{"id":"fd471706-2f82-498d-9aec-7a0d1256bb3c","arxiv_id":"1908.05890","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A 20-year normal-mode coupling analysis of MDI and HMI data characterizes solar Rossby mode frequencies, linewidths, and amplitudes, and validates a spatial leakage correction.","lead":"This paper measures the frequencies, linewidths, and amplitudes of large-scale Rossby waves in the Sun using 20 years of helioseismic data from two space instruments. It also introduces and tests a correction for spatial leakage, which is a main source of systematic error in such measurements.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Leakage-correction scheme is validated only in noiseless tests; the noise test ignores leakage, leaving combined systematics in inferred amplitudes and linewidths unquantified.","rationale":"The reader's weakest assumption concerned the sectoral-only approximation and the neglect of off-diagonal leakage. That is a plausible concern, but it rests on an empirical prior (prior studies found no non-sectoral modes) and on the leakage-frequency argument. The concern I identify is more direct: the paper's own synthetic validation does not test leakage and noise together, even though the stated goal is to quantify systematics. This is an internal gap in the evidence, not a disagreement with prior work. It affects every amplitude and linewidth quoted in Tables 1 and 2, because those errors reflect only statistical scatter and not the systematic leakage error that the paper itself says can reach 'a factor of a few.' The abstract's rms velocity claim (0.5 m/s) also lacks a clear derivation, but that is secondary to the methodological gap. The concern does not overturn the paper's value: the frequencies are largely consistent with theory and previous work, and the leakage modeling is a useful step. However, the reliability claim is conditional on a combined synthetic test being performed and on the systematic error being incorporated into the quoted uncertainties. The reader's CONDITIONAL verdict is therefore appropriate, and my stress test does not move it.","tokens_in":14615,"tokens_out":6513,"duration_ms":62055,"concrete_test":"Run a synthetic recovery experiment that combines the two existing tests: generate B-coefficients using the full forward model of Eq. (5) including the leakage matrix and a known toroidal Rossby profile, add Gaussian noise of amplitude equal to the observed N_{nℓ}^{σ}, then invert with the diagonal-only kernel of Eq. (19). Repeat for many noise realizations and for each harmonic degree s. Compare the mean recovered amplitude and central frequency to the input values. If the amplitude bias exceeds the statistical error bars, or the frequency shift exceeds the fitted linewidth, the leakage correction is insufficient for the claimed precision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central methodological claim is that the novel leakage-correction scheme, validated by synthetic tests, makes the Rossby-mode measurements reliable (abstract and §4.2). The validation, however, is split: Figure 3 tests the diagonal-kernel inversion (Eq. 19) on noiseless synthetic B-coefficients that include leakage; Figure 4 tests inversion with realistic noise but explicitly ignores leakage, using Eq. (7) (the text states 'We then perform inversions assuming Equation (7)'). No synthetic test includes both leakage and noise simultaneously, even though both are present in the actual observations. The paper concedes that ignoring leakage biases amplitudes by 'at worst ... a factor of a few' and that the diagonal-kernel correction only partially recovers the profile (Figure 3). Because the error bars in Tables 1 and 2 reflect only statistical scatter across data chunks, not this systematic leakage error, the quoted uncertainties (e.g., √A = 70 ± 24 cm/s for s=3 HMI) do not fully represent the measurement error. Consequently, the claim that the leakage-correction scheme makes the measurements reliable is not supported by the validation as presented.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies normal-mode coupling to 20 years of MDI and HMI Doppler observations (1999–2018) to measure frequencies, linewidths, and amplitudes of solar Rossby modes. It extends an earlier analysis by Hanasoge & Mandal (2019), using a longer baseline and two instruments, and introduces a leakage-correction scheme based on a diagonal sensitivity kernel (Eq. 19). The method is validated with synthetic inversions: one noiseless test that includes leakage and one noise test that ignores leakage. The authors report frequencies consistent with the classical Rossby dispersion relation for several low-degree modes, compare them with the independent studies of Löptien et al. (2018) and Liang et al. (2018), and quote a surface rms velocity of about 0.5 m/s. They also investigate whether the s=1 mode could be a tracking-rate artifact and conclude it is likely real while remaining cautious. The two datasets are analyzed separately and not combined.","tokens_in":14774,"tokens_out":4975,"duration_ms":49958,"significance":"If the result holds, this paper provides the first long-baseline, two-instrument characterization of solar Rossby-mode frequencies, linewidths, and amplitudes, and it demonstrates a practical way to handle spatial leakage in normal-mode coupling. The strengths are the explicit comparison with the analytic dispersion relation, the use of two independent datasets, the careful discussion of the s=1 systematics, and the synthetic tests that at least partially validate the inversion pipeline. The main caveat is that the validation is split: leakage and noise are never tested together, and the inversion forward model and leakage matrices come from the authors' own earlier papers, so the synthetic tests do not independently validate the forward model. The frequency measurements, however, are checked against external results, which supports the central detection claim.","major_comments":[{"comment":"The validation of the leakage-correction scheme is split. Figure 3 tests the diagonal-kernel inversion (Eq. 19) on noiseless synthetic data that include leakage, while Figure 4 tests inversion with realistic noise but assumes Eq. (7), i.e., no leakage. No test includes both leakage and noise, even though both are present in the actual observations. The paper itself concedes in Section 4.2 that ignoring leakage biases amplitudes by at most a factor of a few, so the statistical error bars in Tables 1 and 2 (e.g., √A = 70 ± 24 cm/s for s=3 HMI) do not include the leakage systematic. The claim that the leakage-correction scheme makes the measurements reliable requires either a combined leakage-plus-noise synthetic test or an explicit propagation of the factor-of-few amplitude uncertainty into the tabulated parameters.","section":"Section 4.2, Figures 3 and 4"},{"comment":"The analysis assumes that only sectoral Rossby modes are present, so b^σ_st ≈ δ_{s,-t}, and that in the 0–0.5 µHz band the off-diagonal leakage terms Θ_{s'}^s with s' ≠ s are negligible, allowing the inversion to use only the diagonal kernel (Eq. 19). The synthetic tests are built from the same sectoral-mode assumption and the same leakage model, so they do not test whether non-sectoral power or non-negligible off-diagonal leakage would bias the recovered frequencies and amplitudes. I ask for a sensitivity test that injects non-sectoral or off-diagonal-leakage components at a few percent of the sectoral amplitude and quantifies the resulting bias.","section":"Section 3, Eq. (8), and Section 4.2"},{"comment":"The asymptotic kernel used in Eq. (7) is stated to be valid only when s ≪ ℓ or s ≪ ℓ′. With ℓ ∈ [10,180] and s ≤ 20, there are contributing pairs with s ≈ ℓ (for example ℓ = 11, s = 11), for which Hanasoge (2018) finds the asymptotic kernel to be less accurate. The paper justifies the asymptotic form only by noting s ≤ 20, which is insufficient for the lowest harmonic degrees. The authors should either restrict the inversion to ℓ ≫ s, or quantify the bias from low-ℓ modes using exact kernels.","section":"Section 3, before Eq. (7)"},{"comment":"Several fitted frequencies deviate strongly from the classical dispersion relation and from the earlier measurements the paper cites. For example, HMI s=11 gives 54 ± 2 nHz versus 75.5 nHz theoretical and 75 ± 7 nHz in Löptien et al., and HMI s=15 gives 18 ± 1 nHz versus 56.6 nHz theoretical. Since the identification of these features as Rossby modes rests partly on agreement with the dispersion relation, these outliers need discussion (e.g., misidentification, line blending, or systematic frequency shifts) before the tabulated frequencies can be taken as a reliable characterization of Rossby-mode properties.","section":"Tables 1 and 2"}],"minor_comments":[{"comment":"Equation (20) uses τ/2 in the Lorentzian denominator, but the text defines Γ as the full width at half maximum. The relationship between τ and Γ is never stated; please use one symbol consistently.","section":"Equation (20)"},{"comment":"The sentence \"Fitted spectrum for HMI and MDI are shown in Figure (6) and (7) respectively\" has a subject-verb mismatch. Also, \"line-widths\" in the abstract and elsewhere should be written consistently as \"linewidths\" or \"line widths\".","section":"Section 4.3"},{"comment":"The notation Θ^{s,-s}_{s,-s} in the right panel is confusing and does not clearly match the kernels defined in Eqs. (17)–(19). Please align the notation between the equations and the figure caption.","section":"Figure 3 caption"},{"comment":"The right panel of Figure 8 shows the s=1, t=1 power spectrum without error bars or a quantitative upper limit. A noise level or significance threshold would make the argument that there is no spurious power at 453 nHz more compelling.","section":"Section 4.4, Figure 8"}],"recommendation":"major_revision","confidential_remarks":"The paper relies heavily on the authors' own forward model (Hanasoge 2018; Hanasoge & Mandal 2019), and the synthetic validations use the same model that is being inverted, so the tests do not independently validate the forward model. This is not by itself grounds for rejection, but the requested combined leakage-plus-noise test should ideally use a forward model or leakage matrix that is not identical to the one used in the inversion. The manuscript also lacks a data/code availability statement; please confirm that this complies with journal policy."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Rossby waves in the Sun get a careful, incremental extension here: 20 years of MDI+HMI data through normal-mode coupling, plus a new diagonal leakage kernel. The low-s frequencies match theory and prior work, and the authors are properly cautious about the s=1 mode and about amplitude uncertainties. The paper is a good fit for a specialist journal after a revision that clarifies a few things.\n\nWhat is actually new: the 20-year catalog of frequencies, linewidths, and amplitudes, the diagonal leakage kernel, and the synthetic tests that compare Eq. (7) with the leakage-aware kernel. The discussion of leakage (Figures 1-2) is useful, and the comparison with Loptien et al. and Liang et al. is helpful. The method is described well enough to reproduce, though code and data are not shipped.\n\nSoft spots, in order of severity. First, the abstract states an rms velocity of order 0.5 m/s, while the body says the observed surface magnitude is ~4 m/s (and Table amplitudes range up to ~5 m/s). That's a factor of eight gap that needs a clear explanation. Second, the synthetic validation never puts leakage and noise in the same test: Figure 3 is noiseless with leakage, Figure 4 has noise but assumes Eq. (7), i.e., no leakage. So the combined systematic effect on linewidths and amplitudes is unquantified; the quoted errors are only scatter across chunks. The paper does say amplitudes could be off by a factor of a few, but the claim that the leakage-correction scheme makes the measurements reliable is stronger than the tests support. Third, the high-s modes (s=9,11,15) show large deviations from the classical dispersion relation (e.g., HMI s=15: 18 vs 56.6 nHz). That isn't discussed, and it raises the question of whether those weak peaks are real or leakage artifacts. Fourth, MDI and HMI are not cross-calibrated, which the authors acknowledge; it limits combined interpretation.\n\nNone of these are fatal for the core result, which is the frequency catalog for low-s sectoral modes. The paper deserves serious peer review; the right referee will push for a joint noise+leakage test, a statement on the amplitude definition, and a discussion of the high-s deviations. I'd probably cite the 20-year catalog once the amplitude number is sorted out.","headline":"A solid incremental extension of the authors' Rossby-wave mode-coupling work to 20 years of data, with a useful leakage kernel, but the abstract's 0.5 m/s amplitude needs reconciling with the body's ~4 m/s, and leakage+noise are never tested together.","tokens_in":15353,"tokens_out":4318,"would_cite":true,"duration_ms":37731,"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":"Twenty years of normal-mode coupling data from two solar observatories yield frequencies, line widths, and amplitudes for sectoral Rossby modes, with surface root-mean-square velocities near 0.5 m/s.","keywords":["solar Rossby waves","normal mode coupling","helioseismology","convection zone","MDI","HMI","leakage correction","r-modes"],"falsifier":"Build a synthetic data set from a known sectoral Rossby depth profile plus a second non-sectoral mode ($s\\neq|t|$) just below the current detection threshold, run the paper's diagonal-only inversion, and check whether the recovered frequency and amplitude shift by more than the quoted uncertainties; any such shift would falsify the sectoral-only assumption. A cheaper check: compare MDI and HMI measurements over their overlapping 2010–2011 data after cross-calibrating the two instruments, since instrument systematics would not produce the same parameter differences as genuine solar-cycle variation.","tokens_in":14362,"feed_emoji":"🌊","tokens_out":9469,"duration_ms":82572,"temperature":0.7,"pith_summary":"Solar Rossby waves are large-scale, retrograde waves in the convection zone whose restoring force is the Coriolis force; in rotating fluids they carry angular momentum, so measuring their properties tests the physics of solar and stellar interiors. This paper tries to measure their frequencies, line widths, and amplitudes by coupling acoustic normal modes over 20 years of space-based Doppler observations: 12 years from MDI and 8 years from HMI. Because we observe only the visible hemisphere, spatial windowing mixes neighboring spherical-harmonic modes, so the authors build a leakage-correction scheme and validate it with synthetic tests before applying it to the data. They report that the measured sectoral modes follow the classical dispersion relation $\\sigma_s = 2\\Omega/(s+1)$ closely enough to identify each ridge with a Rossby mode, and that the root-mean-square velocity at the surface is of order 0.5 m/s. A sympathetic reader would care because this turns a recent detection into a 20-year, two-instrument catalog of mode parameters that can be compared with theory and with independent helioseismic measurements.","feed_headline":"20 years of solar data pin down Rossby-wave speeds","feed_subtitle":"Normal-mode coupling of MDI and HMI observations yields frequencies, widths, and amplitudes for these interior waves.","key_machinery":"The measurement rests on normal-mode coupling: cross-correlating spherical-harmonic coefficients of line-of-sight Doppler velocity, $\\langle \\varphi^*_{\\ell m}(\\omega)\\varphi_{\\ell,m+t}(\\omega+\\sigma)\\rangle$, and condensing the correlations into $B$-coefficients through a weighted least-squares fit. The central object is the leakage matrix $L^{\\ell' m'}_{\\ell m}$, which describes how the spatial window of the visible disk mixes a mode $(\\ell,m)$ into other modes; from it the paper constructs the new diagonal sensitivity kernel $\\Theta^s_s(n,\\ell,\\sigma,r)$ of Eq. (19), which connects the observed $B$-coefficients directly to the toroidal Rossby velocity profile $w_{s,-s}(r)$. A Wigner $3j$ symbol enforces the angular-momentum selection rules in the coupling. This kernel, combined with optimally localized averaging and regularized least-squares inversions, is what lets the authors convert the measured correlations into depth-dependent amplitudes and assess the leakage systematics.","core_discovery":"The paper claims that normal-mode coupling of 12 years of SOHO/MDI and 8 years of SDO/HMI Doppler observations yields a consistent set of solar Rossby-mode parameters for sectoral modes of odd harmonic degree $s=1,3,5,\\ldots,15$ (with $s=13$ not fitted for HMI). The frequencies in the co-rotating frame are close to the sectoral dispersion relation $\\sigma_s=2\\Omega/(s+1)$, for example $233\\pm3$ nHz for $s=3$ from HMI and $249\\pm0.4$ nHz from MDI; line widths are typically 5–70 nHz, amplitudes decline with $s$, and the surface root-mean-square velocity of the modes is about 0.5 m/s. The load-bearing methodological claim is that leakage from observing only part of the Sun can be handled by a new diagonal sensitivity kernel $\\Theta^s_s$ built from the leakage matrix, and that synthetic inversions using this kernel recover input depth profiles better than the earlier no-leakage approximation, which may bias amplitudes by up to a factor of a few. The authors deliberately do not combine the two data sets because MDI and HMI are not cross-calibrated for this measurement, and they stop short of declaring the $s=1$ mode a detection because its frequency coincides with the tracking rate.","pith_inferences":["A reader could push further: inject a non-sectoral mode ($s\\neq|t|$) just below the detection threshold into the paper's synthetic pipeline; if the diagonal-only inversion shifts the recovered sectoral frequency or amplitude beyond the quoted errors, the sectoral-only ansatz would need to be relaxed.","Cross-calibrating MDI and HMI normal-mode coupling over their overlapping years (2010–2011) would turn the two-instrument parameter differences into a clean solar-cycle test rather than an instrument ambiguity.","Coupling acoustic modes of different harmonic degree with $\\delta\\ell=1,3,\\ldots$ should bring the even-harmonic-degree Rossby modes into view, which the identical-degree coupling used here cannot see.","The leakage pattern that moves a mode at $\\sigma_s+2\\Omega$ suggests a template for detecting other large-scale sectoral flows: any rotating sectoral perturbation will reappear at shifted temporal frequencies."],"forward_implications":["If the measurements are right, the tabulated frequencies give a direct test of the sectoral dispersion relation $\\sigma_s=2\\Omega/(s+1)$ for the Sun's interior Rossby waves.","The measured line widths and amplitudes provide the first long-baseline reference set for modeling wave damping and excitation in the convection zone.","A surface root-mean-square velocity of about 0.5 m/s places a concrete scale on the angular-momentum transport that Rossby waves could mediate in the Sun and other stars.","The diagonal leakage kernel offers a reusable correction for future normal-mode-coupling measurements of weakly excited sectoral flows.","The MDI–HMI parameter differences, if not instrument systematics, would encode solar-cycle dependence, but the paper does not claim that without a cross-calibration."],"supporting_citations":[{"why":"It supplies the normal-mode-coupling detection and measurement formalism that this 20-year analysis extends.","marker":"Hanasoge & Mandal (2019)"},{"why":"It derives the leakage-inclusive B-coefficient equation and sensitivity kernels that the diagonal kernel refines.","marker":"Hanasoge (2018)"},{"why":"It provides the independent ring-diagram detection and dispersion-relation measurements used for comparison.","marker":"Löptien et al. (2018)"},{"why":"It provides the independent time-distance helioseismology measurements used for comparison.","marker":"Liang et al. (2018)"},{"why":"It describes the HMI instrument and data products analyzed for the 2010–2018 period.","marker":"Schou et al. (2012)"},{"why":"It supplies the asymptotic kernel factor $f_{\\ell'-\\ell,s}$ on which the inversions rely.","marker":"Vorontsov (2011)"}],"fun_headline_variants":["Solar Rossby waves: new kernel overcomes spatial leakage","20 years of helioseismic data yield Rossby wave frequencies","Leakage-corrected normal mode coupling measures solar Rossby waves","Solar Rossby wave velocities from two decades of oscillations","New diagonal kernel eliminates leakage in Rossby wave inversions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The analysis assumes that only sectoral Rossby waves exist in the low-frequency band and that leakage from neighboring harmonic degrees is negligible there, so the inversion can keep only the diagonal kernel; if non-sectoral waves or that off-diagonal leakage are significant, the inferred frequencies and amplitudes will be biased.","fun_headline_variants_meta":{"raw":{"variants":["Solar Rossby waves: new kernel overcomes spatial leakage","20 years of helioseismic data yield Rossby wave frequencies","Leakage-corrected normal mode coupling measures solar Rossby waves","Solar Rossby wave velocities from two decades of oscillations","New diagonal kernel eliminates leakage in Rossby wave inversions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000339,"raw_usage":{"total_tokens":1904,"prompt_tokens":1010,"completion_tokens":894,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":626,"completion_tokens_details":{"reasoning_tokens":809}},"tokens_in":626,"tokens_out":894,"duration_ms":9262,"temperature":1.0,"reasoning_tokens":809,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:01:52.131192+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build a synthetic data set from a known sectoral Rossby depth profile plus a second non-sectoral mode ($s\\neq|t|$) just below the current detection threshold, run the paper's diagonal-only inversion, and check whether the recovered frequency and amplitude shift by more than the quoted uncertainties; any such shift would falsify the sectoral-only assumption. A cheaper check: compare MDI and HMI measurements over their overlapping 2010–2011 data after cross-calibrating the two instruments, since instrument systematics would not produce the same parameter differences as genuine solar-cycle variation.","supporting_citations":[{"cited_title":"Detection of Rossby waves in the Sun using normal-mode coupling","cited_arxiv_id":"1901.06479","evidence_quote":"It supplies the normal-mode-coupling detection and measurement formalism that this 20-year analysis extends."},{"cited_title":"2018, , 861, 46","cited_arxiv_id":null,"evidence_quote":"It derives the leakage-inclusive B-coefficient equation and sensitivity kernels that the diagonal kernel refines."}],"review_version":1}