Equation of state of nuclear matter and neutron stars: Quark mean-field model versus relativistic mean-field model

The equation of state of neutron-rich nuclear matter is of interest to both nuclear physics and astrophysics. We have demonstrated the consistency between laboratory and astrophysical nuclear matter in neutron stars by considering low-density nuclear physics constraints (from ${}^{208}\mathrm{Pb}$ neutron-skin thickness) and high-density astrophysical constraints (from neutron star global properties). We have used both quark-level and hadron-level models, taking the quark mean-field (QMF) model and the relativistic mean-field (RMF) model as examples, respectively. We have constrained the equation of states of neutron stars and some key nuclear matter parameters within the Bayesian statistical approach, using the first multimessenger event GW170817/AT 2017gfo, as well as the mass-radius simultaneous measurements of PSR $\mathrm{J0030}+0451$ and PSR $\mathrm{J0740}+6620$ from NICER, and the neutron-skin thickness of ${}^{208}\mathrm{Pb}$ from both PREX-II measurement and ab initio calculations. Our results show that, compared with the RMF model, the QMF model's direct coupling of quarks with mesons and gluons leads to the evolution of the in-medium nucleon mass with the quark mass correction. This feature enables the QMF model a wider range of model applicability, as shown by a slow drop of the nucleon mass with density and a large value at saturation that is jointly constrained by nuclear physics and astronomy.

Figure 1

Scalar (vector) potential $U_{\mathrm{S}}$ ($U_{\mathrm{V}}$) (left), effective mass $M_N^{*}$ (middle), and nucleon-$\sigma$ coupling constants (right) as functions of nucleon number density, for the representative case of $K_0$ = 240 MeV, $J_0$ = 31 MeV, $M_N^{*}/M_N$ = 0.77 in symmetric nuclear matter. The calculations are done for both RMF (solid lines) and QMF (dash lines) models. The left panel shows only one line for $U_{\mathrm{V}}$ as its results from RMF and QMF models are identical.

Figure 2

Pressure (upper) and symmetry energy (lower) as functions of density for both the RMF (blue) and QMF (red) models for fixed $K_0$ ($=240$ MeV), $J_0$ ($=31$ MeV), $M_N^{*}/M_N$ ($=0.77$), and three different values of $L_0$ ($=40$, 60, 80 MeV), along with experimental constraints. The orange and grey shaded areas in the upper panel represent the flow [104] and kaon production [105] analyses, respectively, of the heavy-ion experimental data. Meanwhile, in the lower panel, various experimental regions from heavy-ion experiments are included, including the ${\pi }^{-}/{\pi }^{+}$ ratio [106] (lime), the ASY-EOS data with a consistent value of $J_0$[107] (green), and the isospin diffusion data [108] (grey). The orange contour indicates the results of the isobaric analog states (IAS) [109].

Figure 3

Posteriors of the neutron star EoS and mass-radius relation for both the RMF (blue) and QMF (red) models. In all cases, the likelihood is based on observational data (GW170817/AT2017gfo $+$ NICER). The shaded regions and dashed lines represent the 90% confidence interval for the analyses with and without neutron-skin data (PREX-II $+$ EFT), respectively. The dash-dotted and dotted lines indicate the median results for each analysis.

Figure 4

Posterior probability distribution functions of the quantities at saturation density for each analysis (see details in Sec. 2e). The RMF and QMF models are denoted by the blue and red lines, respectively, while solid and dashed lines denote the analyses conducted with and without neutron-skin data.