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New ab initio constrained extended Skyrme equations of state for simulations of neutron stars, supernovae and binary mergers: II. Thermal response in the suprasaturation density domain

Numerical simulations of core-collapse supernovae, mergers of binary neutron stars and formation of stellar black holes, which employed standard Skyrme interactions, established clear correlations between the evolution of these processes, characteristics of the hot compact objects, as well as neutrino and gravitational wave signals, and the value of effective nucleon mass at the saturation density. Unfortunately, the density dependence of the effective mass of nucleons in these models does not align with the predictions of ab initio models with three body forces. In this work, we investigate the thermal response for a set of extended Skyrme interactions that feature widely different density dependencies of the effective mass of the nucleons. Thermal contributions to the energy density and pressure are studied along with a few thermal coefficients over wide domains of density, temperature and isospin asymmetry, relevant for the physics of hot compact objects. For some of the effective interactions, the thermal pressure is negative at high densities. This results in a situation where hot compact stars can support less mass before collapsing into a black hole compared to their cold counterparts. Moreover, the higher the temperature, the lower the maximum mass that the hot star can support.