THE DEPENDENCE OF THE NEUTRINO MECHANISM OF CORE-COLLAPSE SUPERNOVAE ON THE EQUATION OF STATE

We study the dependence of the delayed neutrino-heating mechanism for core-collapse supernovae on the equation of state (EOS). Using a simplified treatment of the neutrino physics with a parameterized neutrino luminosity, we explore the relationship between explosion time, mass accretion rate, and neutrino luminosity for a 15 M-circle dot progenitor in 1D and 2D. We test the EOS most commonly used in core-collapse simulations: the models of Lattimer & Swesty and the model of Shen et al. We find that for a given neutrino luminosity, "stiffer" EOS, where stiffness is determined by a combination of nuclear matter properties not just incompressibility, K, explode later than "softer" EOS. The EOS of Shen et al., being the stiffest EOS, by virtue of larger incompressibility and symmetry energy slope, L, explodes later than any of the Lattimer & Swesty EOS models. Amongst the Lattimer & Swesty EOS that all share the same value of L, the explosion time increases with increasing nuclear incompressibility, K. We find that this holds in both 1D and 2D, while for all of the models, explosions are obtained more easily in 2D than in 1D. We argue that this EOS dependence is due in part to a greater amount of acoustic flux from denser proto-neutron star atmospheres that result from a softer EOS. We also discuss the relevance of approximate instability criteria to realistic simulations.