Comprehensive analysis of time-domain overlapping gravitational wave transients: A Lensing Study

TL;DR

This work systematically probes how temporally overlapping binary black hole signals can mimic gravitational lensing effects in ground-based detectors. Using zero-noise injections and templates for Type-II strong lensing and point-mass microlensing, the authors compare full Bayesian parameter estimation with fast fitting-factor analyses across a broad overlap parameter space. They find that Type-II lensing is only weakly supported in a narrow region where the chirp-mass ratio is near unity and the time offset is very small, while microlensing can produce apparent lensing signatures when the two signals have similar loudness and time delays align with the injection window, though this is often avoided by unlensed models. The study highlights significant overlap-induced biases in recovered masses and SNRs and shows that degeneracies between overlaps and lensing are strongest in specific parameter regimes, which will become more relevant as detector sensitivity grows. The results underscore the need for careful interpretation of waveform modulations, especially to distinguish overlap effects from genuine lensing in future gravitational-wave catalogs.

Abstract

Next-generation GW detectors will produce a high rate of temporally overlapping signals from unrelated compact binary coalescences. Such overlaps can bias parameter estimation (PE) and mimic signatures of other physical effects, such as gravitational lensing. In this work, we investigate how overlapping signals can be degenerate with gravitational lensing by focusing on two scenarios: Type-II strong lensing and microlensing by an isolated point-mass lens. We simulate quasicircular binary black-hole pairs with chirp-mass ratios $\mathscr{M}_{\rm B}/\mathscr{M}_{\rm A}\in\{0.5,\,1,\,2\}$, SNR ratios $\mathrm{SNR}_{\rm B}/\mathrm{SNR}_{\rm A}\in\{0.5,\,1\}$, and coalescence-time offsets $Δt_{\rm c}\in[-0.1,\,0.1]~\mathrm{s}$. Bayesian PE and fitting-factor studies show that the Type-II lensing hypothesis is favored over the unlensed quasicircular hypothesis ($\log_{10}\mathscr{B}^{\rm L}_{\rm U}>1$) only in a small region of the overlapping parameter space with $\mathscr{M}_{\rm B}/\mathscr{M}_{\rm A}\gtrsim1$ and $|Δt_{\rm c}|\leq0.03~\rm{s}$.. Meanwhile, false evidence for microlensing signatures can arise because, to a reasonable approximation, the model produces two superimposed images whose time delay can closely match $|Δt_{\rm c}|$. Overall, the inferred Bayes factor depends on relative chirp-mass ratios, relative loudness, difference in coalescence times, and also the absolute SNRs of the overlapping signals. Cumulatively, our results indicate that overlapping black-hole binaries with nearly equal chirp masses and comparable loudness are likely to be falsely identified as lensed. Such misidentifications are expected to become more common as detector sensitivities improve. While our study focuses on ground-based detectors using appropriate detectability thresholds, the findings naturally extend to next-generation GW observatories.

Figures (11)

• Figure 1: Representation of two BBH signals ($\rm{SINGLES_A}$ and $\rm{SINGLES_B}$) producing an overlapping strain (termed PAIRS). Top: Different SNRs: The primary signal (termed $\rm{SINGLES_A}$, with $\mathrm{SNR}=30$) resembles the GW150914-like merger LIGOScientific:2016vlmLIGOScientific:2016lioLIGOScientific:2018mvr, and the secondary signal (termed $\rm{SINGLES_B}$, with $\mathrm{SNR}=15$) resembles the GW170814-like merger LIGOScientific:2017yccLIGOScientific:2018mvr, which coalesces $\Delta t_{\rm c}=0.15~{\rm s}$ after the merger of the primary signal. The louder signal dominates until its merger-ringdown phase, after which the quieter one becomes visible. Bottom: Similar SNRs: both signals resemble the GW150914-like merger, producing a more strongly modulated waveform with no single signal dominating throughout, with $\Delta t_{\rm c}=0.1~{\rm s}$.
• Figure 2: Illustration of waveform morphology similarities between an overlapping signal and its best-fit lensed counterparts. The injected overlapping waveform at the detector and the corresponding best-fit normalized lensed waveforms obtained from the inferred values from PE are shown. The normalized strain is defined as the ratio of strain $h$ to the maximum amplitude $|h|$. Top: Contains an injected overlapping waveform (termed PAIRS) from a combination of two GW signals ($\rm{SINGLES_A}$ and $\rm{SINGLES_B}$) with relative parameters of chirp mass ratio, $\mathscr{M}_{\rm B}/\mathscr{M}_{\rm A} = 0.5$, SNR ratio, $\mathrm{SNR}_{\rm B}/\mathrm{SNR}_{\rm A} = 1$, and coalescence time difference, $\Delta t_{\rm c} = 0.02~{\rm s}$, and its corresponding inferred Unlensed and Microlensed waveforms. Bottom: Contains the same overlapping strain as above, but with the inferred Type-II lensed waveform. Notably, the microlensed model provides a visibly better match to the modulated structure of the overlapping signal, especially near the merger phase.
• Figure 3: Inferred relative biases in the inferred chirp mass and the recovered SNR from PE on injected overlapping signals, assuming an unlensed quasicircular signal model. The chirp mass bias for each signal is defined as the relative difference between the inferred chirp mass and the mass of the injected signal. Variations in the recovered SNR reflect both the differences in the true injected SNR and the mismatches between the injections and the unlensed templates.
• Figure 4: Results of fitting Type-II lensed templates to overlapping signals as a function of chirp mass ratio, SNR ratio, and coalescence time difference. Left: Inferred Bayes factors for a Type-II image ($n_j=0.5$). Middle and Right: Results when the Morse phase $n_j$ is a free parameter. Circular markers indicate $\log_{10}\mathscr{B}^{\rm L}_{\rm U} \geq 1$, corresponding to strong support for lensing.
• Figure 5: Inferred Morse index $n_j$ densities from parameter estimation under the Type-II lensing hypothesis for all $60$ injections. Posterior medians (purple) and maximum likelihood estimate, MLE (green) values show clustering near $n_j=0.5$, indicating a preference for a saddle-point (Type-II) image. Dashed lines denote the overall medians across the $60$ runs.