The two initial models differed mainly in their angula r momentum distributions: one had the same specific angular momentum profil e as a uniformly rotating, uniform-density sphere; the other had uniform vo rtensity. In both cases, the nonlinear development of the instability resul ted in the formation of a triaxial configuration that was spinning with a w ell-defined pattern speed and exhibited strongly differential, internal mot ions. As viewed from a frame rotating with the pattern frequency of the sys tem, the final configurations are in steady-state, in the sense that their structures are unchanging on a dynamical time scale, and appear to be dynam ically 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 Riema nn S-type ellipsoids. Their steady state configurations are relevant to sel f-consistent models of galaxies, rapidly spinning compact stellar objects, and the structure and evolution of protostellar gas clouds.