Three-dimensional equation of state extension of quark matter in Fermi-liquid theory

TL;DR

This paper develops a method to extend a cold, 1D quark matter equation of state to a comprehensive 3D version considering density, temperature, and electron fraction, improving modeling of neutron star phenomena.

Contribution

The authors introduce a self-consistent 3D extension of the quark matter EoS within Fermi-liquid theory, including thermal and out-of-equilibrium effects, and demonstrate its application with phase transitions.

Findings

The 3D FLT-extended EoS reproduces thermal and compositional effects accurately.

Simulations with the extended EoS match previous results for neutron star and supernova models.

The method effectively incorporates phase transitions into the EoS modeling.

Abstract

The cold, dense matter equation of state (EoS) determines crucial global properties of neutron stars (NSs), including the mass, radius and tidal deformability. However, a one-dimensional (1D), cold, and $\beta$-equilibrated EoS is insufficient to fully describe the interactions or capture the dynamical processes of dense matter as realized in binary neutron star (BNS) mergers or core-collapse supernovae (CCSNe), where thermal and out-of-equilibrium effects play important roles. We develop a method to self-consistently extend a 1D cold and $\beta$-equilibrated EoS of quark matter to a full three-dimensional (3D) version, accounting for density, temperature, and electron fraction dependencies, within the framework of Fermi-liquid theory (FLT), incorporating both thermal and out-of-equilibrium contributions. We compare our FLT-extended EoS with the original bag model and find that our approach successfully reproduces the contributions of thermal and compositional dependencies of the 3D EoS. Furthermore, we construct a 3D EoS with a first-order phase transition (PT) by matching our 3D FLT-extended quark matter EoS to the hadronic DD2 EoS under Maxwell construction, and test it through the GRHD simulations of the TOV-star and CCSN explosion. Both simulations produce consistent results with previous studies, demonstrating the effectiveness and robustness of our 3D EoS construction with PT.