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

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(p1), as a function of the square root of the stellar average density and the parameter (II), 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 less than or similar to fp(1)/f(f) less than or similar to 2.5 (which corresponds to neutron star models with the mass of less than or approximately equal to 0.9 M-circle dot), one could estimate the value of 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.