Inspiral of generic black hole binaries: spin, precession and eccentricity

Given the absence of observations of black hole binaries, it is critical that the full range of accessible parameter space be explored in anticipation of future observation with gravitational-wave detectors. To this end, we compile the Hamiltonian equations of motion describing the conservative dynamics of the most general black hole binaries and incorporate an effective treatment of dissipation through gravitational radiation, as computed by Will and collaborators. We evolve these equations for systems with orbital eccentricity and precessing spins. We find that, while spin-spin coupling corrections can destroy constant radius orbits in principle, the effect is so small that orbits will reliably tend to quasi-spherical orbits as angular momentum and energy are lost to gravitational radiation. Still, binaries that are initially highly eccentric may retain eccentricity as they pass into the detectable bandwidth of ground-based gravitational-wave detectors. We also show that a useful set of natural frequencies for an orbit demonstrating both spin precession and periastron precession is comprised of (1) the frequency of angular motion in the orbital plane, (2) the frequency of the plane precession and (3) the frequency of radial oscillations. These three natural harmonics shape the observed waveform.