Revisiting the Flip-Flop Instability of Hoyle-Lyttleton Accretion

TL;DR

This study uses high-fidelity simulations to analyze the flip-flop instability in Hoyle-Lyttleton accretion, revealing its dependence on accretor size, specific heat ratio, and initial conditions, and confirming it does not require upstream flow gradients.

Contribution

The paper provides detailed numerical analysis of the flip-flop instability, clarifying its growth conditions and independence from upstream flow gradients, and explores the effects of accretor size and thermodynamic properties.

Findings

Growth rate increases with decreasing accretor size.

Instability is insensitive to upstream flow gradients.

Smaller gamma leads to faster instability growth.

Abstract

We revisit the flip-flop instability of two-dimensional planar accretion using high-fidelity numerical simulations. By starting from an initially steady-state axisymmetric solution, we are able to follow the growth of this overstability from small amplitudes. In the small-amplitude limit, before any transient accretion disk is formed, the oscillation period of the accretion shock is comparable to the Keplerian period at the Hoyle-Lyttleton accretion radius (R_a), independent of the size of the accreting object. The growth rate of the overstability increases dramatically with decreasing size of the accretor, but is relatively insensitive to the upstream Mach number of the flow. We confirm that the flip-flop does not require any gradient in the upstream flow. Indeed, a small density gradient as used in the discovery simulations has virtually no influence on the growth rate of the overstability. The ratio of specific heats does influence the overstability, with smaller gamma leading to faster growth of the instability. For a relatively large accretor (a radius of 0.037R_a) planar accretion is unstable for gamma = 4/3, but stable for gamma > 1.6. Planar accretion is unstable even for gamma = 5/3 provided the accretor has a radius of < 0.0025R_a. We also confirm that when the accretor is sufficiently small, the secular evolution is described by sudden jumps between states with counter-rotating quasi-Keplerian accretion disks.