Revisiting the “flip-flop” Instability of Hoyle-lyttleton Accretion

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 (Ra), 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 γ leading to faster growth of the instability. For a relatively large accretor (a radius of 0.037Ra) planar accretion is unstable for γ = 4/3, but stable for γ ≥ 1.6. Planar accretion is unstable even for γ = 5/3 provided the accretor has a radius of < 0.0025Ra. 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. Subject headings: accretion—hydrodynamics—shock waves —turbulence