Distinguishing gravitational lensing from precessional modulation in gravitational-wave events

As the LIGO-Virgo-KAGRA network improves in sensitivity and future space- and ground-based gravitational-wave (GW) detectors come online, GW events will be observed at increasingly higher cosmological redshifts. There is a growing probability that these events will be gravitationally lensed by intervening large-scale structure. In the geometric-optics limit of strong gravitational lensing, multiple images of each GW event can be produced, each with its own magnification and time delay. If in band at the same time, these images can interfere with each other, modulating the observed GW signal. Binary black-hole (BBH) systems may also have spins that are misaligned with the orbital angular momentum, causing the latter to precess about the total angular momentum that generally remains nearly fixed in direction throughout the inspiral. As GW emission is preferentially beamed in the direction of the orbital angular momentum, this precession also modulates the observed GW signal. Using the mismatch between two waveforms, we investigate for which source and lens parameters the two sources of GW modulation can be distinguished. We find that the decreasing time between precessional peaks during the inspiral compared to the fixed lensing time delays generally allows the signals to be distinguished provided they spend enough time in band, but that large degeneracies are possible for appropriate parameter choices.