GWTC-4.0: Searches for Gravitational-Wave Lensing Signatures

TL;DR

This study reports a comprehensive search for gravitational-wave lensing signatures in the O4a portion of LVK data (GWTC-4.0). It implements three complementary strategies: pair-wise strong-lensing searches for multiple images, single-event analyses for Type II and wave-optics distortions, and background modeling to assess unlensed expectations. Across both pair- and single-event analyses, no statistically robust lensing detections emerge, though GW231123_135430 remains an intriguing outlier whose interpretation is sensitive to waveform systematics and noise. The null result constrains strong-lensing event rates and high-redshift BBH merger densities, reinforcing expectations for lensing priors and guiding future observing runs with improved detector networks. Overall, the work advances the methodology for GW lensing searches and provides critical baselines for upcoming data releases.

Abstract

Gravitational waves can be gravitationally lensed by massive objects along their path. Depending on the lens mass and the lens-source geometry, this can lead to the observation of a single distorted signal or multiple repeated events with the same frequency evolution. We present the results for gravitational-wave lensing searches on the data from the first part of the fourth LIGO-Virgo-KAGRA observing run (O4a). We search for strongly lensed events in the newly acquired data by (1) searching for an overall phase shift present in an image formed at a saddle point of the lens potential, (2) looking for pairs of detected candidates with consistent frequency evolution, and (3) identifying sub-threshold counterpart candidates to the detected signals. Beyond strong lensing, we also look for lensing-induced distortions in all detected signals using an isolated point-mass model. We do not find evidence for strongly lensed gravitational-wave signals and use this result to constrain the rate of detectable strongly lensed events and the merger rate density of binary black holes at high redshift. In the search for single distorted lensed signals, we find one outlier: GW231123_135430, for which we report more detailed investigations. While this event is interesting, the associated waveform uncertainties make its interpretation complicated, and future observations of the populations of binary black holes and of gravitational lenses will help determine the probability that this event could be lensed.

Figures (15)

• Figure 1: Flowchart showing the progression of the pairwise analyses and the numbers of pairs that passed each stage of the analysis process. With this approach, only a reduced number of pairs needs to be analyzed with JPE, significantly reducing the computational cost.
• Figure 2: False-positive probability found for all O4a event pairs for Posterior Overlap (PO) and Phazap. The dashed orange line shows the 1% threshold used to select pairs for follow-up. We pass to the second tier all pairs with an FPP below this threshold for at least one of the two approaches.
• Figure 3: Bayes factors $\mathcal{B}^{\rm L}_{\rm U}$ comparing the lensed and unlensed hypotheses for the 50 event pairs passed to the hanabi analysis, computed using three different merger rate density models, namely one that tracks the star formation rate from Madau:2014bja, $R_{\rm min}(z)$ and $R_{\rm max}(z)$ that are described in LIGOScientific:2023bwz, respectively. The color of each marker indicates the value of $p_{\rm astro}^{\rm pair}$, which is the product of the probabilities that each event in a pair has an astrophysical origin as reported in LIGOScientific:ResultsPaper. None of the event pairs shows a preference for the strong-lensing hypothesis over the null hypothesis that the events in a pair are unrelated.
• Figure 4: Distribution of averaged Bayes factors for the type II versus type I or III hypotheses obtained for real data and the unlensed background. No significant outlier candidates are identified.
• Figure 5: Histogram of $\textrm{log}_{10}\mathcal{B}^{\textrm{Mod}}_{\textrm{U}}$ for O4a BBH candidates. Except for GW231123, all Bayes factors found with IMRPhenomXPHM-SpinTaylor fall within the range expected for unlensed events based on the background.