Possible direct method to determine the radius of a star from the spectrum of gravitational wave signals. II. Spectra for various cases

We compute the spectrum and the waveform of gravitational waves generated by the inspiral of a disk or a spherical like dust body into a Kerr black hole. We investigate the effect of the radius R of the body on gravitational waves and conclude that the radius is inferred from the gravitational wave signal irrespective of (1) the form of the body (a disk or a spherical star), (2) the location where the shape of the body is determined, (3) the orbital angular momentum of the body, and (4) a black hole rotation. We find that when R is much larger than the characteristic length of the quasinormal mode frequency, the spectrum has several peaks and the separation of the troughs $\Delta \omega$ is proportional to $R^{-1}.$ Thus, we may directly determine the radius of a star in a coalescing binary black hole–star system from the observed spectrum of gravitational waves. For example, both trough frequencies of neutron stars and white dwarfs are within the detectable frequency range of some laser interferometers and resonant type detectors so that this effect can be observed in the future. We therefore conclude that the spectrum of gravitational waves may provide us important signals in gravitational wave astronomy as in optical astronomy.