Empirical neutron star mass formula based on experimental observables

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 ${}^{132} \mathrm{Sn}$.