Effect of the Landau quantization of electrons on the inner crusts of hot neutron stars

In the present work we study the effects of strongly quantizing magnetic fields and finite temperature on the properties of inner crusts of hot neutron stars. In particular, we study the effects of Landau quantization of electrons on the composition of the NS inner crusts. The inner crust of a neutron star contains neutron-rich nuclei arranged in a lattice and embedded in gases of free neutrons and electrons. We describe the system within the Wigner-Seitz (WS) cell approximation. The nuclear energy is calculated using Skyrme model with SkM* interaction. To isolate the properties of nuclei we follow the subtraction procedure presented by Bonche, Levit, and Vautherin [Nuc. Phys. A 427, 278 (1984); Nuc. Phys. A 436, 265 (1985)], within the Thomas-Fermi approximation. We obtain the equilibrium properties of the inner crust for various density, temperatures, and magnetic fields by minimizing the free energy of the WS cell satisfying the charge neutrality and $\beta$-equilibrium conditions. We infer that at a fixed baryon density and temperature, a strong quantizing magnetic field reduces the cell radii, neutron, and proton numbers in the cell compared with the field free case. However, the nucleon number in the nucleus increases in the presence of a magnetic field. The free energy per nucleon also decreases in the magnetized inner crust. On the other hand, we find that finite temperature tends to smear out the effects of magnetic field. Our results can be important in the context of $r$-process nucleosynthesis in the binary neutron star mergers.

Figure 1

Different contributions to the free energy per nucleon as a function of $R_c$ and $A$ (upper x axis) for $T=0–3$ MeV, $B=0$, and $\langle \rho \rangle =0.001{\mathrm{fm}}^{-3}$.

Figure 2

Same as Fig. 1 but for $T=1–4$ MeV, and $B*={10}^4$.

Figure 3

(a) WS cell radius $R_c$ and (b) proton fraction $Y_p$ as a function of average baryon density for $T=0–4$ MeV with and without quantizing magnetic field.

Figure 4

Total number of neutrons ($N_{\mathrm{cell}}$), protons ($Z_{\mathrm{cell}}$) and $A_{\mathrm{cell}}=N_{\mathrm{cell}}+Z_{\mathrm{cell}}$ in the cell as a function of average baryon density and temperature for (a) $B_{*}=0$ and (b) $B_{*}={10}^4$.

Figure 5

Total number of neutrons ($N$), protons ($Z$), and $A=N+Z$ in the nucleus as a function of average baryon density and temperature for (a) $B_{*}=0$ and (b) $B_{*}={10}^4$.

Figure 6

Free energy per baryon as function of baryonic number density for zero and finite temperature in (a) absence and (b) presence of quantizing magnetic field.