Stellar modeling via the Tolman IV solution: The cases of the massive pulsar J0740+6620 and the HESS J1731-347 compact object

We model compact objects of known stellar mass and radius made of isotropic matter within Einstein's gravity. The interior solution describing hydrostatic equilibrium we are using throughout the manuscript corresponds to the Tolman IV exact analytic solution obtained long time ago. The three free parameters of the solutions are determined imposing the matching conditions for objects of known stellar mass and radius. Finally, using well established criteria it is shown that contrary to the Kohler Chao solution, the Tolman IV solution is compatible with all requirements for well behaved and realistic solutions. except for the relativistic adiabatic index that diverges at the surface of the stars. The divergence of the index $\Gamma$ may be resolved including a thin crust assuming a polytropic equation-of-state, which is precisely the case seen in studies of neutron stars. To the best of our knowledge, we model here for the first time the recently discovered massive pulsar PSR J0740+6620 and the strangely light HESS compact object via the Tolman IV solution. The present work may be of interest to model builders as well as a useful reference for future research.