Can we distinguish lensing and precession effects in gravitational wave signals?

Gravitational lensing is a remarkable consequence of general relativity. About fifty years ago, the first multiply imaged electromagnetic source was discovered. In the past decade, gravitational waves (GWs) have opened a new window into the universe, with the current catalog containing 218 detected events. As GW detectors continue to improve in sensitivity, observed signals will extend to higher redshifts, increasing the likelihood of a lensed GW signal. Strong lensing can produce multiple images with distinct magnifications and arrival times, leading to interference and frequency-domain modulations that depend on the time delays and flux ratios of the images. Meanwhile, spin-orbit misalignments can induce precessional modulations of the GW signal, characterized by precession amplitude and frequency. To explore whether the two modulations can be distinguished, we calculate mismatches between the two waveforms. We examine the parameter space of precession amplitude and frequency, and lensing time delays and flux ratios to identify where the two effects are distinguishable or degenerate. We find that lighter binaries can show distinguishable modulations unless there are a few modulations in band (< 3), while heavier binaries exhibit greater degeneracies. We also find that longer time delays (higher flux ratios) between lensed images are degenerate with greater precession amplitude (frequency) in regularly precessing sources.