Possible Direct Method to Determine the Radius of a Star from the Spectrum of Gravitational Wave Signals

We computed the spectrum of gravitational waves from a dust disk star of radius $R$ inspiraling into a Kerr black hole of mass $M$ and specific angular momentum $a$. We found that when $R$ is much larger than the wave length of the quasinormal mode, the spectrum has several peaks and the separation of peaks $\Delta \omega$ is proportional to $R^{-1\mathrm{}}$ irrespective of $M$ and $a$. This suggests that the radius of the star in coalescing binary black hole–star systems may be determined directly from the observed spectrum of gravitational waves. This also suggests that the spectrum of the radiation may give us important information in gravitational wave astronomy as in optical astronomy.