ON SONIC TRANSITIONS IN ASTROPHYSICAL FLOWS

We study the form of the steady-state solutions to the equations of hy drodynamics. In particular, we investigate the fate of the transonic s ingularity in the steady-state, spherically symmetric equations of hyd rodynamics, when solutions are sought in less constrained geometries. Streamline coordinates demonstrate that the singularity persists: in t he absence of other forces, flows become sonic at necks in the streaml ine pattern (a generalization of the de Laval nozzle). The inclusion o f mass loading adds a term to the flow-speed equation of opposite sign to that from divergence of streamlines. A numerical solution calculat ed on an axisymmetric grid demonstrates the limits of the conclusions drawn for spherical flows. We find that the transonic flow need not be perpendicular to the sonic surface, as assumed in previous work. The form of the solutions close to the sound speed may have implications f or the structure of recombination fronts in ultracompact HII regions.