Transition from inspiral to plunge in precessing binaries of spinning black holes

Abstract

We investigate the non-adiabatic dynamics of spinning black hole binaries by using an analytical Hamiltonian completed with a radiation-reaction force, containing spin couplings, which matches the known rates of energy and angular momentum losses on quasi-circular orbits. We consider both a straightforward post-Newtonian-expanded Hamiltonian (including spin-dependent terms), and a version of the resummed post-Newtonian Hamiltonian defined by the Effective One-Body approach. We focus on the influence of spin terms onto the dynamics and waveforms. We evaluate the energy and angular momentum released during the final stage of inspiral and plunge. For an equal-mass binary the energy released between 40Hz and the frequency beyond which our analytical treatment becomes unreliable is found to be, when using the more reliable Effective One-Body dynamics: 0.6% M for anti-aligned maximally spinning black holes, 5% M for aligned maximally spinning black hole, and 1.8% M for non-spinning configurations. In confirmation of previous results, we find that, for all binaries considered, the dimensionless rotation parameter J/E^2 is always smaller than unity at the end of the inspiral, so that a Kerr black hole can form right after the inspiral phase. By matching a quasi-normal mode ringdown to the last reliable stages of the plunge, we construct complete waveforms approximately describing the gravitational wave signal emitted by the entire process of coalescence of precessing binaries of spinning black holes.Comment: 31 pages, 7 tables, and 13 figure