Neutron star asteroseismology and nuclear saturation parameter

Adopting various unified equations of state (EOSs), we examine the quasinormal modes of gravitational waves from cold neutron stars. We focus on the fundamental ($f$-), 1st pressure ($p_1$-), and 1st spacetime ($w_1$-) modes, and derive the empirical formulae for the frequencies and damping rate of those modes. With the resultant empirical formulae, we find that the value of $\eta$, which is a specific combination of the nuclear saturation parameters, can be estimated within $\sim 30 \%$ accuracy, if the $f$-mode frequency from the neutron star whose mass is known would be observed or if the $f$- and $p_1$-mode frequencies would be simultaneously observed, even though this estimation is applicable only for the low-mass neutron stars. Additionally, we find that the mass and radius of canonical neutron stars can be estimated within a few per cent accuracy via the simultaneous observations of the $f$- and $w_1$-mode frequencies. We also find that, if the $f$-, $p_1$-, and $w_1$-mode frequencies would be simultaneously observed, the mass of canonical neutron stars can be estimated within $2\%$ accuracy, while the radius can be estimated within $1\%$ for the neutron star with $M\ge 1.6M_\odot$ or within $0.6\%$ for the neutron star with $M\ge 1.4M_\odot$ constructed with the EOS constrained via the GW170817 event. Furthermore, we find the strong correlation between the maximum $f$-mode frequency and the neutron star radius with the maximum mass, between the minimum $w_1$-mode frequency and the maximum mass, and between the minimum damping rate of the $w_1$-mode and the stellar compactness for the neutron star with the maximum mass.