Systematics on the high-density nuclear equation of state from relativistic Hartree-Fock theory with Brown-Rho scaling

Using the Brown-Rho (BR) scaling law, several new relativistic Hartree-Fock (RHF) models with chiral limit are thoroughly investigated. The high-density nuclear equation of state (EOS) of RHF with the BR scaling become softer than one without the BR scaling. The EOS of RHF with BR scaling is consistent with the constraint extracted from collective flows and kaon production in heavy-ion collisions. It is found that, with a sizable strength parameter of the mass drop $x=0.126$, the symmetry energy is almost flat at density above 3 times the saturation density ${\rho }_0$, and even decreases slightly. This is caused from the fact that the decline of the potential part of symmetry energy is faster than the increase of the kinetic part of symmetry energy. The decrease of potential part is mainly because the neutron mass $M_n^{*}$ and the proton mass $M_p^{*}$ are close to each other when the density gradually approaches the critical density of chiral limit. For a mass drop of $x=0.092$, since the critical density of chiral limit is higher than one of $x=0.126$, the symmetry energy becomes flat at density above $5{\rho }_0$. While, since the critical density of chiral limit is very high for a small mass drop $x=0.053$, the symmetry energy of RHFs with $x=0.053$ always increases at the entire density domain of this work (below 6 ${\rho }_0$). The maximum mass of neutron star (NS) obtained with present models can satisfy $M=2.08\pm 0.07M_{\odot }$. However, the radius of 1.4 $M_{\odot }$ with the mass drop of $x=0.126$ will surpass the upper limit (13.7 km) extracted from the tidal deformability parameter of coalescence of a NS binary system and the radius of $\text{J0030}+0451$ being $12.{71}_{-1.19}^{+1.14}$ km. The radius of 1.4 $M_{\odot }$ with the mass drop of $x=0.092$ is 13.6 km, closing to 13.7 km and the radius of $\text{J0030}+0451$ being $12.{71}_{-1.19}^{+1.14}$ km. Therefore, the RHF model with BR scaling prefers the mass drop of $x\lesssim 0.092$.

Figure 1

The effective mass as a function of baryon density in symmetric nuclear matter for RHF with different parameters.

Figure 2

The pressure as a function of baryon density in symmetric nuclear matter for RHF with different parameters. The cyan and yellow regions extracted from the collective flows [23] and kaon [24, 25, 26, 27, 28, 29] yields of heavy-ion collisions, respectively.

Figure 3

The symmetry energy as a function of baryon density for RHF with different parameters (upper panel). The lower panel is the kinetic and potential parts of the symmetry energy as a function of baryon density.

Figure 4

The mass-radius trajectories of NSs for RHF with different parameters.