Towards gravitational wave asteroseismology

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 these 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 relations prove to be surprisingly robust, and we show how they can be used to extract the details of the star from observed modes. The results indicate that, should the various pulsation modes be detected by the new generation of gravitational wave detectors that come online in a few years, the mass and the radius of neutron stars can be deduced with errors no larger than a few per cent.