Towards gravitational-wave asteroseismology

TL;DR

This paper calculates neutron star oscillation mode frequencies and derives empirical relations to infer stellar parameters from gravitational-wave observations, aiding asteroseismology.

Contribution

It provides new numerical data and robust empirical relations linking mode frequencies to neutron star properties for multiple equations of state.

Findings

Empirical relations between mode frequencies and star parameters are highly robust.

Mode frequencies can be used to accurately determine neutron star radius and mass.

The study covers twelve realistic equations of state.

Abstract

We present new results for pulsating neutron stars. We have calculated the eigenfrequencies of the modes that one would expect to be the most important gravitational-wave sources: the fundamental fluid f-mode, the first pressure p-mode and the first gravitational-wave w-mode, for twelve realistic equations of state. From this numerical data we have inferred a set of ``empirical relations'' between the mode-frequencies and the parameters of the star (the radius R and the mass M). Some of these relation prove to be surprisingly robust, and we show how they can be used to extract the details of the star (radius, mass, eos) from observed modes with errors no larger than a few percent.