ar X iv : 1 31 0 . 08 03 v 2 [ as tr o - ph . H E ] 1 M ar 2 01 4 Spectral Approach to the Relativistic Inverse Stellar Structure Problem II

The inverse stellar structure problem determines the equation of state of the matter in stars from a knowledge of their macroscopic observables (e.g. their masses and radii). This problem was solved in a previous paper by constructing a spectral representation of the equation of state whose stellar models match a prescribed set of macroscopic observables. This paper improves and extends that work in two significant ways: i) The method is made more robust by accounting for an unexpected feature of the enthalpy based representations of the equations of state used in this work. After making the appropriate modifications, accurate initial guesses for the spectral parameters are no longer needed so Monte-Carlo techniques can now be used to ensure the best fit to the observables. ii) The method is extended here to use masses and tidal deformabilities (which will be measured by gravitational wave observations of neutron-star mergers) as the macroscopic observables instead of masses and radii. The accuracy and reliability of this extended and more robust spectral method is evaluated in this paper using mock data for observables from stars based on 34 different theoretical models of the high density neutron-star equation of state. In qualitative agreement with earlier work, these tests suggest the high density part of the neutron-star equation of state could be determined at the few-percent accuracy level using high quality measurements of the masses and radii (or masses and tidal deformabilities) of just two or three neutron stars.