Dense Matter Equation of State: Neutron Star and Strange Star

The matter state inside neutron stars (NSs) is an exciting problem in nuclear physics, particle physics and astrophysics. The equation of state (EOS) of NSs plays a crucial role in the present multimessenger astronomy, especially after the event of GW170817. Thanks to accruing studies with advanced telescopes and radioactive beam facilities, the unknown EOS of supranuclear matter could soon be understood. We review the current status of the EOS for pulsar-like compact objects, that have been studied with both microscopic many-body approaches and phenomenological models. The appearance of strange baryonic matter and strange quark matter are also discussed. We compare the theoretical predictions with different data coming from both nuclear physics experiments and astrophysical observations. Despite great progresses obtained in dense nuclear matter properties, there are various challenges ahead, such as the model dependence of the constraints extracted from either experimental or observational data, the lack of a consistent and rigorous many-body treatment of all parts of the star, the dependence of many observables on the turbulent dynamics of relevant hot dense system. As LIGO is about to run again and discover more NS merger events, multimessenger observations are expected to finally unravel the mystery of NS structure.