# Equation of State of Supernova

**Gang Shen**

Indiana University

We calculate the equation of state (EoS) of nuclear matter for a wide range of temparatures, densities, and proton fractions for use in supernova simulations. We employ a full relativistic mean field (RMF) calculation for matter at intermediate density and high density, and the Virial expansion of a non-ideal gas for amtter at low density. This is an improvement over the Lattimer-Swesty equation of state that uses a simple liquid drop model and the H. Shen and Toki equation of state that uses the Thomas Fermi and variational approximations. We use the RMF parameter set NL3 with density dependent coupling for scalar meson-nucleon interaction, and approximate the unit cell for non uniform nuclear matter as a spherical Wigner-Seitz cell, wherein the mean fields of nucleons are solved fully self-consistently. The Virial gas sonsists of neutrons, protons, alpha particles, and 8980 species of nuclei with masses from FRDM mass tables. As the density decreases, the mean field results match smoothly to the Virial gas. At very low density, the Virial expansion reduces to nuclear statistical equilibrium. We tabulate the resulting EoS over 100,000 grid points in the temperature range T = 0-8 MeV, the density range nB = 10-8 ~ 1.6 fm^{-3}. and the proton fraction range YP = 0 ~ 0.56.