SUBMITTED TO THE ASTROPHYSICAL JOURNAL Preprint typeset using LATEX style emulateapj v. 12/16/11 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. 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 progenitor in 1D and 2D. We test three different equations of state commonly used in core-collapse simulations: the models of Lattimer & Swesty (1991) with incompressibility of 180 MeV and 220 MeV, and the model of Shen et al. (1998), in order of increasing stiffness. We find that for a given neutrino luminosity the time after bounce until explosion increases with the stiffness of the equation of state: the Lattimer & Swesty EOS explode more easily than that of Shen et al. We find this holds in both 1D and 2D, while for all models explosions are obtained more easily in 2D than in 1D. We also discuss the relevance of approximate instability criteria to realistic simulations