Gravitational wave signals from precessing and nutating binary black holes

Astrophysical black holes are generally spinning. These spins can be misaligned with the orbital angular momentum (L) of the binary leading to precession (azimuthal motion) and nutation (polar motion) of L around the total angular momentum (J) due respectively to spin-orbit and spin-spin coupling. This L motion can cause potentially observable modulation of the amplitude and phase of the gravitational wave (GW) signal. We classify this precession and nutation of the orbit as generic precession, as opposed to regular precession when there is no nutation. We quantify the motion of L using five dimensionless parameters, namely the precession amplitude, precession frequency (the two regular precession parameters that describe the motion of L on a cone around J), nutation amplitude, nutation frequency, and precession-frequency variation (three additional parameters for generic precession which define nutation) using their respective lowest post-Newtonian scaling. We explore this parameter space for a binary population with isotropically oriented spins and generate waveforms. We then compare these generically precessing waveforms with regularly precessing and non-precessing waveforms using match-filtering techniques. We will finally investigate whether current sensitivities yield detectable nutation and assess how better sensitivities across the network can help distinguish precession and nutation.