Ringdown Overtones and Mode Identifiability

Rapidly damped Kerr overtones are present in numerical-relativity ringdowns, but their presence in a basis is not the same as their identification in detector data. At the evidence cutoff of 2026-08-20, GW250114 provides the strongest event-level evidence that an early postmerger signal needs at least two Kerr-consistent modes for roughly one cycle, and GW231028 supplies a separate peer-reviewed positive claim at moderate signal-to-noise ratio. The earlier GW150914 overtone claim is not robust to full time and sky marginalization. Overtone identifiability is therefore supported in particular high-information events, not established as an event-independent fact.

Helpful background. Overtones and Mode Identifiability develops damped-mode conventions, start-time dependence, and generic inference logic. This page compares the dated event evidence and exact public products.

What counts as identifying an overtone

A sum of damped sinusoids can improve a fit for several reasons. A true $(\ell,m,n)=(2,2,1)$ linear quasinormal mode is one; higher angular modes, nonlinear combinations, merger leakage, calibration error, glitches, and colored nonstationary noise are others. Identification requires more than a Bayes factor for “one sinusoid versus two.” The added component’s frequency and damping time should be Kerr-consistent, stable over an admissible start-time range, calibrated in realistic injections, and distinguishable from competing components after nuisance marginalization.

This assessment separates numerical-relativity basis adequacy from detector-data identification; fixed from marginalized merger time and sky; time- from frequency-domain likelihoods; and a required second component from a uniquely labelled overtone. Priors, sample rate, PSD estimation, gating or inpainting, peak-time definition, and the set of searched modes are part of the claim.

Assessment at 2026-08-20	Meaning
Question status	Partially resolved
Evidence status	Supported
Confidence	Moderate because exceptional events are persuasive but mode identity remains model-conditional
Domain	Event-level postmerger analyses of GW150914, GW231028, and GW250114 with declared start-time and noise treatment
What could change the conclusion	A higher-quality event, blind injection campaign, or method-independent identifiability analysis

Entry project: test how a mode claim changes with start time

This topic suits a student who enjoys inference and is willing to study noise conditioning as carefully as Kerr spectra. Preparation includes damped sinusoids, covariance matrices, Bayesian priors, and Monte Carlo calibration. A fit to one numerical waveform is a laptop exercise; credible detector-level evidence needs sampler diagnostics, off-source noise, and a supervisor familiar with gravitational-wave likelihoods.

Begin with Giesler et al. 2019, Figs. 1–5, extracting exactly what the noise-free fit demonstrates. Read Correia et al. 2024, full time-and-sky marginalization analysis next and list the nuisance parameters absent from the simpler exercise. For an inspectable data baseline, use the official LVK GW250114 release, Zenodo 17018009, analysis-specific README files or the RD plotting products in LVK P2600410-v1. Reproduce one released start-time plot before writing a new likelihood.

The finite deliverable is that regenerated plot plus a controlled one-mode/two-mode injection notebook. Fix the tested start times, identification statistic, decision threshold, and priors in advance. First use simulated noise and known signals, including one-mode null injections to calibrate the false-positive rate; report recovered amplitudes and false identifications across repeated realizations. This training notebook does not reproduce the event analysis or measure a new overtone.

A candidate extension, with novelty unchecked, is to repeat the same frozen test with real off-source noise and a competing early-time component. The question is whether apparent extra-mode evidence survives those specific changes. Stop if the likelihood cannot recover its own injections, results depend on sampling resolution, or a favorable start time was selected after looking at the answer. Address those failures before interpreting any event. A rising fit quality alone is not an identification criterion.

What simulations and loud events establish

Numerical relativity makes the theoretical case clear. Multiple $(2,2,n)$ overtones reconstruct the dominant harmonic from near its peak and improve recovery of the remnant mass and spin Giesler et al. 2019, Figs. 1–5 and remnant-recovery analysis. Later high-accuracy simulations find stable overtone amplitudes and simultaneous nonlinear contributions in the early ringdown Giesler et al. 2025, Figs. 1–14. These calculations show that an overtone expansion is physically motivated. Noise-free waveform fits do not supply a detector false-alarm rate.

GW250114 changes the observational balance. The official collaboration analysis finds that at least two postmerger components are required and that the Kerr fundamental plus first overtone describes about one early cycle, with checks across start times, numerical-relativity comparisons, and more than one analysis construction LVK 2026, postmerger two-mode analysis, stability plots, and supplemental tests. Its network signal-to-noise ratio of about 76 makes it qualitatively different from GW150914. The result is a strong, model-conditional identification, not proof that every early damped component is uniquely linear.

GW231028 provides a complementary case. Wang reports a $(2,2,1)$ Bayes factor near 189 and amplitude exclusion above $7\sigma$ for an analysis beginning $10M$ after peak, cross-checking an $\mathcal F$-statistic implementation with full Bayesian time-domain sampling and SXS:BBH:1282 injections Wang 2026, Fig. 1, Table I, § IV, and Appendix B. It is peer reviewed and uses a separate event, but remains one author and pipeline lineage.

Results and open questions at 2026-08-20

Claim or evidence	What it supports	What it does not establish
Near-peak NR overtone fits	Physical presence and basis adequacy of overtones	Detector identifiability or false-positive control
GW150914 original peak-start analysis	A historically important positive claim under fixed choices	Robust evidence after merger-time and sky marginalization
Three GW150914 reanalyses	Strong sensitivity to conditioning, timestamp, start time, and nuisance treatment	Absence of overtones in general relativity
GW231028 two-method analysis	A second positive event and publicly archived analysis	Fully independent pipeline confirmation or global trials control
Official GW250114 multi-analysis result	Strongest high-SNR evidence for two Kerr-consistent modes	Universal uniqueness against every nonlinear merger model
GWTC-5 TGR products	Current catalog context and exact public archives	A universal overtone catalogue with one selection function

The loud-event evidence outweighs the paper count around GW150914, while the GW150914 history determines how cautiously the loud-event Bayes factors must be interpreted.

Strongest competing interpretations

The positive interpretation is that the short-lived component in GW250114 and the reported component in GW231028 have the expected Kerr frequencies, damping, decay with start time, and numerical-relativity counterparts. On this view, black-hole spectroscopy has moved from “suggestive fit” to event-level overtone measurement.

The cautious interpretation is narrower: early-time models need extra degrees of freedom, but nonorthogonal quasinormal modes can trade power, and linear overtone labels compete with nonlinear or merger components. The GW231028 paper itself tests eight alternatives, identifies a nominally decisive $(3,2,0)$ result as spectral leakage, and notes that different mode combinations can reproduce the signal Wang 2026, § IV and supplemental discussion of the $(3,2,0)$ false positive. For GW250114, high signal-to-noise ratio and collaboration cross-checks favor the Kerr label, yet the uniqueness statement remains conditional on the compared model family.

Counterexamples, null results, and failed routes

GW150914 is the decisive counterexample to an easy detection rule. The original peak-start analysis reported evidence for an overtone Isi et al. 2019, Bayesian comparison and peak-start result. Cotesta and collaborators found that support changed sharply under sub-damping-time start shifts and neighboring-noise injections Cotesta et al. 2022, start-time scan and injection study. Correia, Wang, Westerweck, and Capano then marginalized merger time and sky location and obtained low evidence Correia et al. 2024, full-marginalization analysis and conclusion.

A later gating/inpainting study explains part of the disagreement: sample rate, timestamp precision, and PSD resolution can recover moderate support when extrinsic quantities are fixed, but full marginalization again lowers the factor toward unity Wang et al. 2025, conditioning tests and conclusion. This history refutes robust identification in GW150914 under the stronger nuisance treatment. It does not refute overtone physics or the higher-information GW250114 result.

From a required component to a mode label

The best operational hierarchy has three levels. First, does a second component improve predictive performance under injections and off-source noise? Second, is its complex frequency consistent with the Kerr spectrum inferred from the same or independent remnant parameters? Third, is the label stable when nonlinear modes, higher harmonics, and merger-informed models are added? Only the third level supports strong spectroscopic identity.

Start time cannot be optimized silently. Beginning too early risks merger-model error; beginning too late removes the rapidly decaying signal. A rigorous analysis reports the entire start-time curve with merger-time uncertainty and accounts for selection of the most favorable point. The searched-mode family likewise determines a look-elsewhere penalty. These choices are physics-bearing nuisance parameters, not plotting preferences.

What would change the assessment

A blind, preregistered injection campaign in real off-source detector noise would be decisive. It should include Kerr overtones, nonlinear modes, higher angular modes, merger-model errors, calibration excursions, glitches, and no-overtone controls. Independent teams should freeze the start-time treatment, tested-mode set, priors, and false-identification criterion before unblinding, then apply unchanged pipelines to GW231028 and GW250114.

Stable recovery of the same complex frequency and amplitude across independent time- and frequency-domain methods, with calibrated family-wise false-identification rates, would raise confidence. A failure to recover injections at the claimed strength, or a competing nonlinear model with equal predictive performance and no overtone, would lower it.

Research checklist

• Pin strain and calibration releases, detector-frame and geocenter times, sky posterior, PSD segment, sample rate, and line/gate/inpaint operations.
• Define the peak-time waveform model and marginalize its uncertainty rather than fixing a favorable timestamp.
• Declare the complete searched-mode set, priors, amplitude reference time, and Kerr frequency convention.
• Plot evidence, recovered frequencies, and amplitudes across start time; include off-source noise and no-overtone injections.
• Compare at least one independently coded time-domain likelihood with a frequency-domain or otherwise structurally distinct method.
• Test nonlinear modes, higher angular modes, and flexible merger residuals, not only fundamental-versus-overtone models.
• Report family-wise false-identification and coverage, not only the event’s maximum Bayes factor.
• No independent likelihood rerun was performed for this assessment; the public products below define a reproducible prescription.

Source and data map

The Giesler papers establish the numerical-relativity basis. Isi et al. provide the original GW150914 claim; Cotesta et al., Correia et al., and Wang et al. provide adverse and methodological reanalyses. Wang’s 2026 article and Zenodo artifact 17115893 v1.0 provide the GW231028 result. The official GW250114 article is paired with Zenodo release 17018009.

Current catalog context is the GWTC-5 tests-of-general-relativity manuscript DCC P2500781-v17 and exact analysis archive DCC P2600410-v1, especially its RD, QNMRF, and pSEOB products. These releases can reproduce figures and posteriors inside their pipeline families. They do not constitute an external method or test every nonlinear alternative.

Return to the seminar

Record this page’s worksheet, return to Case 3 in the Research Seminar, then continue to Case 4 — Horizon-scale imaging tests of Kerr. Read its seminar instructions before treating it as a reproduction candidate.

References

• Correia, A., Wang, Y.-F., Westerweck, J., and Capano, C. D. “Low evidence for ringdown overtone in GW150914 when marginalizing over time and sky location uncertainty.” Physical Review D 110, L041501 (2024). DOI.
• Cotesta, R., Carullo, G., Berti, E., and Cardoso, V. “Analysis of ringdown overtones in GW150914.” Physical Review Letters 129, 111102 (2022). DOI.
• Giesler, M., et al. “Overtones and nonlinearities in binary black hole ringdowns.” Physical Review D 111, 084041 (2025). DOI.
• Giesler, M., Isi, M., Scheel, M. A., and Teukolsky, S. A. “Black hole ringdown: the importance of overtones.” Physical Review X 9, 041060 (2019). DOI.
• Isi, M., Giesler, M., Farr, W. M., Scheel, M. A., and Teukolsky, S. A. “Testing the no-hair theorem with GW150914.” Physical Review Letters 123, 111102 (2019). DOI.
• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. “Black hole spectroscopy and tests of general relativity with GW250114.” Physical Review Letters 136, 041403 (2026). DOI; manuscript DCC P2500461-v7.
• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. “Black Hole Spectroscopy and Tests of General Relativity with GW250114.” Data release v1, Zenodo (2025). DOI.
• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. “Data release for GWTC-5.0: Tests of General Relativity.” DCC P2600410-v1 (2026). Official archive.
• Wang, H.-T. “First Overtone Mode in the Ringdown Signal of GW231028.” Physical Review Research 8, 033065 (2026). DOI; open preprint v2.
• Wang, H.-T., et al. “Revisiting the evidence for the ringdown overtone in GW150914 with gating and inpainting.” Physical Review D 112, 083023 (2025). DOI.