arxiv: 2604.10698 · v1 · submitted 2026-04-12 · 🌌 astro-ph.SR · physics.space-ph

Recognition: 2 theorem links

· Lean Theorem

Spatio-temporal analysis of helioseismic quasi-biennial oscillations

Amir Hasanzadeh , Anne-Marie Broomhall , Dmitrii Kolotkov , Tishtrya Mehta

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:29 UTC · model grok-4.3

classification 🌌 astro-ph.SR physics.space-ph

keywords quasi-biennial oscillationshelioseismologysolar cyclesp-mode frequency shiftsGONGwavelet analysissolar dynamo

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The pith

Quasi-biennial oscillations show amplitudes partially decoupled from 11-year solar cycle strength

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

This paper examines quasi-biennial oscillations by applying wavelet analysis to p-mode frequency shifts recorded by the GONG network across solar Cycles 23 and 24 and the start of Cycle 25. It finds that QBO periods vary only weakly with latitude, remaining near three years at higher latitudes while appearing shorter and less steady near the equator. QBO amplitudes increase with mode frequency and reach higher values at low latitudes where surface magnetic activity is strongest. The key result is a linear relation between QBO amplitude and cycle amplitude that holds in both cycles, yet the slope is significantly steeper in Cycle 24 than in Cycle 23. This difference demonstrates that QBO strength is not fully determined by the main cycle and points to at least partial independence between the two signals.

Core claim

Wavelet analysis of GONG p-mode frequency shifts shows QBO periods with only weak latitudinal dependence, shorter and less persistent at low latitudes but nearly constant at about three years at higher latitudes. Cycle 24 displays slightly longer periods than Cycle 23 within uncertainties. QBO amplitudes rise with mode frequency at all latitudes and are larger at low latitudes, consistent with the distribution of surface magnetic activity. A linear relation between QBO amplitude and cycle amplitude appears in both cycles, but with significantly different slopes, indicating QBO amplitudes are not wholly governed by solar cycle strength and are at least partially decoupled from it. No evidence

What carries the argument

Wavelet analysis applied to time series of p-mode frequency shifts to extract QBO period and amplitude as functions of latitude and solar cycle

If this is right

QBO amplitudes increase with p-mode frequency at every latitude.
Higher QBO amplitudes occur at low latitudes, matching the distribution of surface magnetic activity.
The ratio of QBO amplitude to cycle amplitude is systematically higher in Cycle 24 than in Cycle 23.
QBO periods show no dependence on QBO amplitude, consistent with a linear oscillation regime.
Above 20 degrees latitude the QBO-to-cycle amplitude ratio is nearly uniform in Cycle 23 but shows modest variations in Cycle 24.

Where Pith is reading between the lines

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

A separate physical mechanism in the solar interior may generate QBOs alongside the primary dynamo.
Continued monitoring through the remainder of Cycle 25 could test whether the differing slopes persist across multiple cycles.
Solar dynamo models may need additional terms to account for this partial decoupling when predicting short-term activity variations.

Load-bearing premise

Wavelet analysis applied to p-mode frequency shifts cleanly isolates QBO periodicities without residual contamination from the dominant 11-year cycle, data gaps, or latitude-dependent noise.

What would settle it

Re-analysis of the same p-mode frequency shift data with cycle-subtracted Fourier methods or empirical mode decomposition that produces identical cycle-dependent slopes in the QBO-cycle amplitude relation.

Figures

Figures reproduced from arXiv: 2604.10698 by Amir Hasanzadeh, Anne-Marie Broomhall, Dmitrii Kolotkov, Tishtrya Mehta.

**Figure 1.** Figure 1: Variation of the averaged-degree mode frequencies based on GONG data for Cycles 23 and 24 and a part of Cycle 25’s rising phase. The errors of the data are of the order of 𝑛Hz and are not visible in the figure. The shifts were obtained by averaging for all common modes in the frequency range 1900 - 4100 μHz and for modes in the range 20 ≤ 𝑙 ≤ 150. The red dashed vertical lines indicate the minima of cycles… view at source ↗

**Figure 3.** Figure 3: Upper Panel: Frequency shift of the 20 ≤ 𝜃 < 30 degree band for the frequency range of 2700 to 3100 μHz. A Savitzky-Golay filter (red line) was applied to capture the 11-year periodic variations. Middle Panel: Shorter-term periodicity that remains after detrending the shifts by subtracting the Savitzky–Golay filtered data. Bottom left panel: Continuous wavelet transform (CWT) power spectrum of the residual… view at source ↗

**Figure 5.** Figure 5: QBO periods (in years) obtained from CWT in latitude bands for Cycles 23 (filled circles) and 24 (open squares). Frequency shifts from which the periods were obtained were determined by averaging over the entire frequency range considered [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: QBO amplitude as a function of frequency and latitude (see legend) for Cycles 23 (lower panel) and 24 (upper). MNRAS 000, 1–13 (2025) [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 7.** Figure 7: Correlation between QBO amplitude and solar cycle shift peak-topeak amplitude observed from the p-mode frequency shifts obtained when averaging over all combinations of frequency and latitude ranges where the QBO was found to be significant (as displayed in Tables A2 and A3). The weighted least-squares linear fits are shown for Cycle 23 (blue solid) and Cycle 24 (dashed orange). • QBO periodicities exhibi… view at source ↗

**Figure 8.** Figure 8: Left panel: Amplitude ratio as a function of frequency for Cycles 23 (solid blue) and 24 (dashed orange line). The amplitudes were determined from shifts using the full solar disk. Right panel: QBO-to-cycle amplitude ratio variations with latitude for Cycles 23 (blue) and 24 (orange). The amplitudes were calculated using the full frequency range [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 9.** Figure 9: QBO period as a function of QBO amplitude for Cycle 23 (filled circles) and 24 (open squares with dashed line error bar) in latitude bands and using modes from the entire frequency range. Error bars in both dimensions reflect the uncertainties in measured QBO amplitudes and periods. Broomhall A. M., Chaplin W. J., Elsworth Y., New R., 2011, MNRAS, 413, 2978 Broomhall A. M., Chaplin W. J., Elsworth Y., Simo… view at source ↗

read the original abstract

Quasi-biennial oscillations (QBOs) are shorter-term periodic signals that occur alongside the dominant 11-year solar cycle. In this study, we examine the spatial and temporal evolution of QBOs using helioseismic p-mode frequency shifts from the Global Oscillation Network Group (GONG) across solar Cycles 23 and 24 and the ascending phase of Cycle 25. By applying wavelet analysis to frequency shifts, we studied the changes in QBO periodicities to determine whether the QBO period and amplitude vary with latitude. Our results show that QBO periods exhibit a weak latitudinal dependence, with shorter and less persistent signals at low latitudes, while at higher latitudes the periods are nearly constant at $\sim$3 years. Cycle 24 tends to display slightly longer periods than Cycle 23, though within uncertainties. At all latitudes, QBO amplitudes increase with mode frequency, which is consistent with previous studies. Higher amplitude QBOs are found at low latitudes, reflecting the distribution of surface magnetic activity. The ratio of QBO to cycle amplitude is systematically higher in Cycle 24 than in Cycle 23, and above $20^\circ$ latitude the amplitude ratio is nearly uniform in Cycle 23 but shows modest variations in Cycle 24. A linear relation between QBO amplitude and cycle amplitude is found in both cycles, but with significantly different slopes, indicating that QBO amplitudes are not wholly governed by the solar cycle strength and are at least partially decoupled from it. Finally, we find no evidence that QBO period depends on QBO amplitude, consistent with a linear oscillation regime.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper maps some new latitudinal and cycle-to-cycle QBO patterns from GONG frequency shifts but the decoupling claim needs checks against possible 11-year leakage.

read the letter

The main things to know are that the authors run wavelet analysis on public GONG p-mode frequency shifts across latitudes for cycles 23 and 24, and they report a linear QBO-cycle amplitude relation whose slope differs between the two cycles, which they interpret as partial decoupling. They also note shorter, less persistent QBO periods at low latitudes and nearly constant ~3-year periods at higher latitudes, plus the usual rise in QBO amplitude with mode frequency and stronger signals at low latitudes where magnetic activity concentrates. Cycle 24 shows a higher QBO-to-cycle amplitude ratio overall. These are concrete empirical extensions of earlier QBO work, and the data handling follows standard practice for the field. The results line up with known surface activity patterns and give dynamo modelers a bit more spatial and cycle-dependent detail to work with. The soft spot is exactly the one the stress test flags. The dominant 11-year signal is far stronger than the QBO band, GONG series have gaps, and continuous wavelets can leak power across scales even with basic masking. Without reported synthetic tests, cycle-subtracted runs, or explicit error bars and wavelet parameters, the slope difference could partly reflect residual cycle modulation rather than true decoupling. The abstract does not address this directly, so the central claim stays plausible but not yet tightly verified. This is narrow-scope work for helioseismologists and solar dynamo people. A reader already following QBO papers will get usable new numbers on period and amplitude variation with latitude and cycle. It is not broad enough for most others. The authors engage the data honestly and cite the relevant prior studies, so the thinking is clear even if the methods section needs tightening. I would send it to peer review once they add the leakage validation and parameter details; the observations themselves are worth referee time.

Referee Report

1 major / 4 minor

Summary. The paper applies continuous wavelet analysis to GONG p-mode frequency shift time series to characterize the spatio-temporal properties of quasi-biennial oscillations (QBOs) during solar Cycles 23 and 24 (plus the ascending phase of Cycle 25). It reports weak latitudinal dependence in QBO periods (shorter and less persistent at low latitudes, ~3 yr at higher latitudes), increasing QBO amplitudes with mode frequency and at low latitudes, a higher QBO-to-cycle amplitude ratio in Cycle 24, and a linear QBO-cycle amplitude relation whose slope differs significantly between the two cycles, interpreted as evidence that QBO amplitudes are at least partially decoupled from overall cycle strength. No period-amplitude dependence is found.

Significance. If the decoupling result holds after validation, the differing slopes between Cycles 23 and 24 would supply a useful observational constraint on QBO generation mechanisms, suggesting they are not entirely slaved to the primary dynamo. The latitudinal and frequency trends add detail to the known distribution of QBO power. The work makes direct use of public GONG data and produces falsifiable, observationally derived quantities rather than fitted parameters.

major comments (1)

The central claim that QBO amplitudes are partially decoupled from cycle strength (abstract and Results section) is based on linear fits to QBO amplitudes extracted in the 2–4 yr band. Because the 11-year cycle is orders of magnitude stronger and GONG series contain gaps, standard CWTs are susceptible to scale leakage even with cone-of-influence masking; any residual 11-year modulation that tracks the cycle envelope would systematically bias the recovered QBO amplitudes and therefore the reported slope difference. No synthetic-signal injection tests, cycle-subtracted comparisons, or gap-filling sensitivity checks are described, leaving the decoupling interpretation vulnerable to this artifact.

minor comments (4)

The abstract asserts that the slope difference is 'significant' but supplies neither the numerical slope values, their uncertainties, nor any statistical measure of the difference; these must be added for the claim to be verifiable.
Exact wavelet parameters (mother wavelet, scale discretization, normalization, and precise cone-of-influence masking procedure) are not stated; these details are required for reproducibility of the period and amplitude extractions.
The manuscript should clarify how data gaps in the GONG frequency-shift series are treated prior to wavelet transformation, as gap-handling choices can affect power leakage across scales.
Error bars or confidence intervals on the reported QBO periods, amplitudes, and amplitude ratios are absent from the abstract and should be included in the figures and text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We address the major comment point by point below, acknowledging the validity of the concern raised and outlining the revisions we will make to strengthen the analysis.

read point-by-point responses

Referee: The central claim that QBO amplitudes are partially decoupled from cycle strength (abstract and Results section) is based on linear fits to QBO amplitudes extracted in the 2–4 yr band. Because the 11-year cycle is orders of magnitude stronger and GONG series contain gaps, standard CWTs are susceptible to scale leakage even with cone-of-influence masking; any residual 11-year modulation that tracks the cycle envelope would systematically bias the recovered QBO amplitudes and therefore the reported slope difference. No synthetic-signal injection tests, cycle-subtracted comparisons, or gap-filling sensitivity checks are described, leaving the decoupling interpretation vulnerable to this artifact.

Authors: We acknowledge the referee's valid concern that scale leakage from the dominant 11-year cycle could potentially bias the extracted QBO amplitudes in the 2–4 yr band, especially given data gaps in the GONG series, and that this might affect the reported difference in linear slopes between Cycles 23 and 24. Although the chosen frequency band is well separated from the 11-year scale and cone-of-influence masking was applied, we agree that the absence of explicit validation tests leaves the decoupling interpretation open to this criticism. In the revised manuscript, we will add synthetic-signal injection tests: we will generate artificial time series containing known 11-year cycle envelopes plus superimposed QBO signals of varying amplitudes, apply the same CWT procedure (including gap handling), and quantify recovery accuracy and any residual leakage into the 2–4 yr band. We will also include cycle-subtracted comparisons and gap-filling sensitivity checks. These additions will directly test whether the observed slope difference remains significant after accounting for possible artifacts. We maintain that the current results support partial decoupling, but the proposed tests will provide the necessary rigor. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct outputs of wavelet analysis on external GONG data

full rationale

The paper applies standard continuous wavelet transforms to p-mode frequency shift time series from the independent GONG network. QBO amplitudes, periods, and ratios are extracted directly from the resulting scalograms at different latitudes and cycles. The reported linear relations and slope differences are ordinary least-squares fits to these extracted quantities versus independently measured cycle amplitudes; neither the extraction nor the fits reduce to the inputs by definition or via self-citation. No uniqueness theorems, ansatzes, or renamings of known results are invoked as load-bearing steps. The derivation chain is therefore self-contained observational analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on standard signal-processing assumptions and prior helioseismic data-reduction pipelines rather than new postulates.

axioms (1)

standard math Wavelet transform isolates quasi-periodic components in non-stationary time series without introducing spurious periods
Invoked implicitly when applying wavelet analysis to frequency-shift time series.

pith-pipeline@v0.9.0 · 5605 in / 1244 out tokens · 58455 ms · 2026-05-10T15:29:19.550779+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

By applying wavelet analysis to frequency shifts, we studied the changes in QBO periodicities... A Savitzky–Golay filter... was applied to capture the 11-year periodic variations... Continuous wavelet transform (CWT) powerspectrum of the residuals.
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

A linear relation between QBO amplitude and cycle amplitude is found in both cycles, but with significantly different slopes

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

4 extracted references · 2 canonical work pages

[1]

J., Elsworth Y., 2012, ApJ, 758, 43 Bazilevskaya G., Broomhall A

Basu S., 2016, Living Reviews in Solar Physics, 13, 2 Basu S., Broomhall A.-M., Chaplin W. J., Elsworth Y., 2012, ApJ, 758, 43 Bazilevskaya G., Broomhall A. M., Elsworth Y., Nakariakov V. M., 2014, Space Sci. Rev., 186, 359 Benevolenskaya E. E., 1998, ApJ, 509, L49 Broomhall A.-M., 2017, Sol. Phys., 292, 67 Broomhall A. M., Nakariakov V. M., 2015, Sol. Ph...

work page doi:10.1007/978-1-4939- 2016
[2]

2, Princeton University Press Deng L

- Vol. 2, Princeton University Press Deng L. H., Fei Y., Deng H., Mei Y., Wang F., 2020, MNRAS, 494, 4930 DikpatiM.,CallyP.S.,McIntoshS.W.,HeifetzE.,2017,ScientificReports, 7, 14750 ElsworthY.,HoweR.,IsaakG.R.,McLeodC.P.,NewR.,1990,Nature,345, 322 FletcherS.T.,BroomhallA.-M.,SalabertD.,BasuS.,ChaplinW.J.,Elsworth Y., Garcia R. A., New R., 2010, ApJ, 718, ...

work page doi:10.1007/3-540-53091-610.1007/3-540-53091-6_93 2020
[3]

For some bands, no periodicity was found with a confidence higher than 0.95, in which case they are marked with "-". Latitude band1900−2300 2100−2500 2300−2700 2500−2900 2700−3100 2900−3300 3100−3500 3300−3700 3500−3900 3700−4100 1900−4100 0−10 3.83 +0.32 −0.38 -1.21 +0.17 −0.22 1.63+0.38 −0.31 1.67+0.46 −0.37 1.56+1.56 −1.04 1.52+1.93 −1.01 1.52+1.93 −1....

1900
[4]

MNRAS000, 1–13 (2025) 14Hasanzadeh et al

Latitude band1900−2300 2100−2500 2300−2700 2500−2900 2700−3100 2900−3300 3100−3500 3300−3700 3500−3900 3700−4100 1900−4100 0−10-2.90 +0.34 −0.49 3.04+0.33 −0.42 - -1.15 +0.33 −0.33 1.21+0.37 −0.47 1.18+0.31 −0.44 - -1.15 +0.30 −0.32 10−20- -2.97 +0.05 −0.06 3.11+0.04 −0.06 3.11+0.34 −0.50 3.11+0.47 −0.60 2.97+0.68 −0.73 2.97+0.74 −0.75 3.11+0.69 −0.84 3.0...

1900