Estimating the nuclear saturation parameter via low-mass neutron star asteroseismology

TL;DR

This paper develops empirical formulas linking neutron star oscillation frequencies to nuclear matter parameters, enabling constraints on the nuclear saturation parameter and neutron star radius through gravitational wave observations.

Contribution

It introduces new empirical relations for $f$- and $p_1$-mode frequencies as functions of nuclear parameters, aiding EOS constraints via gravitational wave data.

Findings

Simultaneous observation of $f$- and $p_1$-modes can estimate the nuclear saturation parameter $ exteta$ within 10%.

The maximum $f$-mode frequency correlates with the minimum neutron star radius.

Empirical formulas relate oscillation frequencies to stellar density and nuclear parameters.

Abstract

We examine the fundamental ($f$-) and the 1st pressure ($p_1$-) mode frequencies in gravitational waves from cold neutron stars constructed with various unified realistic equations of state. With the calculated frequencies, we derive the empirical formulae for the $f$- and $p_1$-mode frequencies, $f_f$ and $f_{p_1}$, as a function of the square root of the stellar average density and the parameter ($\eta$), which is a combination of the nuclear saturation parameters. With our empirical formulae, we show that by simultaneously observing the $f$- and $p_1$-mode gravitational waves, when $1.5\lesssim f_{p_1}/f_f\lesssim 2.5$ (which corresponds to neutron star models with the mass of $\lesssim 0.9M_\odot$), one could estimate the value of $\eta$ within $\sim 10\%$ accuracy, which makes a strong constraint on the EOS for neutron star matter. In addition, we find that the maximum $f$-mode frequency is strongly associated with the minimum radius of neutron star. That is, if one would observe a larger frequency of the $f$-mode, one might constrain the upper limit of the minimum neutron star radius.