GWTC-4.0: Searches for Gravitational-Wave Lensing Signatures

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.

💡 Research Summary

The paper presents a comprehensive search for gravitational‑wave (GW) lensing signatures in the first half of the fourth observing run (O4a) of the LIGO‑Virgo‑KAGRA network. Gravitational waves passing near massive objects can be strongly lensed, producing multiple images with identical intrinsic parameters but different arrival times, magnifications, and characteristic phase shifts (0 or π/2 depending on the image parity). In the wave‑optics regime, especially for point‑mass lenses with masses of order 10⁴–10⁶ M⊙, the GW signal acquires a frequency‑dependent amplification factor that can distort a single event’s waveform. Detecting either of these phenomena would open a new window on the distribution of massive lenses and on the high‑redshift binary‑black‑hole (BBH) population.

To cover both regimes, the authors implemented three largely independent search pipelines:

1. Saddle‑point phase‑shift search – Existing matched‑filter pipelines (PyCBC, GstLAL) were augmented with a discrete phase‑shift parameter that allows the template to be rotated by 0, π/2, π, or 3π/2. Triggers that required a π/2 shift (the signature of a saddle‑point image) were isolated and examined for consistency with the rest of the event’s parameters.

2. Pair‑wise consistency search – All detected candidates were cross‑matched to find pairs whose sky location, masses, spins, and waveform morphology were compatible within statistical uncertainties, while allowing for a time delay ranging from seconds to days. Bayesian model selection was used to compute a Bayes factor comparing the hypothesis “two images of the same source” against the null hypothesis of two unrelated events.

3. Sub‑threshold counterpart search – Below‑threshold triggers (SNR < 8) were re‑analysed in the vicinity of each high‑significance event. By coherently stacking these low‑SNR candidates and looking for the magnification pattern expected from strong lensing, the authors probed whether any bright events had faint, lensed counterparts that fell under the usual detection threshold.

In parallel, the authors modeled lensing using both geometric‑optics approximations (magnification μ, time delay Δt, parity‑dependent phase) and a full wave‑optics point‑mass model. The latter employs the complex amplification factor
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