Impact of higher-order modes on eccentricity measurement in binary black hole gravitational waves

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 explore representative 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 relatively high total mass ($M^{\rm det}\gtrsim120M_\odot$), highly asymmetric mass ratios ($q \gtrsim 4$), large inclinations ($\theta_\textrm{JN} \gtrsim 30^\circ$), and high SNRs ($\rho^N_\textrm{mf}\approx50$). Notably, for quasicircular BBHs with approximately $M^{\rm det}\gtrsim140M_\odot$, our results suggest that 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 relatively massive, asymmetric, or edge-on systems--require HOM-inclusive waveforms to avoid substantial systematic errors.