Impact of strong magnetic fields on the inner crust of neutron stars

We study the impact of strong magnetic fields on the pasta phases that are expected to exist in the inner crust of neutron stars. We employ the relativistic mean field model to describe the nucleon interaction and use the self-consistent Thomas-Fermi approximation to calculate the nonuniform matter in neutron star crust. The properties of pasta phases and crust-core transition are examined. It is found that as the magnetic field strength $B$ is less than ${10}^{17}$ G, the effects of magnetic field are not evident comparing with the results without magnetic field. As $B$ is stronger than ${10}^{18}$ G, the onset densities of pasta phases and crust-core transition density decrease significantly, and the density distributions of nucleons and electrons are also changed obviously.

Figure 1

Binding energy per nucleon $E/N$ of pasta phases as a function of baryon density $n_b$ for TM1 (upper panel) and IUFSU (lower panel) models with different magnetic field strength, $B=0$ (dashed line), $B={10}^{17}$ G (dotted line), and $B={10}^{18}$ G (solid line). The results with $B={10}^{18}$ G ignoring the anomalous magnetic moments of nucleons for IUFSU model are also plotted by dash-dotted line for comparison. The onset densities of various nonspherical pasta phases are indicated by the circle dots.

Figure 2

Same as Fig. 1, but for binding energy per nucleon of pasta phases relative to that of homogeneous matter $\mathrm{\Delta }E$.

Figure 3

Proton fractions of pasta phases $Y_p$ as a function of baryon density $n_b$ for TM1 (upper panel) and IUFSU (lower panel) models with magnetic fields $B={10}^{18}$ G (solid line) and $B=0$ (dashed line). The results with $B={10}^{18}$ G ignoring the anomalous magnetic moments of nucleons are also plotted by dash-dotted line for comparison. Different colors correspond to various pasta structures.

Figure 4

Chemical potentials of neutrons, ${\mu }_n$ (a), protons, ${\mu }_p$ (b), and electrons, ${\mu }_e$ (c), as functions of baryon density $n_b$ for TM1 (upper panel) and IUFSU (lower panel) models with magnetic fields $B={10}^{18}$ G (solid line) and $B=0$ (dashed line).

Figure 5

Radius of WS cell $r_{\mathrm{ws}}$ (thick line) and nucleus $r_{\mathrm{in}}$ (thin line) as a function of baryon density $n_b$ for TM1 (upper panel) and IUFSU (lower panel) models with magnetic fields $B={10}^{18}$ G (solid line) and $B=0$ (dashed line). The jumps in $r_{\mathrm{ws}}$ and $r_{\mathrm{in}}$ correspond to shape transitions in pasta phases.

Figure 6

Properties of spherical nuclei in droplet phase, such as the charge number $Z_d$ (a) and the nucleon number $A_d$ (b), as a function of baryon density $n_b$ for TM1 (upper panel) and IUFSU (lower panel) models with magnetic fields $B=0$ G (dashed line) and $B={10}^{18}$ G (solid line).

Figure 7

Density distributions of protons, ${\rho }_p$ (a), neutrons, ${\rho }_n$ (b), and baryons, ${\rho }_b$ (c), in the WS cell at $n_b=0.01,0.02,0.03{\mathrm{fm}}^{-3}$ (top to bottom) obtained in the TF approximation for TM1 model with magnetic fields $B=0$ (dashed line) and $B={10}^{18}$ G (solid line). The cell boundary is indicated by the hatching.

Figure 8

Same as Fig. 7, but for IUFSU model.

Figure 9

Density distributions of neutrons, ${\rho }_n$ (a), protons, ${\rho }_p$ (b), and electrons, ${\rho }_e$ (c), in the WS cell at $n_b=0.03,0.05,0.07,0.08,0.09{\mathrm{fm}}^{-3}$ (top to bottom) obtained in the TF approximation for IUFSU model with magnetic fields $B=0$ (dashed line) and $B={10}^{18}$ G (solid line). The cell boundary is indicated by the hatching.

Figure 10

Neutron density of liquid phase $n_{n,L}$ and gas phase $n_{n,G}$ in WS cell (a) and proton density of liquid phase $n_{p,L}$ in WS cell (b), as a function of baryon density $n_b$ for IUFSU model with magnetic fields $B=0$ (dashed line) and $B={10}^{18}$ G (solid line). The kinks correspond to shape transitions of different pasta phases.