Can Eccentric Binary Black Hole Signals Mimic Gravitational-Wave Microlensing?

TL;DR

This work probes whether orbital eccentricity in binary black-hole GW signals can impersonate wave-optics microlensing by a point mass. By combining high-fidelity numerical-relativity injections and TEOBResumS-Dalí eccentric waveforms with Bayesian model comparison and mismatch analyses, the authors quantify where eccentricity masquerades as microlensing (notably at high eccentricity, low total mass, and high SNR) and demonstrate that incorporating eccentric waveform models eliminates the false-positive microlensing signal. The results underscore the need to analyze potential microlensing events with eccentric waveform templates to avoid biased astrophysical inference in the precision GW era. The study provides a practical framework for robust interpretation of GW signals, with implications for microlensing searches in current and future detectors and for disentangling waveform physics such as eccentricity, precession, and lensing.

Abstract

Gravitational lensing in the wave-optics regime imprints characteristic frequency-dependent amplitude and phase modulations on gravitational-wave (GW) signals, yet to be detected by ground-based interferometers. Similar modulations may also arise from orbital eccentricity, raising the possibility of degeneracies that could lead to false microlensing claims. We investigate the extent to which eccentric binary black hole (BBH) signals can mimic microlensing signatures produced by an isolated point-mass lens. With a simulated population of eccentric signals using numerical relativity simulations and \texttt{TEOBResumS-Dalí} waveform model, we perform a Bayesian model-comparison study, supported by a complementary \textit{mismatch} analysis. We find a strong degeneracy for high eccentricities, low total masses, and high signal-to-noise ratios (SNRs): under these conditions, quasicircular microlensed model can be strongly favored over quasicircular unlensed model, even when the true signal is unlensed. For moderate SNRs ($\sim 30$), binaries with $M_\mathrm{tot}\lesssim 100\,M_\odot$ and eccentricity $e \gtrsim 0.4$ are particularly susceptible to misclassifications. In such cases, inferred microlens parameters exhibit well-constrained posteriors despite being unphysical. Crucially, the degeneracy is completely removed when the recovery uses waveform models that incorporate eccentricity, which overwhelmingly favors the eccentric hypothesis over microlensing. Our results demonstrate that any event exhibiting strong Bayesian evidence for microlensing should also be analyzed with eccentric waveform models and vice-versa to avoid false positives and biased astrophysical inference. This work contributes to developing robust strategies for interpreting signals in the era of precision GW astronomy.

Figures (6)

• Figure 1: Inferred microlens parameters, $\log_{10}M^{\rm z}_{\rm L}$ and $y$, for three non-spinning QCUL NR injections (left panel) and three non-spinning EccUL NR injections (right panel), generated using SXS simulations (SXS IDs mentioned in the legend). The bottom-left subpanels display the inferred $1\sigma$ credible regions for the lens parameters, while the adjacent panels show the corresponding $1$D marginalized posteriors. For eccentric simulations, we additionally report the gauge-independent eccentricity measured at $20~\mathrm{Hz}$$(e^{\mathrm{gw}}_{20~\mathrm{Hz}})$ using the gw_eccentricity package.
• Figure 2: Bias in microlensing searches arising from the presence of eccentricity in the signal. The variation in the Bayes factors between the QCML and QCUL hypotheses, $\log_{10}\mathcal{B}^\mathrm{QCML}_\mathrm{QCUL}$, is shown as a function of the eccentricity $(e)$ (x-axis), total binary mass $(M_\mathrm{tot})$ (color scale), and mass ratio $(q)$ (solid vs. dashed lines). Eccentricity is defined at a dimensionless frequency of $\sim 0.003$ at apastron. The uncertainty in the estimated $\log_{10}\mathcal{B}^\mathrm{QCML}_\mathrm{QCUL}$ is represented by the translucent bands around each curve. The injections are performed using the TEOBResumS-Dalí waveform model, while the recovery (evidence computation) is done using two different quasicircular models: (a) TEOBResumS-Dalí with eccentricity and related parameters fixed to zero, and (b) IMRPhenomXPHM-SpinTaylor allowing all 15 parameters to vary. These results demonstrate that neglecting eccentricity in waveform modeling can lead to spurious support for the microlensing hypothesis, especially at higher eccentricities.
• Figure 3: Comparison of the inferred intrinsic parameters as a function of eccentricity ($e_{M f \approx 0.003}$) when eccentric injections are analyzed under the quasicircular microlensed (QCML; $\mathcal{H}_{\rm QCML}$) and quasicircular unlensed (QCUL; $\mathcal{H}_{\rm QCUL}$) hypotheses. For the TEOBResumS-Dalí waveform model [panel (a)], the intrinsic parameters shown are the total mass $(M_\mathrm{tot})$, mass ratio $(q)$, and aligned spin components $(\chi_{1z}, \chi_{2z})$. For the IMRPhenomXPHM-SpinTaylor model [panel (b)], we instead show the total mass $(M_\mathrm{tot})$, mass ratio $(q)$, effective precession spin parameter $(\chi_{\rm p})$, and effective aligned-spin parameter $(\chi_{\rm eff})$. All results correspond to non-spinning injections with $\{M_\mathrm{tot} = 30~{\rm M}_\odot, q = 1\}$. The points denote the median values of the one-dimensional marginalized posteriors, and the shaded bands indicate the corresponding $1\sigma$ uncertainties. In panel (a), in-plane spins, eccentricity, and true anomaly are fixed to zero during inference, whereas in panel (b), all 15 parameters are varied.
• Figure 4: Inferred microlens parameters, $\log_{10}M^{\rm z}_{\rm L}$ and $y$, for non-spinning eccentric injections with $\{M_\mathrm{tot} = 30~{\rm M}_\odot, q = 1\}$, analyzed using IMRPhenomXPHM-SpinTaylor. We show results only for cases with $\log_{10}\mathcal{B}^\mathrm{QCML}_\mathrm{QCUL}>1$, with the $e=0$ case included for reference. The bottom-left panel displays the inferred $1\sigma$ credible regions for the lens parameters, while the adjacent panels show the corresponding one-dimensional marginalized posteriors.
• Figure 5: Variation in the Bayes factors between the EccUL and QCUL hypotheses, $\log_{10}\mathcal{B}^\mathrm{EccUL}_\mathrm{QCUL}$, shown as a function of the eccentricity $(e)$ (x-axis), total binary mass $(M_\mathrm{tot})$ (color scale), and mass ratio $(q)$ (solid vs. dashed lines). Eccentricity is defined at a dimensionless frequency of $\sim 0.003$ at apastron. The uncertainty in the estimated Bayes factors are represented by the translucent bands around each curve.