Search for Strong Lensing of Gravitational Waves in the Binary Black Hole Events from O1–O4a

Abstract A small fraction of the gravitational waves (GWs) currently observable by LIGO, Virgo, and KAGRA (LVK) may be strongly lensed by intervening galaxies and galaxy clusters, potentially producing multiple copies of the same signal. We search for lensed pairs of binary black hole signals detected during the first observing run (O1) to the first part of the fourth observing run (O4a). We include the events identified by the LVK collaboration, as well as additional events found by external groups (Institute for Advanced Study and Open Gravitational-wave Catalog). Our search is based on Posterior Overlap 2.0 , a fast and efficient Bayesian model-selection pipeline to identify lensed candidates. The search is supplemented by realistic background and foreground simulations to characterize the robustness and detection efficiency of the pipeline, as well as the statistical significance of lensed candidates. We define new metrics to assess the statistical significance of lensing both at the individual and population levels. Our work addresses some of the limitations of previous searches. With the probability of lensing < 0.6% for all pairs, we find no evidence for strong lensing in the data and consequently place a 90% upper bound on the lensing fraction of 1.4%. With five out of the top nine lensed candidate pairs being from non-LVK catalogs, we also highlight the importance of searching among events reported by multiple GW catalogs. We forecast that the probabilities of making a 3 σ detection in the fourth (O4), intermediate (IR1), and fifth (O5) observing runs are ∼20%, 23%, and 67%, respectively.