Density-dependent quark mean-field model for nuclear matter and neutron stars

We develop a density-dependent quark mean-field (DDQMF) model to study the properties of nuclear matter and neutron stars, where the coupling strength between $\sigma$ meson and nucleon is generated by the degree of freedom of quarks, while other meson coupling constants are regarded as density-dependent ones. Two values for the nucleon effective mass, $M_{N0}^{*}/M_N=0.556,0.70$ at the saturation density are chosen based on the consideration of the core-collapse supernova simulation and finite nuclei when the meson-nucleon coupling constants are fixed. We find that the equation of state (EOS) of nuclear matter, the symmetry energy, the mass-radius relations, and the tidal deformabilities of neutron stars with larger nucleon effective mass are more sensitive to the skewness coefficient $J_0$. The EOSs with $M_{N0}^{*}/M_N=0.70$ are softer when the skewness coefficient $J_0=-800$ MeV. However, the maximum masses of the neutron star can be around $2.32M_{\odot }$ with $J_0=400$ MeV regardless of the value of the nucleon effective mass. By manipulating the coupling strength of the isovector meson to generate different slopes of symmetry energy, we construct the neutron star EOSs that can satisfy the different variables from the simultaneous mass-radius measurements of PSR $\mathrm{J}0030+0451$, PSR $\mathrm{J}0740+6620$ by the NICER collaboration, the mass-radius relations of HESS J1731-347, and the radius constraints from the gravitational-wave signal GW170817 in the framework of a DDQMF model. At the same time, most of these constructed EOSs can also satisfy the constraints of the tidal deformability from GW170817 event.

Figure 1

The density-dependent behaviors of coupling constants, ${\mathrm{\Gamma }}_{\sigma N}\left({\rho }_B\right)$ and ${\mathrm{\Gamma }}_{\omega N}\left({\rho }_B\right)$, the effective mass, $M_N^{*}$, and the scalar(vector) potential at $M_{N0}^{*}/M_N=0.556,0.70$ as functions of the baryon density for symmetric nuclear matter with DDQMF parameters in Table 2.

Figure 2

(a) The binding energies per nucleon and (b) pressures as functions of vector density for symmetric nuclear matter with DDQMF parameters in Table 2.

Figure 3

Mass-radius relations of neutron stars at $M_{N0}^{*}/M_N=0.556,0.70$ with the DDQMF model.

Figure 4

Tidal deformabilities of neutron stars at $M_{N0}^{*}/M_N=0.556,0.70$ with the DDQMF model.

Figure 5

The density-dependent behaviors of the symmetry energy for $L_0=30,40,60,80$ MeV of the DDQMF model.

Figure 6

Mass-radius relations of neutron stars with different $L_0$ for the core EOS with the DDQMF model.

Figure 7

Tidal deformabilities of neutron stars with different $L_0$ for the core EOS with the DDQMF model.