Time-dependent fluid flow in a central gravitational field

Similarity arguments are used to obtain exact solutions of the time-dependent equations of motion for a polytropic fluid in a central gravitational field; these equations are a simplifed model for unsteady accretion and stellar wind flows. The spherically symmetric self-similar polytropic flows with a finite number of shocks always evolve toward a steady state in the large time limit. Actual accretion and stellar wind flows are thus expected to show a general tendency to evolve toward a steady state even in the absence of dissipation.For polytropic index n>3/2, the similarity solutions approach either hydrostatic equilibrium or a steady state with vanishing density and with velocity equal to +- (2GMr-1)1/2. For n=3/2, the solutions may in addition approach one of a continuum of steady-state solutions with generally nonzero mass flux at the origin. The n=3/2 solutions approach a steady state as t-2/3 for t→infinity at fixed r. The steady-state solutions for n>3/2 are stable against self-similar perturbations for large time at fixed r. However, the steady-state solutions for n=3/2 are not stable against self-similar perturbations.The nature of self-similar shocks is discussed, and the conditions for a smooth transition between subsonic and supersonic flow are obtained. Examples of solutions describing unsteady accretion and stellar wind flows are given. When applied to X-ray objects, the unsteady accretion solutions typically describe flaring behavior