Searching for lensed gravitational waves with unlensed templates

Abstract

Gravitational lensing can split the signal of a binary merger into two images, which either overlap and interfere or arrive as separate events. We show that the matched-filter output of every two-image template can be straightforwardly constructed from the signal-to-noise ratio (SNR) time series that searches already compute with unlensed templates. This enables a marginalized detection statistic that increases search sensitivity without additional matched filtering and is more than 150 times faster than an explicit lensed template bank. For overlapping images in the geometric-optics regime, our two-image method recovers $\gtrsim97\%$ of the optimal SNR from point-mass and singular isothermal lenses, compared with as little as $67\%$ captured by unlensed templates, with substantial gains also for Chang-Refsdal and cored isothermal lenses. Overlapping lensed signals moreover fail the signal-consistency test that is used to down-rank noise transients. Our two-image method restores the consistency and increases the sensitive volume by roughly $2$-$4\times$ for the strongly down-ranked signals. For separated images, our method enables an efficient coherent search for pairs in which neither image is significant alone. Near fold caustics, this increases the sensitive volume by factors of 1.8-2.6 over requiring two independent detections, and up to 1.6 over a targeted counterpart search. Our method is applicable to any matched-filtering search.