The Role of Doubly Diffusive Instabilities in the Core-Collapse Supernova Mechanism

Abstract

We investigate doubly diffusive instabilities in hot, dense stellar material by examining its behavior in response to small perturbations. These instabilities, particularly neutron fingers, have been suggested to arise in the postcollapse cores of massive stars, where entropy and lepton gradients are stabilizing and destabilizing, respectively, and to be important for the supernova explosion mechanism. We model neutrino-mediated equilibration of energy and leptons as a linear system characterized by four response functions. These latter are evaluated for a given thermodynamic state by detailed neutrino-transport experiments. Our results indicate that regions in a postcollapse stellar core may be semiconvectively rather than neutron-finger unstable but that these regions shrink with time as more and more of the lepton profile of the core falls below the critical lepton number for which a negative lepton gradient becomes stabilizing. Because these results differ from what has been assumed before, the role of doubly diffusive instabilities in the supernova explosion mechanism will have to be reexamined.