Impact of Higher-Order Modes on Eccentricity Measurement in Binary Black Hole Gravitational Waves

TL;DR

This study asks whether neglecting higher-order modes (HOMs) biases eccentricity measurements of binary black-hole mergers. It compares HOM-inclusive SEOBNRv5EHM against dominant-mode SEOBNRv5E across six eccentric GW candidates and conducts zero-noise injections over a parameter grid to map where HOM omission may bias $e_0$, using Bayesian inference with Bilby/dynesty. The main finding is that no significant HOM-induced eccentricity bias appears for the six events, but biases emerge in high-mass, highly asymmetric, or edge-on systems at high SNR, including possible false eccentricity for quasi-circular high-mass binaries; lower-mass systems show negligible bias. The results underscore the necessity of HOM-inclusive waveforms for robust eccentricity measurements in future detections and guide waveform modeling and data-analysis strategies for current and next-generation GW Observatories. The work also highlights limitations such as the spin-aligned constraint and the need to test additional waveform families.

Abstract

We investigate the systematic biases in measuring orbital eccentricity for binary black hole (BBH) mergers that arise when higher-order modes (HOMs) of gravitational waves are neglected in waveform modeling. Using Bayesian inference with the state-of-the-art eccentric, spin-aligned, higher-mode effective-one-body model SEOBNRv5EHM, we reanalyze six previously suggested eccentric gravitational-wave events--GW190521, GW190620, GW190701, GW191109, GW200129, and GW200208\_222617. Comparing results with its dominant-mode-only counterpart SEOBNRv5E, we find no statistically significant HOM-induced bias in eccentricity for any of these events, including GW190521, whose eccentricity has been debated in the literature. To identify parameter regimes vulnerable to HOM omission, we perform a broad zero-noise injection campaign varying detector-frame total mass, mass ratio, eccentricity, inclination, and network SNR. We find that significant systematic biases ($Δ_e/σ> 1$) arise predominantly in systems with high total mass ($M^{\rm det}\gtrsim120M_\odot$), highly asymmetric mass ratios ($q \gtrsim 4$), near edge-on orientations ($θ_\textrm{JN} \gtrsim 30^\circ$), and high SNRs ($ρ^N_\textrm{mf}\approx50$). Notably, for quasi-circular BBHs with $M^{\rm det}\gtrsim140M_\odot$, neglecting HOMs may lead to strong false-positive evidence for nonzero eccentricity. By contrast, for lower-mass systems ($M^{\rm det}\sim100 M_\odot$), HOM exclusion produces negligible eccentricity biases. Our results demonstrate that although current eccentric candidates are not impacted by HOM omission, future eccentricity measurements--particularly for massive, asymmetric, or edge-on systems--require HOM-inclusive waveforms to avoid substantial systematic errors.

Figures (8)

• Figure 1: The eccentricity posteriors for an example injected GW signal generated with SEOBNRv5EHM. The left panel shows the result recovered with SEOBNRv5EHM, while the right panel shows the result obtained with SEOBNRv5E. The red solid line indicates the true eccentricity. The colored dashed lines and circular markers show the median and MAP estimates of eccentricity, respectively. The colored dotted lines indicate the 90% credible interval of eccentricity posteriors. As shown in the figures, the exclusion of HOMs significantly biases the estimated orbital eccentricity. This GW signal is generated with $M=160M_\odot$, $q=6$, $e_0=0.3$, $\theta_\textrm{JN}=90^\circ$, $\rho^N_\textrm{mf}=50$, and $f_\textrm{ref}=10~\textrm{Hz}$.
• Figure 2: Marginalized posterior distributions of initial eccentricity $e_0$ for all six GW events: GW190521, GW190620, GW190701, GW191109, GW200129, and GW200208_222617. Each panel presents the eccentricity posteriors obtained with SEOBNRv5EHM (green) and SEOBNRv5E (orange). Colored dashed lines represent the median eccentricities estimated, and colored circular markers denote the MAP point for each model. Colored dotted lines indicate the 90% credible interval of the eccentricity posteriors.
• Figure 3: Median-based normalized systematic errors $\Delta_e/\sigma$ for all injection analyses. Rows compare results with different total masses, and columns compare results with different network SNRs and eccentricities. The block colors correspond to the values of normalized $\Delta_e/\sigma$. Every block with $\Delta_e/\sigma>1$ is marked with a red box.
• Figure 4: The same as in Fig. \ref{['fig:norm-erro-median']} but for normalized systematic errors calculated using MAP.
• Figure 5: Eccentricity posteriors recovered with HOM-excluded SEOBNRv5E for injections generated with HOM-included SEOBNRv5EHM. We show results for systems with different total masses $M$ and compare two network matched-filter SNRs, $\rho^N_\textrm{mf}=20$ (lighter color) and $\rho^N_\textrm{mf}=50$ (darker color). The top panel presents the case of $e_0=0.3$, $q=2$, and $\theta_\textrm{JN}=90^\circ$; the bottom panel presents the case of $e_0=0.0$, $q=2$, and $\theta_\textrm{JN}=90^\circ$. The gray dashed lines indicate injected values of eccentricity, and the colored solid lines represent the 90% credible interval of each corresponding eccentricity posteriors. The median and MAP eccentricities are marked with red crosses and blue plus signs, respectively.