Empirical neutron star mass formula based on experimental observables

Abstract

We derive the empirical formulae expressing the mass and gravitational redshift of a neutron star, whose central density is less than threefold the nuclear saturation density, as a function of the neutron-skin thickness or the dipole polarizability of $ {}^{208} \mathrm{Pb} $ or $ {}^{132} \mathrm{Sn} $, especially focusing on the 8 Skyrme-type effective interactions. The neutron star mass and its gravitational redshift can be estimated within $ \approx 10 \, \% $ errors with our formulae, while the neutron star radius is also expected within a few $\%$ errors by combining the derived formulae. Owing to the resultant empirical formulae, we find that the neutron star mass and radius are more sensitive to the neutron-skin thickness of $ {}^{208} \mathrm{Pb} $ than the dipole polarizability of $ {}^{208} \mathrm{Pb} $ or $ {}^{132} \mathrm{Sn} $.