Detecting nutation of the orbital angular momentum in the gravitational waves emitted during binary black-hole inspirals

Generic binary black hole (BBH) systems consist of two black holes, each with a mass and spin, orbiting about their center of mass. The BBH spins are generally misaligned with the orbital angular momentum, implying that the total angular momentum will be misaligned as well. As the BBHs emit GWs and inspiral towards merger, the orbital angular momentum precesses and nutates about the total angular momentum whose direction stays nearly fixed. We develop a new model for the gravitational waves emitted by generically precessing binaries parameterized by precession and nutation amplitudes and frequencies, the variation of the precession frequency, and precession and nutation nuisance phases. We explore the distinguishability of generically precessing sources from non-precessing and regularly precessing templates, then determine the fraction of BBH systems in which nutation can be detected as a function of redshift for different BBH populations characterized by the mass and spin distributions.