Identifying precession in gravitational wave signals from binary black hole inspirals

Gravitational waves (GW), ripples in the fabric of spacetime predicted by Einstein's theory of general relativity, have provided us with unique insights into astrophysics and the dynamics of compact binary systems ever since their direct observation in 2015 by the Laser Interferometer Gravitational Observatory (LIGO) from a binary black hole (BBH) merger. The analysis of GW signals emitted by these compact binary coalescing systems has yielded invaluable information about the properties of the binary systems themselves. Dynamics in such a system are complex as black holes would generally have spins in random directions, which would cause the orbital angular momentum to be misaligned with total angular momentum (which is the sum of orbital angular momentum and spins of the black holes). Such misalignment will induce precession, i.e., the orbital angular momentum will move in a cone centered around the total angular momentum on a precessional timescale. Precession introduces modulations in the gravitational wave signals in the frequency domain. Our focus is to quantitatively analyze these modulations and understand the role of different precession parameters: amplitude, frequency, and phase of the precession on these signals. We investigate how these parameters and different sky localizations of the source give us different waveforms and how we can distinguish such signals from non-precessing signals using match-filtering techniques. In particular, we investigate the relationship between these parameters and the mismatch between precessing and non-precessing signals. Mismatch quantifies the differences in the waveforms, and from the Lindblom criterion, it provides a relation between the distinguishability of signals and the signal-to-noise ratio.