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

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 formulas 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 ($\ensuremath{\eta}$), which is a combination of the nuclear saturation parameters. With our empirical formulas, we show that by simultaneously observing the $f$- and ${p}_{1}$-mode gravitational waves, when $1.5\ensuremath{\lesssim}{f}_{{p}_{1}}/{f}_{f}\ensuremath{\lesssim}2.5$ (which corresponds to neutron star models with the mass of less than or approximately equal to $0.9\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$), one could estimate the value of $\ensuremath{\eta}$ within approximately 10% accuracy, which makes a strong constraint on the equation of state 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.