Gravitational wave asteroseismology for low-mass neutron stars

TL;DR

This paper develops empirical formulas relating the $f$-mode gravitational wave frequencies of low-mass neutron stars to nuclear saturation parameters, enabling constraints on the neutron star equation of state through observations.

Contribution

It introduces new empirical relations connecting $f$-mode frequencies with nuclear saturation parameters and central density ratios, aiding EOS constraints from gravitational wave data.

Findings

Empirical formulas for $f$-mode frequency as a function of nuclear parameters and density.

Relations enabling EOS constraints from gravitational wave observations.

Analysis of avoided crossing phenomena in neutron star oscillation modes.

Abstract

The fundamental ($f$-) mode gravitational waves from cold low-mass neutron stars are systematically studied with various equations of state (EOSs) characterized by the nuclear saturation parameters, especially focusing on the phenomena of the avoided crossing with the first pressure ($p_1$-) mode. We find that the $f$-mode frequency and the average density for the neutron star at the avoided crossing can be expressed as a function of the parameter, $\eta$, which is the specific combination of the nuclear saturation parameters. Owing to these relations, we can derive the empirical formula expressing the $f$-mode frequency for a low-mass neutron star, whose central density is larger than that for the neutron star at the avoided crossing, as a function of $\eta$ and the square root of the stellar average density, $x$. On the other hand, we also derive the empirical formula expressing the $f$-mode frequency for a neutron star, whose central density is less than that for the neutron star at the avoided crossing, as a function of $x$ independently of the adopted EOS. Furthermore, adopting the empirical formula of $x$ as a function of $\eta$ and $u_c$, which is the ratio of the stellar central density to the saturation density, we can also rewrite our empirical formula for the $f$-mode frequency to a function of $\eta$ and $u_c$. So, by observing the $f$-mode gravitational wave from a low-mass neutron star, whose mass or gravitational redshift is known, one could evaluate the values of $\eta$ and $u_c$, which enables us to severely constrain the EOS for neutron star matter.