On the stability of isothermal shocks in black hole accretion disks

TL;DR

This paper analyzes the stability of isothermal shocks in thin black hole accretion disks, revealing that inner shocks are always unstable while outer shocks are stable, with implications for accretion regimes.

Contribution

First explicit calculation of isothermal shock stability in black hole accretion disks using matched asymptotic methods.

Findings

Inner shocks are always unstable.

Outer shocks are always stable.

Stability depends on flow parameters and angular momentum dissipation.

Abstract

Most black holes possess accretion disks. Models of such disks inform observations and constrain the properties of the black holes and their surrounding medium. Here, we study isothermal shocks in a thin black hole accretion flow. Modelling infinitesimal molecular viscosity allows the use of multiple-scales matched asymptotic methods. We thus derive the first explicit calculations of isothermal shock stability. We find that the inner shock is always unstable, and the outer shock is always stable. The growth/decay rates of perturbations depend only on an effective potential and the incoming--outgoing flow difference at the shock location. We give a prescription of accretion regimes in terms of angular momentum and black hole radius. Accounting for angular momentum dissipation implies unstable outer shocks in much of parameter space, even for realistic viscous Reynolds numbers of the order $\approx 10^{20}$.