The orbital statistics of stellar inspiral and relaxation near a massive black hole: characterizing gravitational wave sources

We study the orbital parameters distribution of stars that are scattered into nearly radial orbits and then spiral into a massive black hole (MBH) due to dissipation, in particular by emission of gravitational waves (GW). This is important for GW detection, e.g. by the Laser Interferometer Space Antenna (LISA). Signal identification requires knowledge of the waveforms, which depend on the orbital parameters. We use analytical and Monte Carlo methods to analyze the interplay between GW dissipation and scattering in the presence of a mass sink during the transition from the initial scattering-dominated phase to the final dissipation-dominated phase of the inspiral. Our main results are (1) Stars typically enter the GW-emitting phase with high eccentricities. (2) The GW event rate per galaxy is a few per Gyr for typical central stellar cusps, almost independently of the relaxation time or the MBH mass. (3) For intermediate mass black holes (IBHs) of ~a thousand solar masses such as may exist in dense stellar clusters, the orbits are very eccentric and the inspiral is rapid, so the sources are very short-lived.