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Assessing the imprint of eccentricity in GW signatures using two independent waveform models

This study analyzes 162 gravitational wave sources from the O3 and O4a observing runs using two independent eccentric waveform models (SEOBNRv5EHM and TEOBResumS-Dali) to conclude that while most events disfavor eccentricity, three binary black hole candidates (GW200129, GW200101, and GW231123) show potential, though sometimes ambiguous, evidence for orbital eccentricity.

Original authors: Natalie Malagon, Richard O'Shaughnessy

Published 2026-05-14

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CC BY 4.0

Original authors: Natalie Malagon, Richard O'Shaughnessy

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is a giant, silent concert hall. For years, we've been listening to the "music" of black holes colliding, but until recently, our musical score (the mathematical models we use to understand the sound) assumed the black holes were dancing in perfect, circular circles.

However, scientists suspect that sometimes, these cosmic dancers might be moving in wobbly, oval-shaped paths (eccentric orbits) before they crash together. This paper is like a massive, high-tech audit where researchers checked 162 of these cosmic collisions to see if any of them were actually dancing in those wobbly, oval patterns.

Here is a breakdown of what they found, using simple analogies:

1. The Setup: Two Different "Translators"

To understand the music, the researchers used two different "translators" (waveform models): SEOBNRv5EHM and TEOBResumS-Dali.

Think of these as two different experts trying to translate a foreign language. They both know the grammar of gravity, but they have slightly different dictionaries.
The goal was to see if both experts agreed on the story. If they both say, "This black hole was wobbly," we can be pretty sure it was. If one says "wobbly" and the other says "perfect circle," we have a problem.

2. The General Verdict: "Mostly Perfect Circles"

After listening to all 162 events, the two experts mostly agreed on one thing: The vast majority of black holes are dancing in perfect circles.

For almost every event, the "wobble" (eccentricity) was so tiny it was indistinguishable from zero.
The two translators gave very similar stories for almost everything, which gives us confidence that our understanding of the "perfect circle" dance is solid.

3. The Exceptions: Three "Suspicious" Dancers

While most were perfect circles, the researchers found three events where the music might have had a wobble. However, the story gets a bit messy here:

Event 1: GW200129 (The Strongest Candidate)
- Both translators agreed this one was likely wobbly.
- The Catch: This event is known to be "noisy" (like trying to hear a whisper in a room with a loud fan). The researchers found that if you change the settings of your listening equipment (like the sampling rate), the story changes slightly. It's a strong hint, but the noise makes it hard to be 100% certain.
Event 2: GW231001 (The Confused Candidate)
- One translator said, "Definitely wobbly!"
- The other translator said, "Nah, probably a circle."
- Because they disagreed so much, the researchers can't claim this is a confirmed wobble. It's an ambiguous signal.
Event 3: GW231123 (The Heavyweight Candidate)
- This was a very heavy pair of black holes. One translator saw a huge wobble, while the other saw almost none.
- The researchers suspect this disagreement isn't because the black hole was actually wobbly, but because the "translator" (the mathematical model) gets confused when dealing with very heavy objects moving fast. It's like a GPS getting lost in a dense city; the map itself might be the issue, not the car's path.

4. The "Glitch" Warning

The paper emphasizes that sometimes the data itself has "glitches" (like a sudden pop in a recording).

For the most promising candidate (GW200129), the researchers showed that how you handle these glitches changes the result.
It's like trying to identify a specific instrument in a song; if you filter out the static noise differently, you might hear a different instrument. This means we need to be very careful before declaring a "wobble" found.

5. The Bottom Line

The researchers built a massive catalog of these events to see if the "wobbly dance" is common.

The Result: They found no strong, undeniable proof that black holes merge in wobbly orbits, except for that one tricky case (GW200129) which needs more study.
The Takeaway: Most black holes seem to tidy up their orbits into perfect circles long before they collide. The few times we thought we saw a wobble, it turned out to be either a noisy signal, a disagreement between our math models, or a glitch in the data.

In short: The universe's black hole dancers are mostly sticking to the perfect circle choreography. We haven't found enough evidence yet to say they are doing the wobbly, oval-step dance, though we are keeping an eye on a few suspicious suspects.

Technical Summary: Assessing the Imprint of Eccentricity in GW Signatures

Problem Statement
Gravitational wave (GW) signals from merging compact binaries encode information about their orbital and intrinsic properties. While orbital eccentricity is a key discriminator between formation channels—specifically distinguishing isolated binary evolution (expected to be quasi-circular) from dynamic assembly in dense stellar environments (which may retain measurable eccentricity)—detecting this imprint is challenging. Previous analyses have identified candidate events with potential eccentricity, but results have often been sensitive to analysis settings, waveform models, and data conditioning (e.g., glitch mitigation). Furthermore, substantial differences in parameter inference can arise when using different waveform models, complicating the reliable discernment of source parameters. This work addresses the need for a comprehensive, consistent assessment of eccentricity across a large population of GW events using state-of-the-art waveform models that account for orbital eccentricity and aligned spins.

Methodology
The authors performed parameter inference on 162 confident GW sources identified during the O3 and O4a observing runs of the LIGO-Virgo-KAGRA (LVK) network. The sample includes all events with a false alarm rate (FAR) of less than one per year, plus 11 additional O3 events with tentative eccentricity indications.

Inference Engine: The study utilized the RIFT (Rapid Inference Framework for Transients) parameter inference engine, which employs a two-step iterative process to compute marginal likelihoods and construct posterior distributions efficiently, mitigating the high computational cost of evaluating complex waveforms.
Waveform Models: Two independently implemented, state-of-the-art waveform models were employed to assess eccentricity: SEOBNRv5EHM and TEOBResumS-Dali. Both models account for orbital eccentricity and aligned compact object spins, utilizing available higher-order modes.
Analysis Settings:
- Spins were constrained to be aligned with the orbital angular momentum ("z prior").
- Sampling rates were set to at least 4096 Hz (8192 Hz for some events) to accommodate RIFT's internal discrete time sampling.
- Eccentricity ( $e$ ) and mean anomaly ( $\ell$ ) were included as parameters with uniform priors. For GWTC-3 events, the prior range was $e \in [0, 0.9]$ (truncated to $e \in [0, 0.5]$ for final posteriors to reflect model validity); for GWTC-4 events, the prior was $e \in [0, 0.5]$ .
- Starting frequencies varied (13.33 Hz for GWTC-4, 20 Hz or 10 Hz for older events) based on event characteristics and prior analysis choices.
- Noise Power Spectral Density (PSD) estimates were generated independently for each event using Bayeswave.
Comparison Metrics: The study compared results between the two waveform models and against previously published quasi-circular (QC) results. Consistency was quantified using Jensen-Shannon (JS) divergences between marginal posterior distributions. Bayes factors were calculated using the Savage-Dickey density ratio to quantify support for the eccentric hypothesis versus the quasi-circular hypothesis.

Key Contributions

Comprehensive Population Analysis: This work provides the first systematic parameter inference of eccentricity for a large, consistent sample of 162 events using two distinct, high-fidelity eccentric waveform models within a single analysis framework (RIFT).
Model Consistency Assessment: By employing two independent waveform implementations, the study rigorously tests the robustness of eccentricity inferences against waveform systematics.
Identification of Systematics: The paper identifies specific events where conclusions regarding eccentricity and other intrinsic parameters differ significantly between waveform models, highlighting regions of parameter space (particularly high-mass systems) where waveform systematics are substantial.
Re-evaluation of Candidates: The study re-evaluates previously identified eccentric candidates (e.g., GW200129, GW190521) and new candidates, providing updated Bayes factors and posterior distributions.

Results

General Consistency: For the vast majority of the 162 events, the SEOBNRv5EHM and TEOBResumS-Dali models yield highly consistent conclusions, with posterior distributions for chirp mass, mass ratio, effective spin, and eccentricity showing strong agreement. Most events are consistent with zero eccentricity.
Eccentricity Candidates:
- GW200129 065458: Both waveform models found positive evidence for eccentricity. SEOBNRv5EHM yielded $\log_{10} B \approx 3.12$ with $e \approx 0.12$ , and TEOBResumS-Dali yielded $\log_{10} B \approx 3.59$ with $e \approx 0.11$ . However, the authors note that conclusions for this event are sensitive to analysis settings (e.g., sampling frequency, reference frequency, and glitch mitigation), consistent with previous literature.
- GW231001 140220: TEOBResumS-Dali showed a modest peak in eccentricity ( $e \approx 0.36$ ) with $\log_{10} B \approx 0.30$ , while SEOBNRv5EHM found no significant evidence ( $\log_{10} B \approx -0.12$ ). The authors attribute the TEOB feature partly to waveform systematics in high-mass systems.
- GW231123 135430: TEOBResumS-Dali showed strong support for eccentricity ( $\log_{10} B \approx 6.05$ , $e \approx 0.46$ ), with the distribution "railing" against the upper prior limit. In contrast, SEOBNRv5EHM found no significant evidence ( $\log_{10} B \approx 0.04$ ). The authors conclude this event exhibits substantial waveform systematics and do not consider it a confirmed eccentric candidate based on the discrepancy.
Systematics: Significant discrepancies (JS divergences > 0.2) were observed between models for a few high-mass events (GW230814, GW231001, GW231123), particularly in the eccentricity and effective spin parameters. TEOBResumS-Dali tended to assign non-negligible probability to high eccentricities ( $e \gtrsim 0.5$ ) in high-mass systems, a behavior the authors suggest may be a waveform systematic.
Comparison with Other Works: The study's conclusions often differ from previous reports that found stronger evidence for eccentricity in events like GW190521 074359 or GW190701 203306. The authors attribute these differences to variations in analysis settings, waveform models, and data conditioning (e.g., deglitching strategies).

Significance
The paper establishes a comprehensive catalog of eccentric parameter estimation for the current GW event catalog using a consistent framework. The primary significance lies in demonstrating that while two independent, state-of-the-art eccentric waveform models largely agree on the quasi-circular nature of most binary black hole mergers, significant systematics can arise in specific high-mass cases. The authors conclude that, with the exception of the well-studied and setting-sensitive GW200129 065458, no other binary black hole candidates in their sample exhibit significant evidence for eccentricity. This work underscores the critical importance of assessing analysis settings and waveform systematics when interpreting potential eccentricity signatures, cautioning against over-interpreting features that may be artifacts of the models or analysis choices rather than astrophysical reality. The results provide a robust baseline for future population-level studies of compact binary formation channels.