Entropic-acoustic instability of shocked Bondi accretion I. What does perturbed Bondi accretion sound like?

In the radial flow of gas into a black hole (i.e. Bondi accretion), the inf all of any entropy or vorticity perturbation produces acoustic waves propag ating outward. The dependence of this acoustic flux on the shape of the per turbation is investigated in detail. This is the key process in the mechani sm of the entropic-acoustic instability proposed by Foglizzo & Tagger (2000 ) to explain the instability of Bondi-Hoyle-Lyttleton accretion. These acou stic waves create new entropy and vorticity perturbations when they reach t he shock, thus closing the entropic-acoustic cycle. With an adiabatic index 1 < <gamma> less than or equal to 5/3, the linearized equations describing the perturbations of the Bondi flow are studied analytically and solved nu merically. The fundamental frequency of this problem is the cut-off frequen cy of acoustic refraction, below which ingoing acoustic waves are refracted out. This cut-off is significantly smaller than the Keplerian frequency at the sonic radius and depends on the latitudinal number I of the perturbati ons. When advected adiabatically inward, entropy and vorticity perturbation s trigger acoustic waves propagating outward, with an efficiency which is h ighest for non radial perturbations l = 1. The outgoing acoustic flux produ ced by the advection of vorticity perturbations is always moderate and peak s at rather low frequency. By contrast, the acoustic flux produced by an en tropy wave is highest close to the refraction cut-off. It can be very large if gamma is close to 5/3. These results suggest that the shocked Bondi flo w with gamma = 5/3 is strongly unstable with respect to the entropic-acoust ic mechanism.