On the Azimuthal Stability of Shock Waves around Black Holes

Analytical studies and numerical simulations of time-dependent axially symmetric flows onto black holes have shown that it is possible to produce stationary shock waves with a stable position for both ideal inviscid and moderately viscous accretion disks. We perform several two-dimensional numerical simulations of accretion flows in the equatorial plane to study shock stability against nonaxisymmetric azimuthal perturbations. We find a peculiar new result. A very small perturbation seems to produce an instability as it crosses the shock, but after some small oscillations, the shock wave suddenly transforms into an asymmetric closed pattern and stabilizes with a finite radial extent, despite the fact that the inflow and outflow boundary conditions are perfectly symmetric. The main characteristics of the final flow are: (1) The deformed shock rotates steadily without any damping. It is a permanent feature, and the thermal energy content and the emitted energy vary periodically with time. (2) This behavior is also stable against further perturbations. (3) The average shock is still very strong and well defined, and its average radial distance is somewhat larger than that of the original axially symmetric circular shock. (4) Shocks obtained with larger angular momentum exhibit more frequencies and beating phenomena. (5) The oscillations occur in a wide range of parameters, so this new effect may have relevant observational consequences, such as (quasi-) periodic oscillations, for the accretion of matter onto black holes. Typical timescales for the periods are 0.01 and 1000 s for black holes with 10 and 106 M, respectively.