False positives for gravitational lensing: the gravitational-wave perspective

Abstract: For the first detection of a novel astrophysical phenomenon, scientific standards are particularly high. Especially in a multi-messenger context, there are also opportunity costs to follow-up observations on any detection claims. So in searching for the still elusive lensed gravitational waves, care needs to be taken in controlling false positives. In particular, many methods for identifying strong lensing rely on some form of parameter similarity or waveform consistency, which under rapidly growing catalog sizes can expose them to false positives from coincident but unlensed events if proper care is not taken. And searches for waveform deformations in all lensing regimes are subject to degeneracies we need to mitigate between lensing, intrinsic parameters, insufficiently modelled effects such as orbital eccentricity, or even deviations from general relativity. Robust lensing studies also require understanding and mitigating glitches and non-stationarities in the detector data. This article reviews sources of possible false positives (and their flip side: false negatives) in gravitational-wave lensing searches and the main approaches the community is pursuing to mitigate them.

• The paper’s main contribution is to identify and categorize potential false positives in gravitational-wave lensing by analyzing multi-image events and single-image waveform deformations.
• It demonstrates how noise fluctuations, waveform systematics, and intrinsic parameter degeneracies can mimic lensing signatures in low SNR detections.
• It proposes mitigation strategies such as astrophysical time-delay priors, higher multiple tests, and robust Bayesian analyses to reduce the false-positive rate.

Gravitational lensing of gravitational waves (GWs) is an exciting prospect for future detections, but identifying these rare events amongst a growing catalog of transient GW signals requires careful control of false positives. This paper reviews the various sources of potential false positives and mitigation strategies being developed by the GW lensing community.

The challenge stems from the relatively low signal-to-noise ratios (SNRs) of current GW detections and the poor sky localization compared to electromagnetic observations, which lack the geometric information (image positions and shapes) crucial for identifying lensed sources. Instead, GW lensing searches rely on amplitude, phase, and time delay information encoded in the GW waveforms.

The paper discusses false positives in two main categories of lensing searches:

1. Multiple Images from Strong Lensing

In the geometric optics regime, strong lensing can produce multiple images of the same source, appearing as GW events with nearly identical waveforms, differing primarily in magnification, time delays, and potentially phase shifts (due to higher modes). The primary detection method is to identify pairs (or higher multiples) of events with consistent intrinsic parameters (mass, spin, etc.) and sky location.

• Sources of False Positives (FA):
  • Noise fluctuations: Mistaking detector noise transients for astrophysical signals is a basic source of FA, but standard GW searches are designed to control this. However, sub-threshold searches targeting fainter lensed images require extra vigilance regarding data quality.
  • Unlensed coincident signals: This is identified as the main challenge. As the catalog of detected GW events grows quadratically with the number of events, the number of potential coincident pairs also grows quadratically. Physically unrelated sources can coincidentally have similar parameters, especially given clustering in the mass/spin space of observed binary black holes.
  • Contaminated GWs: Real GW signals contaminated by detector glitches can be distorted, potentially causing them to falsely resemble other signals and appear lensed. Deglitching techniques are crucial for robust analysis.
  • Waveform Systematics: Imperfections in theoretical waveform models, particularly for signals from complex sources like those with high spins, large mass ratios, or orbital eccentricity, can lead to biased parameter estimation. This can cause parameter consistency checks between purported images to yield false positives or false negatives.
• Mitigation Strategies:
  • Astrophysical Time Delay Priors: Incorporating priors on the expected time delays from galaxy or cluster lenses significantly reduces the per-pair FA and can suppress the quadratic growth of catalog-level FA with detection rate, bringing it closer to a linear growth rate, especially for galaxy lenses with shorter time delays.
  • Higher Multiples: Searching for three or four images instead of just pairs drastically reduces the chance of false positives from unrelated coincidences. Higher multiples also allow for more stringent tests of consistency with expected lens geometries (time delays, phase differences, image ordering).
  • Smoking Guns (GW-only): Specific waveform features can provide additional evidence. For binary neutron star mergers, tidal effects can distinguish between nearby heavy unlensed sources and lensed distant lighter sources. For binary black holes, evidence for Type-II image parity flips or wave-optics effects on individual images can strengthen the lensing hypothesis for a multiple-image candidate.
  • Combined GW+EM Observations: While challenging due to poor GW sky localization, detecting an electromagnetic counterpart (for BNS) or identifying a consistent host galaxy (for BBH) through improved sky localization from joint GW analysis can provide strong, independent confirmation.
  • Improved Data and Analyses: Higher SNR events from more sensitive detectors yield tighter parameter constraints. Continued development of glitch identification and mitigation is essential. Advanced analysis techniques like machine learning and phase consistency checks can complement initial posterior overlap methods, and full joint Bayesian parameter estimation under specific lens models provides the most rigorous test. Incorporating expectations from lens simulations into search strategies also helps.

2. Deformed Waveforms (Single Images)

Searches for lensing signatures in single GW events focus on frequency-dependent waveform deformations. These include the parity change expected for Type-II images in strong lensing (detectable with higher modes and precessing spins) and wave-optics effects or beating patterns characteristic of milli- and microlensing. These effects are typically searched for using Bayesian evidence comparisons between lensed and unlensed waveform models. In this case, the number of tests grows linearly with the catalog size.

• Sources of False Positives (FA):
  • Noise Issues: Glitches or other non-Gaussian noise transients can mimic the subtle distortions expected from lensing, potentially leading to an incorrect preference for a lensed model in Bayesian analysis. Robust background studies with noisy data are critical.
  • Waveform Systematics: As with multi-image searches, incomplete or inaccurate waveform models for unlensed signals (e.g., lacking eccentricity or full precession effects) can cause real signals to appear deformed in a way that resembles lensing.
  • Degeneracies with Intrinsic Parameters: Certain intrinsic properties of the compact binary source can produce waveform features that are degenerate with lensing effects.
  • Spin Precession: Precessing spins can cause waveform modulations similar to those from microlensing. While full parameter estimation can often distinguish them, degeneracies exist in some parameter space regions.
  • Orbital Eccentricity: Eccentric orbits also introduce waveform modulations that can potentially be mistaken for microlensing effects. This poses a significant risk of false positives, although highly eccentric binaries may be astrophysically rare.
  • Degeneracies with GR Violations: Hypothetical deviations from general relativity could, in principle, produce waveform distortions that mimic lensing signatures. However, it's argued that lensing is a more likely explanation than a deviation from GR, and lensing is more likely to be a source of false positives for GR tests than vice versa.
• Mitigation Strategies: Investigations into these degeneracies are ongoing. Key approaches include developing more complete waveform models that incorporate lensing, precession, and eccentricity simultaneously, and performing systematic studies to identify the regions of parameter space where degeneracies are most significant. Robust background studies using simulations incorporating realistic source populations and noise properties are essential for setting detection thresholds.

Conclusions:

Detecting lensed GWs requires overcoming the limitations imposed by current detector sensitivity and poor sky localization. The primary challenge for multi-image searches is distinguishing true lensed pairs from coincidental unrelated events. Strategies like time-delay priors, identifying higher multiples, joint parameter estimation, incorporating lens models, and multi-messenger follow-up are crucial. For single-image searches, distinguishing subtle lensing deformations from noise artifacts, waveform systematics, and degeneracies with intrinsic source parameters like spin precession and orbital eccentricity is key. Ongoing research into these degeneracies, improved waveform modeling, and comprehensive background studies are necessary.

As the sensitivity of the global GW detector network (LIGO, Virgo, KAGRA, future additions) increases in upcoming observing runs (O4, O5) and transitions to next-generation detectors (Einstein Telescope, Cosmic Explorer, LISA), the rate of GW detections will increase dramatically. This increases the opportunities for finding lensed signals but also exacerbates the false positive problem if mitigation strategies do not keep pace. The expansion of the network will improve sky localization, aiding in multi-messenger follow-up and reducing chance coincidences. Robust background studies, simulating all potential confounding factors, are paramount for assigning credible significance to any potential lensed GW candidate.