Enhanced adiabatic index for hot neutron-rich matter from microscopic nuclear forces

We investigate the adiabatic index $\Gamma_{\mathrm{th}}$ of hot and dense nuclear matter from chiral effective field theory and find that the results are systematically larger than from typical mean field models. We start by constructing the finite-temperature equation of state from chiral two- and three-nucleon forces, which we then use to fit a class of extended Skyrme energy density functionals. This allows for modeling the thermal index across the full range of densities and temperatures that may be probed in simulations of core-collapse supernovae and neutron star mergers, including the low-density inhomogeneous mixed phase. For uniform matter we compare the results to analytical expressions for $\Gamma_{\mathrm{th}}$ based on Fermi liquid theory. The correlation between the thermal index and the effective masses at nuclear saturation density is studied systematically through Bayesian modeling of the nuclear equation of state. We then study the behavior of $\Gamma_{\mathrm{th}}$ in both relativistic and non-relativistic mean field models used in the astrophysical simulation community to complement those based on chiral effective field theory constraints from our own study. We derive compact parameterization formulas for $\Gamma_{\mathrm{th}}$ across the range of densities and temperatures encountered in core collapse supernovae and binary neutron star mergers, which we suggest may be useful for the numerical simulation community.