Perturbations in the self-similar Bondi flow

Context.The question of the stability of steady spherical accretion has been studied for many years and, recently, the concept of spatial instability has been introduced.Aims.Here we study the perturbations of steady spherical accretion flows (Bondi solutions), restricting ourselves to the case of a self-similar flow, as a case that is amenable to analytic treatment and that is of physical interest. We restrict ourselves further to its acoustic perturbations.Methods.The radial perturbation equation can be solved in terms of Bessel functions. We study the formulation of adequate boundary conditions and decide to use no matter-flux-perturbation conditions (at the Bondi radius and at $r=0$). We also consider the problems of initial conditions and time evolution, and concentrate more particularly on radial perturbations.Results.No spatial instability at $r=0$ is found. The time evolution is such that perturbations eventually become ergodic-like and show no trace of instability or of acquiring any remarkable pattern