Instability of a stalled accretion shock: evidence for the advective-acoustic cycle

We analyze the linear stability of a stalled accretion shock in a perfect gas with a parametrized cooling function L ∝ ρP . The instability is dominated by the l = 1 mode if the shock radius exceeds 2−3 times the accretor radius, depending on the parameters of the cooling function. The growth rate and oscillation period are comparable to those observed in the numerical simulations of Blondin & Mezzacappa (2006). The instability mechanism is analyzed by separately measuring the efficiencies of the purely acoustic cycle and the advective-acoustic cycle. These efficiencies are estimated directly from the eigenspectrum, and also through a WKB analysis in the high frequency limit. Both methods prove that the advective-acoustic cycle is unstable, and that the purely acoustic cycle is stable. Extrapolating these results to low frequency leads us to interpret the dominant mode as an advective-acoustic instability, different from the purely acoustic interpretation of Blondin & Mezzacappa (2006). A simplified characterization of the instability is proposed, based on an advectiveacoustic cycle between the shock and the radius r∇ where the velocity gradients of the stationary flow are strongest. The importance of the coupling region in this mechanism calls for a better understanding of the conditions for an efficient advective-acoustic coupling in a decelerated, nonadiabatic flow, in order to extend these results to core-collapse supernovae. Subject headings: accretion – hydrodynamics – instabilities – shock waves – supernovae