{"id":"b8644baf-edc5-42b6-a2af-731ad631d2e9","arxiv_id":"2505.10756","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Zonal-flow dynamo wave patterns and a near-surface rotation gradient close to -1 are confirmed across GONG, MDI, and HMI helioseismic data using a new time-radius inversion method.","lead":"This paper analyzes decades of helioseismic data to map bands of faster and slower solar rotation as they travel through the convection zone over the solar cycle. It introduces an inversion method that smooths in time and radius together, and finds the same dynamo-wave patterns in zonal acceleration and zonal flow across three independent data sets.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central dynamo-wave detection lacks a null test and a same-epoch cross-instrument zonal-flow comparison; Section 3.2's admitted high-latitude systematics leave open that the 5-6 yr inclined pattern is a regularization/systematics artifact rather than a confirmed solar signal.","rationale":"The reader's weakest assumption concerns systematics in the splitting coefficients. I partially agree but locate the load-bearing issue one step earlier: the time-dependent regularized inversion itself is the only pipeline used for the main maps, and no null test is provided. A synthetic forward-inversion check with a dynamo-model input (Figure 12) is real evidence, but it tests recovery of a known pattern, not the false-positive rate under the same regularization. Since the paper explicitly reports instrument-dependent systematics at high latitudes and the key dynamo-wave maps are GONG-only (or MDI+HMI combined), the claim of cross-instrument confirmation is broader than the figures demonstrate. The correct response is to keep CONDITIONAL: request the null test and a same-epoch cross-instrument zonal-acceleration comparison. There is no reason to reject: multi-window GONG persistence and the independent MDI/HMI Figure 2 give genuine support. UNCHANGED is appropriate because the reader's conditional verdict already captures the needed additional validation.","tokens_in":16756,"tokens_out":4820,"duration_ms":52912,"concrete_test":"Re-run the Section 2.2 time-dependent RLS inversion (same lambda_r, lambda_t, B-spline knots, data cadence, and noise level) on synthetic a-coefficients generated from a fixed, time-independent rotation profile plus observationally realistic noise, and also on a copy of the observed a-coefficients with time segments randomly shuffled. If either null case yields inclined 5-6 yr bands in zonal acceleration with amplitudes comparable to Figures 3-5 (roughly 0.2-0.5 m/s), the central detection must be regarded as an inversion or systematics artifact; if both null cases produce only unstructured noise, the regularization concern is settled.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing assertion (Section 4) is that dynamo-wave signatures in zonal flow and acceleration are robust across GONG, MDI and HMI, with a 5-6 yr low-latitude rise time. The weakest link is not the forward-model check itself but the absence of any demonstration that the inclined patterns in Figures 3-5 would not be produced by the inversion procedure from data without such a pattern. Equation 6 adds first-derivative time regularization (lambda_t) and second-derivative radial regularization (lambda_r); no L-curve, grid scan, or null realization is shown for the main choices (f=g=1). Figure 12 validates recovery only on a dynamo-model input from the same modeling family used to interpret the data, so it does not establish that artificial wave-like structure is absent. The paper itself states in Section 3.2 that high-latitude differences 'exceed significantly' between instruments and 'indicate potential systematics' (Figure 9), and in Section 4 that mean gradient discrepancies exist above 60 degrees. If similar, smaller systematics contaminate lower latitudes or specific depths, the ~0.5 m/s zonal-flow signal and the tilted 5-6 yr branch could be biased. Moreover, although the abstract and conclusions claim three-instrument confirmation, the zonal-flow/acceleration maps shown (Figures 3-7) are exclusively GONG, except Figure 2 which combines MDI+HMI; no same-epoch cross-instrument map of the wave pattern is presented. The post hoc MDI l<120 cut and GONG l<150 cut further complicate direct comparison. These gaps do not disprove the detection, but they make 'unambiguously confirming' outrun the shown evidence.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a time-dependent regularized least-squares inversion that carries out the inversion jointly in radius and time using B-spline basis functions, thereby avoiding separate post-hoc temporal smoothing. The method is applied to p-mode frequency-splitting coefficients from GONG, MDI, and HMI, using both the Korzennik (2023) sets and JSOC pipeline products at several time-window lengths (1x72-day through 8x72-day). The authors report dynamo-wave-like signatures in both zonal flow and zonal acceleration throughout the convection zone, with a low-latitude branch that takes approximately 5-6 years to rise from the base of the convection zone to the surface, and a nearly vertical pattern at high latitudes. They also analyze the dimensionless radial gradient of rotation in the near-surface shear layer, finding values near -1 that increase with depth and show torsional-oscillation-like temporal variations, while acknowledging high-latitude results as inconclusive. The inversion is validated with forward-modeled synthetic splittings from the Pipin & Kosovichev (2020) dynamo model.","tokens_in":17100,"tokens_out":6553,"duration_ms":59591,"significance":"If the central detection holds, the paper provides a useful methodological contribution with the first simultaneous time-radius RLS inversion for global helioseismology, and it places a concrete constraint on dynamo-wave propagation: a 5-6 year rise time at low latitudes. The use of multiple independent instruments and window lengths strengthens the earlier detection by Kosovichev & Pipin (2019). The paper also honestly reports high-latitude inter-instrument discrepancies and inconclusive high-latitude gradient results. However, the strong claims in the abstract and conclusions are not fully supported by the displayed evidence: the main pattern figures come from GONG only, no null test is shown for the temporal regularization, and the central figures do not display error bars. The forward-model validation uses the authors' own dynamo model for both the input and the interpretation, which limits its ability to rule out inversion artifacts.","major_comments":[{"comment":"The regularization weights λ_r and λ_t are selected without a documented procedure, and the only validation shown assumes f(r)=g(r)=1. Because the central claim is the inclined 5-6 year pattern in Figures 3-5, please provide an L-curve or grid scan for λ_r and λ_t and, crucially, a null test in which synthetic splittings from a time-independent rotation profile with realistic noise are inverted and the recovered time-dependent residual is shown to be consistent with zero. Without such a test, the tilted branches could be an artifact of temporal regularization.","section":"Section 2.2, Eq. (6)"},{"comment":"The maps that directly display the dynamo-wave pattern are produced from GONG data only, with Figure 2 combining MDI and HMI. The abstract and Section 4 claim confirmation across all three instruments, but no same-epoch cross-instrument zonal-flow map is shown. Please add an apples-to-apples comparison over overlapping MDI/HMI/GONG epochs with identical inversion settings to demonstrate that the tilted branches are not an artifact of a particular dataset or pipeline.","section":"Section 3.1, Figures 3-7"},{"comment":"The manuscript states that high-latitude (>60°) differences between instruments 'exceed significantly' and 'indicate potential systematics' in the frequency measurements. Since the same mode sets are used for the lower-latitude dynamo-wave detection, the paper needs to show that these systematics are confined to high latitudes. For example, present inter-instrument residuals in the latitude range 0-60° and depths 0.75-0.98 R⊙, or repeat the central inversions after applying a more conservative mode selection.","section":"Section 3.2, Figure 9"},{"comment":"The Monte Carlo error estimation is described but the resulting uncertainties are not displayed on the figures that support the central claim. Because the zonal-flow signals are of order 0.5 m/s, the reader needs error bars or shaded uncertainty regions (or an explicit statement of the typical 1σ error amplitude) to judge whether the reported branches are significant.","section":"Section 2.2, Figures 3-7 and 11"},{"comment":"The choice to exclude MDI modes with ℓ>120 is justified as a consistency requirement with other instruments, which is a post hoc selection. The same applies to the GONG ℓ<150 limit. Please repeat the time-dependent inversion for several degree cutoffs (e.g., MDI with ℓ_max = 120, 150, 180) and confirm that the 5-6 year rise time and the branch directions remain unchanged, to rule out that the consistency cut removes modes that would otherwise alter the inferred wave pattern.","section":"Section 3.1, MDI harmonic-degree cut"}],"minor_comments":[{"comment":"The word 'Equatuon' should read 'Equation'.","section":"Appendix A"},{"comment":"The sentence 'and a third temporal grid point as a knot in the time direction' is ambiguous; please clarify whether the time knots are equally spaced and how many knots are used.","section":"Section 2.2"},{"comment":"The vertical axes are labeled 'dv/dt' and 'v' without units; please add m/s year⁻¹ and m/s, respectively.","section":"Figures 3 and 4"},{"comment":"The statement that error bars are 'very small' is not quantitative; please report the actual 1σ uncertainty in ∇rΩ.","section":"Section 3.2"},{"comment":"The caption mentions an online video; please specify the URL or repository where it can be accessed.","section":"Figure 5 caption"},{"comment":"The phrase 'unambiguously confirming the original detection' is stronger than the evidence presented given the high-latitude systematics acknowledged in Section 3.2; consider tempering this wording and the corresponding abstract phrase.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal. The main concern for the editor is that the abstract and conclusion claim three-instrument confirmation while the supporting figures are mostly single-instrument (GONG) and the paper's own Section 3.2 reports inter-instrument systematics at high latitudes. The central claim is defensible, but the manuscript's strong assertions should be paired with the missing null tests, error bars, and cross-instrument maps, or softened accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Genuinely new here is the time-dependent RLS inversion that solves for ws(r,t) jointly, with first-derivative smoothing in time built into the misfit. That is a real methodological contribution, and the synthetic recovery in Figure 12 shows it works on the dynamo-model input. The multi-window, multi-instrument comparison using Korzennik (2023) splittings is also a step beyond earlier work. The NSSL gradient analysis is careful and mostly agrees with Antia & Basu (2022) and Komm (2023); the bump near 0.98 R is worth following up.\n\nThe dynamo-wave detection is not new: it confirms Kosovichev & Pipin (2019) and Mandal et al. (2024). Confirmation is legitimate, and the persistence across 72-day to 8x72-day windows is real support. But the paper overstates what is shown. The abstract and conclusions say three-instrument confirmation, yet the wave-pattern maps are GONG-only apart from the combined MDI+HMI snapshots in Figure 2. No same-epoch cross-instrument map of the tilted branch is presented. That makes 'unambiguously confirming' outrun the displayed evidence.\n\nThe bigger methodological soft spot is the absence of a null test. The tilted 5-6 year low-latitude branches in Figures 3-5 could be partly produced by the temporal regularization, especially with lambda_t and f=g=1 chosen without an L-curve or grid scan. The forward-model check in Figure 12 uses the authors' own dynamo model both to generate splittings and to define the expected wave pattern; it shows recovery of a smooth wave-like input, not whether the inversion would invent inclined structure from pattern-less data. A simple scrambled-data or synthetic no-wave run would close that gap. The paper honestly reports high-latitude systematics (Fig 9, Sec 3.2), but that admission also leaves open the possibility that smaller systematics contaminate lower latitudes. The MDI l<120 cut is a consistency-based selection, not an independent criterion—minor, but should be justified.\n\nNone of this kills the central claim. The observed detection is not fitted to the model, and the low-latitude 5-6 yr rise time is consistent across window lengths in GONG. If I worked on torsional oscillations or NSSL constraints, I would want this reviewed properly. My recommendation: send to peer review, with a request for error bars on the central figures, a same-epoch cross-instrument comparison, and at least one null test for the inversion. Conditional accept after revision.","headline":"A genuinely useful time-radius inversion and a mostly confirmatory multi-instrument dynamo-wave study that overclaims three-instrument confirmation and needs a null test.","tokens_in":17707,"tokens_out":3286,"would_cite":true,"duration_ms":30141,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims the dynamo-wave signature in solar torsional oscillations is genuine and persistent, appearing in both zonal flow and zonal acceleration across GONG, MDI, and HMI data, with low-latitude branches taking about 5–6 years…","keywords":["solar differential rotation","torsional oscillations","zonal flows","helioseismology","dynamo waves","regularized least squares inversion","near-surface shear layer","solar cycle"],"falsifier":"Invert a synthetic dataset built from a time-independent rotation profile plus noise matching the observed uncertainties using the same time-dependent inversion; if tilted patterns resembling 5–6-year propagation appear in the recovered zonal flow or acceleration, the claimed dynamo-wave pattern is an artifact of the regularization. Alternatively, if independent local-helioseismology measurements of zonal flows at 0.8–0.98 R⊙ disagree with the global-inversion propagation speeds by more than the combined uncertainties, the pattern does not survive.","tokens_in":16517,"feed_emoji":"🌞","tokens_out":6472,"duration_ms":57574,"temperature":0.7,"pith_summary":"The paper sets out to establish that the recently discovered dynamo-wave signature in the Sun's torsional oscillations is real, not a quirk of one instrument or one analysis pipeline. Using p-mode frequency-splitting data from GONG, MDI, and HMI, with time series from 72 days to eight times that length, the authors report the same tilted wave pattern in both the zonal flow and its time derivative, the zonal acceleration, throughout the convection zone: low-latitude branches take about 5–6 years to rise from the base of the convection zone to the surface, while high-latitude changes appear almost simultaneously at all depths. To achieve this, they introduce a time-dependent inversion that smooths the solution in radius and time jointly, eliminating the need for separate post-processing smoothing. The paper also characterizes the dimensionless radial gradient of rotation in the near-surface shear layer, finding values near −1 at the surface that increase with depth and show a torsional-oscillation-like variation, with high-latitude results left inconclusive because of inter-instrument systematics.","feed_headline":"Dynamo waves confirmed in the Sun's rotation by all three datasets","feed_subtitle":"Joint time-radius inversions of GONG, MDI, and HMI data show the same 5–6-year rise pattern.","key_machinery":"The load-bearing tool is a time-dependent Regularized Least Squares inversion: the misfit function (Eq. 6) adds second-derivative smoothing in radius and first-derivative smoothing in time to a fit of the frequency-splitting coefficients, with rotation expanded in cubic B-splines along both acoustic depth and time. Smoothing in time is thus internal to the inversion, controlled by a regularization weight rather than applied afterward as a Gaussian filter, and it can be made depth-dependent through the radial weighting function f(r). This device turns the 72-day time series into a continuous time–radius solution for the zonal flow coefficients ws(r,t), from which both the flow and its acceleration are reconstructed and the dynamo-wave tilt is measured.","core_discovery":"The central claim is that the dynamo-wave pattern first reported by Kosovichev & Pipin (2019) appears unambiguously in every dataset analyzed here: GONG, MDI, and HMI frequency splittings, binned in 72-day, 4×72-day, 5×72-day, and 8×72-day segments, and processed both by the Korzennik (2023) pipeline and by the JSOC pipeline. The pattern is visible in the zonal flow itself and in its acceleration, and the two are phase-shifted; the tachocline onset at high latitudes correlates in sign and timing with the approach of the next solar cycle. For the near-surface shear layer, the paper claims the logarithmic radial gradient of rotation is close to −1 at the surface, rises toward zero with depth, stays nearly constant from equator to mid-latitudes in the top 13–35 Mm, and exhibits a torsional-oscillation-like variation whose equatorward branch matches the magnetic butterfly diagram.","pith_inferences":["An implication the authors leave implicit: comparing the measured travel-time and phase-lag pattern against flux-transport versus distributed dynamo models could discriminate between dynamo families, because the two predict different relations between deep magnetic torque and surface flow.","The high-latitude inter-instrument discrepancies suggest the systematics may be depth-dependent; resolving them with high-degree modes (ℓ > 300) or local helioseismology would test whether the polar branch of the dynamo wave is real.","The bump in the rotation gradient near 0.98 R⊙, attributed to the He II ionization transition, is testable with independent ring-diagram measurements; a matching bump in their gradient profiles would strengthen the interpretation.","Extending the same joint time–radius inversion to meridional flows could reveal whether the dynamo-wave coupling inferred for zonal flows also organizes the meridional circulation on similar timescales."],"forward_implications":["Dynamo models must reproduce a low-latitude branch that takes about 5–6 years to travel from the base of the convection zone to the surface and a nearly instantaneous high-latitude branch, because the same phase pattern appears in zonal flow and zonal acceleration.","The time-dependent inversion removes post-processing temporal smoothing and produces consistent features from 72-day to 8×72-day datasets, so it can be reused for other time-varying helioseismic inversions.","The dimensionless radial rotation gradient near −1 at the surface, increasing with depth and nearly constant from equator to mid-latitudes in the top 13–35 Mm, gives a quantitative target for models of the near-surface shear layer and its role in the dynamo.","The torsional-oscillation-like variation of the radial gradient, with an equatorward branch matching the butterfly diagram, ties the near-surface shear layer's cycle variations to the same dynamo-wave process.","The phase difference between zonal flow and acceleration near the tachocline may provide timing and strength information for the upcoming solar cycle, though the paper notes that the correlation with magnetic field must first be established."],"supporting_citations":[{"why":"original detection of dynamo-wave signatures in HMI torsional oscillations that this paper claims to confirm","marker":"Kosovichev & Pipin (2019)"},{"why":"earlier GONG detection and the generalized-spherical-harmonic sensitivity kernel and inversion setup this work extends","marker":"Mandal et al. (2024)"},{"why":"source of the frequency-splitting coefficients for GONG, MDI, and HMI at multiple time-series lengths","marker":"Korzennik (2023)"},{"why":"dynamo model whose time-varying rotation profile is used for forward modeling and validation of the inversion","marker":"Pipin & Kosovichev (2020)"},{"why":"justifies the MDI harmonic-degree cut ℓ < 120 needed to align instruments","marker":"Antia et al. (2008)"},{"why":"independent ring-diagram measurement of the radial rotation gradient whose bump near 0.95 R⊙ is compared with this paper's finding","marker":"Komm (2023)"}],"fun_headline_variants":["Dynamo waves in Sun's rotation confirmed across GONG, MDI, HMI","New helioseismic inversion reveals consistent dynamo wave patterns","Solar zonal flow shows same dynamo wave signal in three datasets","All three solar datasets show identical dynamo wave pattern"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument stands on the assumption that the measured frequency-splitting coefficients, after pipeline-specific cuts such as limiting MDI to harmonic degrees below 120 and GONG below 150, represent solar rotation with systematic errors smaller than the roughly 0.5 m/s zonal-flow signals being interpreted.","fun_headline_variants_meta":{"raw":{"variants":["Dynamo waves in Sun's rotation confirmed across GONG, MDI, HMI","New helioseismic inversion reveals consistent dynamo wave patterns","Solar zonal flow shows same dynamo wave signal in three datasets","All three solar datasets show identical dynamo wave pattern"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000281,"raw_usage":{"total_tokens":1705,"prompt_tokens":1025,"completion_tokens":680,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":641,"completion_tokens_details":{"reasoning_tokens":604}},"tokens_in":641,"tokens_out":680,"duration_ms":6834,"temperature":1.0,"reasoning_tokens":604,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:05:24.353248+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Invert a synthetic dataset built from a time-independent rotation profile plus noise matching the observed uncertainties using the same time-dependent inversion; if tilted patterns resembling 5–6-year propagation appear in the recovered zonal flow or acceleration, the claimed dynamo-wave pattern is an artifact of the regularization. Alternatively, if independent local-helioseismology measurements of zonal flows at 0.8–0.98 R⊙ disagree with the global-inversion propagation speeds by more than the combined uncertainties, the pattern does not survive.","supporting_citations":[{"cited_title":"M., Basu , S., & Chitre , S","cited_arxiv_id":null,"evidence_quote":"justifies the MDI harmonic-degree cut ℓ < 120 needed to align instruments"},{"cited_title":"2023, , 298, 119, 10.1007/s11207-023-02213-7","cited_arxiv_id":null,"evidence_quote":"independent ring-diagram measurement of the radial rotation gradient whose bump near 0.95 R⊙ is compared with this paper's finding"}],"review_version":1}