Analysis of non-Axisymmetric shock stability in black hole geometry by numerical simulation and linear analysis

We study about the multidimensional stability of standing shock waves in advectiondominated accretion flows into a Schwarzschild black hole by 2D general relativistic hydrodynamical simulations and linear analysis in the equatorial plane. We demonstrate that the accretion shock is stable against axisymmetric perturbations but becomes unstable to non-axisymmetric perturbations. The results of dynamical simulations are good consistent with linear analysis such as stability, oscillation and growing timescale. However, our analysis does not support previous work suggestion which is the instability mechanism is based on Papaloizou-Pringle type. It seems due to the wavelength of perturbation is too large for discussion about reflection point. In non-linear phases, it is found not only short-term random fluctuations by turbulent motions but also quasi periodic oscillations taking place on longer time scales in the latter phase. We discuss possible implications of Black Hole SASI for Quasi Periodic Oscillation (QPO) and central engine for Gamma Ray Bursts (GRB).