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

TL;DR

This study probes the thermal response of dense nuclear matter using ab initio constrained Brussels extended Skyrme EOSs to span wide ranges of density, temperature, and isospin. It highlights how non-monotonic density dependence of the nucleon effective mass $m_{ m eff}(n)$, particularly U-shaped behaviors, shapes thermal contributions to energy and pressure, sometimes producing negative thermal pressure $P_{ m th}$ at suprasaturation densities and significantly influencing hot-star stability. By comparing two NM ensembles, S1 and S2, derived from Bayesian inference, the work shows that stricter constraints (S2) reduce dispersion in $m_{ m eff}(n)$ and moderate extreme thermal responses, though substantial model dependence persists, especially in $S/A$- and $Y_p$-dependent outcomes for proto-neutron stars and merger remnants. The findings have direct implications for CCSNe, BNS mergers, and BH formation, stressing the importance of realistic finite-temperature NM modeling and the potential value of Brussels-Skyrme EOS tables in simulations and multimessenger interpretation. Overall, the paper advances understanding of how thermal NM properties govern hot compact-object evolution and provides a framework to constrain thermal behavior in dense matter.

Abstract

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.

Figures (13)

• Figure 1: Neutron effective mass ($m_{\mathrm{eff;}n}$) in SNM (top) and PNM (bottom) in units of bare neutron mass ($m_n$) as a function of density. Medians and upper and lower quantiles at 90% CI of the two sets of models in Sec. \ref{['sec:NM']} are depicted with solid and short dashed curves, respectively. The other curves correspond to BBSk1 - BBSk5 forces, see Paper I.
• Figure 2: Neutron ($m_{\mathrm{eff;}n}$) and proton ($m_{\mathrm{eff;}p}$) effective masses in units of bare neutron ($m_n$) and proton ($m_p$) masses, respectively as functions of density in NM matter with $Y_p=0.2$. For the legend, see Fig. \ref{['Fig:meffn']}.
• Figure 3: The same as in Fig. \ref{['Fig:meffn']} but for $Q_n$, see Eq. \ref{['eq:Qi']}.
• Figure 4: Proton fraction ($Y_p$) as a function of density in NS matter.
• Figure 5: ${e}_{\mathrm{th}}(n)$ in PNM and SNM matter at $T=20~\mathrm{MeV}$.