DYNAMIC AND DIFFUSIVE INSTABILITIES IN-CORE COLLAPSE SUPERNOVAE

The instabilities that are believed to play an important role in the supernova mechanism are reviewed. We then investigate the dynamics of two of these instabilities, prompt convection and neutron fingers, and its consequences for the supernova outcome. We find that prompt convection occurs immediately after shock propagation and is primarily entropy driven. A number of detailed one-dimensional spherically symmetric simulations of prompt convection are performed using a mixing length algorithm in a code coupling the core hydrodynamics with multigroup flux-limited diffusion of neutrinos of all types. We find that prompt convection does not have a significant effect on the neutrino luminosities or spectra and, furthermore, that the core is not amenable to shock revival at this time. Consequently, we do not find that prompt convection is important for the supernova mechanism. Our analysis of neutron fingers begins with a simple model of doubly diffusive instabilities, applicable to salt and water, and is then extended to describe matter and neutrinos in a postshock core. The equations describing the stability of the latter are nonlinear, requiring a numerical approach. However, on general grounds, we find that, in the usual thermodynamic setting that gets established beneath the neutrinospheres in the postshock core, there is a critical value of Y-l, depending on rho and s, below which matter is stable to doubly diffusive instabilities. Above this critical value, numerous numerical experiments show that the postshock core is most likely stable or, at worst, unstable to semiconvection father than neutron fingers. We therefore conclude that the core is unlikely at any time to be unstable to neutron fingers and, consequently, that the latter play no role in the supernova mechanism.