A Spectral Approach to the Relativistic Inverse Stellar Structure Problem

TL;DR

This paper introduces a spectral method for accurately determining the high-density equation of state of neutron stars from a few mass-radius measurements, significantly improving inverse stellar structure analysis.

Contribution

The paper presents a novel spectral approach that efficiently reconstructs the neutron-star equation of state from limited observational data, outperforming previous methods in accuracy and data efficiency.

Findings

Spectral representations require only a few parameters for high accuracy.

The method accurately recovers original equations of state from mock data.

Higher data points improve the precision of the reconstructed equations of state.

Abstract

A new method for solving the relativistic inverse stellar structure problem is presented. This method determines a spectral representation of the unknown high density portion of the stellar equation of state from a knowledge of the total masses M and radii R of the stars. Spectral representations of the equation of state are very efficient, generally requiring only a few spectral parameters to achieve good accuracy. This new method is able, therefore, to determine the high density equation of state quite accurately from only a few accurately measured [M,R] data points. This method is tested here by determining the equations of state from mock [M,R] data computed from tabulated "realistic" neutron-star equations of state. The spectral equations of state obtained from these mock data are shown to agree on average with the originals to within a few percent (over the entire high density range of the neutron-star interior) using only two [M,R] data points. Higher accuracies are achieved when more data are used. The accuracies of the equations of state determined in these examples are shown to be nearly optimal, in the sense that their errors are comparable to the errors of the best-fit spectral representations of these realistic equations of state.