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Abstract Noise in various interferometer systems can sometimes couple non-linearly to create excess noise in the gravitational wave (GW) strain data. Third-order statistics, such as bicoherence and biphase, can identify these couplings and help discriminate those occurrences from astrophysical GW signals. However, the conventional analysis can yield large bicoherence values even when no phase-coupling is present, thereby, resulting in false identifications. Introducing artificial phase randomization in computing the bicoherence reduces such occurrences with negligible impact on its effectiveness for detecting true phase-coupled disturbances. We demonstrate this property with simulated disturbances—focusing only on short-duration ones (lasting up to a few seconds) and employing mainly the auto-bicoherence in this work. Statistical hypothesis testing is used for distinguishing phase-coupled disturbances from non-phase coupled ones when employing the phase-randomized bicoherence. We also obtain an expression for the bicoherence value that minimizes the sum of the probabilities of false positives and false negatives. This can be chosen as a threshold for shortlisting bicoherence triggers for further scrutiny for the presence of non-linear coupling. Finally, the utility of the phase-randomized bicoherence analysis in GW time-series data is demonstrated for the following three scenarios: (1) Finding third-order statistical similarities within categories of noise transients, such as blips and koi fish. If these non-Gaussian noise transients, or glitches, have a common source, their bicoherence maps can have similarities arising from common bifrequencies related to that source. (2) Differentiating linear or non-linear phase-coupled glitches from compact binary coalescence signals through their bicoherence maps. This is explained with a simulated signal. (3) Identifying repeated bifrequencies in the second and third observation runs (i.e. O2 and O3) of LIGO and Virgo. 

ABSTRACT In this study, we investigate the impact of microlensing on gravitational wave (GW) signals in the LIGO−Virgo sensitivity band. Microlensing caused by an isolated point lens, with (redshifted) mass ranging from MLz ∈ (1,  105) M⊙ and impact parameter y ∈ (0.01,  5), can result in a maximum mismatch of $$\sim 30~{{\ \rm per\ cent}}$$ with their unlensed counterparts. When y < 1, it strongly anticorrelates with the luminosity distance enhancing the detection horizon and signal-to-noise ratio (SNR). Biases in inferred source parameters are assessed, with in-plane spin components being the most affected intrinsic parameters. The luminosity distance is often underestimated, while sky-localization and trigger times are mostly well-recovered. Study of a population of microlensed signals due to an isolated point lens primarily reveals: (i) using unlensed templates during the search causes fractional loss (20 per cent to 30 per cent) of potentially identifiable microlensed signals; (ii) the observed distribution of y challenges the notion of its high improbability at low values (y ≲ 1), especially for y ≲ 0.1; (iii) Bayes factor analysis of the population indicates that certain region in MLz − y parameter space have a higher probability of being detected and accurately identified as microlensed. Notably, the microlens parameters for the most compelling candidate identified in previous microlensing searches, GW200208_130117, fall within a 1σ range of the aforementioned higher probability region. Identifying microlensing signatures from MLz < 100 M⊙ remains challenging due to small microlensing effects at typical SNR values. Additionally, we also examined how microlensing from a population of microlenses influences the detection of strong lensing signatures in pairs of GW events, particularly in the posterior-overlap analysis. 

We introduce the rapidly emerging field of multi-messenger gravitational lensing—the discovery and science of gravitationally lensed phenomena in the distant universe through the combination of multiple messengers. This is framed by gravitational lensing phenomenology that has grown since the first discoveries in the twentieth century, messengers that span 30 orders of magnitude in energy from high-energy neutrinos to gravitational waves, and powerful ‘survey facilities’ that are capable of continually scanning the sky for transient and variable sources. Within this context, the main focus is on discoveries and science that are feasible in the next 5–10 years with current and imminent technology including the LIGO–Virgo–KAGRA network of gravitational wave detectors, the Vera C. Rubin Observatory and contemporaneous gamma/X-ray satellites and radio surveys. The scientific impact of even one multi-messenger gravitational lensing discovery will be transformational and reach across fundamental physics, cosmology and astrophysics. We describe these scientific opportunities and the key challenges along the path to achieving them. This article therefore describes the consensus that emerged at the eponymous Theo Murphy meeting in March 2024, and also serves as an introduction to this Theo Murphy meeting issue. This article is part of the Theo Murphy meeting issue ‘Multi-messenger gravitational lensing (Part 2)’.