Improved Analytic Modeling of Neutron Star Interiors

Studies of neutron star (NS) observations are extremely timely given the recent detection of gravitational waves from a binary NS merger GW170817, and an International Space Station payload NICER currently in operation aiming to determine radii of NS to a precision better than 5%. In many cases, NS solutions are constructed numerically since realistic equations of state are given in tables. However, to relate observables like the NS mass and radius to interior quantities like central density and pressure, it would be useful to provide an analytic model of NS interior. One such solution for static and isolated NS is the Tolman VII solution characterized only by two parameters (e.g. mass and radius), though its agreement with numerical solutions is not perfect. We here introduce an improved model based on Tolman VII solution by introducing an additional parameter (related to the central density) to make the analytic density profile agree better with the numerical results. The pressure, gravitational potential and interior mass profiles improve typically by a factor of 3 compared to the original one for typical NS. Our results are first-step calculations towards constructing more realistic NS under rotation or tidal deformation.