Lensing, not luck! Detection prospects of strongly lensed gravitational waves

TL;DR

The work addresses detecting strongly lensed gravitational waves in large GW catalogs, where true lensed pairs grow linearly with detections while false positives grow quadratically. It leverages the Posterior Overlap 2.0 (PO2.0) Bayesian approach to efficiently compute the lensing Bayes factor $\mathcal{B}^L_U$ and links background and lensed distributions to forecast performance. The authors forecast the first $3\sigma$ lensing detection in the LVK O5 run under realistic assumptions and project a rapid expansion of high-purity lensing catalogs in the XG era, while proposing practical strategies to manage computational costs, including using catalog purity thresholds. These results have significant implications for cosmology, astrophysics, and multi-messenger opportunities, enabling early warning, improved localization, and new tests of gravity as more sensitive detectors come online.

Abstract

A small fraction of gravitational-wave (GW) signals detected by ground-based observatories will be strongly lensed by intervening galaxies or clusters. This may produce multiple copies of the signals (i.e., lensed images) arriving at different times at the detector. These, if observed, could offer new probes of astrophysics and cosmology. However, identification of lensed image pairs among a large number of unrelated GW events is challenging. Though the number of lensed events increases with improved detector sensitivity, the false alarms increase quadratically faster. While this "lensing or luck" problem would appear to be insurmountable, we show that the expected increase in measurement precision of source parameters will efficiently weed out false alarms. Based on current astrophysical models and anticipated sensitivities, we predict that the first confident detection could occur in the fifth observing run of LIGO, Virgo, and KAGRA. We expect computational costs to be a major hurdle in achieving such a detection, and show that the Posterior Overlap 2.0 method may offer a near-optimal solution to this challenge.

Figures (8)

• Figure 1: The efficiency of identifying strongly lensed GWs plotted against the significance of detection for various observing scenarios. Solid lines show the expectation based on realistic assumptions of BBH merger rate and lensing fraction, while shaded regions show the range between more pessimistic and optimistic assumptions as defined in Appendix \ref{['sec:sim_strong_lensing']}.
• Figure 2: The expected number of lensed GWs present in the data (unfilled black boxes) and the number of confident identifications (colored bars) in various observing scenarios. We show results for standard frequentist significance thresholds as well as those based on the purity of lensed catalogs. Results under pessimistic, realistic and optimistic assumptions of BBH merger rate and lensing fraction (as defined in Appendix \ref{['sec:sim_strong_lensing']}) are differentiated using hatches and edge styles.
• Figure 3: The computational cost of various components of GW strong lensing search (i.e., that of computing ${\mathcal{B}^L_U}$'s of all observed pairs), and background simulations needed to reach $3\sigma$ and $5\sigma$ significance (i.e., that of computing ${\mathcal{B}^L_U}$'s of the required number of simulated unlensed pairs). Solid lines correspond to the analysis using PO2.0, while the dashed lines correspond to analysing 1% of the event pairs using joint parameter estimation methods. For comparison, the total resource utilization of LVK's O3 run bagnasco2024ligo is also shown.
• Figure 4: The probability density of simulated strong lensing Bayes factors under the lensed and unlensed hypotheses, $P(\log_{10}{\mathcal{B}^L_U} \mid {\mathcal{H}_L})$, $P(\log_{10}{\mathcal{B}^L_U} \mid {\mathcal{H}_U})$, along with $P(\log_{10}{\mathcal{B}^L_U} \mid {\mathcal{H}_L}) / {\mathcal{B}^L_U}$. Shaded regions show $90\%$ multinomial error bounds. These ${\mathcal{B}^L_U}$'s, computed using barsode2025fast's PO2.0 method, verify Equation \ref{['eq:blu_distribution_relationship_inverted']} within an accuracy of a factor of 2.
• Figure 5: The Bayes factor-Bayes factor ($B-B$) plot showing $P({\mathcal{B}^L_U} | {\mathcal{H}_L}) / P({\mathcal{B}^L_U} | {\mathcal{H}_U})$ as a function of ${\mathcal{B}^L_U}$ for different Bayesian model selection methods: 1) haris2018identifying's ${\mathcal{R}^L_U}$ incorporating consistency of time delays, 2) sky localization overlap, 3) haris2018identifying's PO method taking posterior overlap of selected BBH parameters assuming flat priors, and 4) barsode2025fast's PO2.0 method utilizing all the available information from dominant-mode aligned-spin posteriors with correct astrophysical priors.