Inverting neutron star structure equations: Constraints on equation of state of neutron star matter via the gridded parameter scanning

How to constrain the equation of state (EOS) of neutron star matter is a shared goal in the community of nuclear physics and astrophysical physics. Due to the poor knowledge about nuclear interactions at short distances, the density dependence of nuclear symmetry energy is among the most uncertain parts of the EOS for traditional neutron stars made of nuclear matter and it can affect the pressure of neutron star matter, the crust-core transition density, and the cooling of neutron stars. If the phase transition from hadron matter to quark matter exists, i.e., a hybrid star, the mass-radius relation can be varied significantly and show many exotic phenomena, such as the twin star. The possible existence of a phase transition can be potentially identified from the high-frequency gravitational waves from the post merger phase of colliding neutron stars. With the accumulation of observations of neutron stars and terrestrial nuclear experiments, it is possible to constrain the EOS of neutron star matter from directing inverting neutron star observables. Our recent work about constraining the properties of neutron star matter from inverting observations of neutron stars is summarized in this review based on an isospin dependent parameterized EOS, including: (1) The combined constraints on EOS and symmetry energy of neutron star matter from the observations of mass, radii, and tidal deformability after the detection of GW170817, mainly focusing on how the increase of maximum observed mass affects the constraints on EOS and symmetry energy; (2) the impact of simultaneous mass and radius measurement of massive neutron star on the constraints on EOS and symmetry energy; (3) the possibility of the secondary component of GW190814 being a fast rotating neutron star; (4) constraints on the phase transition properties from inverting the observations of neutron stars; (5) the impact of the nuclear equation of state on the formation of twin stars. Overall, thanks to the hard work of many people in the astrophysics and nuclear physics community, new data of neutron star observations since the discovery of GW170817 have significantly enriched our knowledge about the symmetry energy of neutron star matter.