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

TL;DR

This study assesses how neglecting higher-order modes in gravitational wave models affects eccentricity measurements of binary black hole mergers, finding minimal bias in current events but significant biases in certain high-mass, asymmetric, or edge-on systems.

Contribution

It provides a comprehensive analysis of the impact of higher-order modes on eccentricity estimation, highlighting parameter regimes where HOM omission causes significant biases.

Findings

No significant HOM-induced bias in current events.

Biases are significant for high-mass, asymmetric, edge-on, high-SNR systems.

Neglecting HOMs can cause false-positive eccentricity in massive, nearly circular binaries.

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 ($\Delta_e/\sigma > 1$) arise predominantly in systems with high total mass ($M^{\rm det}\gtrsim120M_\odot$), highly asymmetric mass ratios ($q \gtrsim 4$), near edge-on orientations ($\theta_\textrm{JN} \gtrsim 30^\circ$), and high SNRs ($\rho^N_\textrm{mf}\approx50$). 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.