Neutron star equations of state and their applications

This paper reviews the properties of neutron stars based on the recent multi-messenger observations including electromagnetic waves from the low-mass X-ray binaries and gravitational waves from the merger of neutron star binaries. Based on these observations, we investigate theoretical models for dense nuclear matter and discuss their implications to the neutron star observations such as mass, radius, cooling, and tidal deformability. We also discuss the uncertainties in the neutron star cooling, neutron star properties with Bayesian approaches, and an expansion scheme applied to the nuclear energy density functional theory.