Improved Identification of Strongly Lensed Gravitational Waves with Host Galaxy Locations

Abstract

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.

Figures (4)

• Figure 1: Simulated Euclid lens galaxy catalog for informed positional priors in gravitational lensing analysis. The 5 deg$^2$ field contains $\sim77$ galaxies with a density of 15 deg$^{-2}$, matching ET's sky localization uncertainty. The field center ($\alpha=1.375$ rad, $\delta=-1.2108$ rad) corresponds to the injection position of simulated GW events.
• Figure 2: Reweighted Euclid lens galaxy prior after incorporating gravitational wave posterior information. The initial uniform weights $w_i^{(0)} = 1/N$ have been updated to $w_i$ based on the consistency between galaxy positions $(\alpha_i, \delta_i)$ and the GW sky localization, implementing the mixture model $P_{\rm Euclid}(\alpha, \delta \, | \, \mathcal{G}) = \sum_{i=1}^{N} w_i \,K(\Delta \alpha_i, \Delta \delta_i)$. The colorbar indicates the relative probability mass assigned to each galaxy, reflecting the combined evidence from both Euclid catalog and GW parameter estimation.
• Figure 3: Combined corner plot comparing posterior distributions for lensed gravitational wave signal parameters under different prior assumptions. The royal blue contours show ET lensed GW signal 1 with uniform priors, dark orange contours show ET lensed GW signal 2 with uniform priors, crimson contours show ET lensed GW signal 1 with Euclid priors, and light green contours show ET lensed GW signal 2 with Euclid priors. All contours represent the 68% and 95% credible regions. The injection values are marked by colored lines corresponding to each analysis (gray for uniform prior analyses, crimson and light green for Euclid prior analyses), illustrating the impact of prior information on parameter estimation accuracy. The near-perfect overlap of contours confirms that intrinsic parameter estimates are robust to prior choice for high-SNR ET signals.
• Figure 4: Comparison of the restricted Bayes factors $\log_{10}\mathcal{B}^{(5)}$ computed under uniform and Euclid-informed priors. The Bayes factors are computed using only the five common parameters ($\mathcal{M}_c$, $q$, $\theta_{\rm JN}$, $a_1$, $a_2$) to isolate the effect of incorporating positional information. Blue points represent unlensed event pairs, while red points represent lensed event pairs. The dashed diagonal line indicates equality between the two priors. The systematic shift of lensed pairs above the diagonal demonstrates the enhanced sensitivity provided by the Euclid-informed prior, while the shift of unlensed pairs below the diagonal shows suppression of false positives.