Using overlap of sky localization probability maps for filtering potentially lensed pairs of gravitational-wave signals

Abstract

Strong gravitational lensing creates multiple images of a gravitational wave transient. The current state-of-the-art method for identifying such lensing events is a computationally expensive full Bayesian analysis. In this paper, we investigate the feasibility and efficiency of using the overlap of sky localization probability maps (skymaps) to quickly filter potentially lensed gravitational wave signal pairs. We introduce three overlap statistics and test their performance using 200 simulated lensed pairs of gravitational-wave signals across five sets of signal-to-noise ratios. By setting a threshold with a false positive rate of $\mathrm{FPR} = 10^{-2}$ for the three overlap statistics, we find that we can filter out over $99\%$ of nonlensed events while retaining all lensed events. The statistics for each event pair can be computed instantly, and can be used in practice to quickly analyze existing events using the skymaps from the low-latency localization pipelines when results from the full parameter estimation are not available.