Astroseismology of neutron stars from gravitational waves in the limit of perfect measurement

TL;DR

This paper demonstrates that, under perfect measurement conditions, the gravitational wave spectrum from oscillating neutron stars uniquely determines their internal structure, unlike the classical spectral geometry result for drums.

Contribution

It proves that for axial perturbations of static, perfect fluid neutron stars, the quasi-normal mode spectrum uniquely identifies the star's profile, unlike the non-uniqueness in spectral geometry.

Findings

Eigenfrequency spectrum uniquely determines neutron star profiles.

Two neutron stars with different structures cannot have identical oscillation spectra.

Perfect measurement allows complete inference of stellar properties from gravitational waves.

Abstract

The oscillation spectrum of a perturbed neutron star is intimately related to the physical properties of the star, such as the equation of state. Observing pulsating neutron stars therefore allows one to place constraints on these physical properties. However, it is not obvious exactly how much can be learnt from such measurements. If we observe for long enough, and precisely enough, is it possible to learn everything about the star? A classical result in the theory of spectral geometry states that one cannot uniquely `hear the shape of a drum'. More formally, it is known that an eigenfrequency spectrum may not uniquely correspond to a particular geometry; some `drums' may be indistinguishable from a normal-mode perspective. In contrast, we show that the drum result does not extend to perturbations of simple neutron stars within general relativity -- in the case of axial (toroidal) perturbations of static, perfect fluid stars, a quasi-normal mode spectrum uniquely corresponds to a stellar profile. We show in this paper that it is not possible for two neutron stars, with distinct fluid profiles, to oscillate in an identical manner. This result has the information-theoretic consequence that gravitational waves completely encode the properties of any given oscillating star: unique identifications are possible in the limit of perfect measurement.