Entropic-Acoustic instability in shocked accretion flows

Abstract

A new instability mechanism is described in accretion flows where the gas is accelerated from a stationary shock to a sonic surface. The instability is based on a cycle of acoustic and entropic waves in this subsonic region of the flow. When advected adiabatically inward, entropy perturbations trigger acoustic waves propagating outward. If a shock is present at the outer boundary, acoustic waves reaching the shock produce new entropy perturbations, thus creating an entropic-acoustic cycle between the shock and the sonic surface. The interplay of acoustic and entropy perturbations is estimated analytically using a simplified model based on the compact nozzle approximation. According to this model, the entropic-acoustic cycle is unstable if the sound speed at the sonic surface significantly exceeds the sound speed immediately after the shock. The growth rate scales like the inverse of the advection time from the outer shock to the sonic point. The frequency of the most unstable perturbations is comparable to the refraction cutoff, defined as the frequency below which acoustic waves propagating inward are significantly refracted outward. This generic mechanism should occur in Bondi-Hoyle-Lyttleton accretion, and also in shocked accretion discs.