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~ rhoᵇeta Tᵃlpha. A new formulation of the boundary conditions at the shock is proposed, different from Houck & Chevalier (1992). 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. Both methods indicate that the instability is due to an unstable advective-acoustic cycle, and that the purely acoustic cycle is stable. These results do not support the purely acoustic interpretation of Blondin & Mezzacappa (2006). A simplified characterization of the instability is proposed, based on an advective-acoustic cycle between the shock and the radius rₙabla 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.