General Relativistic Hydrodynamic Simulations and Linear Analysis of the Standing Accretion Shock Instability around a Black Hole

doi: 10.1086/590325 ABSTRACT We study the stability of standing shock waves in advection-dominated accretion flows into a Schwarzschild black hole using two-dimensional general relativistic hydrodynamic simulations, as well as linear analysis, in the equatorial plane. We demonstrate that the accretion shock is stable against axisymmetric perturbations but becomes unstable to nonaxisymmetric perturbations. The results of the dynamical simulations show good agreement with the linear analysis on the stability and the oscillation and growth timescales. A comparison of different wave-travel times with the growth timescales of the instability suggests that it is likely to be of the Papaloizou-Pringle type, induced by the repeated propagations of acoustic waves. However, the wavelengths of the perturbations are too long to allow a clear definition of the reflection point. By analyzing the nonlinear phase in the dynamical simulations, we show that quadratic mode couplings precede the nonlinear saturation. It is also found that not only short-term random fluctuations due to turbulent motion, but also quasi-periodic oscillations on longer timescales, take place in the nonlinear phase. We give some possible implications of the instability for black hole quasi-periodic oscillations and the central engine in gamma-ray bursts.