Eccentricity signatures in LIGO-Virgo-KAGRA's BNS and NSBH binaries

TL;DR

The study targets the measurement of orbital eccentricity in low-mass gravitational-wave binaries to illuminate their formation channels. It employs two state-of-the-art eccentric waveform models, SEOBNRv5EHM and TEOBResumS-Dali, each with higher-order modes, within a Bayesian framework to analyze seven LVK-detected events at $f_ ext{ref}=20$ Hz. Six events show no significant eccentricity, yielding tight upper limits, while GW200105 shows moderate evidence for $e\sim\mathcal{O}(0.1)$ with Bayes factors of $\sim6$–$7$ (uniform $e$ prior) that drop under a log-prior, highlighting strong prior dependence and a multi-modal posterior structure. The work underscores the challenges of eccentricity inference in high-dimensional, multi-modal spaces and calls for improved waveform models, reduced waveform costs, and advanced marginalization techniques to enable robust eccentricity measurements for current and next-generation detectors.

Abstract

Measurement of eccentricity in low-mass binary systems through gravitational waves is crucial to distinguish between various formation channels. Detecting eccentricity in these systems is challenging due to a lack of accurate eccentric waveform models and the high computational cost of Bayesian inferences. We access the eccentricities of six previously observed low-mass gravitational wave events using publicly available data from the first four observing runs of the LIGO and Virgo collaboration. We analyze the events using the new eccentric waveform model, SEOBNRv5EHM, and compare our results with the existing model, TEOBResumS-Dali. We also present the first eccentricity constraints for GW190814. To improve accuracy, we include higher-order modes in both models and optimize inference using efficient marginalization and parallelization techniques. We find that GW200105 exhibits non-negligible eccentricity, with a measured eccentricity of $e=0.135^{+0.019}_{-0.088}$ at 20 Hz (90% credible level) for TEOBResumS-Dali and $e=0.125^{+0.029}_{-0.082}$ for SEOBNRv5EHM, given a uniform eccentricity prior from 0 to 0.2. This provides moderate support for the eccentric hypothesis, with a Bayes factor of $\sim6-7$ in favor of the eccentric model. With a uniform log prior on eccentricity, the Bayes factor is reduced to 2.35. The remaining five sources are consistent with low eccentricity, with 90% upper limits from $e \leq 0.011$ to $e \leq 0.066$. We find no support for non-negligible eccentricity in GW190814. Finally, we discuss the challenges of performing Bayesian inference in eccentric, multi-modal parameter spaces, including issues related to sampling efficiency and waveform systematics.

Figures (4)

• Figure 1: Normalized one-dimensional posterior distributions for the orbital eccentricity $e$ at 20 Hz for seven low-mass gravitational wave events, using SEOBNRv5EHM and TEOBResumS-Dali depicted in blue and orange for the dominant (2,2) waveform mode (SEOB,TEOB) and with HOMs included depicted in green and red (SEOBHM, TEOBHM). The posteriors have been smoothed using a Gaussian kernel density estimate. The dotted vertical line indicates the bounds of the 90% confidence interval in each panel. For GW200105, the dashed lines represent the 90% credible interval.
• Figure 2: Corner plot comparing marginalized posterior distributions for GW200105. The parameters shown are chirp mass $\mathcal{M}$, mass ratio $q = m_1/m_2$ where $m_1,m_2$ are the masses of the primary and secondary object, eccentricity $e$ defined at 20 Hz, aligned spin components $\chi_{1z}$ and $\chi_{2z}$, and mean or relativistic anomaly $\ell$ which is different depending on the model. The distributions are plotted for dominant modes of SEOBNRv5EHM (dominant mode green solid line), SEOBNRv5EHM (HOM blue solid line), TEOBResumS-Dali (dominant mode yellow dash-dot line), and TEOBResumS-Dali (HOM red dash-dot line). The two-dimensional panels display contours representing the 90% credible regions. The one-dimensional histograms along the diagonal show the marginalized posterior distributions for chirp mass, mass ratio, eccentricity, spins, and anomaly, with the quoted numbers representing the 90% credible interval. For additional comparison, published results from 2025arXiv250315393M using pyEFPE (purple dashed line) and planas2025eccentricinspiralmergerringdownanalysisneutron using IMRPhenomTEHM (pink dotted line) are also included. planas2025eccentricinspiralmergerringdownanalysisneutron reports the only results with no second island on the eccentricity and chirp mass or mass ratio posteriors, or a mild peak near $e\sim0.05$. 2025arXiv250315393M reports the only result with no secondary peak $e \sim 0.12$ in the posterior distribution.
• Figure 3: Comparison of eccentricity posteriors for GW200105 using different priors. None of the waveforms include HOMs in the plots. The orange curve shows the posterior assuming a uniform prior on eccentricity. The yellow dashed curve corresponds to a posterior assuming a log-uniform prior, with a minimum bound of $e_{\mathrm{min}} = 10^{-4}$. The dark blue curve represents the posterior on eccentricity with a uniform prior using SEOBNRv5EHM, while the dashed dark blue line shows the corresponding posterior under a log-uniform prior with the same lower bound. Vertical dashed lines indicate the median and 90% credible intervals for each corresponding uniform distribution. The 90% credible intervals are depicted in the legend.
• Figure 4: Marginalized posterior distributions and matches for two configurations: one with only eccentricity and anomaly varied (top), and the second with chirp mass and eccentricity varied (bottom). The model used for the plot is the dominant (2,2) mode SEOBNRv5EHM. The same test was performed for TEOBResumS-Dali and the same distribution is present in both waveforms. Multiple distinct modes are visible in parameters such as eccentricity, anomaly, and masses, illustrating the complex structure of the likelihood surface. The left plots show the inferred posteriors from parameter estimation, while the right plots show waveform matches for a fixed reference waveform depicted with the red point. The multi-modal structure in parameter space reflects underlying features of the waveform evolution.