False Alarm Rates in Detecting Gravitational Wave Lensing from Astrophysical Coincidences: Insights with Model-independent Technique GLANCE

Lensing of gravitational waves (GWs) due to intervening massive astrophysical systems between the source and the observer is an inevitable consequence of the general theory of relativity, which can produce multiple GW events with overlapping sky localization error. However, the confirmed detection of such a unique astrophysical phenomenon is challenging due to several sources of contamination, ranging from detector noise to astrophysical uncertainties. Robust model-independent search techniques that can mitigate noise contamination have been developed in the past. In this study, we explore the astrophysical uncertainty associated with incorrectly classifying a pair of unlensed GW events as a lensed pair and the associated false alarm rate (FAR) depending on the GW source properties. To understand the effect of unlensed astrophysical GW sources in producing false lensing detections, we perform a model-independent test using the pipeline GLANCE on a simulated population of merging binary black holes. We find that ∼0.01% of the pair of events can be falsely classified as lensed with a lensing threshold signal-to-noise ratio of 1.5, appearing at a time delay between the pair of events of ∼1000 days or more. We show the FAR distribution for the parameter space of the GW source masses, delay time, and lensing magnification parameter over which the model-independent technique GLANCE can confidently detect a lensed GW pair with the current Laser Interferometer Gravitational-wave Observatorie detector sensitivity. In the future, this technique will be useful in understanding the lensing FAR for next-generation GW detectors, which can observe more GW sources.