Framework for phase transitions between the Maxwell and Gibbs constructions at finite temperature

TL;DR

This paper extends a framework describing phase transitions between Maxwell and Gibbs constructions at finite temperature, crucial for modeling astrophysical phenomena like supernovae and neutron star mergers.

Contribution

It introduces a finite-temperature extension of a previously developed framework for phase transitions, applicable to out-of-$eta$ equilibrium conditions in astrophysical simulations.

Findings

Pressure in the mixed phase varies when matter is not in $eta$-equilibrium.

Constant thermal index may be ill-defined in mixed phases at finite temperature.

The framework enables more accurate modeling of phase transitions in astrophysical environments.

Abstract

The characteristics of the hadron-to-quark first-order phase transition differ depending on whether charge neutrality is locally or globally fulfilled. In $\beta$-equilibrated matter, these two possibilities correspond to the Maxwell and Gibbs constructions. Recently, we presented a new framework in which a continuously-varying parameter allows one to describe a first-order phase transition in intermediate scenarios to the two extremes of fully local and fully global charge neutrality. In this work, we extend the previous framework to finite temperatures and out-of-$\beta$ equilibrium conditions, making it available for simulations of core-collapse supernovae and binary neutron star mergers. We investigate its impact on key thermodynamic quantities across a range of baryon densities, temperatures, and electron fractions. We find that when matter is not in $\beta$-equilibrium, the pressure in the mixed phase is not constant even for the case of fully-local charge neutrality. Moreover, we compute the thermal index using three different approaches, demonstrating that the finite-temperature extension of an equation of state using a constant thermal index can be ill-defined when applied to the mixed phase.