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arxiv: 2404.14286 · v3 · submitted 2024-04-22 · 🌀 gr-qc · astro-ph.HE

Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA

Nihar Gupte , Antoni Ramos-Buades , Alessandra Buonanno , Jonathan Gair , M. Coleman Miller , Maximilian Dax , Stephen R. Green , Michael P\"urrer
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Jonas Wildberger Jakob Macke Isobel M. Romero-Shaw Bernhard Sch\"olkopf
This is my paper

Pith reviewed 2026-05-24 01:27 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords binary black holesgravitational wavesorbital eccentricityLIGO-Virgo-KAGRABayesian model selectiondynamical formationwaveform modeling
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The pith

Bayesian analysis of 57 gravitational-wave events indicates over 99.5% probability that at least one binary black hole has nonzero orbital eccentricity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper analyzes 57 binary black hole merger events detected in LIGO-Virgo-KAGRA runs O1-O3 with a waveform model that adds orbital eccentricity and relativistic anomaly to a multipolar aligned-spin inspiral-merger-ringdown framework. Bayes factors are computed between eccentric aligned-spin models and both quasi-circular aligned-spin and precessing-spin models, yielding moderate support for eccentricity in three specific events. With a uniform eccentricity prior the individual signals remain inconclusive, yet an astrophysically motivated prior on the eccentric rate lifts the population probability that at least one of the 57 events is eccentric above 99.5 percent. This result would indicate that dynamical formation channels operate in the observed population. The analysis also quantifies biases that appear when eccentricity is omitted from standard quasi-circular templates.

Core claim

The central claim is that, when spin-precession is neglected and an astrophysically-motivated prior on the eccentric binary black hole rate is adopted, the probability that one of the 57 events is eccentric exceeds 99.5 percent. For GW200129 the eccentric aligned-spin versus quasi-circular aligned-spin log10 Bayes factor reaches 1.84-4.75, with eccentricity at 10 Hz inferred near 0.27; comparable support appears for GW190701 and GW200208_22, while GW190521 shows none. The same events retain positive but lower Bayes factors when compared against precessing quasi-circular models.

What carries the argument

A multipolar aligned-spin inspiral-merger-ringdown waveform extended by two eccentric parameters (eccentricity and relativistic anomaly) under the assumption of a quasi-circular merger-ringdown, evaluated with the DINGO machine-learning code to enable rapid Bayesian inference.

If this is right

  • Eccentric parameters must be included in binary black hole characterization for upcoming LVK runs and future detectors.
  • Neglecting eccentricity in quasi-circular models produces biases in recovered parameters.
  • Higher modes in eccentric models affect the accuracy of parameter estimation.
  • The results provide evidence for dynamical formation channels among observed binary black holes.
  • Future space-based detectors probing more diverse populations will require eccentric waveform models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Confirmation would strengthen the interpretation that a measurable fraction of black hole binaries form through dynamical interactions rather than isolated evolution.
  • Larger catalogs could permit direct measurement of the eccentric fraction without relying on an external rate prior.
  • The same Bayesian comparison framework could be applied to joint eccentricity and spin-precession inference in future data releases.

Load-bearing premise

The merger-ringdown phase remains quasi-circular even when the inspiral is eccentric, and the astrophysically-motivated prior on the eccentric binary black hole rate matches the true population fraction.

What would settle it

Repeating the full analysis on the identical 57 events with the same rate prior and obtaining a posterior probability below 50 percent that at least one event is eccentric would falsify the population-level claim.

Figures

Figures reproduced from arXiv: 2404.14286 by Alessandra Buonanno, Antoni Ramos-Buades, Bernhard Sch\"olkopf, Isobel M. Romero-Shaw, Jakob Macke, Jonas Wildberger, Jonathan Gair, Maximilian Dax, M. Coleman Miller, Michael P\"urrer, Nihar Gupte, Stephen R. Green.

Figure 1
Figure 1. Figure 1: Zero-noise injections of SEOBNRv4EHM with parameters χeff = −0.23, Mdet = 28M⊙, q = 1/3 and initial eccentricities e10Hz = 0.1 and e10Hz = 0.2 for the top and bottom figures, respectively. The injections are recovered with both DINGO, DINGO-IS (DINGO with importance sampling) and pBilby. C. GW200129 There has been considerable interest around GW200129 due to the fact that it has shown signs of orbital prec… view at source ↗
Figure 2
Figure 2. Figure 2: Shown on the left are the log10 BEAS/QCAS and 90% highest-density intervals on egw, 10Hz for the 57 events analyzed. Many events have log10 BEAS/QCAS < 1 and we color these green and reduce their opacity. However, there are 3 events GW200129, GW190701 and GW200208 22 which have log10 BEAS/QCAS > 1 which are labelled in the legend. We compute egw, 10Hz only for these three events since for events with low s… view at source ↗
Figure 3
Figure 3. Figure 3: Posteriors of GW200129 using different glitch mitiga￾tion techniques. In green is the analysis with gwsubtract, which uses auxillary detector channels and transfer functions to subtract glitches. Shown in orange, blue and pink is the analysis carried out using BayesWave de-glitching. This method involves generating a posterior of glitches using and then drawing individual glitches from this “glitch posteri… view at source ↗
Figure 4
Figure 4. Figure 4: The 90% credible interval of the projected waveforms of GW200129 analyzed with [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Radial separation as a function of the coordinate angle of [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Eccentric violin plots for all events with log [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Posterior distributions for the 3 candidate eccentric events analyzed with [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: JSDs of 1D marginals when including or not including higher modes in GWs. Each point represents a GW event and contains [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Posterior distribution for the rate of eccentric [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Analysis of GW200129 using LIGO-Hanford and LIGO [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Significance levels of GW200129, GW190701 and [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Kick velocity of GW200129 in km/s. Shown on the top (bottom) figure is the posterior distribution of the kick velocity using samples from the SEOBNRv4EHM and SEOBNRv4HM (NRSur7dq4) analyses using gwsubtract glitch mitigation. The green (grey) vertical lines show the typical escape velocity of a globular (nuclear) cluster as shown in Ref. [204]. 0.50 0.75 1.00 q -0.2 0.0 0.2 Â e ff 24 28 32 Msrc [M¯ ] 0.4 … view at source ↗
Figure 14
Figure 14. Figure 14: Posterior distributions obtained with NRSur7dq4 (left) and SEOBNRv4EHM (right) when injecting SEOBNRv4EHM (left) or NRSur7dq4 (right). The injection parameters were chosen to be the maximum likelihood point of GW200129 with gwsubtract glitch mitigation analyzed with SEOBNRv4EHM (left) and NRSur7dq4 (right) [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗
read the original abstract

Binary black holes (BBHs) in eccentric orbits produce distinct modulations in gravitational waves (GWs); measuring orbital eccentricity provides evidence for dynamical binary formation channels. We analyze 57 GW events from the LIGO-Virgo-KAGRA (LVK) O1-O3 observing runs using a multipolar aligned-spin inspiral-merger-ringdown waveform with two eccentric parameters: eccentricity and relativistic anomaly (assuming a quasi-circular merger-ringdown), made computationally feasible by the machine-learning code \texttt{DINGO}, which accelerates inference by 2-3 orders of magnitude. First, with a uniform eccentricity prior, eccentric vs. quasi-circular aligned-spin $\log_{10}$ Bayes factors are 1.84-4.75 (depending on glitch mitigation) for GW200129, 3.0 for GW190701 and 1.77 for GW200208_22. We infer $e_{\text{gw, 10Hz}}$ $(e_{\text{gw, 20Hz}})$ to be $0.27_{-0.12}^{+0.10}$ ($0.16_{-0.05}^{+0.04}$) to $0.17_{-0.13}^{+0.14}$ ($0.1_{-0.04}^{+0.05}$) for GW200129, $0.54_{-0.30}^{+0.12}$ ($0.31_{-0.13}^{+0.12}$) for GW190701 and $0.39_{-0.23}^{+0.23}$ ($0.21_{-0.08}^{+0.08}$) for GW200208_22. Second, eccentric aligned-spin vs. quasi-circular precessing-spin $\log_{10}$ Bayes factors are 1.43-4.92 for GW200129, 2.61 for GW190701 and 1.23 for GW200208_22. Third, GW190521 shows no evidence for eccentricity ($\log_{10}$ Bayes factor 0.04). Fourth, neglecting spin-precession with an astrophysically-motivated prior on the eccentric BBH rate, the probability of one of the 57 events being eccentric exceeds 99.5\% or $(100-8.4\times10^{-4})$\% (depending on glitch mitigation). Fifth, we study parameter estimation impacts of neglecting eccentricity in quasi-circular models or higher modes in eccentric models. These results underscore the inclusion of eccentric parameters in BBH characterization for upcoming LVK runs and future ground- and space-based detectors probing more diverse BBH populations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes 57 LVK O1-O3 binary black hole events with a multipolar aligned-spin eccentric inspiral-merger-ringdown waveform (implemented via the DINGO machine-learning code) that includes eccentricity and relativistic anomaly parameters under a quasi-circular merger-ringdown assumption. It reports log10 Bayes factors favoring eccentricity (uniform prior) of 1.84-4.75 for GW200129, 3.0 for GW190701 and 1.77 for GW200208_22, with corresponding eccentricity posteriors at 10 Hz and 20 Hz; compares to precessing-spin models; finds no eccentricity evidence for GW190521; and concludes that, neglecting spin-precession and adopting an astrophysically-motivated prior on the eccentric BBH rate, the probability of at least one eccentric event among the 57 exceeds 99.5%. The work stresses the need to include eccentricity in future BBH analyses.

Significance. If the central population result holds after full specification of the rate prior, the paper would supply quantitative evidence that dynamical channels contribute to the observed BBH population. The 2-3 order-of-magnitude acceleration of eccentric inference via DINGO is a clear methodological strength that enables the scale of the analysis. The individual-event Bayes factors and eccentricity measurements are concrete and falsifiable, though their interpretation for the population statement depends on the unspecified prior.

major comments (2)
  1. [Abstract (fourth point)] Abstract (fourth point): The headline claim that 'neglecting spin-precession with an astrophysically-motivated prior on the eccentric BBH rate, the probability of one of the 57 events being eccentric exceeds 99.5%' is load-bearing for the paper's central population inference. The prior's functional form, hyperparameters, and derivation are not supplied, yet this prior directly scales the combination of the reported per-event Bayes factors into the joint probability. Without its explicit construction the 99.5% figure cannot be reproduced or tested for sensitivity to reasonable variations in the rate.
  2. [Abstract (waveform description)] Abstract (waveform description): The analysis assumes the merger-ringdown remains quasi-circular even when the inspiral is eccentric. This modeling choice underpins the eccentricity posteriors and Bayes factors quoted for GW200129, GW190701 and GW200208_22; its quantitative impact on those results (e.g., via injection studies or alternative waveforms) must be demonstrated to support the robustness of the individual-event evidence.
minor comments (2)
  1. [Abstract] The range of log10 Bayes factors for GW200129 (1.84-4.75) depends on glitch mitigation; the specific methods, their justification, and the resulting data-quality cuts should be stated explicitly.
  2. [Abstract] Eccentricity is reported at both 10 Hz and 20 Hz; the reference-frequency convention and its relation to the waveform model should be clarified for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review. We address each major comment below and indicate the revisions we will implement.

read point-by-point responses

  1. Referee: [Abstract (fourth point)] Abstract (fourth point): The headline claim that 'neglecting spin-precession with an astrophysically-motivated prior on the eccentric BBH rate, the probability of one of the 57 events being eccentric exceeds 99.5%' is load-bearing for the paper's central population inference. The prior's functional form, hyperparameters, and derivation are not supplied, yet this prior directly scales the combination of the reported per-event Bayes factors into the joint probability. Without its explicit construction the 99.5% figure cannot be reproduced or tested for sensitivity to reasonable variations in the rate.

    Authors: We agree that the explicit functional form, hyperparameters, and derivation of the astrophysically-motivated prior are required for reproducibility. The main text derives this prior from rate estimates for dynamical channels (modeled as a Poisson process with hyperparameters set by population synthesis predictions), but we acknowledge the abstract does not state them. We will revise the abstract to include a concise description of the prior and add an explicit reference to the relevant methods section, allowing direct reproduction and sensitivity tests. revision: yes

  2. Referee: [Abstract (waveform description)] Abstract (waveform description): The analysis assumes the merger-ringdown remains quasi-circular even when the inspiral is eccentric. This modeling choice underpins the eccentricity posteriors and Bayes factors quoted for GW200129, GW190701 and GW200208_22; its quantitative impact on those results (e.g., via injection studies or alternative waveforms) must be demonstrated to support the robustness of the individual-event evidence.

    Authors: The quasi-circular merger-ringdown assumption is an inherent limitation of the eccentric IMR model implemented in DINGO. While the manuscript discusses this approximation, we agree that its quantitative effect on the reported posteriors and Bayes factors should be demonstrated. We will add injection-recovery studies (using available fully eccentric waveforms where feasible) to quantify any bias in eccentricity measurements and Bayes factors for the three events, and report the results in a new subsection. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's headline population probability is obtained by combining per-event Bayes factors (computed via standard Bayesian inference on strain data against external DINGO waveform models) with an astrophysically-motivated prior on the eccentric BBH rate. The abstract supplies no equations, self-definitions, or fitted inputs that reduce this probability to the paper's own data or ansatzes by construction. The prior is presented as external astrophysical input rather than derived within the work, and no self-citation load-bearing or uniqueness theorem is invoked in the provided text. The derivation remains self-contained against external benchmarks and waveform models.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The analysis rests on the quasi-circular merger-ringdown assumption inside the waveform model and on an external astrophysically motivated rate prior whose detailed construction is not shown.

free parameters (2)
  • uniform eccentricity prior
    Used for the first set of model comparisons
  • astrophysically-motivated eccentric BBH rate prior
    Used for the population probability calculation
axioms (1)
  • domain assumption Merger-ringdown phase is quasi-circular even for eccentric inspirals
    Explicitly stated in the waveform description

pith-pipeline@v0.9.0 · 6046 in / 1319 out tokens · 36856 ms · 2026-05-24T01:27:15.677553+00:00 · methodology

discussion (0)

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