On the Azimuthal Stability of Shock Waves around Black Holes

Abstract

Analytical studies and numerical simulations of time dependent axially\nsymmetric flows onto black holes have shown that it is possible to produce\nstationary shock waves with a stable position both for ideal inviscid and for\nmoderately viscous accretion disks.\n We perform several two dimensional numerical simulations of accretion flows\nin the equatorial plane to study shock stability against non-axisymmetric\nazimuthal perturbations. We find a peculiar new result. A very small\nperturbation seems to produce an instability as it crosses the shock, but after\nsome small oscillations, the shock wave suddenly transforms into an asymmetric\nclosed pattern, and it stabilizes with a finite radial extent, despite the\ninflow and outflow boundary conditions are perfectly symmetric. The main\ncharacteristics of the final flow are: 1) The deformed shock rotates steadily\nwithout any damping. It is a permanent feature and the thermal energy content\nand the emitted energy vary periodically with time. 2) This behavior is also\nstable against further perturbations. 3) The average shock is still very strong\nand well defined, and its average radial distance is somewhat larger than that\nof the original axially symmetric circular shock. 4) Shocks obtained with\nlarger angular momentum exhibit more frequencies and beating phenomena. 5) The\noscillations occur in a wide range of parameters, so this new effect may have\nrelevant observational consequences, like (quasi) periodic oscillations, for\nthe accretion of matter onto black holes. Typical time scales for the periods\nare 0.01 and 1000 seconds for black holes with 10 and 1 million solar mass,\nrespectively.\n