Spin Precession Signatures as an Indicator of Microlensing in Strongly Lensed Gravitational Waves

Microlensing by the stellar field in a strong-lensing galaxy can introduce wave-optics distortions into the waveforms of strongly lensed gravitational waves (SLGWs). If these signals are analyzed with waveform templates that do not include microlensing, the lensing-induced modulation may be misinterpreted as intrinsic source physics. In particular, microlensing can mimic spin precession, since both effects can produce beat-pattern-like features in the waveform. In this work, we study the degeneracy between stellar-field microlensing and spin precession, and ask to what extent microlensed SLGWs may show false evidence of precession. We analyze simulated SLGW events for two detector sensitivities, O5 and a lower-noise configuration with a power spectral density reduced by a factor of 4 (named O5 Plus), assuming binary black holes with parallel spins. We find that microlensing can indeed produce apparent evidence for precession, and that this effect becomes more visible at higher signal-to-noise ratios. Under O5 sensitivity, 4.88% of microlensed events lie above the one-sided Gaussian-equivalent 3$\sigma$ background threshold, corresponding to the 99.9th percentile of the unlensed-background distribution, while under O5 Plus sensitivity this fraction increases to 14.91%. We also find that the evidence for precession is positively correlated with the strength of microlensing. This correlation is weak under O5 sensitivity, but becomes clear under O5 Plus sensitivity. In addition, Type II (saddle-point) images show a stronger correlation than Type I (minimum-point) images. These results show that evidence for precession in GW data should be interpreted with care, as it may also arise from microlensing wave effects in SLGWs.