Crustal properties of a neutron star within an effective relativistic mean-field model

We use the effective relativistic mean-field (E-RMF) model to study the crustal properties of the neutron star. The unified equations of state (EoS) are constructed using recently developed E-RMF parameter sets, such as FSUGarnet, IOPB-I, and G3. The outer crust composition is determined using the atomic mass evaluation 2020 data [Huang et al. Chin. Phys. C 45, 030002 (2021) along with the available Hartree-Fock-Bogoliubov mass models [Goriely et al. Phys. Rev. C 88, 024308 (2013) for neutron-rich nuclei. The structure of the inner crust is estimated by performing the compressible liquid drop model calculations using the same E-RMF functional as that for the uniform nuclear matter in the liquid core. Various neutron star properties such as mass-radius ($M-R$) relation, the moment of inertia ($I$), the fractional crustal moment of inertia ($I_{\text{crust}}/I$), mass ($M_{\text{crust}}$) and thickness ($l_{\text{crust}}$) of the crust are calculated with three unified EoSs. The crustal properties are found to be sensitive to the density-dependent symmetry energy and slope parameter advocating the importance of the unified treatment of neutron star EoS. The three unified EoSs, IOPB-I-U, FSUGarnet-U, and G3-U, reproduced the observational data obtained with different pulsars, NICER, and glitch activity and are found suitable for further description of the structure of the neutron star.

Figure 1

The proton ($Z$) and neutron number ($N$) in the outer crust as a function of density. The experimental data are taken from AME2020 when available [38]. The unknown mass are taken from microscopic calculations HFB-14 [41], HFB-24, HFB-26 [42] along with the FRDM(2012) mass table [96]. A comparison with BCPM [7] and D1M [97] is also shown. In addition the experimental mass of ${}^{82}\mathrm{Zn}$ [57], ${}^{77–79}\mathrm{Cu}$ [58] and ${}^{151–157}\mathrm{Yb}$ [59] are also considered. Vertical dashed line represent the boundary where prediction from experimental masses ends.

Figure 2

In the upper panel the EoS of outer crust is shown for different mass model. The lower panel shows the global asymmetry as a function of density. Vertical dashed line represent the boundary where prediction from experimental masses ends.

Figure 3

EoSs of the Nuclear matter for NL3 set with other three considered sets.

Figure 4

The variation of mass number $A$, proton number $Z$, asymmetry $\alpha$, average cluster density ${\rho }_0$, the neutron gas density ${\rho }_g$ and the radius of cell with the baryon density ${\rho }_b$ in the inner crust of neutron star with FSUGarnet, IOPB-I, and G3 E-RMF parameter set. The quantum calculation by Negele and Vautherin [43] and Onsi et al. [45] are also shown.

Figure 5

The density dependent symmetry energy ($J$) and slope parameter ($L$) for different E-RMF parametrizations.

Figure 6

Crust-core transition density and pressure as a function of slope parameter $L$ and $p$ [Eq. (14)] for the FSUGarnet, IOPB-I, and G3 parameter sets.

Figure 7

The EoS for the inner crust and equilibrium value of WS cell energy using the E-RMF parameter sets FSUGarnet, IOPB-I and G3.

Figure 8

The effective shear and compression modulus for BCC lattice in the inner crust of neutron stare using the FSUGarnet, IOPB-I, and G3 parameter sets.

Figure 9

Adiabatic index of the inner crust calculated from the FSUGarnet, IOPB-I, and G3 E-RMF forces.

Figure 10

The unified EoSs for FSUGarnet-U, IOPB-I-U, and G3-U sets. The green line represents the outer-inner crust transition.

Figure 11

The $M-R$ relations for three unified EoSs such as FSUGarnet-U, IOPB-I-U, and G3-U. The horizontal bars represents the PSR $\mathrm{J}0740+6620$ [22] (light orange) and PSR $\mathrm{J}0348+0432$ [23] (light violet). The old NICER data are also shown with two boxes from two different analysis [18, 122]. The double-headed red line represents the radius constraints by the Miller et al. [123] for $1.4M_{\odot }$ neutron star termed as new NICER data.

Figure 12

Upper: the mass of the crust as a function of mass for three unified EoSs. Lower: the length of the crust as a function of mass. The black dotted line represents the canonical neutron star mass.

Figure 13

Upper: the normalized moment of inertia as a function of mass for three unified EoSs. Lower: the fractional moment of inertia as a function of mass. The dashed dark magenta and dark blue lines represent the Vela pulsar data (see text for details).

Figure 14

Distribution of $I_{\text{crust}}/I$ calculated using 581 glitches [131]. The vertical lines are the FMI for FSUGarnet-U, IOPB-I-U, and G3-U EoSs.