{"id":"9883d4ee-46c6-4d60-b8c7-14eab19d11de","arxiv_id":"2509.02047","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"The ringdown of GW231123 contains a detectable 200 quasinormal mode in addition to the fundamental 220 mode, with log10 Bayes factor 5.3, and the inferred remnant mass and spin agree with general relativity.","lead":"An analysis of a gravitational wave event reports a second 'ringing' mode in a black hole's post-merger signal, with strong statistical support. The work also upgrades a faster search method so it can produce model-comparison evidence, opening new tests of general relativity on real data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"A200≈20×A220 at Δt=12M is inconsistent with a linear-perturbation origin; the fitted '200 mode' may be absorbing merger nonlinearity, which would invalidate the detection and all derived conclusions. An IMR/NR injection-recovery test would settle it.","rationale":"I read the paper's central claim as an empirical statement about GW231123's ringdown: a 220+200 Kerr QNM superposition with log10 BF≈5.3 at Δt=12M, leading to remnant parameters consistent with IMR analyses and a no-hair null result. The load-bearing premise is that the chosen window is in the linear regime, so the recovered modes are genuine Kerr QNMs. The weakest point is not the 12M start time per se but the recovered amplitudes: A200/A220≈20 at 12M. With τ200≈6M, the linear model implies an unphysically large amplitude at the merger peak, comparable to or exceeding the total observed signal strength. This is the signature of a fast-decaying template absorbing the nonlinear merger-ringdown transient at the start of the window—the failure mode identified by Baibhav, Nee, Zhu and others, whose work the paper cites. The authors' own Fig. 4 shows the 200 frequency is biased away from GR at Δt=8M and 10M, showing that the transient contaminates the fit up to at least 10M. I therefore regard this as more load-bearing than the reader's primary concern (fixed sky location and same-model comparison): those affect the parameter-consistency argument but do not by themselves falsify the detection, whereas a nonlinearity artifact would falsify the entire claim. I credit the paper's real strengths: two independent methods agree (log10 BF 5.3 vs 5.9), the F-statistic evidence reconstruction is a novel contribution, the inferred remnant matches both NRSur7dq4 and SEOBNRv5PHM IMR results, and Abac et al.'s independent 200-mode evidence at later times is corroborative. But those do not settle linearity at 12M, since Abac started later and found A200/A220≈3. The decisive, concrete check is injection-recovery on IMR/NR waveforms consistent with GW231123; no such test is presented anywhere in the paper. Until it is run, the detection claim remains conditional, and the condition should be the injection test.","tokens_in":15714,"tokens_out":27306,"duration_ms":285578,"concrete_test":"Inject the maximum-likelihood NRSur7dq4 waveform for GW231123 (the same model that fixes RA/DEC/ψ/tpol in Sec. II) into the real GW231123 noise realization and into ~100 Gaussian-noise realizations with the paper's ACF; run the identical TTD and F-statistic 220 and 220+200 analyses over Δt=8–18M. If the injected IMR waveform—which has negligible linear-regime 200 content—yields log10 B_{220+200/220}≳3 and A200/A220≳1 at Δt=12M, the detection is a nonlinearity artifact. Cross-check with a high-mass/high-spin NR waveform (e.g., SXS catalog) to rule out waveform-model dependence.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim—detection of a genuine 200 Kerr QNM at Δt=12M in the linear regime—requires the fitted 200 mode to be a small, linear perturbation of the remnant. The recovered ML amplitudes are A200=2.9e-20 vs A220=1.4e-21 at Δt=12M for Fs (3.9e-20 vs 3.1e-21 for TTD), i.e. A200/A220≈20. Since the m=0 mode's damping time for χf≈0.84 is τ≈6M (Schwarzschild-like; Refs. [44,45]), the linear model extrapolates to A200(peak)≈2e-19 at the merger peak—comparable to or larger than the total observed signal strength of GW231123, impossible for a subdominant linear mode. The authors flag this anomaly themselves ('The pronounced dominance of the 200 mode raises questions about its origin', Sec. III) and offer exotic explanations (precession, eccentricity, boson stars) that are not tested. The established alternative, documented in the references they cite (Baibhav et al. 2023 [18], Nee et al. 2023 [19], Zhu et al. 2024 [20]), is that early-time fits of fast-decaying modes absorb the nonlinear merger transient. Consistent with that, their own no-hair test (Fig. 4) shows δf200 deviating from GR at Δt=8M and 10M—nonlinear contamination 2M before the preferred start time, in a mode recovered at 20× the fundamental amplitude. If the 200 template is fitting a transient rather than a QNM, the log10 BF=5.3 detection, the inferred (Mf,χf), the claimed IMR consistency, and the no-hair null are all consequences of the same artifact.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a Bayesian time-domain ringdown analysis of GW231123 using two methods: a traditional stochastic sampler (TTD) and a newly extended F-statistic framework. It reports that the model containing the 220 and 200 quasinormal modes is strongly preferred over a 220-only model, with log10 Bayes factor 5.3 (F-statistic) at Δt=12M after the polarization peak, and that the two methods agree. The inferred remnant parameters are Mf=305.6^{+35.7}_{-47.3} Msun and χf=0.84^{+0.07}_{-0.14} (F-statistic), overlapping with full IMR results. A no-hair test allowing deviations in the 200 mode frequency and damping time finds no deviation at the preferred start time. A search for a third mode finds no compelling evidence.","tokens_in":16227,"tokens_out":9246,"duration_ms":104916,"significance":"If the detection is real, it would be an important result: a higher harmonic (200) mode in a ringdown, enabling a multimode no-hair test. The extension of the F-statistic to compute evidences and posteriors is a useful methodological contribution, and the cross-check between TTD and F-statistic is a strength. The authors are candid about the anomaly of the large 200 amplitude. However, the central claim depends on the assumption that at Δt=12M the signal is a linear superposition of Kerr QNMs; the paper does not yet provide the validation needed to exclude the alternative explanation that the fast-decaying 200 template absorbs the nonlinear merger transient.","major_comments":[{"comment":"The linear-regime assumption at Δt=12M is load-bearing and is not validated. The recovered amplitudes are A200=(2.9–3.9)e-20 and A220=(1.4–3.1)e-21, so A200/A220≈20. For the m=0 mode with τ≈6M, the corresponding peak amplitude would be far larger than the 220 mode, which is difficult to reconcile with a subdominant linear perturbation. The authors themselves write that 'The pronounced dominance of the 200 mode raises questions about its origin' and offer untested explanations. Moreover, Fig. 4 shows δf200 deviating from GR at Δt=8M and 10M, demonstrating sensitivity to non-linear contamination at nearby start times. I ask for an NR/IMR injection-recovery test showing that (i) a known 200 mode with moderate amplitude is recovered without bias at 12M, and (ii) a non-linear merger residual does not produce a spurious 200 detection with log10 BF≈5. Without such a test, the detection and the","section":"Sec. III; Fig. 4"},{"comment":"The headline log10 BF=5.3 is the maximum over a scan of start times (8 to 18M in 2M steps) and seven mode combinations. No trials-factor or look-elsewhere correction is applied. This inflates the statistical significance of the 200 detection. Please report the evidence integrated over the scan or a corrected Bayes factor. If the trials factor is applied, the evidence may remain large, but it must be quantified.","section":"Sec. II; Fig. 1"},{"comment":"The analysis fixes RA, DEC, ψ, and the polarization peak time to the NRSur7dq4 maximum-likelihood values and then compares the resulting posteriors with NRSur7dq4 IMR posteriors. This makes the claimed consistency partially built in and can bias ringdown amplitudes and evidence if the extrinsic parameters are inaccurate. A marginalization over these nuisance parameters, or an injection test demonstrating that fixing them does not bias the 200 amplitude and evidence, is needed. Comparing with SEOBNRv5PHM is helpful but is not a substitute.","section":"Sec. II"},{"comment":"The F-statistic evidence reconstruction is a new contribution, but no validation on simulated injections is shown. The cross-check with TTD is reassuring, but an explicit test that the importance-sampling evidence estimator is unbiased for the adopted priors and ACF would strengthen the methodological claim and the model comparison.","section":"Appendix A, Eqs. (A13)–(A15)"}],"minor_comments":[{"comment":"The caption says '220 + 201' in the bottom-right panel; it should be '220 + 200'.","section":"Fig. 5 caption"},{"comment":"Typo: 'NRSurd7q4' should be 'NRSur7dq4'.","section":"Introduction"},{"comment":"The statement that the 200 amplitude is 'approximately an order of magnitude larger' is imprecise; the maximum-likelihood ratio is about 20.","section":"Sec. III"},{"comment":"The sentence 'To isolate the ringdown signal and mitigate contamination from the pre-merger phase, we fix the sky location...' is confusing: fixing extrinsic parameters does not by itself remove pre-merger contamination. Please clarify.","section":"Sec. II"},{"comment":"The no-hair deviation parameters δf200 and δτ200 are introduced only in words; please include their definitions in the model equations and specify their priors.","section":"Sec. II / Appendix A"}],"recommendation":"major_revision","confidential_remarks":"This is a borderline case. The anomaly of A200≈20×A220 and the lack of injection-recovery tests make me unable to accept the paper as is. I would not reject because the methods are sound and the issue is testable, but the authors must either rule out the nonlinear-transient interpretation or substantially soften the detection claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the methodological core is worth your time, but the headline detection is shaky. The F-statistic extension is a real contribution: they show how to compute Bayesian evidence and reconstruct posteriors for the analytically maximized linear parameters, which prior F-stat ringdown papers didn't do. That the two independent time-domain methods agree is also a point in their favor. And to their credit, they flag the big anomaly themselves: the fitted 200 amplitude is an order of magnitude larger than the 220 at 12M, and they float precession, eccentricity, even boson stars.\n\nBut that amplitude ratio is exactly the problem. For a Kerr remnant with χf ≈ 0.84, the 200 mode damps on a timescale of roughly 6M, so an observed ratio A200/A220 ≈ 20 at Δt = 12M extrapolates to a peak ratio of about 100. That is not a subdominant linear perturbation; it is the dominant signal. The literature they cite (Baibhav, Nee, Zhu) already makes the case that early-time fits of fast-decaying modes absorb merger nonlinearity, and their own no-hair test shows δf200 deviating at 8 and 10M, which is consistent with contamination. Their preferred 12M start is not clearly past it. Without an injection-recovery test or noise-only trials, I can't take the log10BF = 5.3 at face value.\n\nThere are also two standard soft spots: they fix sky location, polarization, and peak time to the NRSur7dq4 maximum-likelihood values, then compare against that same model's posteriors; and the headline Bayes factor is the maximum over a start-time/mode scan with no trials factor. Neither kills the result by itself, but both push toward caution.\n\nSo my honest take: the F-statistic evidence formalism is a solid piece of methods work and will be useful beyond this event. But the physical detection claim needs another paper's worth of testing—inject realistic IMR waveforms, check whether the 200 appears in noise, and address the amplitude ratio head-on. It deserves a serious referee, because if the detection survives, it's important; if it doesn't, the method still stands. I'd send it to review with a request for those tests.","headline":"A clever new F-statistic evidence formalism wrapped around a ringdown detection whose headline claim looks physically doubtful because the 200 mode would have to be about a hundred times the fundamental at the merger peak.","tokens_in":16719,"tokens_out":3727,"would_cite":true,"duration_ms":42842,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.30.-w","04.70.-s"],"model":"deepseek-v4-flash","headline":"The ringdown of GW231123 contains the fundamental 220 quasinormal mode and a statistically significant 200 mode, with log10 Bayes factor 5.3 at a start time 12 M after peak, and the pair passes a no-hair test.","keywords":["black hole spectroscopy","quasinormal modes","ringdown","GW231123","F-statistic","Bayes factor","no-hair theorem","gravitational wave data analysis"],"falsifier":"Re-analyze the same data while marginalizing over sky location, polarization angle, and peak time rather than fixing them, and check whether the log10 Bayes factor for 220+200 over 220 stays above about 3 and the mass-spin posterior still overlaps the inspiral-merger-ringdown posteriors; alternatively, inject a 220-only signal into the same noise realization and ask how often the pipeline reports comparable 200-mode evidence.","tokens_in":15605,"feed_emoji":"🕳️","tokens_out":8651,"duration_ms":89066,"temperature":0.7,"pith_summary":"The paper analyzes the ringdown of the binary black hole merger GW231123 and claims that, in addition to the expected fundamental 220 quasinormal mode, the signal contains a statistically significant 200 mode. The evidence peaks at a start time 12 M after the peak, with log10 Bayes factors of 5.3 (F-statistic) and 5.9 (traditional time-domain) over a fundamental-mode-only model; at the maximum-likelihood point the 200 amplitude is about an order of magnitude larger than the 220 amplitude. Using the two modes, the authors recover a redshifted remnant mass of 305.6^{+35.7}_{-47.3} solar masses and spin 0.84^{+0.07}_{-0.14}, consistent with full inspiral-merger-ringdown analyses with two independent waveform models, and a no-hair test returns no deviation from general relativity. If correct, this would be a rare secure detection of a subdominant ringdown mode inside the linear regime and a demonstration that the F-statistic can do full Bayesian model comparison.","feed_headline":"GW231123 ringdown shows a second black-hole tone at 200,000-to-1 odds","feed_subtitle":"A second ringdown tone at 18 ms after peak agrees with whole-signal models and passes Einstein's no-hair test.","key_machinery":"The load-bearing mechanism is the F-statistic extended to time-domain ringdown analysis. The quasinormal-mode waveform is split into linear amplitude/phase parameters and nonlinear parameters such as remnant mass, spin, inclination, sky location, and peak time; the linear parameters are maximized analytically, giving a profile likelihood in a low-dimensional nonlinear parameter space. The paper adds a Gaussian reconstruction of the linear-parameter posteriors plus an importance-sampling formula for the full Bayesian evidence, making model comparison possible. The central physical object is the (ell, |m|, n) = (2, 0, 0) Kerr quasinormal mode, the higher harmonic whose presence is claimed in t","core_discovery":"The central claim is that GW231123's ringdown contains at least two Kerr quasinormal modes: the fundamental 220 mode and the higher harmonic 200 mode, with the latter strongly preferred by the data at a start time 12 M after the polarization peak. The paper estimates the detection significance as log10 Bayes factor 5.3 with the F-statistic and 5.9 with the traditional time-domain sampler, and finds the 200-mode amplitude roughly ten times the 220-mode amplitude at the maximum likelihood. From the two-mode fit it derives remnant mass and spin, reports consistency with the NRSur7dq4 and SEOBNRv5PHM inspiral-merger-ringdown posteriors, and finds the frequency and damping time of the 200 mode co","pith_inferences":["Because the sky location, polarization angle, and peak time are fixed to the NRSur7dq4 maximum-likelihood values rather than marginalized, the 200-mode evidence could change under a fully marginalized analysis; re-running with those parameters varying would give the cleanest test.","The 200-to-220 amplitude ratio at 12 M is so large that it implies an even larger ratio at earlier times unless the 200 mode decays much faster; this points toward a strongly precessing or non-quasi-circular source, and comparing the measured mode amplitudes with precessing numerical-relativity templates would discriminate among the scenarios the paper lists.","The same F-statistic evidence and posterior reconstruction could be applied to other disputed ringdown claims, such as the earlier subdominant-mode detection in GW190521, where the conservative start time was a central issue.","If the 200-mode dominance is reproduced by independent pipelines, it would imply that some binary black holes ring down with mode energies quite different from quasi-circular aligned-spin expectations, informing ringdown templates for future detectors."],"forward_implications":["GW231123 becomes a two-tone black-hole spectroscopy source: the ringdown alone fixes the remnant's mass and spin, and those values agree with full inspiral-merger-ringdown analyses without the bimodal posteriors seen in fundamental-mode-only fits.","Start times as early as 12 M after peak can be used for ringdown model selection when subdominant modes are included, extending the usable ringdown data.","The no-hair test with the two detected modes places a direct observational constraint on the 200-mode frequency and damping time, and finds them compatible with Kerr predictions.","The F-statistic evidence-reconstruction formalism makes Bayesian model comparison between different quasinormal-mode combinations computationally practical, so scanning many mode combinations becomes feasible.","No three-mode combination, including 220+200+330, beats the two-mode model at safe start times, so the claimed spectrum is exactly two resolved tones."],"supporting_citations":[{"why":"Supplies the GW231123 event, the IMR maximum-likelihood values used to fix sky location, polarization angle, and peak time, and the comparison IMR posteriors.","marker":"[33]"},{"why":"Introduces the time-domain F-statistic for ringdowns whose evidence and posterior reconstruction this paper extends.","marker":"[14]"},{"why":"Establishes the efficiency and robustness of the F-statistic ringdown analysis, providing the performance baseline.","marker":"[32]"},{"why":"Provides the time-domain likelihood and ACF-based noise covariance validation used by both the TTD and F-statistic analyses.","marker":"[13]"},{"why":"Defines the NRSur7dq4 waveform model used both to set extrinsic parameters and as an IMR comparison posterior.","marker":"[34]"},{"why":"Defines the independent SEOBNRv5PHM waveform model used to cross-check remnant mass and spin consistency.","marker":"[35]"},{"why":"Supports the linear perturbation framework at early post-merger times by showing higher overtones and second-order modes in numerical waveforms.","marker":"[22]"},{"why":"Motivates the physical origin of the detected 200 mode by showing that strong precession amplifies subdominant modes.","marker":"[36]"}],"fun_headline_variants":["GW231123 ringdown reveals a second black-hole tone","Second ringdown tone in GW231123 passes no-hair test","Gravitational wave GW231123 shows higher harmonic mode","Higher harmonic detected in GW231123 ringdown","Two-tone ringdown in GW231123 matches Einstein's prediction"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The detection rests on assuming that at 12 M after peak (about 18 ms) the signal is a linear Kerr ringdown, and that fixing sky location, polarization angle, and peak time to the NRSur7dq4 maximum-likelihood values does not bias the comparison.","fun_headline_variants_meta":{"raw":{"variants":["GW231123 ringdown reveals a second black-hole tone","Second ringdown tone in GW231123 passes no-hair test","Gravitational wave GW231123 shows higher harmonic mode","Higher harmonic detected in GW231123 ringdown","Two-tone ringdown in GW231123 matches Einstein's prediction"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000629,"raw_usage":{"total_tokens":2787,"prompt_tokens":828,"completion_tokens":1959,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":572,"completion_tokens_details":{"reasoning_tokens":1876}},"tokens_in":572,"tokens_out":1959,"duration_ms":14082,"temperature":1.0,"reasoning_tokens":1876,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T11:56:24.829735+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-analyze the same data while marginalizing over sky location, polarization angle, and peak time rather than fixing them, and check whether the log10 Bayes factor for 220+200 over 220 stays above about 3 and the mass-spin posterior still overlaps the inspiral-merger-ringdown posteriors; alternatively, inject a 220-only signal into the same noise realization and ask how often the pipeline reports comparable 200-mode evidence.","supporting_citations":[{"cited_title":"Effect of Noise Estimation in Time-Domain Ringdown Analysis: A Case Study with GW150914","cited_arxiv_id":"2311.13300","evidence_quote":"Provides the time-domain likelihood and ACF-based noise covariance validation used by both the TTD and F-statistic analyses."}],"review_version":1}