Improved Identification of Strongly Lensed Gravitational Waves with Host Galaxy Locations

We present a Bayesian framework that enhances the identification of strongly lensed gravitational waves (GWs) by incorporating informative positional priors from the Euclid galaxy lens catalog. The core of our method introduces a two-step reweighting scheme: first, gravitational wave parameter estimation is performed under a uniform sky prior; the resulting posterior is then used to reweight galaxy positions within the Euclid catalog, constructing an astrophysically informed positional prior. Comparing this Euclid-informed prior against a uniform prior within our framework reveals distinct behaviors. While the posterior estimates of the intrinsic waveform parameters show little sensitivity to the prior change, the Bayes factor for lensing identification exhibits significant prior dependence. Crucially, for truly lensed event pairs, the Bayes factor systematically increases, whereas for unlensed pairs it decreases. This dual effect is vital for robust discrimination. Our analysis demonstrates that this multi-messenger approach significantly improves the confidence of lensing searches. For lensed pairs, the method boosts the Bayes factor by an average factor of $\sim 10$, while effectively suppressing false positives for unlensed coincidences. This underscores the critical importance of prior specification and showcases the substantial gains achievable by synergizing gravitational-wave data with electromagnetic survey information.