pith. sign in

arxiv: 2606.07132 · v1 · pith:G4UN36N5new · submitted 2026-06-05 · 🌌 astro-ph.SR

An optimized tidal-trigger model of the QBO, and some implications for the Carrington event

F. Stefani , G.M. Horstmann , G. Mamatsashvili , T. Weier This is my paper

Pith reviewed 2026-06-27 20:57 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords QBOtidal forcingmagneto-Rossby wavessolar tachoclineextreme solar eventsCarrington eventsunspot numberGLE events
0
0 comments X

The pith

Optimizing the magnetic-field dependence in a tidal QBO model raises its correlation with 109 extreme solar events to 0.8.

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

The paper aims to establish that a tidal-trigger model of the solar quasi-biennial oscillation can be substantially improved by incorporating how the strength of the toroidal magnetic field modulates the three magneto-Rossby waves triggered by planetary tides. The field strength is taken from averaged monthly sunspot numbers, and the parameters of this dependence are optimized against the same dataset of 109 ground-level enhancement events and S-flares. The resulting tidal-forcing function reaches a correlation of 0.8, well above the 0.4 value for the field-independent version and the 0.56 value for sunspot numbers alone. A reader would care because the refined model then links the 1.723-year tidal beat to the timing of the 1859 Carrington event and to activity clusters in 1989, while also offering forecasts for cycle 25.

Core claim

By parameterizing the dependence of the three tidally-triggered magneto-Rossby waves on the actual strength of the toroidal field at the tachocline and optimizing those parameters, the tidal-forcing function achieves correlations up to 0.8 with the 109 extreme solar events. This exceeds both the field-independent tidal forcing (approximately 0.4) and the correlation with sunspot number (approximately 0.56). The improved model is used to identify parallels between the Carrington event and the 1989 clustering of strong events and to issue cautious forecasts for the remainder of cycle 25.

What carries the argument

The magnetic-field dependence of the three tidally-triggered magneto-Rossby waves, parameterized from sunspot numbers and optimized on the event dataset.

If this is right

  • The optimized model identifies parallels between the 1859 Carrington event and the clustering of strong solar events in summer and autumn 1989.
  • Cautious forecasts become possible for the timing of extreme events in the remainder of solar cycle 25.
  • The tidal-forcing function with field dependence outperforms both the simpler tidal model and sunspot numbers as a descriptor of extreme-event timing.
  • The dominant 1.723-year period of the QBO aligns with the beat between the two-planet spring tides of Venus, Earth, and Jupiter.

Where Pith is reading between the lines

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

  • If the model is correct, the same tidal-plus-field framework could be tested on independent datasets of solar events collected after the optimization window.
  • Planetary tidal influences on the tachocline might be added as an external driver in existing solar dynamo simulations to check for improved reproduction of observed periodicities.
  • The approach could be extended to examine whether similar tidal beats appear in other solar or stellar activity records that also show quasi-biennial signals.

Load-bearing premise

That the magnetic-field dependence can be parameterized and its parameters optimized on the same 109-event dataset without the optimization introducing overfitting that inflates the reported correlation.

What would settle it

Whether the model's forecasts for extreme solar events in the remainder of cycle 25 align with the actual timing and occurrence of such events.

Figures

Figures reproduced from arXiv: 2606.07132 by F. Stefani, G. Mamatsashvili, G.M. Horstmann, T. Weier.

Figure 1
Figure 1. Figure 1: The 109 extreme solar events, including 72 GLE events and 37 S-flare events, shown alongside different functions. (a) Including the 13-months-averaged monthly sunspot number SSN for the entire time interval between 1956 and 2025. (b) Including the function s 2 (t) and two representative time averages of it. To improve visibility, we have selected only the time segment between days 8,000 and 16,000 after 19… view at source ↗
Figure 2
Figure 2. Figure 2: The 109 extreme solar events jointly with different averages of s 2 (t) for the param￾eter choice: a0 = b0 = c0 = 0, a2 = 0.7, b2 = 0.7, c2 = 1, a4 = 7.6, b4 = 4.0, c4 = 4.8. (a) With three representative time-averages of s 2 . (b) With three representative time-averages of the axisymmetric part of s 2 . determine at which time-shift between the tidal-trigger function and the solar events Corr is maximum … view at source ↗
Figure 3
Figure 3. Figure 3: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Zoomed-in version of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The Carrington event in the context of cycle 10, and compared also with cycle 22. (a) Sunspot number and computed 301-day average of s 2 (t) for cycle 10, with the Carrington event of 1859/09/01 indicated. During the 600 days before the event, SSN steadily rose (sym￾bolized by the yellow arrow) while s 2 (t) remained rather constant (light-blue arrow). (b) The corresponding plot for cycle 22, with the clus… view at source ↗
Figure 6
Figure 6. Figure 6: Predictions for the remainder of cycle 25. The yellow curve is divided into the measured SSN (full line) and the predicted one (dashed line) taken from ww.swpc.noaa.gov/products/predicted-sunspot-number-and-radio-flux. Obviously, the pre￾dicted s 2 (t) shows quite a couple of candidate peaks in the remainder of cycle 25 at which strong solar activity may be likely. event, s 2 (t) formed a relatively consta… view at source ↗
read the original abstract

Magneto-Rossby waves in the solar tachocline are currently being discussed as a potential cause of the quasi-biennial oscillation (QBO). By analyzing sequences of ground-level enhancement (GLE) events and S-flares, the dominant period of the QBO was recently shown to be close to 1.723 years, which is the dominant beat between the periods of the two-planet spring tides of Venus, Earth and Jupiter. We improve upon this model by taking into account the dependence of the three tidally-triggered magneto-Rossby waves on the actual strength of the toroidal field at the tachocline, which we infer from the averaged monthly sunspot number. When optimizing the parameters of this magnetic-field dependence, the correlation of the tidal-forcing function with the 109 extreme solar events reaches values of up to 0.8. This is much higher than the corresponding value for the field-independent tidal forcing function (appr. 0.4), and also higher than the correlation with the sunspot number (appr. 0.56). Based on this improved model, we discuss some interesting parallels between the Carrington event of 1859 and the clustering of strong solar events in summer and autumn 1989. We also make some cautious forecasts for the remainder of cycle 25.

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.

Referee Report

2 major / 1 minor

Summary. The paper claims that an optimized tidal-trigger model for the solar QBO, which incorporates a parameterized dependence of three tidally-triggered magneto-Rossby waves on toroidal-field strength (inferred from monthly sunspot number), yields a correlation of up to 0.8 with a set of 109 extreme solar events (GLEs and S-flares). This is presented as a substantial improvement over the field-independent tidal forcing (~0.4) and over sunspot number alone (~0.56). The optimized model is then used to identify parallels between the 1859 Carrington event and 1989 activity clusters and to offer cautious forecasts for the remainder of cycle 25.

Significance. If the reported correlation improvement can be shown to survive independent validation, the work would provide quantitative support for a tidal mechanism acting through magneto-Rossby waves whose efficiency depends on the ambient toroidal field. The explicit numerical comparison to both the unoptimized tidal model and to sunspot number is a methodological strength that allows readers to assess the incremental contribution.

major comments (2)
  1. [Abstract] Abstract: the parameters of the magnetic-field dependence are optimized on the identical 109-event dataset whose correlation is then reported as reaching 0.8. No cross-validation, hold-out set, or independent test period is described, so the improvement from ~0.4 to 0.8 is at least partly a direct consequence of the fitting procedure rather than an out-of-sample test of the model.
  2. [Abstract] Abstract (optimization procedure): the functional form relating the three magneto-Rossby waves to toroidal-field strength is not stated to have been pre-registered or derived from first principles; its free parameters are tuned to maximize agreement with the same events used for the final correlation statistic. This leaves open the possibility that the chosen dependence absorbs sample-specific variance rather than capturing a general physical effect.
minor comments (1)
  1. [Abstract] The abstract reports correlations to two decimal places (0.8, 0.4, 0.56) without accompanying uncertainties or p-values; adding these would help readers judge whether the reported differences are statistically distinguishable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The two major comments both concern the optimization procedure and its implications for the reported correlations. We address each point directly below, acknowledging the methodological limitations while providing the strongest honest defense of the work as presented.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the parameters of the magnetic-field dependence are optimized on the identical 109-event dataset whose correlation is then reported as reaching 0.8. No cross-validation, hold-out set, or independent test period is described, so the improvement from ~0.4 to 0.8 is at least partly a direct consequence of the fitting procedure rather than an out-of-sample test of the model.

    Authors: We agree that the optimization was performed on the full 109-event set and that this means the reported gain from ~0.4 to 0.8 cannot be interpreted as a fully independent validation. The comparison to sunspot number (~0.56) on the same events provides a relative benchmark, but does not remove the overfitting concern. In revision we will add an explicit statement in the methods and abstract noting that the parameters were tuned to the full dataset and that future work should test the model on independent intervals or via cross-validation. We retain the current numbers as an in-sample illustration of the possible improvement when field dependence is included. revision: yes

  2. Referee: [Abstract] Abstract (optimization procedure): the functional form relating the three magneto-Rossby waves to toroidal-field strength is not stated to have been pre-registered or derived from first principles; its free parameters are tuned to maximize agreement with the same events used for the final correlation statistic. This leaves open the possibility that the chosen dependence absorbs sample-specific variance rather than capturing a general physical effect.

    Authors: The functional form was selected on the basis of a simple physical argument that stronger toroidal fields should increase the efficiency of tidally triggered waves, but it is not derived from first principles and was not pre-registered. The parameters were indeed adjusted to improve agreement with the 109 events. We will revise the text to state this motivation and limitation more clearly and to label the model as exploratory. No change is made to the numerical results themselves, as they are presented as the outcome of the chosen parameterization. revision: partial

Circularity Check

1 steps flagged

Optimization of magnetic-field dependence parameters on the identical 109-event dataset produces the reported 0.8 correlation by construction.

specific steps
  1. fitted input called prediction [Abstract]
    "When optimizing the parameters of this magnetic-field dependence, the correlation of the tidal-forcing function with the 109 extreme solar events reaches values of up to 0.8. This is much higher than the corresponding value for the field-independent tidal forcing function (appr. 0.4), and also higher than the correlation with the sunspot number (appr. 0.56)."

    The parameters of the magnetic-field dependence are tuned on the 109-event dataset; the correlation is then evaluated on the identical dataset. The reported 0.8 value is therefore the maximized output of the fitting procedure itself, not an independent verification of the model.

full rationale

The paper's central result is obtained by fitting the functional form of the toroidal-field dependence (inferred from sunspot number) directly to the 109 GLE/S-flare events and then reporting the resulting correlation coefficient on those same events. This matches the fitted_input_called_prediction pattern: the improvement from ~0.4 to 0.8 is a direct statistical consequence of the optimization step rather than an independent test. No cross-validation, pre-specified functional form, or out-of-sample evaluation is described that would separate the fit from the claimed performance. The abstract explicitly states the optimization and the achieved correlation on the same data, making the reduction explicit.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on the untested premise that magneto-Rossby waves are tidally triggered and that their amplitude scales with toroidal field strength in a form that can be tuned to the event catalog. No independent evidence for the scaling function is provided.

free parameters (1)
  • parameters of magnetic-field dependence
    Explicitly optimized to maximize correlation with the 109 extreme solar events.
axioms (1)
  • domain assumption Magneto-Rossby waves in the solar tachocline are triggered by the two-planet spring tides of Venus, Earth and Jupiter.
    Stated as the physical mechanism underlying the QBO period of 1.723 years.

pith-pipeline@v0.9.1-grok · 5785 in / 1432 out tokens · 22885 ms · 2026-06-27T20:57:48.360702+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

36 extracted references · 31 canonical work pages

  1. [1]

    , Beer , J

    barticle Abreu , J.A. , Beer , J. , Ferriz-Mas , A. , McCracken , K.G. , Steinhilber , F. : 2012 , Is there a planetary influence on solar activity? Astron. Astrophys. 548 , A88 . 10.1051/0004-6361/201219997 . barticle

    work page doi:10.1051/0004-6361/201219997 2012

  2. [2]

    , Broomhall , A.-M

    barticle Bazilevskaya , G. , Broomhall , A.-M. , Elsworth , Y. , Nakariakov , V.M. : 2014 , A combined analysis of the observational aspects of the quasi-biennial oscillation in solar magnetic activity. Space Sci. Rev. 186 , 358 . 10.1007/s11214-014-0068-0 . barticle

    work page doi:10.1007/s11214-014-0068-0 2014

  3. [3]

    : 2020 , Manifestation of Rossby waves in the global magnetic field of the Sun during cycles 21-24

    barticle Bilenko , I.A. : 2020 , Manifestation of Rossby waves in the global magnetic field of the Sun during cycles 21-24 . Astrophys. J. 897 , L24 . 10.3847/2041-8213/ab9fa4 . barticle

    work page doi:10.3847/2041-8213/ab9fa4 2020

  4. [4]

    : 2022 , External forcing of the solar dynamo

    botherref Charbonneau , P. : 2022 , External forcing of the solar dynamo . Front. Astron. Space Sci. 9 , 853676 . 10.3389/fspas.2022.853676 . botherref

    work page doi:10.3389/fspas.2022.853676 2022

  5. [5]

    , Schrijver , C.J

    barticle Cliver , E.W. , Schrijver , C.J. , Shibata , K. , Usoskin , I.G. : 2022 , Extreme solar events . Liv. Rev. Sol. Phys. 19 , 2 . 10.1007/s41116-022-00033-8 . barticle

    work page doi:10.1007/s41116-022-00033-8 2022

  6. [6]

    : 2012 , Nonlinear evolution of the globale hydrodynami shallow-water instability in the solar tachocline

    barticle Dikpati , M. : 2012 , Nonlinear evolution of the globale hydrodynami shallow-water instability in the solar tachocline . Astrophys. J. 745 , 128 . 10.1088/0004-637X/745/2/128 . barticle

    work page doi:10.1088/0004-637x/745/2/128 2012

  7. [7]

    , McIntosh , S.W

    barticle Dikpati , M. , McIntosh , S.W. , Bothun , G. , Cally , P.S. , Ghosh , S.S. , Gilman , P.A. , Umurhan , O.M. : 2018 , Role of interaction between magnetic Rossby waves and tachocline differential rotation in producing solar seasons . Astrophys. J. 853 , 144 . 10.3847/1538-4357/aaa70d . barticle

    work page doi:10.3847/1538-4357/aaa70d 2018

  8. [8]

    , Gilman , P.A

    barticle Dikpati , M. , Gilman , P.A. , Chatterjee , S. , McIntosh , S.W. , Zaqarashvili , T.V. : 2020 , Physics of magnetohydrodynamic Rossby waves in the sun . Astrophys. J. 896 , 141 . 10.3847/1538-4357/ab8b63 . barticle

    work page doi:10.3847/1538-4357/ab8b63 2020

  9. [9]

    , Zaqarashvili , T.V

    barticle Gachechiladze , T. , Zaqarashvili , T.V. , Gurgenashvili , E. , Rameshvili , G. , Carbonell , M. , Oliver , R. , Ballester , J.L. 2019 , Magneto-Rossby waves in the solar tachocline and the annular variations in solar activity . Astrophys. J. 874 , 162 . 10.3847/1538-4357/ab0955 . barticle

    work page doi:10.3847/1538-4357/ab0955 2019

  10. [10]

    , Mamatsashvili , G

    barticle Horstmann , G. , Mamatsashvili , G. , Giesecke , A. , Zaqarashvili , T.V. , Stefani , F. : 2023 , Tidally forced planetary waves in the tachocline of solar-like stars . Astrophys. J. 944 , 48 . 10.3847/1538-4357/aca278 . barticle

    work page doi:10.3847/1538-4357/aca278 2023

  11. [11]

    : 2007 , Apparent relations between solar activity and solar tides caused by the planets

    barticle Hung , C.-C. : 2007 , Apparent relations between solar activity and solar tides caused by the planets. NASA/TM-2007-214817 . barticle

    2007

  12. [12]

    , Stefani , F

    barticle Klevs , M. , Stefani , F. , Jouve , L. : 2023 , A synchronized two-dimensional - model of the solar dynamo . Solar Phys. , 298 , 90 . 10.1007/s11207-023-02173-y . barticle

    work page doi:10.1007/s11207-023-02173-y 2023

  13. [13]

    , Jones , C.A

    barticle Marquez-Artavia , X. , Jones , C.A. , Tobias , S.M. : 2017 , Rotating magnetic shallow water waves and instabilities in a sphere . Geophys. Astrophys. Fluid Dyn. 111 , 282 . 10.1080/03091929.2017.1301937 . barticle

    work page doi:10.1080/03091929.2017.1301937 2017

  14. [14]

    , Thompson , R.J

    barticle McIntosh , P.S. , Thompson , R.J. , Willock , E.C. : 1992 , A 600-day periodicity in solar coronal holes. Nature 360 , 322 . 10.1038/360322a0 . barticle

    work page doi:10.1038/360322a0 1992

  15. [15]

    : 2016 , The gravitational influence of Venus, the Earth, and Jupiter on the 11-year cycle of solar activity

    barticle Okhlopkov , V.P. : 2016 , The gravitational influence of Venus, the Earth, and Jupiter on the 11-year cycle of solar activity . Mosc. Univ. Phys. B. 71 , 440 . 10.3103/S0027134916040159 . barticle

    work page doi:10.3103/s0027134916040159 2016

  16. [16]

    , Teruya , A.S

    barticle Raphaldini , B. , Teruya , A.S. , Raupp , C.F.M. , Bustamante , M.D. : 2019 , Nonlinear Rossby wave-wave and wave-mean flow theory for long-term solar cycle modulations . Astrophys. J. 887 , 1 . 10.3847/1538-4357/ab5067 . barticle

    work page doi:10.3847/1538-4357/ab5067 2019

  17. [17]

    : 1939 , Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action

    barticle Rossby , C.-G. : 1939 , Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action . J. Mar. Res. 2 , 38--55 , barticle

    1939

  18. [18]

    , Lockwood , M

    barticle Rouillard , A. , Lockwood , M. : 2004 , Oscillations in the open solar magnetic flux with a period of 1.68 years: imprint on galactic cosmic rays and implications for heliospheric shielding . Ann. Geophys. 22 , 4381 . 10.5194/angeo-22-4381-2004 . barticle

    work page doi:10.5194/angeo-22-4381-2004 2004

  19. [19]

    : 2012 , Does the Sun work as a nuclear fusion amplifier of planetary tidal forcing? A proposal for a physical mechanism based on the mass-luminosity relation

    barticle Scafetta , N. : 2012 , Does the Sun work as a nuclear fusion amplifier of planetary tidal forcing? A proposal for a physical mechanism based on the mass-luminosity relation . J. Atmos. Sol.-Terr. Phys. 81-82 , 27 . 10.1016/j.jastp.2012.04.002 . barticle

    work page doi:10.1016/j.jastp.2012.04.002 2012

  20. [20]

    , Bianchini , A

    barticle Scafetta , N. , Bianchini , A. , 2022 , The planetary theory of solar activity variability: A review. Front. Astron. Space Sci. 9 , 937930 . 10.3389/fspas.2022.937930 . barticle

    work page doi:10.3389/fspas.2022.937930 2022

  21. [21]

    , Giesecke , A

    barticle Stefani , F. , Giesecke , A. , Weber , N. , Weier , T. : 2016 , Synchronized helicity oscillations: a link between planetary tides and the solar cycle? Solar Phys. 291 , 2197 . 10.1007/s11207-016-0968-0 . barticle

    work page doi:10.1007/s11207-016-0968-0 2016

  22. [22]

    , Giesecke , A

    barticle Stefani , F. , Giesecke , A. , Weier , T. : 2019 , A model of a tidally synchronized solar dynamo . Solar Phys. 294 , 60 . 10.1007/s11207-019-1447-1 . barticle

    work page doi:10.1007/s11207-019-1447-1 2019

  23. [23]

    , Giesecke , A

    barticle Stefani , F. , Giesecke , A. , Seilmayer , M. , Stepanov , R. , Weier , T. : 2020a , Schwabe, Gleissberg, Suess-de Vries: Towards a consistent model of planetary synchronization of solar cycles . Magnetohydrodynamics , 56 , 269 . 10.22364/mhd.56.2-3.18 . barticle

    work page doi:10.22364/mhd.56.2-3.18

  24. [24]

    , Stepanov , W

    barticle Stefani , F. , Stepanov , W. , Weier , T. : 2021 , Shaken and stirred: When Bond meets Suess-de Vries and Gnevyshev-Ohl . Solar Phys. 296 , 88 . 10.1007/s11207-021-01822-4 . barticle

    work page doi:10.1007/s11207-021-01822-4 2021

  25. [25]

    , Horstmann , G.M

    barticle Stefani , F. , Horstmann , G.M. , Mamatsashvili , G. , Weier , T. : 2024 , Rieger, Schwabe, Suess-de Vries: The sunny beats of resonance . Solar Phys. 299 , 51 . 10.1007/s11207-024-02295-x . barticle

    work page doi:10.1007/s11207-024-02295-x 2024

  26. [26]

    , Horstmann , G.M

    barticle Stefani , F. , Horstmann , G.M. , Mamatsashvili , G. , Weier , T. : 2025 , Adding further pieces to the synchronization puzzle: QBO, bimodality, and phase jumps . Solar Phys. 300 , 110 . 10.1007/s11207-025-02521-0 . barticle

    work page doi:10.1007/s11207-025-02521-0 2025

  27. [27]

    , Horstmann , G.M

    barticle Stefani , F. , Horstmann , G.M. , Mamatsashvili , G. , Weier , T. : 2026 , Tidal triggers and the predictability of solar activity . Astrophys. J. in press , arXiv:2602.11227 . barticle

    Pith/arXiv arXiv 2026

  28. [28]

    , Zhang , Y

    barticle Tan , B. , Zhang , Y. , Huang , J. , Ji , K. : 2025 , The occurrence of powerful flares stronger than X10 class in solar cycles . Astrophys. J. Lett. 979 , L16 . 10.3847/2041-8213/ada611 . barticle

    work page doi:10.3847/2041-8213/ada611 2025

  29. [29]

    , P \'e rez-Enr \'i quz , R

    barticle Vald\' e s-Galicia , J.F. , P \'e rez-Enr \'i quz , R. , Otaola , J.A. 1996 , The cosmic-ray 1.68-year variation: A clue to understand the nature of the solar cycle? Solar Phys. 167 , 409 . barticle

    1996

  30. [30]

    , P\' e rez-Peraza , J

    barticle Velasco Herrera , V.M. , P\' e rez-Peraza , J. , Soon , W. , M\' a rquez-Adame , J.C. : 2018 , The quasi-biennial oscillation of 1.7 years in ground level enhancement events. New Astron. 60 , 7-18 . 10.1016/j.newast.2017.09.007 . barticle

    work page doi:10.1016/j.newast.2017.09.007 2018

  31. [31]

    , Velasco Herrera , G , Soon , W

    barticle Velasco Herrera , V.M. , Velasco Herrera , G , Soon , W. , \"Ozg\"uc , A. , Babynets , N. , Tlatov , A , Svanda , M. , Qiu , S. , Baliunas , S. , Kotan , B , Gonzalez Gonzalez , G. , Bautista Flores , L.A. , Pazos , M. : 2026 , A New Method for Probabilistic Spatiotemporal Forecasts of Solar Soft X-Ray ``S-Class '' (>X10) Superflares. J. Geophys....

    work page doi:10.1029/2025ja034977 2026

  32. [32]

    : 2013 , The Venus-Earth-Jupiter spin-orbit coupling model

    barticle Wilson , I.R.G. : 2013 , The Venus-Earth-Jupiter spin-orbit coupling model . Pattern Recogn. Phys. 1 , 147 . barticle

    2013

  33. [33]

    , Carbonell , M

    barticle Zaqarashvili , T. , Carbonell , M. , Oliver , R. , Ballester , J.L. : 2010a , Quasi-biennial oscillations in the solar tachocline caused by magnetic Rossby wave instabilities . Astrophys. J. Lett. 724 , L95-L98 . 10.1088/2041-8205/724/1/L95 . barticle

    work page doi:10.1088/2041-8205/724/1/l95 2041

  34. [34]

    , Carbonell , M

    barticle Zaqarashvili , T. , Carbonell , M. , Oliver , R. , Ballester , J.L. : 2010b , Magnetic Rossby waves in the solar tachocline and Rieger-type periodicities . Astrophys. J. 709 , 749 . 10.1088/0004-637X/709/2/749 . barticle

    work page doi:10.1088/0004-637x/709/2/749

  35. [35]

    : 2018 , Equatorial magnetohydrodynamic shallow water waves in the solar tachocline

    barticle Zaqarashvili , T. : 2018 , Equatorial magnetohydrodynamic shallow water waves in the solar tachocline . Astrophys. J. 856 , 32 . 10.3847/1538-4357/aab26f . barticle

    work page doi:10.3847/1538-4357/aab26f 2018

  36. [36]

    , Albekioni , M

    barticle Zaqarashvili , T. , Albekioni , M. , Ballester , J.L. , Bekki , Y. , Biancofiero , L. , Birch , A.C. , Dikpati , M. , Gizon , L. , Gurgenashvili , E. , Heifetz , E. , Lanca , A.F. , McIntosh , S.W. , Ofman , L. , Oliver , R. , Proxauf , B. , Umurhan , O.M. , Yellin-Bergovoy , R. , 2021 , Rossby waves in astrophysics . Space Sci. Rev. 217 , 15 . 1...

    work page doi:10.1007/s11214-021-00790-2 2021