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

TL;DR

This study combines 2D general relativistic hydrodynamic simulations and linear analysis to investigate the stability of standing accretion shocks around a Schwarzschild black hole, revealing non-axisymmetric instabilities and their potential link to astrophysical phenomena.

Contribution

It provides the first combined simulation and linear analysis of shock stability in relativistic accretion flows, identifying the Papaloizou-Pringle type instability and its nonlinear evolution.

Findings

Shock stable against axisymmetric perturbations

Non-axisymmetric perturbations cause instability

Quasi periodic oscillations observed in nonlinear phase

Abstract

We study the stability of standing shock waves in advection-dominated accretion flows into a Schwarzschild black hole by 2D 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 non-axisymmetric perturbations. The results of dynamical simulations show good agreement with linear analysis on the stability, oscillation and growing time scales. The comparison of different wave-travel times with the growth time scales of the instability suggests that the instability is likely to be of the Papaloizou-Pringle type, induced by the repeated propagations of acoustic waves. However, the wavelengths of perturbations are too long to clearly define the reflection point. By analyzing the non-linear phase in the dynamical simulations, it is shown that quadratic mode couplings precede the non-linear saturation. It is also found that not only short-term random fluctuations by turbulent motions but also quasi periodic oscillations take place on longer time scales in the non-linear phase. We give some possible implications of the instability for quasi periodic oscillations (QPOs) and the central engine for gamma ray bursts (GRBs).