Identifying strongly lensed gravitational waves using phase consistency

Strongly lensed gravitational waves (GWs) are detected as repeated chirps of the original binary merger. At each of the detectors, the phase of the lensed GWs will be consistent modulo a fixed constant phase shift (multiples of π/2) which depends on the part of the lensing potential crossed by each copy. We develop a fast and reliable method to identify strongly lensed GWs exploiting that phases at each detector are the best measured GW parameter, with errors only of a fraction of a radian (ΔΦ ~ 1/SNR). Our basic statistic determining the consistency of two GW events with the lensing hypothesis is the distance between the posterior distribution of phases at each of the detectors. The posterior distribution of phases at detectors can be well approximated by Gaussian distributions, and therefore the distance can be trivially computed. This method avoids the shortcoming of looking for overlaps in highly non-Gaussian sky-maps, as well as the issue with the prior volume of the masses and other intrinsic parameters of the binary not being well defined.