Empirical neutron star mass formula based on experimental observables

We derive the empirical formulas 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 ²⁰⁸Pb or ¹³²Sn, especially focusing on the eight Skyrme-type effective interactions. The neutron star mass and its gravitational redshift can be estimated within ≈10 % errors with our formulas, while the neutron star radius is also expected within a few % errors by combining the derived formulas. Owing to the resultant empirical formulas, we find that the neutron star mass and radius are more sensitive to the neutron-skin thickness of ²⁰⁸Pb than the dipole polarizability of ²⁰⁸Pb or ¹³²Sn.