Neutron star properties in density-dependent relativistic Hartree-Fock theory

With the equations of state provided by the newly developed density-dependent relativistic Hartree-Fock (DDRHF) theory for hadronic matter, the properties of the static and $\beta$-equilibrium neutron stars without hyperons are studied for the first time and compared to the predictions of the relativistic mean-field models and recent observational data. The influences of Fock terms on properties of asymmetric nuclear matter at high densities are discussed in detail. Because of the significant contributions from the σ- and ω-exchange terms to the symmetry energy, large proton fractions in neutron stars are predicted by the DDRHF calculations, which strongly affect the cooling process of the star. A critical mass of about $1.45M_{\odot }$, close to the limit of $1.5M_{\odot }$ determined by modern soft X-ray data analysis, is obtained by DDRHF with the effective interactions PKO2 and PKO3 for the occurrence of the direct Urca process in neutron stars. The maximum masses of neutron stars given by the DDRHF calculations lie between $2.45M_{\odot }$ and $2.49M_{\odot }$, which are in reasonable agreement with the high pulsar mass of $(2.08\pm 0.19)M_{\odot }$ from PSR B1516 $+$ 02B. It is also found that the mass-radius relations of neutron stars determined by DDRHF are consistent with the observational data from thermal radiation measurements in the isolated neutron star RX J1856, quasiperiodic brightness oscillations in the low-mass X-ray binaries 4U 0614 $+$ 09 and 4U 1636-536, and the redshift determined in the low-mass X-ray binary EXO 0748-676.

Figure 1

The coupling constants $g_{\sigma }$, $g_{\omega }$, $g_{\rho }$, and $f_{\pi }$ as functions of the baryonic density ${\rho }_b$ (${\mathrm{fm}}^{-3}$) for the DDRHF effective interactions PKO1, PKO2, and PKO3 and the RMF ones PKDD, TW99, and DD-ME2. The shadowed area represents the empirical saturation region ${\rho }_b=0.166\pm 0.018\hspace{0.5em}{\mathrm{fm}}^{-3}$.

Figure 2

The binding energy per particle, $E_B/A$, as a function of the baryonic density ${\rho }_b$ for symmetric nuclear matter. The results are calculated by DDRHF with PKO1, PKO2, and PKO3, in comparison with those by RMF with TW99, DD-ME2, and PKDD.

Figure 3

Similar to Fig. 2 but for pure neutron matter.

Figure 4

The nuclear symmetry energy $E_S$ (MeV) as a function of the baryon density ${\rho }_b$ (${\mathrm{fm}}^{-3}$). The results are calculated by DDRHF with PKO1, PKO2, and PKO3, in comparison to those by RMF with TW99, DD-ME2, and PKDD.

Figure 5

Contributions from different channels to the symmetry energy as a function of the baryon density ${\rho }_b$. The left panel gives the contributions from the kinetic energy and isoscalar channels; the ones from ρ mesons are shown in the right panel. See text for details.

Figure 6

The neutron (upper left panel), proton (upper right panel), electron (lower left panel), and muon (lower right panel) densities in neutron star matter as functions of the baryon density ${\rho }_b$ (${\mathrm{fm}}^{-3}$). The results are calculated by DDRHF with PKO1, PKO2, and PKO3, in comparison to those by RMF with TW99, DD-ME2, and PKDD.

Figure 7

Proton fractions $x={\rho }_p/({\rho }_p+{\rho }_n)$ in neutron star matter for different DDRHF and DDRMF effective interactions. The dotted line labeled with $x^{\mathrm{DU}}$ is the threshold for the direct Urca process to occur. Here $x^{\mathrm{DU}}=14.8\%$ is taken by assuming muons in the massless limit.

Figure 8

The pressure of neutron star matter as a function of the baryon density ${\rho }_b$ (${\mathrm{fm}}^{-3}$). The results are calculated by DDRHF with PKO1, PKO2, and PKO3, in comparison to those by RMF with GL-97, NL3, PK1, TW99, DD-ME2, and PKDD.

Figure 9

Neutron star mass as a function of the central density for different DDRHF and RMF effective interactions. Filled stars denote the maximum mass configurations; filled squares mark the critical mass $M^{\mathrm{DU}}$ and central density values ${\rho }^{\mathrm{DU}}(0)$ where the DU cooling process becomes possible. The light gray horizontal bands around $2.08M_{\odot }$ denote the $1\sigma$ confidence level for the mass measurement of PSR B1516$+$02B [14]. The mass region of typical neutron stars is between $1.0M_{\odot }$ and $1.5M_{\odot }$.

Figure 10

Mass-radius relations of neutron stars provided by the DDRHF and RMF calculations and the corresponding maximum masses ( marked by filled star symbols). For comparison are also shown the four separate observational constraints from RX J1856 (gray grided region), 4U 0614 $+$ 09 (cyan grided area), 4U 1636-536 (yellow grided area), and EXO 0748-676 (error bar for $1\sigma$ error). The black region is excluded by causality that $R>2.9\hspace{0.5em}\mathit{GM}/c^2$ [78, 79]. See the text for details.