Systematic Study of Pasta Nuclei in Neutron Stars with Families of the Empirical Nuclear Equations of State

The structures of pasta nuclei in the crust of a neutron star are investigated systematically by using a family of the equations of state (EOSs) of nuclear matter within the framework of the Thomas-Fermi theory. This EOS family is given as a function of the incompressibility K 0 of symmetric nuclear matter and the parameter L that characterizes the density dependence of the symmetry energy. The remaining saturation parameters are chosen so that the masses and radii of stable nuclei calculated within the framework are consistent with the empirical values. The structure of a neutron-rich nucleus is determined by the local pressure balance of asymmetric nuclear matter, which is mainly controlled by L and K 0. With this EOS family, we calculate the structure of pasta nuclei in the crust of a neutron star, and examine its (K 0, L) dependence. It is found that the existence of pasta nuclei is mainly determined by L. For sufficiently small L, as the matter density increases, the shape of the nuclei changes from sphere to cylinder, slab, cylindrical hole and spherical hole successively. For larger L, this sequence of the shape change may end before reaching spherical hole. All the pasta shape can exist for L ≤ 70 MeV, while no pasta shape appears for L ≥ 110 MeV. The density width of each pasta phase, the energy and volume fraction at the onset of each pasta phase have a clear correlation with L while the onset density also has an appreciable Ko dependence.