Correlations between the Neutron Star Mass-Radius Relation and the Equation of State of Dense Matter

TL;DR

This paper introduces an analytic method to invert neutron star mass-radius relations to accurately determine the underlying dense matter equation of state, facilitating EOS inference from observational data.

Contribution

The authors develop a semi-universal power-law based analytic inversion technique linking mass-radius curves to the EOS, improving accuracy over previous methods.

Findings

Achieves ~0.5% accuracy for non-phase transition EOSs

Effectively reconstructs hybrid star EOSs with phase transitions

Provides a new analytic alternative to Bayesian EOS inference

Abstract

We develop an analytic method of inverting the Tolman-Oppenheimer-Volkoff (TOV) relations to high accuracy. In principle, a specified $\mathcal{E}\mbox{-}P$ relation gives a unique $M\mbox{-}R$ 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. Root-mean-square 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 mass-radius 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.