Dynamic and Diiusive 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 ngers, and its consequences for the supernova outcome. We nd 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 ux-limited di usion of neutrinos of all types. We nd that prompt convection does not have a signi cant e ect on the neutrino luminosities or spectra and, furthermore, that the core is not amenable to shock revival at this time. Consequently, we do not nd that prompt convection is important for the supernova mechanism. Our analysis of neutron ngers begins with a simple model of doubly di usive 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 nd that, in the usual thermodynamic setting that gets established beneath the neutrinospheres in the postshock core, there is a critical value of Y`, depending on and s, below which matter is stable to doubly di usive instabilities. Above this critical value, numerous numerical experiments show that the postshock core is most likely stable or, at worst, unstable to semiconvection rather than neutron ngers. We therefore conclude that the core is unlikely at any time to be unstable to neutron ngers and, consequently, that the latter play no role in the supernova mechanism.