2025ApJ...984...30S

We develop an analytic method of inverting the Tolman-Oppenheimer-Volkoff relations to high accuracy. In principle, a specified energy density-pressure relation gives a unique mass-radius (M-R) relation and vice versa. Our method is developed from the strong correlations that are shown to exist between the neutron star mass-radius curve and the equation of state (EOS) or pressure-energy density relation. Selecting points that have masses equal to fixed fractions of the maximum mass, we find a semi-universal power-law relation between the central energy densities, pressures, sound speeds, chemical potentials, and number densities of those stars, with the maximum mass and the radii of one or more fractional maximum mass points. Rms fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5% for all quantities at all mass points. The method also works well, although less accurately, in reconstructing the EOS of hybrid stars with first-order phase transitions. These results permit, in effect, an analytic method of inverting an arbitrary M-R curve to yield its underlying EOS. We discuss applications of this inversion technique to the inference of the dense matter EOS from measurements of neutron star masses and radii as a possible alternative to traditional Bayesian approaches.