False Alarm Rates in Detecting Gravitational Wave Lensing from Astrophysical Coincidences: Insights with Model-Independent Technique GLANCE

TL;DR

This work quantifies false-alarm rates for detecting strong gravitational-wave lensing using the model-independent GLANCE cross-correlation method, by simulating an unlensed BBH population and identifying sky-overlapping pairs that could masquerade as lensed images. Using GWSIM to generate a three-year LVK-like BBH catalog and GLANCE to cross-correlate reconstructed polarizations, the study maps the region in magnification–time-delay space free from astrophysical contaminants. It finds that false lensing alarms are rare, with about $0.01\\%$ of pairs falsely flagged at a 1.5$\,\sigma$ threshold and delays around $oldsymbol{\ frac{1000}{ m days}}$, while the contaminated region clusters around chirp masses $oldsymbol{ ilde{M}\,\sim 35-55\,M_otive}$ and short delays. These results provide a quantitative FAR framework for current detectors and set the stage for evaluating lensing claims with next-generation gravitational-wave observatories.

Abstract

The strong lensing gravitational waves (GWs) due to intervening massive astrophysical systems between the source and an observer are an inevitable consequence of the general theory of relativity, which can produce multiple GW events in overlapping sky localization error. However, the confirmed detection of such a unique astrophysical phenomenon is challenging due to several sources of contamination, arising from detector noise to astrophysical uncertainties. Robust model-independent search techniques that can mitigate noise contamination were developed in the past. In this study, we explore the astrophysical uncertainty associated with incorrectly classifying a pair of unlensed GW events as a lensed event, and the associated False Alarm Rate (FAR) depending on the GW source properties. To understand the effect of unlensed astrophysical GW sources in producing false lensing detections, we have performed a model-independent test using the pipeline GLANCE on a simulated population of merging binary-black holes (BBHs). We find that $\sim$ 0.01\% of the event pairs can be falsely classified as lensed with a lensing threshold signal-to-noise ratio of 1.5, appearing at a time delay between the event pairs of $\sim$ 1000 days or more. We show the FAR distribution for the parameter space of GW source masses, delay time, and lensing magnification parameter over which the model-independent technique GLANCE can confidently detect lensed GW pair with the current LIGO detector sensitivity. In the future, this technique will be useful for understanding the FAR of the upcoming next-generation GW detectors, which can observe many more GW sources.

Figures (10)

• Figure 1: In this figure, we present the outline of the workflow for GW lensing false alarm rate (FAR) estimation with GLANCE. Given a cosmology model, we generate an astrophysical population of merging binary black holes (BBHs), emitting GWs. This is done using the Python-based BBH population simulation tool GWSIMKarathanasis:2022hrb. From these BBH mergers, we select GW events with a matched-filter signal-to-noise ratio (SNR) of at least 8 in at least two detectors at the current sensitivity of the Hanford-Livingston-Virgo (HLV) network with observational run-4 (O4) sensitivities. To identify overlapping GW events in their estimated sky patches, we perform parameter estimation of the sky-localization errors using BILBYAshton:2018jfp. We then select event pairs whose 90% credible sky regions overlap. These sky-overlapping pairs are analysed using the cross-correlation-based technique GLANCE. Event pairs with a similar chirping behaviour , are picked up in a cross-correlation based strain overlapping. In an unlensed population, two events appearing to be strongly correlated, creates confusion for a detection of a truly strongly lensed GW pair. Since such false lensing alarms are generated by chance coincidence, greater the time-delay between a strongly-correlated pair, higher the chances of the event(s) being underlying unlensed astrophysical population. Therefore, a confident detection of strongly lensed images can be made only in the low-delay time regime, when events from the population have not started to pop up.
• Figure 2: In this figure, we show a schematic diagram of GW lensing by a massive object in the GO-lensing regime. All distances are measured here are angular-diameter distances. The distances between the source-observer, lens-observer and lens-source are denoted by $D_{s}$, $D_{l}$ and $D_{ls}$ respectively. $\vec{\eta}$ captures the misalignment parameter between the source and the lens and $\vec{\xi}$ denotes the impact parameter of the ray in the lens-plane.
• Figure 3: In this figure, we show that given a pair of 'similar' GW sources, there can be two way to explain. First guess is that they are coming from two different sources of similar characteristics arising from the underlying population of GW sources. The second guess is that they are lensed images, counterparts to one another formed by some massive astronomical object. Thus the detection of a truly lensed event pair is thus always prone to false alarms from unlensed GW sources of similar source properties. Higher the probability of a GW source (say, a certain mass range) in the population, higher is the false positive probability associated with its lensing detection.
• Figure 4: In this figure, we have categorized the possible scenarios that can account for the false positives when detecting lensing of GWs. For strong lensing, the primary concern for false positives is the unlensed astrophysical population of GW sources and the merger rates associated. For microlensing, the concern is around the modelling of GW waveforms that is not able to incorporate all the source effects (like in orbital-plane spins arising to precession and/or eccentricity of the binary orbit) and environmental effects (like dephasing of GW due to dynamical friction, when encompassing matter slows down the orbital motion of the BBH), resulting in any beyond-modelled effects falsely classified as microlensing effects. In both GO-lensing and WO-lensing cases, noise profile, matching the characteristics of a signal can also create false alarms.
• Figure 5: In this figure, we have demonstrated the sky-localization error for two events (blue and red regions) and the region where their 90% credibility interval (C.I.) regions are overlapping (green shaded). For the events with disjoint sky-localization errors, further false alarm checks are not performed, since lensed GW images are supposed to appear from very close positions ($\approx$ arcsec to few arcmin lens_size) in the sky. The common sky-region is used to extract the two polarizations of GW from the strains and thereafter GLANCE is applied to these sky-overlapping events to find the fraction of unlensed merging BBH population that falsely appear as lensed.