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Abstract

A small fraction of the gravitational-wave (GW) signals from binary black
holes observable by ground-based detectors will be strongly lensed by
intervening objects such as galaxies and clusters. Strong lensing will produce
nearly identical copies of the GW signals separated in time. These lensed
signals must be identified against a background of unlensed pairs GW events,
some of which may appear similar by accident. This is usually done using fast,
but approximate methods that, for example, check for the overlap between the
posterior distributions of a subset of binary parameters, or using slow, but
accurate joint Bayesian parameter estimation. In this work, we present a
modified version of the posterior overlap method dubbed "PO2.0" that is
mathematically equivalent to joint parameter estimation while still remaining
fast. We achieve a significant gain in efficiency by incorporating informative
priors about the binary and lensing populations, selection effects, and all the
inferred parameters of the binary. For binary black hole signals lensed by
galaxies, our improved method can detect 65% lensed events at a pair-wise false
alarm probability of $\sim 2\times 10^{-6}$. Consequently, we have a 13%
probability of detecting a strongly lensed event above $2.25\sigma$
significance during 18 months of observation by the LIGO-Virgo detectors at
their current sensitivity. We also show how we can compute the joint posteriors
of the lens and source parameters from a pair of lensed events by reweighting
the posteriors of individual events in a computationally inexpensive way.