Neutron star mass formula with nuclear saturation parameters

TL;DR

This paper presents empirical formulas linking neutron star mass, radius, and gravitational redshift to nuclear saturation parameters, enabling estimates within 10% accuracy based on nuclear experimental constraints.

Contribution

It introduces new empirical formulas that connect neutron star properties directly to nuclear saturation parameters, applicable up to three times nuclear saturation density.

Findings

Neutron star mass and radius can be estimated within ~10% accuracy.

Empirical formulas are valid for central densities up to threefold nuclear saturation density.

The formulas facilitate discussion of neutron star properties based on nuclear experimental data.

Abstract

We derive the empirical formulas for the neutron star mass and gravitational redshift as a function of the central density and specific combination of the nuclear saturation parameters, which are applicable to the stellar models constructed with the central density up to threefold nuclear saturation density. Combining the both empirical formulas, one also estimates the neutron star radius. In practice, we find that the neutron star mass (radius) can be estimated within $\sim 10\%$ (a few percent) accuracy by comparing the mass and radius evaluated with our empirical formulas to those determined with the specific equation of state. Since our empirical formulas directly connect the neutron star mass and radius to the nuclear saturation parameters, one can discuss the neutron star properties with the specific values of nuclear saturation parameters constrained via nuclear experiments.