We study the influence of astrophysical formation scenarios on the precessional dynamics of spinning black-hole binaries by the time they enter the observational window of second- and third-generation gravitational-wave detectors, such as Advanced LIGO/Virgo, LIGO-India, KAGRA, and the Einstein Telescope. Under the plausible assumption that tidal interactions are efficient at aligning the spins of few-solar mass black-hole progenitors with the orbital angular momentum, we find that black-hole spins should be expected to preferentially lie in a plane when they become detectable by gravitational-wave interferometers. This “resonant plane” is identified by the conditions $\Delta \Phi =0°$ or $\Delta \Phi =\pm 180°$, where $\Delta \Phi$ is the angle between the components of the black-hole spins in the plane orthogonal to the orbital angular momentum. If the angles $\Delta \Phi$ can be accurately measured for a large sample of gravitational-wave detections, their distribution will constrain models of compact binary formation. In particular, it will tell us whether tidal interactions are efficient and whether a mechanism such as mass transfer, stellar winds, or supernovae can induce a mass-ratio reversal (so that the heavier black hole is produced by the initially lighter stellar progenitor). Therefore, our model offers a concrete observational link between gravitational-wave measurements and astrophysics. We also hope that it will stimulate further studies of precessional dynamics, gravitational-wave template placement, and parameter estimation for binaries locked in the resonant plane.

• Received 17 February 2013

DOI:https://doi.org/10.1103/PhysRevD.87.104028