Pasta properties of the neutron star within effective relativistic mean-field model

We study the properties of pasta structures and their influence on the neutron star observables employing the effective relativistic mean-field (E-RMF) model. The compressible liquid drop model is used to incorporate the finite size effects, considering the possibility of nonspherical structures in the inner crust. The unified equation of state are constructed for several E-RMF parameters to study various properties such as pasta mass and thickness in the neutron star’s crust. The majority of the pasta properties are sensitive to the symmetry energy in the subsaturation density region. Using the results from Monte Carlo simulations, we estimate the shear modulus of the crust in context of quasiperiodic oscillations from soft gamma-ray repeaters and calculate the frequency of fundamental torsional oscillation mode in the inner crust. Global properties of the neutron star such as mass-radius profile, the moment of inertia, crustal mass, crustal thickness and fractional crustal moment of inertia are worked out. The results are consistent with various observational and theoretical constraints.

Figure 1

Comparison of the sequence of ground state pasta phase appearance for various functional.

Figure 2

Symmetry energy of the models considered in Fig. 1.

Figure 3

The equilibrium value of WS cell energy for various parameter sets considered in Fig. 1 with the range of different pasta structures.

Figure 4

The crust-core transition pressure $P_c$, chemical potential ${\mu }_c$, and density ${\rho }_c$ as a function of symmetry energy $J$, slope parameter $L$ and $K_{\mathrm{sym}}$. The orange band represent the median range obtained in Newton et al. [29] for the uniform $\mathrm{Prior}+\mathrm{PREX}$ [111] data while the purple band represent the uniform $\mathrm{Prior}+\mathrm{PNM}$ band from the Balliet et al. [37] for 95% credible range. The verticals cyan band for the empirical/experimental range of symmetry energy and its slope parameter constraints given By Danielwicz et al. [121]. The olive vertical band represents the $K_{\mathrm{sym}}$ constraints by Zimmerman et al. [122].

Figure 5

The mass/moment of inertia and thickness fractions of pasta as a function of symmetry energy $J$, slope parameter $L$ and $K_{\mathrm{sym}}$.

Figure 6

Upper panel show the relative mass of the different layer of pasta structures and lower panel shows the relative thickness as compared to the total crust.

Figure 7

Correlation heat map of the bulk properties with the crustal properties and surface parameters. The color map signify the strength of the correlation while the values represent the associated $p$-values.

Figure 8

Shear modulus ($\mu$) of the inner crust for various E-RMF sets.

Figure 9

The shear velocity ($V_s$) as a function of the mass density for the various E-RMF models.

Figure 10

Frequency of fundamental torsional oscillation mode ($l=2$) in the crust for the maximum mass with $J$ and $L$. The two horizontal lines corresponds to the observed value of 18 and 26 Hz.