Studies of neutron stars are extremely timely given the recent detection of gravitational waves from a binary neutron star merger GW170817, and an International Space Station payload NICER currently in operation that aims to determine radii of neutron stars to a precision better than 5%. In many cases, neutron star solutions are constructed numerically due to the complexity of the field equations with realistic equations of state. However, in order to relate observables like the neutron star mass and radius to interior quantities like central density and pressure, it would be useful to provide an accurate, analytic modeling of a neutron star interior. One such solution for static and isolated neutron stars 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 analytic model based on the Tolman VII solution by introducing an additional parameter to make the analytic density profile agree better with the numerically obtained one. This additional parameter can be fitted in terms of the stellar mass, radius and central density in an equation-of-state-insensitive way. In most cases, we find that the new model more accurately describes realistic profiles than the original Tolman VII solution by a factor of 2-5. Our results are first-step calculations towards constructing analytic interior solutions for more realistic neutron stars under rotation or tidal deformation.

10 pages, 6 figures; There is a modification of central density in the caption of FIG.1. Some typos in Table 3 are fixed. A typo in Eq.(16) corrected