Axisymmetric Bondi-Hoyle accretion on to a Schwarzschild black hole: shock cone vibrations

We study numerically the axisymmetric relativistic Bondi-Hoyle accretion of a supersonic ideal gas on to a fixed Schwarzschild background space-time described with horizon penetrating coordinates. We verify that a nearly stationary shock cone forms and that the properties of the shock cone are consistent with previous results in Newtonian gravity and former relativistic studies. The fact that the evolution of the gas is tracked on a spatial domain that contains a portion of the inner part of the black hole avoids the need to impose boundary conditions on a time-like boundary as done in the past. Thus, our approach contributes to the solution to the Bondi-Hoyle accretion problem at the length-scale of the accretor in the sense that the gas is genuinely entering the black hole. As an astrophysical application, we study for a set of particular physical parameters, the spectrum of the shock cone vibrations and their potential association with Quasi Periodic Oscillations sources.