Standing Shock Instability in Advection-Dominated Accretion Flows

TL;DR

This study investigates the stability of standing shocks in advection-dominated accretion flows, revealing conditions for stability and instability, and suggesting possible origins of observed quasi-periodic oscillations in black hole systems.

Contribution

It applies linear stability analysis to classify shock configurations in accretion flows and predicts the existence of QPOs with specific frequency ratios.

Findings

Preshock deceleration is unstable to the zeroth mode but stable to higher modes.

Preshock acceleration is always unstable to the zeroth mode.

Stable shocks may still produce QPOs with 2:3 and 3:5 ratios.

Abstract

Depending on the values of the energy and angular momentum per unit mass in the gas supplied at large radii, inviscid advection-dominated accretion flows can display velocity profiles with either preshock deceleration or preshock acceleration. Nakayama has shown that these two types of flow configurations are expected to have different stability properties. By employing the Chevalier \& Imamura linearization method and the Nakayama instability boundary conditions, we discover that there are regions of parameter space where disks/shocks with outflows can be stable or unstable. In regions of instability, we find that preshock deceleration is always unstable to the zeroth mode with zero frequency of oscillation, but is always stable to the fundamental mode and overtones. Furthermore, we also find that preshock acceleration is always unstable to the zeroth mode and that the fundamental mode and overtones become increasingly less stable as the shock location moves away from the horizon when the disk half-height expands above $\sim 12$ gravitational radii at the shock radius. In regions of stability, we demonstrate the zeroth mode to be stable for the velocity profiles that exhibit preshock acceleration and deceleration. Moreover, for models that are linearly unstable, our model suggests the possible existence of quasi-periodic oscillations (QPOs) with ratios 2:3 and 3:5. These ratios are believed to occur in stellar and supermassive black hole candidates, for example, in GRS 1915+105 and Sgr A*, respectively. We expect that similar QPO ratios also exist in regions of stable shocks.