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.

💡 Research Summary

The authors present a Bayesian framework that leverages positional information from the Euclid galaxy lens catalog to improve the identification of strongly lensed gravitational‑wave (GW) events. The method consists of a two‑step re‑weighting scheme. First, standard GW parameter estimation is performed with a uniform sky prior, yielding a posterior distribution for the source sky location, P_uni(α,δ|d). Second, this posterior is used to re‑weight the discrete set of galaxies in the simulated Euclid catalog: each galaxy i receives a weight w_i ∝ w_i^(0)·P_uni(α_i,δ_i|d), where w_i^(0)=1/N is the initial uniform weight. The weighted galaxies are then smoothed with an isotropic Gaussian kernel K(Δα,Δδ) of width σ_match=50″, producing a continuous, astrophysically informed positional prior P_Euclid(α,δ|G)=∑_i w_i K(Δα_i,Δδ_i). This prior concentrates probability mass around galaxies that are consistent with the GW localization while remaining broader than Euclid’s astrometric errors and narrower than the typical ET sky‑localization region, thereby enabling meaningful discrimination among many candidate lenses.

The core of the lens‑identification problem is the comparison of two hypotheses: (H_L) the two GW triggers are lensed images of the same binary black‑hole merger, and (H_U) they are independent, unrelated events. The Bayes factor B_LU = Z_L / Z_U quantifies the evidence ratio, where Z_L and Z_U are the marginalized likelihoods under each hypothesis. In the standard formulation B_LU = ∫ dθ P(θ|d₁) P(θ|d₂) P(θ), the prior P(θ) plays a crucial role. The authors evaluate B_LU under two prior choices: (1) a uniform prior (B_uni) and (2) the Euclid‑informed prior (B_Euclid). Non‑positional parameters (masses, spins, etc.) are kept identical in both cases, ensuring that any difference in the Bayes factor stems solely from the positional component.

To test the approach, the authors simulate a realistic Euclid‑like lens galaxy catalog over a 5 deg² field, populating it with ~77 galaxies at a surface density of 15 gal deg⁻². They generate strongly lensed GW signals using a Singular Isothermal Ellipsoid lens model and IMRPhenomPv2 waveforms, injecting the two brightest images (either double or quad configurations) into colored Gaussian noise consistent with the Einstein Telescope (ET‑D) power spectral density. Each event has a high signal‑to‑noise ratio (≈80). Parameter estimation is performed with LALInferenceNest within the Bilby framework, employing the dynesty nested sampler and marginalizing over time delays, Morse phase shifts, and magnification‑altered luminosity distances.

The results are striking. For genuinely lensed event pairs, the Euclid‑informed Bayes factor B_Euclid exceeds the uniform‑prior value B_uni by an average factor of ~10, reflecting the strong alignment between the GW posterior and the cataloged galaxy positions. Conversely, for unrelated (unlensed) event pairs, B_Euclid is systematically lower than B_uni, effectively suppressing false positives. Importantly, the posterior distributions of intrinsic waveform parameters (masses, spins, inclination) remain virtually unchanged between the two prior choices, confirming that the improvement is driven purely by the added astrophysical positional information.

This work demonstrates that incorporating external electromagnetic survey data into GW analyses can dramatically enhance the confidence of lensing searches without compromising parameter estimation. It underscores the sensitivity of Bayes factors to prior specification and provides a concrete, quantitative pathway for multi‑messenger synergy between next‑generation GW detectors (such as ET) and deep optical/near‑infrared surveys (Euclid). The authors suggest future extensions to include real Euclid data, incorporate lens‑mass models, and explore additional priors (e.g., time‑delay distributions) to further refine the lensing identification pipeline.