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 \mathrm { few \times 10 ^ { -9 } } \mathrm { yr ^ { -1 } } for typical central stellar cusps , almost independently of the relaxation time or the MBH mass .
( 3 ) For intermediate mass black holes ( IBHs ) of \sim 10 ^ { 3 } M _ { \odot } 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 .