Finite-Temperature Equations of State for Neutron-Star Mergers within the Quark Mean-Field Model

Abstract

We extend the quark mean-field (QMF) model to finite temperature and systematically investigate the thermodynamic properties of uniform nuclear matter, using the relativistic mean-field (RMF) model as a reference. For each model, we consider two parameter sets calibrated to the same selected nuclear-matter saturation properties but with different nucleon Dirac effective-mass ratios at saturation. We examine the effective nucleon mass and the composition of $β$-equilibrium matter, together with the free energy, energy density, pressure, entropy, and heat capacities of symmetric nuclear matter, pure neutron matter, and $β$-equilibrium matter. The QMF and RMF models exhibit similar qualitative trends, but their predictions increasingly differ at high density, where the effective masses have distinct density dependences. These differences are particularly evident in the thermal pressure and thermal index. For the two parameter sets considered in this work, we further provide compact analytical representations of the thermal index, $Γ_{\rm th}(ρ_{\rm b},T,β)$ over baryon densities of 0.08-1.0 $\rm fm^{-3}$, temperatures of 5-100 MeV, and isospin asymmetries of 0-1. The fits reproduce the numerical results with an accuracy better than $2\%$ and can be directly implemented in binary neutron-star merger simulations. This study establishes a finite-temperature extension of the QMF framework and provides a basis for future assessments of how a quark-structure-based description of nuclear matter affects thermal support and post-merger dynamics in binary neutron-star mergers.