Multi-dimensional Radiation/hydrodynamic Simulations of Protoneutron Star Convection

Based on multi-dimensional multi-group radiation hydrodynamic simulations of core-collapse supernovae with the VULCAN/2D code, we study the physical conditions within and in the vicinity of the nascent protoneutron star (PNS). Conclusions of this work are threefold: First, as before, we do not see any large-scale overturn of the inner PNS material. Second, we see no evidence of doubly-diffusive instabilities in the PNS, expected to operate on diffusion timescales of at least a second, but instead observe the presence of convection, within a radius range of 10-20km, operating with a timescale of a few milliseconds. Third, we identify unambiguously the presence of gravity waves, predominantly at 200-300milliseconds (ms) past core bounce, in the region separating the convective zones inside the PNS and between the PNS surface and the shocked region. Our numerical study is an improvement over past work in a number of ways: we follow the evolution of the collapsing envelope from ∼200ms before bounce to ∼500ms after bounce; the spatial grid switches from Cartesian inside to spherical outside, permitting a handling of the inner PNS region at good spatial resolution, all the way inside to the center, and without severe Courant-time limitation; neutrino-transport is treated with a Multi-Group, Flux-Limited-Diffusion (MGFLD) approach, well suited for the study of the PNS, i.e., in regions where the neutrino mean-free-path is small. With this configuration, VULCAN/2D has the ability to simulate doubly-diffusive instabilities, if present. Convection, directly connected to the PNS, is found to occur in two distinct regions: between 10 and 20 km, coincident with the region of negative lepton gradient, and exterior to the PNS above 50 km. These two regions are separated by an interface, which shows no sizable outward or inward motion and efficiently shelters the inner PNS. The PNS is also the site of gravity waves, excited by the convection in the outer convective zone. In the PNS, convection is always confined to a region between 10 and 20 km, i.e., within the neutrinospheric radii for all neutrino energies above just a few MeV. We find that such motions do not appreciably enhance the νe neutrino luminosity, and that they can enhance the ν̄e and “νμ” luminosities by no more than ∼15% and ∼30%, respectively, during the first post-bounce ∼100 ms, after which the optical depth barrier between the inner convection and the neutrinospheres effectively isolates one from the other, terminating even this modest enhancement. PNS convection is thus found to be a secondary feature of the core-collapse phenomenon, rather than a decisive ingredient for a successful explosion. Furthermore, the typical timescale associated with such convective transport is of the order of a few milliseconds, and thus is at least a thousand times faster than typical growth rates for instabilities associated with neutrino-mediated thermal and lepton diffusion. Such doubly-diffusive instabilities are, therefore, unlikely to play a substantial role in the early critical phases of the PNS. We conclude that inner PNS motions do not bear importantly on the potential success of core-collapse supernovae explosions. Subject headings: convection – hydrodynamics – neutrinos – stars: neutron – stars: supernovae: