An effective method to search for sub-threshold lensed gravitational waves with a targeted population model

Strong gravitational lensing of gravitation waves (GW) from the same source can produce identical signals (with the same intrinsic parameters, e.g., masses and spins) with varying amplitudes and arrival times. One scenario is when some signals are magnified that are strong enough to be identified as GWs (super-threshold), and some are demagnified and buried in the noise, remaining unidentified (sub-threshold). There have been efforts that assume confirmed GWs as strongly lensed signals and attempt to search for their sub-threshold lensed counterparts. As LVK detectors' sensitivities improve, we expect to observe more super-threshold GWs in upcoming observing runs. We present an effective method built based on the traditional targeted search method to search for possible sub-threshold lensed GWs for a given target event efficiently, with a targeted population model created based on the component-mass posterior distribution of the target. Without additional re-filtering, the likelihood of being a real GW is re-evaluated for each candidate from the general search for GWs using the targeted population model. Candidates with masses similar to the target will be up-ranked, and those that are not will be down-ranked. Candidates in the reranked list with ranking statistics passing a given threshold will then be identified as possible lensed counterparts and followed up with other analyses to determine how likely they are lensed counterparts to the given target. This method will be applied in future LVK collaboration-wide lensing analyses.