Determination of the internal structure of neutron stars from gravitational wave spectra

TL;DR

This paper presents a method to infer the internal structure and equation of state of neutron stars from their gravitational wave spectra by using an inverse scheme based on stellar pulsation modes.

Contribution

It introduces an iterative inverse scheme for neutron star analysis that determines mass, radius, and internal structure from gravitational wave data, including explicit formulas for axial w-mode oscillations.

Findings

Successfully applied the method to different neutron star models

Accurately determines the equation of state of nuclear matter

Provides explicit formulas for axial w-mode oscillations

Abstract

In this paper the internal structure of a neutron star is shown to be inferrable from its gravitational-wave spectrum. Iteratively applying the inverse scheme of the scaled coordinate logarithmic perturbation method for neutron stars proposed by Tsui and Leung [Astrophys. J. {\bf 631}, 495 (2005)], we are able to determine the mass, the radius and the mass distribution of a star from its quasi-normal mode frequencies of stellar pulsation. In addition, accurate equation of state of nuclear matter can be obtained from such inversion scheme. Explicit formulas for the case of axial $w$-mode oscillation are derived here and numerical results for neutron stars characterized by different equations of state are shown.