Quark mean-field model for nuclear matter with or without bag

We propose the quark mean-field bag (QMFB) model by incorporating the bag confinement mechanism in the original quark mean-field model. Nuclear matter and neutron star properties are studied with the QMFB model. For the study of the bag effect, we fit 12 parameter sets by reproducing the empirical saturation properties of nuclear matter. Quark confinement is found to be mainly demonstrated by the bag after it is included in the model, instead of the confining potential. For nuclear matter, the bag decreases the binding energy and increases the symmetry energy. For neutron stars, the bag affects significantly the radius $R$ of a $1.4M_{\odot }$ star, with the maximum mass only slightly modified. The bag also has a large suppression effect on the well-accepted $R$ versus $L$ dependence, with $L$ the symmetry energy slope at the saturation density.

Figure 1

Effective nucleon mass (upper panel) and radius (lower panel) as functions of baryon density for nuclear matter. The model with bag (red) and without bag (black), $K=240$ MeV (solid) and $K=260$ MeV (dashed) are included for comparison.

Figure 2

Density dependence of binding energy per nucleon (upper panel) and pressure (lower panel) for nuclear matter. The denotation for models and $K$ is the same as in previous figure.

Figure 3

Symmetry energy as a function of density, with $L=40$ (solid), 60 (dashed), and 80 MeV (dotted) for both QMF models with bag (red) and without bag (black). The incompressibility $K$ is fixed at 240 MeV for all sets. The colorful shadow regions denote the constraints from IAS (silver) and IAS+skin (gold) [33], from the ${\alpha }_{\mathrm{D}}$ (cyan) [34], and from HIC (pink) [35], respectively.

Figure 4

Mass-radius relations of neutron stars for QMF models with bag (red) and without bag (black). The sets with different value of $K$ are also included for comparison, while the $L$ is fixed at 40 MeV. The colorful shadow regions represent the measured mass of two massive neutron stars $\mathrm{PSR}\mathrm{J}0348+0432$ [27] and $\mathrm{PSR}\mathrm{J}1614-2230$ [28, 29] and the radius constraints for a $1.4M_{\odot }$ star from GW170817 [36].

Figure 5

Equations of state (left panel) and mass-radius relations (right panel) of neutron stars for QMF models with bag (red) and without bag (black), with fixed $K=240$ MeV and three values of $L=40,60,80$ MeV. The radius constraints are also shown as in Fig. 4.