Diversity of neutron star properties at the fixed neutron-skin thickness of ${}^{208}\mathrm{Pb}$

We study the diversities in the properties of the neutron stars arising due to the different choices for the cross coupling between various mesons, which governs the density dependence of the nuclear symmetry energy in the extended relativistic mean-field (RMF) model. For this purpose, we obtain two different families of the extended RMF model corresponding to different nonlinear cross-coupling terms in the isovector part of the effective Lagrangian density. The lowest-order contributions for the $\delta$ mesons are also included. The different models within the same family yield wide variation in the value of neutron-skin thickness in the ${}^{208}\mathrm{Pb}$ nucleus. These models are employed to compute the neutron-star properties such as core-crust transition density, radius and red shift at canonical mass $(1.4M_{\odot })$, tidal polarizability parameter, and threshold mass required for the enhanced cooling through the direct Urca process. Most of the neutron-star properties considered are significantly different(10–40%) for the different families of models at a smaller neutron-skin thickness $(\sim 0.15\mathrm{fm})$ in the ${}^{208}\mathrm{Pb}$ nucleus.

Figure 1

Color-coded contours in the $g_{\delta }-{\eta }_{\rho }$(upper panel) and $g_{\delta }-{\eta }_{2\rho }$ (lower panel) planes correspond to the $F_{\rho }$ and $F_{2\rho }$ families, respectively. The value of $g_{\rho }$ are color coded according to the scale on the right side.

Figure 2

Same as Fig. 1, but for the symmetry energy at the saturation density $(J=S\left({\rho }_0\right))$ fixed along the contour. The values of $J$ are in MeV.

Figure 3

Same as Fig. 1, but for the neutron-skin thickness $\mathrm{\Delta }{r}_{\mathrm{np}}$ in the ${}^{208}\mathrm{Pb}$ nucleus fixed along the contour. The values of $\mathrm{\Delta }{r}_{\mathrm{np}}$ are in femtometers.

Figure 4

The density dependence of symmetry energy $S\left(\rho \right)$ for some representative cases of $F_{\rho }$ and $F_{2\rho }$ families of the models. The labels SET1 and SET2 correspond to the two different parameterizations for the $F_{\rho }$ family, whereas SET3 and SET4 correspond to the $F_{2\rho }$ family. SET1 and SET3 are associated with $\mathrm{\Delta }{r}_{\mathrm{np}}=0.22\text{fm}$ and SET2 and SET4 yield $\mathrm{\Delta }{r}_{\mathrm{np}}=0.15\text{fm}$ (see also Tables 1 and 2).

Figure 5

The variations of symmetry energy slope parameter $L$ with neutron-skin thickness $\mathrm{\Delta }{r}_{\mathrm{np}}$ in the ${}^{208}\mathrm{Pb}$ nucleus for the $F_{\rho }$ and $F_{2\rho }$ families of models. The solid and hollow symbols represent the results obtained with $g_{\delta }\ne 0$ and with $g_{\delta }=0$, respectively.

Figure 6

The variation of core-crust transition density (upper panel) and the corresponding pressure (lower panel) with the neutron-skin thickness $\mathrm{\Delta }{r}_{\mathrm{np}}$ in ${}^{208}\mathrm{Pb}$ nucleus for the $F_{\rho }$ and $F_{2\rho }$ families of the extended RMF models.

Figure 7

The mass-radius relationship for the $F_{\rho }$ (left panel) and $F_{2\rho }$ (right panel) families of the models. The solid squares represent the masses and the corresponding radii for the neutron stars with the central density to be $3{\rho }_0$.

Figure 8

Plots for the radius $R_{1.4}$ for the neutron stars with the canonical mass $1.4M_{\odot }$ (upper panel) and the corresponding red shift (lower panel) as a function of $\mathrm{\Delta }{r}_{\mathrm{np}}$ in the ${}^{208}\mathrm{Pb}$ nucleus obtained for the $F_{\rho }$ and $F_{2\rho }$ families of models.

Figure 9

The dependence of the threshold neutron star mass $M_{DU}$ on the neutron-skin thickness in ${}^{208}\mathrm{Pb}$ nucleus. The neutron stars with masses equal to or larger than $M_{DU}$ undergo enhanced cooling through the direct Urca process for the cooling.

Figure 10

Variations in the tidal polarizability parameter $\lambda$ with the neutron-star mass for the different parametrizations of $F_{\rho }$ and $F_{2\rho }$ families corresponding to neutron-skin thickness $\mathrm{\Delta }{r}_{\mathrm{np}}=0.15$ fm in the ${}^{208}\mathrm{Pb}$ nucleus.