Impact of nuclear symmetry energy on neutron star structure and crustal oscillations

Neutron stars are a good candidate for studying physics in the extreme states. Since the density inside the star significantly exceeds the normal nuclear density. Considering that the density at the crust-core boundary becomes around (1/3-1) times normal nuclear density, the nuclear properties around the saturation density play an important role in the phenomena inside the crust and in the low-mass neutron star itself. In this presentation, a theoretical approach to the question of how the poorly known density dependence of nuclear symmetry energy affects the mass-radius relation of neutron stars, as well as the eigenfrequencies of crustal torsional oscillations, will be discussed, together with astrophysical implications. In particular, we will show a combination of nuclear saturation parameters, which can express well low-mass neutron stars. With this new parameter, we also discuss the possible maximum mass of neutron stars. In addition, by comparing the frequencies of crustal torsional oscillations to the quasi-periodic oscillations observed in giant flares, we will constrain not only the nuclear saturation parameters but also the neutron star model for one of the giant flares.