Fluid Stability below the Neutrinospheres of Supernova Progenitors and the Dominant Role of Lepto-entropy Fingers

Instabilities driven by thermal and lepton diffusion (doubly diffusive instabilities) in a Ledoux stable fluid will, if present below the neutrinosphere of the collapsed core of a supernova progenitor (protosupernova), induce convective-like fluid motions there. These fluid motions may enhance the neutrino emission by advecting neutrinos outward toward the neutrinosphere, and may thus play an important role in the supernova mechanism. “Neutron fingers,” in particular, have been suggested as being critical for producing explosions in the sophisticated spherically symmetric supernova simulations by the Livermore group (Wilson & Mayle 1993, e.g.,). These have been argued to arise in an extensive region below the neutrinosphere of a proto-supernova where entropy and lepton gradients are stabilizing and destabilizing, respectively, if, as they assert, the rate of neutrino-mediated thermal equilibration greatly exceeds that of neutrino-mediated lepton equilibration. Application of the Livermore group’s criteria to models derived from core collapse simulations using both their equation of state and the Lattimer-Swesty equation of state do indeed show a large region below the neutrinosphere unstable to neutron fingers. Because of the potential importance of fluid instabilities for the supernova mechanism, and the desire to understand the origin of convective-like fluid motions that may arise in upcoming multidimensional radiation-hydrodynamical simulations of core collapse, we develop a methodology introduced by Bruenn & Dineva (1996) for analyzing the stability of a fluid in the presence of neutrinos of all flavors and in the presence of a gravitational field. Neutrino-mediated thermal and lepton equilibration between a fluid element and its surroundings (background) is modeled as a linear system characterized by four response functions (i.e., thermal and lepton equilibration driven by entropy and lepton fraction differences between a fluid element and the background), the latter evaluated for a given thermodynamic state and fluid element radius by detailed neutrino transport simulations. These transport simulations employ both traditional and improved neutrino physics. When applied to an extensive two-dimensional grid of core radii and fluid element sizes for each of several time slices of a number of proto-supernovae, we find no evidence for the neutron finger instability as described by the Livermore group. We find, instead, that the rate of lepton equilibration always exceeds that of thermal equilibration. Furthermore, we find that neither of the “cross” response functions, that is, entropy equilibration driven by a lepton fraction difference, and lepton equilibration driven by an entropy difference, is zero and that the first of these tends to be the largest of the four response functions in magnitude. These cross response functions play a critical role in the dynamics of the equilibration of a fluid element with the background. An important consequence of this is the presence of a doubly diffusive instability, which we refer to as “lepto-entropy fingers,” in an extensive region below the neutrinosphere where the lepton number, Yl, is small. This instability is driven by a mechanism very different from that giving rise to neutron fingers, and may play an important role in enhancing the neutrino emission. Deep in the core where the entropy is low and the lepton number higher, our analysis indicates a region unstable to another instability, also involving the cross response functions, which we refer to as “lepto-entropy semiconvection.” These instabilities, particularly lepto-entropy fingers, may have already been seen in some multi-dimensional core collapse simulations described in the literature. Subject headings: (stars:) supernovae: general – neutrinos – fluid instabilities