Improved statistic to identify strongly lensed gravitational wave events

As the number of detected gravitational wave sources increase with increasing sensitivity of the gravitational wave observatories, observing strongly lensed pair of events will become a real possibility. Lensed GW events will have very accurately measured time delays, as well as magnification ratios. If the corresponding lens system can be identified electromagnetically and the redshifts of the lens and the host galaxy can be measured, such events can be used to constrain important astrophysical parameters of the lens system. As most lensing events will have image separations that will be significantly smaller than the GW event localization uncertainties, it is important that we develop diagnostics that will aid in the robust identification of such lensed events. We define a new statistic based on the joint probability of lensing observables that can be used to discriminate lensed pair of events from the unlensed ones. To this end, we carry out simulations of lensed GW events to infer the distribution of the relative time delays, relative magnifications sub-divided by the type of lensed images. We compare this distribution to a similar one obtained for random unlensed event pairs. Our improved statistic can be used to improve the existing ranking approach adopted by the search pipelines in order to down-select event pairs for joint parameter estimates. The distributions we obtain can further be used to define more informative priors in joint parameter estimation analyses for candidate lensed events.Comment: 8 pages, 6 figure