Performing two-dimensional hydrodynamic simulations including a detailed treatment of the equation of state of the stellar plasma and for the neutrino transport and interactions, we investigate here the interplay between different kinds of non-radial hydrodynamic instabilities that can play a role during the postbounce accretion phase of collapsing stellar cores. The convective mode of instability, which is driven by the negative entropy gradients caused by neutrino heating or by variations in the shock strength in transient phases of shock expansion and contraction, can be identified clearly by the development of typical Rayleigh-Taylor mushrooms. However, in those cases where the gas in the postshock region is rapidly advected towards the gain radius, the growth of such a buoyancy instability can be suppressed. In this situation the shock and postshock flow can nevertheless develop non-radial asymmetry with an oscillatory growth in the amplitude. This phenomenon has been termed "standing (or spherical) accretion shock instability" (SASI). It is shown here that the SASI oscillations can trigger convective instability, and like the latter, they lead to an increase in the average shock radius and in the mass of the gain layer. Both hydrodynamic instabilities in combination stretch the advection time of matter accreted through the neutrino-heating layer and thus enhance the neutrino energy deposition in support of the neutrino-driven explosion mechanism. A rapidly contracting and more compact nascent neutron star turns out to be favorable for explosions, because the accretion luminosity and neutrino heating are greater and the growth rate of the SASI is higher. Moreover, we show that the oscillation period of the SASI observed in our simulations agrees with the one estimated for the advective-acoustic cycle (AAC), in which perturbations are carried by the accretion flow from the shock to the neutron star and pressure waves close an amplifying global feedback loop. A variety of other features in our models, as well as differences in their behavior, can also be understood on the basis of the AAC hypothesis. The interpretation of the SASI in our simulations as a purely acoustic phenomenon, however, appears difficult.

We analyze the linear stability of a stalled accretion shock in a perfect gas with a parameterized cooling function L / À P . The instability is dominated by the l ¼ 1 mode if the shock radius exceeds 2Y3 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. 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. A simplified characterization of the instability is proposed, based on an advective-acoustic cycle between the shock and the radius r 9 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.