Stability of Self-Similar Spherical Accretion

Spherical accretion flows are simple enough for analytical study, by solution of the corresponding fluid dynamic equations. The solutions of stationary spherical flow are due to Bondi. The questions of the choice of a physical solution and of stability have been widely discussed. The answer to these questions is very dependent on the problem of boundary conditions, which vary according to whether the accretor is a compact object or a black hole. We introduce a particular, simple form of stationary spherical flow, namely, self-similar Bondi flow, as a case with physical interest in which analytic solutions for perturbations can be found. With suitable no matter-flux-perturbation boundary conditions, we will show that acoustic modes are stable in time and have no spatial instability at r=0. Furthermore, their evolution eventually becomes ergodic-like and shows no trace of instability or of acquiring any remarkable pattern.