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REVIEW 4 major objections 6 minor 1 cited by

The ringdown of GW231028 contains the first overtone quasinormal mode alongside the fundamental, with a Bayes factor near 190 supporting the two-mode fit.

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2026-08-04 20:16 UTC pith:CVKVCTDQ

load-bearing objection Potentially important overtone claim in GW231028, but the abstract overstates what the body supports: the cited injection validation is missing and the detection sits on a steeply decaying Bayes factor. the 4 major comments →

arxiv 2509.08657 v2 pith:CVKVCTDQ submitted 2025-09-10 gr-qc astro-ph.HE

First Overtone Mode in the Ringdown Signal of GW231028

Hai-Tian Wang This is my paper
classification gr-qc astro-ph.HE PACS 04.30.Tv
keywords gravitational-wave ringdownquasinormal modesfirst overtone modeblack hole spectroscopyno-hair theoremF-statisticGW231028Bayes factor
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper claims that the ringdown of the binary black hole merger GW231028 contains a second quasinormal mode — the first overtone (221) — alongside the fundamental (220) mode. Using a time-domain F-statistic analysis that starts 10M (about 12 ms) after the signal peak, the two-mode model beats the fundamental-only model by a Bayes factor of about 190, with the overtone amplitude excluding zero at more than 7σ. The two-mode fit yields a redshifted remnant mass of about 243 M⊙ and spin of about 0.8 that agree with full inspiral-merger-ringdown waveform analyses, and a no-hair test of the two modes agrees with general relativity. If correct, this is the first decisive overtone detection in a binary black hole ringdown, and it matters because measuring two distinct modes from one remnant is the minimum needed to test the claim that a black hole's vibrations are fixed entirely by its mass and spin. The statistical support is steeply time-dependent — the log-Bayes factor falls from about 5.2 at 8M to about zero at 14–16M — so the adopted 10M start boundary carries the result.

Core claim

On the paper's own terms: the ringdown of GW231028 is best described by the superposition of the fundamental quadrupole mode (220) and its first overtone (221). With the F-statistic starting 10M after the polarization peak, the 220+221 model beats the fundamental-only model by a Bayes factor near 190, the overtone amplitude is non-zero at more than 7σ, and the inferred remnant — mass 243.0+22.7/−22.7 M⊙, spin 0.80+0.07/−0.11 — agrees with two independent full IMR waveform posteriors. The numerical-relativity injection SXS:BBH:1282 is cited as showing this multimode content is physically expected for this remnant's spin and mass ratio. The paper calls this the first decisive overtone detectio

What carries the argument

The engine is the F-statistic, a time-domain likelihood method that analytically maximizes the ringdown fit over each mode's linear parameters (amplitude and phase), leaving only the nonlinear parameters — remnant mass, spin, and any frequency or damping deviations — to the search; this dimensionality reduction is what lets a sub-dominant mode as faint as the 221 overtone compete with the noise at a network SNR near 10.5. The signal model is a superposition of damped sinusoids (quasinormal modes), each indexed by (ℓ, m, n), whose complex frequency is fixed uniquely by the remnant's mass and spin — so every additional detected mode is an independent measurement of the same two parameters, whi

Load-bearing premise

The load-bearing premise is that at Δt = 10M after the SEOBNRv5PHM-defined peak, GW231028's ringdown is already in the linear perturbation regime, so the extra power modeled as the 221 overtone is a genuine quasinormal mode rather than nonlinear or transient merger content; the reported Bayes factor falls from about 193 at 10M to essentially zero by 14–16M, so a slightly later linearity boundary erases the detection.

What would settle it

Run the same pipeline on noise-only stretches of the same detector data and on injections containing only the 220 mode, and count how often the 220+221 model wins with a Bayes factor above 190 when no overtone is present; a false-alarm rate much above 1/190 would undercut 'decisive'. Separately, repeat the 10M analysis starting at 12M and 14M: Fig. 1 of the paper shows log10 B dropping from ≈2.3 at 10M to ≈0 at 14–16M, so the >7σ amplitude exclusion must survive those later, uncontroversially linear start times for the detection to stand.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the detection holds, black-hole spectroscopy becomes a two-mode discipline: remnant mass and spin can be pinned from the ringdown alone, as done here, without needing the inspiral part of the signal.
  • The two-mode no-hair test becomes usable on real events; the paper's 90% bounds on the overtone frequency and damping-time deviations (δf221, δτ221) are the template for future tests.
  • Mode content becomes a diagnostic of merger dynamics: GW231028 shows the 221 overtone with no 200 mode, whereas GW231123's ringdown was 200-dominated, which the paper links to different merger geometries and formation channels.
  • Ringdown-only remnant parameters that agree with two independent full IMR waveform models give gravitational-wave astronomy a cross-check on inspiral-merger-ringdown waveform accuracy.
  • The evidence landscape across start times (log10 B ≈ 5.2 at 8M, ≈2.3 at 10M, ≈0 at 14–16M) maps where overtone searches should look: as early in the linear regime as the data allow.

Where Pith is reading between the lines

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

  • My read: the steep decay of the Bayes factor between 8M and 16M puts the whole detection on the question of where linearity begins for this specific event; an event-specific numerical-relativity injection study at the inferred mass and spin — rather than the generic ≈8M rule — would settle whether the 10M boundary is safe.
  • My read: the >7σ amplitude exclusion is quoted for 10M, but the mode's SNR decays from 10.5 at 10M to 5.9 at 20M; checking the overtone amplitude posterior at 12M and 14M would show how quickly that significance decays.
  • My read: the peak time, sky location, and polarization are anchored to the SEOBNRv5PHM waveform; redoing the analysis with the NRSur7dq4 anchor or marginalizing over sky position would reveal how much of the Bayes factor depends on that single-model choice.
  • My read: a genuine overtone implies a predictable A221/A220 excitation ratio from numerical relativity; measuring that ratio across a population of high-mass, high-spin remnants would turn this single detection into a calibration of overtone excitation physics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper analyzes the ringdown of GW231028_153006 using a time-domain F-statistic method that fixes the sky location and polarization and varies the analysis start time from 8M to 20M after the SEOBNRv5PHM polarization peak. It claims a decisive detection of the first overtone 221 in addition to the fundamental 220, with a Bayes factor of 193 at Δt=10M, remnant parameters Mf=243.0^{+22.7}_{-22.7} M⊙ and χf=0.80^{+0.07}_{-0.11} consistent with full IMR analyses, and a no-hair test consistent with GR. The abstract additionally claims validation against the NR injection SXS:BBH:1282 and an amplitude exclusion from zero at >7σ, and reports slightly different numerical values (BF 189.2, Mf=246.2, χf=0.81). The main evidence is summarized in Fig. 1 (Bayes factors for several two-mode combinations) and in the start-time dependence of the 220+221 evidence and amplitudes (Fig. 3).

Significance. If correct, this would be the first decisive detection of an overtone in a BBH ringdown and would enable a two-mode no-hair test; the result is therefore of considerable interest for BH spectroscopy. The manuscript has several genuine strengths: the QNM frequencies and damping times are fixed by GR and the inferred remnant parameters rather than fitted; the F-statistic reduces the search dimension; and the supplementary figures show the full start-time and model dependence of the posteriors, which is good practice. The significance statement is however weakened by the steep start-time dependence of the evidence, the absent NR-injection validation promised in the abstract, and the unresolved model-selection degeneracy between the 221 overtone and the 210 harmonic. These issues, not the method itself, currently prevent the result from being verified as stated.

major comments (4)
  1. [Abstract vs §II–IV] The abstract states the findings are 'rigorously validated against the numerical relativity injection SXS:BBH:1282'. The body never mentions this injection or any injection-recovery test; the only calibration invoked is that the pipeline is 'identical' to that validated for GW231123 [28], a different event with different mass, spin, SNR, and noise. The false-alarm rate and amplitude bias of the F-statistic are therefore uncalibrated for GW231028, and the claimed BF=193 and >7σ significance are unsupported. Also, abstract and body disagree on BF (189.2 vs 193), Mf (246.2 vs 243.0), and χf (0.81 vs 0.80). Either include the SXS:BBH:1282 validation or retract the claim, and reconcile the numbers.
  2. [§III, Fig. 1; §II start-time choices] The evidence for 220+221 decays steeply with start time: log10B is ≈5.2 at Δt=8M, ≈2.3 at 10M (BF=193), ≈1.5 at 12M, and near zero by 14–16M. The choice Δt=10M as 'firmly within the linear perturbation regime' is asserted with citations [11–15] but no event-specific check is given: no NR injection into GW231028's noise, no stability test of the 221 amplitude or phase across start times, and no marginalization over the linear-regime boundary. The peak time t_pol_c=1382542224.18917 s is fixed (Sec. II). Given this steep gradient, a slightly later linearity boundary erases the detection. The authors should demonstrate linearity for this event (e.g., recover an injected NR waveform at 10M) or report a start-time-marginalized Bayes factor; otherwise the 'decisive' claim is not robust.
  3. [§III, model selection] Sec. III states that the 220+210 model is 'marginally favored' over 220+221 by evidence (Fig. 1) but is rejected because it 'fails to provide meaningful constraints' on Mf and χf. The reported BF=193 is only for 220+221 vs 220. Since the data do not clearly prefer 221 over 210, the specific claim of an overtone (n=1) identification requires a direct comparison of 220+221 vs 220+210, or a model average over the candidate set with explicit priors. As written, the selection of 221 over 210 rests on consistency with IMR posteriors—an external physical expectation—rather than on the evidence. This is not circular, but it must be quantified and reported so the reader can see the posterior weight of each candidate.
  4. [Abstract vs §III (amplitude significance)] The abstract claims an amplitude exclusion from zero at '>7σ credibility' for the 221 mode, but the body never reports this significance level or the A221 posterior at Δt=10M. Fig. 3 shows that the 221 amplitude posterior is consistent with zero at later start times, so the σ value is a headline result that must be derived or explicitly stated. The abstract also says the analysis uses 'both a time-domain F-statistic framework and full Bayesian time-domain sampling', but Sec. II describes only the F-statistic method; either the Bayesian analysis must be reported or the abstract corrected.
minor comments (6)
  1. [§II, Eq. (1)] Clarify the handling of the azimuth angle δ and its relation to the fixed polarization angle ψ; the notation ℓ|m|n in the introduction is ambiguous (e.g., '22' should be '220').
  2. [§III header] Typo in the section header: 'MUL TIMODE SEARCH' should be 'MULTIMODE SEARCH'.
  3. [§II] The paper should state the noise model and PSD estimation used, even if identical to [28], for reproducibility.
  4. [§II, Eq. (1)] The spherical-harmonic approximation should be quantified for χf≈0.8; spheroidal corrections for the 221 mode could bias the amplitudes or Bayes factor at the claimed precision.
  5. [Abstract vs §III] The abstract's 'decisive evidence for multimode content' also names the 210 mode, but the body does not claim a 210 detection; clarify the status of 210.
  6. [Fig. 3] The top-panel axis label 'log10B220+221 220' is hard to read; use explicit subscript/superscript formatting.

Circularity Check

0 steps flagged

No constructional circularity: the 221 detection is a genuine model comparison; the SXS-injection validation promised in the abstract is absent, and the pipeline calibration is sourced to the same author's prior work, but these are validation/reproducibility gaps, not by-construction reductions.

full rationale

I walked the derivation chain. The ringdown model (Eq. 1) is a superposition of damped sinusoids whose complex frequencies are fixed by GR for given M_f and chi_f; the amplitudes and phases are free parameters maximized by the F-statistic. The 221 detection therefore does not reduce to a fitted input: the Bayes factor in Fig. 1 is a genuine comparison of 220+221 versus 220-only, and the >7 sigma amplitude claim is a posterior constraint, not a renaming of the model choice. The remnant parameters (M_f=243.0, chi_f=0.80) are inferred from the ringdown data and compared with independent IMR posteriors; the sky location and peak time are imported from SEOBNRv5PHM, but M_f and chi_f are not, so the consistency check is an external benchmark rather than an input to the likelihood. The 8-10M linear-regime rule is cited to external NR studies, not to the author's own work. I explicitly flag two concerns that are not constructional circularity. First, the abstract states the findings are 'rigorously validated against the numerical relativity injection SXS:BBH:1282', but this validation never appears in the body; instead, Section II says the implementation is 'identical to the validated pipeline detailed in Wang et al. [28]', a same-first-author paper. Thus the calibration of the reported Bayes factor and amplitude significance is imported from a self-citation rather than demonstrated for GW231028 in this manuscript. This is a missing-support/reproducibility problem, not an equivalence-by-construction. Second, Section III prefers 220+221 over 220+210 partly because 210 gives IMR-inconsistent remnant posteriors, a post-hoc physicality criterion; however, the 221 model's Bayes factor of 193 is reported independently, so the central claim does not reduce to that criterion. No equation is defined in terms of its own conclusion, and no fitted parameter is relabeled as a prediction. Score 2 reflects the self-citation and the absent SXS validation without inflating them into circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

No new physical entities are proposed. The free parameters are the choices that shape the detection claim: the start time, the imported IMR sky location and peak time, and the deferred priors. The axioms are the standard QNM framework plus the linear-regime assumption that carries most of the risk.

free parameters (4)
  • Analysis start time Δt = 10M = 10M post-peak
    Chosen after inspecting the Bayes factor as a function of start time (Fig. 1); the evidence peaks at 8M and decays steeply, so the 'conservative' 10M choice is load-bearing for the detection claim.
  • Fixed sky location and polarization angle (RA, DEC, psi) = (0.04, -0.10, 1.26) = Maximum-likelihood values from IMR analysis with SEOBNRv5PHM
    Section II: fixing these avoids contamination but imports IMR-derived values from the same event into the ringdown analysis, coupling the two analyses.
  • Peak reference time t_pol_c = 1382542224.18917 GPS = From SEOBNRv5PHM analysis of the same event
    Section II: all start times are measured from this peak; its uncertainty is not propagated into the ringdown analysis.
  • Remnant mass and spin priors and amplitude priors = Mass uniform [50,300] Msun; remaining priors 'identical to Wang et al. [28]'
    Section II: prior choices are not specified in this paper but deferred to the same-author companion paper; the amplitude prior affects the reported '>7 sigma' statement.
axioms (4)
  • standard math Kerr QNM frequencies and damping times are uniquely determined by Mf and chi_f (Leaver; Berti et al.)
    Used in Eq. (1) and Section II; this is the theoretical backbone of the mode models.
  • domain assumption The signal is in the linear perturbation regime at Δt ≥ 8M after the peak
    Section III: the paper relies on refs [11-15] to claim 8M-10M is safe; this assumption is exactly where the evidence decays fastest, and it is not validated for this event in the text.
  • domain assumption Noise is stationary and Gaussian over the analyzed stretch, and the noise PSD is correctly estimated by the pipeline of Wang et al. [28]
    Section II defers noise estimation to the companion paper; the F-statistic likelihood and all Bayes factors depend on it.
  • domain assumption Approximating spheroidal harmonics by spin-weighted spherical harmonics is adequate here
    Section II states this approximation explicitly; it introduces a systematic error in mode amplitudes that is not quantified.

pith-pipeline@v1.3.0-alltime-deepseek · 8741 in / 18883 out tokens · 185686 ms · 2026-08-04T20:16:28.371823+00:00 · methodology

0 comments
read the original abstract

The properties of a remnant black hole can be probed by analyzing the gravitational waves emitted during its ringdown phase. This signal provides a direct test of general relativity in the strong-field regime. In this study, we apply both a time-domain F-statistic framework and full Bayesian time-domain sampling to the ringdown of GW231028\_153006. We report decisive evidence for multimode content, specifically identifying both the first overtone ($\ell|m|n=221$) and the higher order ($\ell|m|n=210$). The detection of the $221$ mode is statistically significant, achieving a Bayes factor of $\sim 189.2$ and an amplitude exclusion from zero at $>7\sigma$ credibility for an analysis beginning at $10\,M$ postpeak. These findings are rigorously validated against the numerical relativity injection SXS:BBH:1282, which confirms that such multimode features are physically expected for a remnant with the inferred high spin and mass ratio. The inclusion of the overtone mode allows for precise constraints on the remnant's properties, yielding a redshifted final mass of $246.2^{+22.3}_{-22.4}\,{\rm M}_{\odot}$ and a final spin of $0.81_{-0.10}^{+0.07}$ (at $90\%$ credibility), consistent with full inspiral-merger-ringdown predictions. A test of the no-hair theorem, enabled by this robust multimode detection, shows consistency with general relativity.

Figures

Figures reproduced from arXiv: 2509.08657 by Hai-Tian Wang.

Figure 1
Figure 1. Figure 1: FIG. 1: Bayesian evidence for various two-mode QNM com [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Posterior distributions for the redshifted final mass [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Results for the 220 + 221 mode analysis as a function of the analysis start time ∆ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Tests of the no-hair theorem using the 220 + 221 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The posterior distributions of the redshifted final mass [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. GW250114 reveals black hole horizon signatures

    gr-qc 2025-10 conditional novelty 6.0

    The merger signal of GW250114 contains a residual 'direct wave' component whose frequency and damping match the remnant horizon's rotation frequency and surface gravity.

Reference graph

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    R. Abbottet al.(KAGRA, VIRGO, LIGO Scientific), Astrophys. J. Suppl.267, 29 (2023), arXiv:2302.03676 [gr-qc]. Appendix A: Results of Different Combinations To supplement the model comparison discussed in the main text, this appendix presents a detailed ex- amination of the posterior distributions for the final mass and spin under various ringdown models. ...

    Pith/arXiv arXiv 2023