Neutron star inner crust and symmetry energy

The cell structure of clusters in the inner crust of a cold $\beta$-equilibrium neutron star is studied within a Thomas-Fermi approach and compared with other approaches that include shell effects. Relativistic nuclear models are considered. We conclude that the symmetry energy slope $L$ may have quite dramatic effefcts on the cell structure if it is very large or small. Rodlike and slablike pasta clusters have been obtained in all models except one with a large slope $L$.

Figure 1

Symmetry energy $E_{\mathrm{sym}}$ (a) and its slope $L$ (b) as a function of the density $\rho$.

Figure 2

Surface tension as a function of the proton fraction $x$ for all the models considered in this study except SLy4.

Figure 3

Neutron density at the cell center and border (a), cluster proton fraction at the cluster center (b), and neutron skin thickness (c) for all the models considered in this study.

Figure 4

Proton number $Z$ (a), neutron number $N$ (b), Wigner-Seitz cell radius $R_{ws}$ (c), proton fraction $x$ (d), the baryon number in the nucleus $A$ (e), and the proton fraction in the nucleus $Z/A$ (f) as a function of the density $\rho$. HFB SLy4, HF N$\&$V, and CLD SLy4 refer to the results found in Refs. [1, 3, 9].

Figure 5

Proton number (a), neutron number (b), and Wigner-Seitz cell radius (c) in the pasta-phase regions. CLD SLy4 refers to the results found in Ref. [3].