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

TL;DR

This work presents a self-consistent method to extend a cold, β-equilibrated quark-matter EoS to a full three-dimensional EoS that depends on density, temperature, and electron fraction by employing multi-component Fermi-liquid theory. The approach incorporates thermal excitations and out-of-equilibrium effects through Landau parameters and single-particle energies, enabling $p(\varepsilon,T,Y_e)$ descriptions suitable for CCSNe and BNS merger simulations. It demonstrates close agreement with the bag model for thermal and composition-dependent contributions and develops a 3D hybrid EoS with a first-order hadron-quark phase transition via Maxwell construction, ensuring thermodynamic consistency through free-energy-based recomputations. The authors validate the framework with GRHD tests, including a PT-triggered TOV star evolution and CCSN explosions, showing robust performance and results consistent with prior studies. This framework thus provides a versatile, thermodynamically coherent tool for exploring finite-temperature and out-of-equilibrium effects in dense matter relevant to neutron stars and their dynamical events.

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 $β$-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 $β$-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.

Figures (10)

• Figure 1: Pressure as a function of the number density for quark matter EoS using the bag model (left), the mass-radius relation (middle), and the tidal deformability (right) of the corresponding quark stars with two parameter sets are displayed. The blue lines refer to results obtained with $B^{1/4}=136\ {\rm MeV}, \alpha_s=0.5$, and the oranges ones $B^{1/4}=140\ {\rm MeV}, \alpha_s=0$.
• Figure 2: Comparison between total pressures in the FLT-extended EoSs (solid and dashed lines) and the original bag model ones (triangular markers) at $Y_e=0.2$ (left) and $Y_e=0.5$ (right); the temperature is held at $T=0.01$ MeV. Note that results for FLT-extended EoSs with $M_{\rm diff}=0$ MeV (solid) and $M_{\rm diff}=-20$ MeV (dashed) nearly overlap with each other and thus indistinguishable on the upper panels, implying the minor effects of the Dirac effective mass. The lower panels show the deviation of the FLT pressures from those in the corresponding bag model EoSs.
• Figure 3: Entropy per baryon as a function of temperature at $Y_e=0.5$ and $n_{\rm B}=0.49$ fm$^{-3}$. Results from both the bag model EoSs and FLT extensions are shown for comparison, with the same labels as in Fig. \ref{['fig:out_of_equilibrium']}. Additionally, we include the result of an FLT model with negative squared Dirac effective masses $M_i^2$; see text for details.
• Figure 4: Thermal pressures of the bag model and FLT-extended EoSs (upper panel) and their relative errors (lower panel). Labels are the same as those in previous figures.
• Figure 5: Thermal pressure as a function of number density at $Y_e=0.5$. Triangular and diamond markers denote the results of the bag model (with the same parameter sets as shown in previous figures), for $T=20.7$ MeV and $T=52.4$ MeV, respectively, whereas solid and dotted lines represent the FLT results. For all FLT extensions, we set $M_{\rm diff}=0$ MeV, except for the one with negative $M_i^2$ (dash-dotted).