Study of Neutron Star Properties under the Two-Flavor Quark NJL Model
Chunran Zhu, Bolin Li
TL;DR
This work develops a self-consistent hadron-quark hybrid EOS by coupling the BSR6 RMF hadronic EOS with a two-flavor NJL quark matter model that includes vector interactions. A quintic polynomial interpolation ensures a thermodynamically smooth $C^2$ crossover between phases, enabling TOV-based neutron star structure calculations and tidal deformability predictions. The benchmark Set 1 yields $M_{\max} = 2.20\,M_\odot$, $R_{1.4} = 12.27$ km, and $\Lambda_{1.4} = 353$, consistent with PSR J0740+6620, NICER, and GW170817 constraints, respectively. The analysis reveals that the vector coupling $G_V$ primarily controls high-density stiffness (max mass), while the phase-transition endpoint $BU$ modulates intermediate-density softness (radius and $\Lambda$), with causality imposing a robust bound on the crossover width. This decoupled control framework supports the hadron-quark crossover scenario in neutron stars and demonstrates how multi-messenger data can jointly constrain dense-matter models.
Abstract
The Equation of State (EOS) of matter within neutron stars is a central topic in nuclear physics and astrophysics. A precise understanding of the composition and phase behavior of matter under such extreme conditions is crucial for uncovering the fundamental laws of the strong interaction. This study investigates hadron-quark hybrid stars using a two-flavor Nambu-Jona-Lasinio (NJL) model. As an effective theory, this model can describe the generation of dynamical quark masses and chiral symmetry restoration characteristic of dense quark matter. We construct the hybrid EOS by joining the BSR6 relativistic mean-field model for hadronic matter with the NJL model for quark matter. A quintic polynomial interpolation ensures a smooth ($C^2$ continuity) and thermodynamically consistent crossover between the phases. Based on this hybrid EOS, we solve the Tolman-Oppenheimer-Volkoff (TOV) equations to calculate macroscopic properties of neutron stars, such as the mass-radius ($M-R$) relationship and the tidal deformability parameter ($Λ$). By exploring key model parameters, we identify a region satisfying a wide range of multi-messenger constraints. Our resulting EOS supports a maximum mass consistent with PSR J0740+6620, while simultaneously predicting radii and tidal deformabilities for a $1.4M_{\odot}$ star that agree with NICER observations and limits from GW170817. This work thus presents a self-consistent model that resolves the tension between high-mass pulsars and small tidal deformabilities, deepening our understanding of the hadron-quark crossover.