Neutron star mass formula with nuclear saturation parameters for asymmetric nuclear matter

Abstract

Low-mass neutron stars are directly associated with the nuclear saturation parameters because their central density is definitely low. We have already found a suitable combination of nuclear saturation parameters for expressing the neutron star mass and gravitational redshift, i.e., $\eta\equiv (K_0L^2)^{1/3}$ with the incompressibility for symmetric nuclear matter, $K_0$, and the density-dependent nuclear symmetry energy, $L$. In this study, we newly find another suitable combination given by $\eta_\tau\equiv (-K_\tau L^5)^{1/6}$ with the isospin dependence of incompressibility for asymmetric nuclear matter, $K_\tau$, and derive the empirical relations for the neutron star mass and gravitational redshift as a function of $\eta_\tau$ and the normalized central number density. With these empirical relations, one can evaluate the mass and gravitational redshift of the neutron star, whose central number density is less than threefold the saturation density, within $\sim 10\%$ accuracy, and the radius within a few \% accuracies. In addition, we discuss the neutron star mass and radius constraints from the terrestrial experiments, using the empirical relations, together with those from the astronomical observations. Furthermore, we find a tight correlation between $\eta_\tau$ and $\eta$. With this correlation, we derive the constraint on $K_\tau$ as $-348\le K_\tau\le -237$ MeV, assuming that $L=60\pm 20$ and $K_0=240\pm 20$ MeV.