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Binary-black-hole orbits precess when the black-hole spins are mis-alignedwith the binary's orbital angular momentum. The apparently complicated dynamicscan in most cases be described as simple precession of the orbital angularmomentum about an approximately fixed total angular momentum. However, theimprint of the precession on the observed gravitational-wave signal is yet morecomplicated, with a non-trivial time-varying dependence on black-hole dynamics,the binary's orientation and the detector polarization. As a result, it isdifficult to predict under which conditions precession effects are measurablein gravitational-wave observations, and their impact on both signal detectionand source characterization. We show that the observed waveform can besimplified by decomposing it as a power series in a new precession parameter $b= \tan(\beta/2)$, where $\beta$ is the opening angle between the orbital andtotal angular momenta. The power series is made up of five harmonics, withfrequencies that differ by the binary's precession frequency, and individuallydo not exhibit amplitude and phase modulations. In many cases, the waveform canbe well approximated by the two leading harmonics. In this approximation we areable to obtain a simple picture of precession as caused by the beating of twowaveforms of similar frequency. This enables us to identify regions of theparameter space where precession is likely to have an observable effect on thewaveform, and to propose a new approach to searching for signals fromprecessing binaries, based upon the two-harmonic approximation.

Two-harmonic approximation for gravitational waveforms from precessing binaries