An analytic study of Bondi-Hoyle-Lyttleton accretion

TL;DR

This paper analytically investigates the stability of Bondi-Hoyle-Lyttleton accretion flows, focusing on shock-induced entropy and vorticity, and compares theoretical predictions with numerical simulations to understand flow destabilization mechanisms.

Contribution

It provides an analytical assessment of linear instabilities in accretion flows and compares these with numerical simulations, highlighting the conditions under which instabilities develop.

Findings

Instability occurs only for supersonic accretors.

Instability is nonaxisymmetric and starts near the equatorial region.

Growth times of instabilities are comparable to advection times.

Abstract

The adiabatic shock produced by a compact object moving supersonically relative to a gas with uniform entropy and no vorticity is a source of entropy gradients and vorticity. We investigate these analytically. The non-axisymmetric Rayleigh-Taylor and axisymmetric Kelvin-Helmholtz linear instabilities are potential sources of destabilization of the subsonic accretion flow after the shock. A local Lagrangian approach is used in order to evaluate the efficiency of these linear instabilities. However, the conditions required for such a WKB type approximation are fulfilled only marginally: a quantitative estimate of their local growth rate integrated along a flow line shows that their growth time is at best comparable to the time needed for advection onto the accretor, even at high Mach number and for a small accretor size. Despite this apparently low efficiency, several features of these mechanisms qualitatively match those observed in numerical simulations: in a gas with uniform entropy, the instability occurs only for supersonic accretors. It is nonaxisymmetric, and begins close to the accretor in the equatorial region perpendicular to the symmetry axis. The mechanism is more efficient for a small, highly supersonic accretor, and also if the shock is detached. We also show by a 3-D numerical simulation an example of unstable accretion of a subsonic flow with non-uniform entropy at infinity. This instability is qualitatively similar to the one observed in 3-D simulations of the Bondi-Hoyle-Lyttleton flow, although it involves neither a bow shock nor an accretion line.