Doubly diffusive instabilities in postcollapsed stellar matter

We use a semianalytical approach to derive criteria for the presence of doubly diffusive instabilities in postcollapsed stellar matter believed to be essential for producing a supernova explosion. Critical stability equations are obtained from both Boltzmann Equation Moment formalism and Single Particle Eigenvalue approach. Computer experiments are performed to numerically evaluate the key equilibration timescales contained in these equations. Contrary to the widely accepted view, we find that the core, if unstable, is unstable to semiconvection, rather than to neutron fingers. We also find for a given density and entropy there is a critical value for the lepton fraction Y1, below which the stellar core is completely stable to doubly diffusive instabilities of either kind. A considerable fraction of the core proves to lie below the critical Y1, immediately following shock propagation. As the core evolves this fraction quickly encompasses the entire core. We conclude that doubly diffusive instabilities of any kind are unlikely to play a role in the supernova explosion mechanism.