Structure of neutron star crusts from new Skyrme effective interactions constrained by chiral effective field theory

We investigate the structure of neutron star crusts, including the crust-core boundary, based on new Skyrme mean field models constrained by the bulk-matter equation of state from chiral effective field theory and the ground-state energies of doubly-magic nuclei. Nuclear pasta phases are studied using both the liquid drop model as well as the Thomas-Fermi approximation. We compare the energy per nucleon for each geometry (spherical nuclei, cylindrical nuclei, nuclear slabs, cylindrical holes, and spherical holes) to obtain the ground state phase as a function of density. We find that the size of the Wigner-Seitz cell depends strongly on the model parameters, especially the coefficients of the density gradient interaction terms. We employ also the thermodynamic instability method to check the validity of the numerical solutions based on energy comparisons.

Figure 1

Comparison of the energy per baryon in asymmetric nuclear matter from chiral EFT ($\mathrm{\Lambda }=450\mathrm{MeV}$) and its Skyrme fitting model. The isospin asymmetry is denoted by $\delta =(n_n-n_p)/(n_n+n_p)$.

Figure 2

Density profiles of neutron and proton in ${}^{208}\mathrm{Pb}$ using Skyrme Hartree-Fock calculations. Experimental charge density is also added for comparison.

Figure 3

Mass-radius curves from the Skyrme mean field models constructed in the present work.

Figure 4

Shape function $\mathcal{D}\left(u\right)$ for discrete dimension and continuous dimension. The continuous dimension curve always lies below those of the discrete geometries.

Figure 5

Energy per nucleon as a function of baryon number density in beta-stable nuclear matter employing the liquid drop model with the $\mathrm{Sk}\chi 450$ Skyrme mean field model.

Figure 6

Pressure as a function of baryon number density in beta-stable nuclear matter employing the liquid drop model with the $\mathrm{Sk}\chi 450$ Skyrme mean field model. At each transition density the pressure is almost continuous in the case of the LDM approach.

Figure 7

Volume fraction of the dense phase in the Wigner-Seitz cell. The volume fraction indicates which dimension is the ground state for a given baryon number density.

Figure 8

Energy per baryon using the TF approximation with the $\mathrm{Sk}\chi 450$ Skyrme fit model.

Figure 9

Pressure vs baryon number density using in the TF approximation. A discontinuity in the pressure occurs at the shape transition densities, but the discontinuity region (shown in the inset) is very narrow.

Figure 10

Atomic number of heavy nucleus in the Wigner Seitz cell. The dotted line around $\rho =0.064{\mathrm{fm}}^{-3}$ indicates the transition between 3D nuclei and 2D nuclei.

Figure 11

Neutron and proton density profiles using three different numerical methods with the $\mathrm{Sk}\chi 450$ Skyrme mean field model.

Figure 12

Transition density contour plot for the core-crust boundary obtained from thermodynamic instability. The individual points are taken from the modified Skyrme interactions obtained in Ref. [81].