The Spherical Accretion Shock Instability in the Linear Regime

We use time-dependent, axisymmetric, hydrodynamic simulations to study thelinear stability of the stalled, spherical accretion shock that arises in thepost-bounce phase of core-collapse supernovae. We show that this accretionshock is stable to radial modes, with decay rates and oscillation frequenciesin close agreement with the linear stability analysis of Houck and Chevalier.For non-spherical perturbations we find that the l=1 mode is always unstablefor parameters appropriate to core-collapse supernovae. We also find that thel=2 mode is unstable, but typically has a growth rate smaller than that forl=1. Furthermore, the l=1 mode is the only mode found to transition into anonlinear stage in our simulations. This result provides a possible explanationfor the dominance of an l=1 'sloshing' mode seen in many two-dimensionalsimulations of core-collapse supernovae