Neutron star properties in density-dependent relativistic mean field theory with consideration of an isovector scalar meson

Based on the density-dependent relativistic mean field theory, the properties for nuclear matter and neutron stars with the effective interaction $\mathrm{DD}\text{−}\mathrm{ME}\delta$ including the isovector scalar channel which disentangle the effects of isovector scalar and isovector vector channels by fitting microscopic calculations. The influences of the isovector scalar $\delta$ meson on properties of asymmetric nuclear matter at high densities are discussed in detail. The results support that the isovector scalar channel can soften the equation of state through the effects on the nucleon effective mass and the scalar $\sigma$ field and impact the behavior of the nuclear matter symmetry energy. Because of the influence on the symmetry energy by the $\delta$ meson, a larger proton fraction in neutron stars is predicted by the $\mathrm{DD}\text{−}\mathrm{ME}\delta$ calculation, which strongly affects the cooling process of the star. The maximum masses of neutron stars given by the $\mathrm{DD}\text{−}\mathrm{ME}\delta$ calculation is $1.97M_{⨀}$ which is in reasonable agreement with PSR J1614 − 2230 ($1.97 \pm 0.04 M_{⨀}$) and PSR J0348 + 0432 $(2.01 \pm 0.04 M_{⨀})$. Among all the selected interactions, $\mathrm{DD}\text{−}\mathrm{ME}\delta$ gives the smallest radius range. The radius for the 1.4 solar mass neutron star calculated by $\mathrm{DD}\text{−}\mathrm{ME}\delta$ is in good agreement with the prediction [Astrophys. J. Lett. 765, L5 (2013)] according to the resent observations.

Figure 1

The binding energy per nucleon $E_B/A$, as a function of the nucleon density $\rho$ for symmetric nuclear matter (upper panel) and pure neutron matter (lower panel). The results are calculated by DD-ME2, TW99, PKDD without the isovector scalar meson $\delta$ and $\mathrm{DD}\text{−}\mathrm{ME}\delta$ with the $\delta$ meson.

Figure 2

The contributions from different channels to the $E_B/A$ as functions of the nucleon density $\rho$ for the pure neutron matter. The results calculated by $\mathrm{DD}\text{−}\mathrm{ME}\delta$ (solid black lines) and $\mathrm{DD}\text{−}\mathrm{ME}\delta$ (dashed pink lines) but switching off the $\delta$ channel.

Figure 3

Neutron and proton effective masses as a function of the nucleon density with three different $\beta$.

Figure 4

The nuclear matter symmetry energy $E_{\mathrm{sym}}$(MeV) as a function of the nucleon density $\rho \left(\mathrm{fm}{}^{-3}\right)$.

Figure 5

Proton fractions $x={\rho }_p/({\rho }_p+{\rho }_n)$ in neutron star given by different effective interactions. The dotted line labeled with $x^{\mathrm{DU}}=14.8\%$ is the threshold for the direct Urca process to occur.

Figure 6

The pressure of neutron star matter as a function of the energy density $\varepsilon$ (MeV $\mathrm{fm}{}^{-3}$).

Figure 7

Neutron star mass as a function of the central density for different effective interactions. The filled squares mark the critical mass $M^{\mathrm{DU}}$ and central density values ${\rho }^{\mathrm{DU}}\left(0\right)$ where the DU cooling process becomes possible. The mass region of typical neutron stars is between $1.0M_{⨀}$ and $1.5M_{⨀}$.

Figure 8

Mass radius of neutron stars calculated by the interactions without the $\delta$ meson and the interaction $\mathrm{DD}\text{−}\mathrm{ME}\delta$ with the $\delta$ meson. The two shaded areas are 68% and 95% confidence contours extracted from the analysis of Ref. [11].