Neutron star asteroseismology and nuclear saturation parameter

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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.