REVIEW 3 major objections 6 minor 87 references
Analyses of features of magnetic cycles at different amounts of dynamo supercriticality: Solar dynamo is about two times critical
T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash
Pith's one-line read Sun's magnetic dynamo runs only about twice past its critical threshold
desk verdict A plausible but not tightly pinned-down estimate that the solar dynamo is about two times critical, supported by multi-model consistency but limited by single runs and fixed noise levels. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The quantity that carries the argument is $\hat{\alpha}_0 = \alpha_0/\alpha_0^{\rm crit}$, the amplitude of the Babcock-Leighton α effect normalized by the value at which each model first sustains a growing magnetic field. The models are axisymmetric flux-transport dynamos (Models I-III) and truncated time-delay dynamos (Models IV-V), all kinematic with prescribed nonlinear quenching and stochastic fluctuations in the α source. Each model is run at $\hat{\alpha}_0 = 2, 4, 8$ for 11,000 years, and the resulting cycle statistics are compared with reconstructed solar activity and with the observed recovery slope after the Maunder minimum. This comparison is what lets the authors translate cycle statistics into a statement about how far the Sun is from the dynamo threshold.
What would settle it
Measure the rise slope of every well-resolved grand-minimum recovery in the 11,000-year cosmogenic record and compare the distribution with the model slopes at $\hat{\alpha}_0=2,4,8$; a distribution centered above the $\hat{\alpha}_0=2$ predictions would falsify the claim.
Extended reading notes
Core claim
The central claim is that the solar dynamo's supercriticality, measured by $\hat{\alpha}_0 = \alpha_0/\alpha_0^{\rm crit}$, is only about 2 rather than a large value. In all four models that were tested for recovery, the rise of sunspot number after an imposed Maunder-like suppression matches the observed 1700-1730 recovery only at $\hat{\alpha}_0 = 2$; at higher values the model rebounds too quickly. The 11,000-year simulations also produce roughly the observed number of grand minima (27) and maxima (23) only near $\hat{\alpha}_0 = 2$, while higher supercriticality makes deep minima rarer and shorter. The paper also argues that the observed weak correlation between polar-field proxies and the amplitude of cycles two and three ahead, and the Gnevyshev-Ohl pairing statistics, are compatible with a two-times-critical dynamo rather than contradicting it.
Load-bearing premise
The inference assumes the Sun's fluctuation level in the α (poloidal-source) effect is the same as the fixed values inherited from earlier calibrations; if the real fluctuation amplitude differs, the inferred supercriticality of about two would shift.
Editorial extensions
If this is right
- The Sun's dynamo is only weakly supercritical, so a modest further decline in rotation with age could push it below the threshold and end large-scale magnetic activity.
- Grand minima like the Maunder minimum should be comparatively frequent and long at $\hat{\alpha}_0 \approx 2$, consistent with the historical record.
- Recovery from any future deep minimum should be gradual, taking roughly 30 years, as in the 1700-1730 recovery.
- Polar-field memory in the dynamo should extend only weakly beyond one cycle, so cycle prediction based on the polar field at minimum should not expect strong skill two or three cycles ahead.
- The Gnevyshev-Ohl even-odd pattern should continue to hold with occasional violations, matching the observed pairing statistics.
Reading between the lines
- Editorial inference: if $\hat{\alpha}_0 \approx 2$ is robust, stellar samples should show a relatively sharp drop in magnetic activity as rotation slows past the equivalent threshold, and stars slightly above it should show frequent Maunder-like minima.
- Editorial inference: the paper's noise amplitudes are fixed; a testable extension would vary the fluctuation level jointly with $\hat{\alpha}_0$ to map the degeneracy and see whether the inferred factor of two broadens.
- Editorial inference: the same comparison could be applied to the historical cosmogenic isotope records of other Sun-like stars once their dynamo numbers are constrained, offering a stellar check on weakly supercritical operation.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper estimates the solar dynamo's supercriticality, defined as alpha_hat = alpha0 / alpha0_crit, by running five Babcock-Leighton type kinematic dynamo models (flux transport and time-delay variants) at alpha_hat = 2, 4, and 8 with fixed stochastic fluctuation amplitudes. It compares three diagnostics against observations: the recovery rate from a Maunder-like grand minimum, the number and duration of grand minima and maxima in 11,000-year simulations, and consistency checks using polar-field memory correlations and the Gnevyshev-Ohl rule. The authors conclude that the solar dynamo is only about two times critical. The manuscript is clearly written and makes an interesting, observationally grounded claim, but the central inference currently rests on statistical and degeneracy assumptions that are not fully addressed.
Significance. If correct, the conclusion that the solar dynamo operates at roughly twice the critical dynamo threshold would support a weakly supercritical regime consistent with frequent grand minima and gradual Maunder recovery, with implications for stellar activity evolution and gyrochronology. The study's strengths include the use of multiple independent dynamo models, long 11,000-year simulations comparable to cosmogenic reconstructions, and explicit matching to observed grand-minima counts. The authors also acknowledge kinematic limitations and their results align with several previous independent estimates. However, the significance is currently limited by the absence of ensemble statistics and by the fixed noise amplitudes inherited from prior calibrations, which are degenerate with supercriticality in controlling rare-event statistics.
major comments (3)
- [Section 3.2, Table 1] The central statistical comparison uses a single 11,000-year realization per (model, alpha_hat) cell, with no ensemble spread or error bars. For counting statistics, Poisson fluctuations of sqrt(N) are roughly 4-5 events, which is comparable to the differences between alpha_hat = 2 and alpha_hat = 4 in several models (e.g., Model I: 20 vs 8; Model II: 18 vs 8; Model III: 16 vs 9). Without multiple realizations or a properly propagated uncertainty estimate, the claim that alpha_hat = 2 is statistically preferred over alpha_hat = 4 is not supported by the presented data. This is a load-bearing issue for the main conclusion.
- [Section 2.1 and Table 1] The fluctuation amplitudes of the alpha effect are fixed at values inherited from previous calibrations (e.g., Gaussian sigma = 2.67 for Models I and II; 200%, 100%, and 70% uniform fluctuations for Models III, IV, and V) and are never varied. Grand-minima statistics depend jointly on supercriticality and noise amplitude, so the observed 27 grand minima in 11,000 years could plausibly be reproduced at alpha_hat = 4 with a somewhat lower noise level than assumed. Because the paper does not explore this degeneracy, the inference 'alpha_hat = 2' is not uniquely identified by the statistics. The sentence in Section 3, 'for each model, the level of fluctuations in alpha remains the same,' confirms the fixed-noise assumption but does not justify it for the supercriticality sweep.
- [Section 3.1, Figures 1-2] The Maunder-minimum recovery comparison is qualitative and based on a single observed event and a single imposed initial perturbation (multiplying the polar field by gamma_p = 0.1). No quantitative goodness-of-fit measure is given, the sensitivity to gamma_p is not explored, and the results for Models II, III, and IV are only asserted in the text with no figures or numerical values. The exclusion of Model V is explained, but the overall constraint from this diagnostic is weak and should be framed accordingly.
minor comments (6)
- [Section 3.1] The text states 'the robust result in all four models (I–VI)' — the parenthetical appears to be a typo for 'I–IV' (or 'I–V' with V excluded), and should be corrected.
- [Section 3.2] The phrase 'namely, Models III-VI' should read 'Models III-V', since only five models are used in total.
- [Table 2 and Section 3.2] For the time-delay models (IV and V), durations in Table 2 are not reported because the time unit is dimensionless; this makes comparison with the flux-transport models and observations difficult. A conversion or a clear statement of the cycle-length normalization would improve readability.
- [Section 3.3.1, Table 3] The correlation coefficients for Models I and II in Table 3 are taken from Kumar, Karak, and Vashishth (2021) at alpha_hat = 2 and are not computed in the present study; this should be stated in the table caption to avoid implying new calculations.
- [Section 3.3.2 and Figure 6] The Gnevyshev-Ohl comparison is based on Model IV alone and on observed data with large reconstruction uncertainties; the authors correctly note that the comparison is not robust. This section is appropriately cautious, but the caveat should also appear in the Conclusions where the GO rule is listed as a supporting feature.
- [Abstract and Introduction] The abstract contains a grammatical error: 'with that of observations and we show' should be 'with observations, we show'. Also, Eq. (1) defines the dynamo number D, but subsequent analysis uses alpha_hat = alpha0/alpha0_crit; the relationship between these two measures should be clarified earlier.
Circularity Check
The alpha_hat = 2 conclusion is partly degenerate with the fixed, previously calibrated alpha-fluctuation amplitude used to drive grand minima; other diagnostics are independent, so circularity is partial.
-
fitted input called prediction
[Section 1 (fluctuations explain grand minima), Section 2.1 (Gaussian sigma = 2.67), Section 3 and Section 3.2 / Table 1 (same fluctuation level for all alpha_hat0; grand-minima count comparison)]
"These fluctuations in the Babcock–Leighton dynamo models explain majority of the irregular features of solar cycle, including long-term modulation and grand minima ... When we introduce fluctuations in these models, we multiply α0 by a Gaussian of unity mean and 2.67 standard deviation as inspired by the study of Olemskoy, Choudhuri, and Kitchatinov (2013) ... In our study, for each model, we perform a set of solar cycle simulations at ˆα0 = 2, 4, and 8, and for each model, the level of fluctuations in α remains the same."
The central selection of alpha_hat = 2 rests on matching the 11,000-year grand-minima/maxima counts (observed 27/23) to models with fixed fluctuation amplitudes. But the grand-minima frequency is a joint function of supercriticality and noise amplitude, and the paper varies only alpha_hat while importing sigma from prior calibrations that, by the paper's own statement, were already used to reproduce 'long-term modulation and grand minima.' Thus the count comparison is not an independent test of supercriticality: a different sigma would shift the best-matching alpha_hat. The inference is partially degenerate with the inherited noise input, although the Maunder-recovery rate, duration statistics, and polar-field consistency checks provide separate evidence for weak supercriticality.
full rationale
The paper's main claim is that the solar dynamo is only about twice critical (alpha_hat = 2). The inference is drawn from several diagnostics, with the grand-minima/maxima counts in Section 3.2 acting as the strongest quantitative discriminator. Those counts are produced by models in which the stochastic alpha-fluctuation amplitude is a fixed input inherited from earlier studies, several by the same authors, and the paper explicitly states that these fluctuations were designed to explain 'long-term modulation and grand minima.' Consequently, the comparison of counts is partly circular: it constrains a combination of supercriticality and noise, not supercriticality alone. However, the paper also compares the Maunder-minimum recovery slope (Section 3.1) and grand-minima durations (Table 2), which are not governed by the same fitted noise parameter, and it uses the polar-field memory and Gnevyshev–Ohl assessments only as consistency checks. These independent diagnostics support the same conclusion, so the circularity is local to the count comparison and does not make the entire derivation tautological. The score of 4 reflects partial circularity of the central claim without full reduction by construction.
Assumptions & free parameters
free parameters (8)
- Fluctuation amplitude of alpha effect (Models I and II) =
Gaussian, sigma = 2.67
- Fluctuation level (Model III) =
200% uniform
- Fluctuation level (Model IV) =
100% uniform
- Fluctuation level (Model V) =
70% uniform
- Mean-field alpha amplitude (Model III) =
alpha0MF = 0.4
- Mean-field alpha amplitude (Model IV) =
alpha_mf = 0.2
- Polar-field suppression factor for Maunder recovery =
gamma_p = 0.1
- Supercriticality grid =
alpha_hat = 2, 4, 8
assumptions (5)
- domain assumption The Babcock-Leighton mechanism, with observationally motivated fluctuations, is the dominant poloidal-field source for the solar dynamo.
- domain assumption Kinematic dynamo models with prescribed nonlinear quenching capture the relevant dynamics for long-term cycle statistics.
- domain assumption The reconstructed grand-minima and maxima statistics from cosmogenic isotopes (27 minima, 23 maxima in 11,000 years) are accurate.
- ad hoc to paper A single 11,000-year run per model and supercriticality is representative of the stochastic statistics.
- ad hoc to paper The fluctuation amplitudes inherited from prior calibrations are applicable at all supercriticality values tested.
Cite this review
Pith. "Pith review of Analyses of features of magnetic cycles at different amounts of dynamo supercriticality: Solar dynamo is about two times critical." pith.science (2026). https://pith.science/paper/KAC5BNXQ
@misc{pith2026250102262,
author = {Pith},
title = {Pith review of: Analyses of features of magnetic cycles at different amounts of dynamo supercriticality: Solar dynamo is about two times critical},
year = {2026},
howpublished = {\url{https://pith.science/paper/KAC5BNXQ}},
note = {Machine review of arXiv:2501.02262}
}
read the original abstract
The growth of a large-scale magnetic field in the Sun and stars is usually possible when the dynamo number (D) is above a critical value Dc. As the star ages, its rotation rate and thus D decrease. Hence, the question is how far the solar dynamo is from the critical dynamo transition. To answer this question, we have performed a set of simulations using Babcock-Leighton type dynamo models at different values of dynamo supercriticality and analyzed various features of magnetic cycle. By comparing the recovery rates of the dynamo from the Maunder minimum and statistics (numbers and durations) of the grand minima and maxima with that of observations and we show that the solar dynamo is only about two times critical and thus not highly supercritical. The observed correlation between the polar field proxy and the following cycle amplitudes and Gnevyshev-Ohl rule are also compatible with this conclusion.
Figures
Figures from the paper (5 more)
Reference graph
Works this paper leans on
-
[1]
barticle Albert , C. , Ferriz-Mas , A. , Gaia , F. , Ulzega , S. : 2021 , Can Stochastic Resonance Explain Recurrence of Grand Minima? 916 , L9 . https://doi.org/10.3847/2041-8213/ac0fd6 . 2021ApJ...916L...9A . barticle
-
[2]
barticle Augustson , K. , Brun , A.S. , Miesch , M. , Toomre , J. : 2015 , Grand Minima and Equatorward Propagation in a Cycling Stellar Convective Dynamo . 809 , 149 . https://doi.org/10.1088/0004-637X/809/2/149 . 2015ApJ...809..149A . barticle
-
[3]
: 1961 , The Topology of the Sun's Magnetic Field and the 22-YEAR Cycle
barticle Babcock , H.W. : 1961 , The Topology of the Sun's Magnetic Field and the 22-YEAR Cycle. 133 , 572 . https://doi.org/10.1086/147060 . 1961ApJ...133..572B . barticle
doi:10.1086/147060 1961
-
[4]
barticle Bhowmik , P. , Nandy , D. : 2018 , Prediction of the strength and timing of sunspot cycle 25 reveal decadal-scale space environmental conditions . Nature Communications 9 , 5209 . https://doi.org/10.1038/s41467-018-07690-0 . 2018NatCo...9.5209B . barticle
-
[5]
barticle Biswas , A. , Karak , B.B. , Kumar , P. : 2023 , Exploring the reliability of polar field rise rate as a precursor for an early prediction of solar cycle . 526 , 3994 . https://doi.org/10.1093/mnras/stad2966 . 2023MNRAS.526.3994B . barticle
-
[6]
barticle Biswas , A. , Karak , B.B. , Usoskin , I. , Weisshaar , E. : 2023 , Long-Term Modulation of Solar Cycles . 219 , 19 . https://doi.org/10.1007/s11214-023-00968-w . 2023SSRv..219...19B . barticle
-
[7]
barticle Brun , A.S. , Browning , M.K. : 2017 , Magnetism, dynamo action and the solar-stellar connection . Living Reviews in Solar Physics 14 , 4 . https://doi.org/10.1007/s41116-017-0007-8 . 2017LRSP...14....4B . barticle
-
[8]
barticle Brun , A.S. , Miesch , M.S. , Toomre , J. : 2004 , Global-Scale Turbulent Convection and Magnetic Dynamo Action in the Solar Envelope . 614 , 1073 . https://doi.org/10.1086/423835 . 2004ApJ...614.1073B . barticle
doi:10.1086/423835 2004
Show all 87 references
-
[9]
, Strugarek , A
barticle Brun , A.S. , Strugarek , A. , Varela , J. , Matt , S.P. , Augustson , K.C. , Emeriau , C. , DoCao , O.L. , Brown , B. , Toomre , J. : 2017 , On Differential Rotation and Overshooting in Solar-like Stars . 836 , 192 . https://doi.org/10.3847/1538-4357/aa5c40 . 2017ApJ...
2017 doi
-
[10]
, Strugarek , A
barticle Brun , A.S. , Strugarek , A. , Noraz , Q. , Perri , B. , Varela , J. , Augustson , K. , Charbonneau , P. , Toomre , J. : 2022 , Powering Stellar Magnetism: Energy Transfers in Cyclic Dynamos of Sun-like Stars . 926 , 21 . https://doi.org/10.3847/1538-4357/ac469b . 202...
2022 doi
-
[11]
, Sch \"u ssler , M
barticle Cameron , R. , Sch \"u ssler , M. : 2015 , The crucial role of surface magnetic fields for the solar dynamo . Science 347 , 1333 . https://doi.org/10.1126/science.1261470 . 2015Sci...347.1333C . barticle
2015 doi
-
[12]
, Sch \"u ssler , M
barticle Cameron , R.H. , Sch \"u ssler , M. : 2017 , Understanding Solar Cycle Variability . 843 , 111 . https://doi.org/10.3847/1538-4357/aa767a . 2017ApJ...843..111C . barticle
2017 doi
-
[13]
, Sch \"u ssler , M
barticle Cameron , R.H. , Sch \"u ssler , M. : 2019 , Solar activity: periodicities beyond 11 years are consistent with random forcing . 625 , A28 . https://doi.org/10.1051/0004-6361/201935290 . 2019A&A...625A..28C . barticle
2019 doi
-
[14]
, Sch \"u ssler , M
barticle Cameron , R.H. , Sch \"u ssler , M. : 2023 , Observationally Guided Models for the Solar Dynamo and the Role of the Surface Field . 219 , 60 . https://doi.org/10.1007/s11214-023-01004-7 . 2023SSRv..219...60C . barticle
2023 doi
-
[15]
: 2020 , Dynamo models of the solar cycle
barticle Charbonneau , P. : 2020 , Dynamo models of the solar cycle . Living Reviews in Solar Physics 17 , 4 . https://doi.org/10.1007/s41116-020-00025-6 . 2020LRSP...17....4C . barticle
2020 doi
-
[16]
, Barlet , G
barticle Charbonneau , P. , Barlet , G. : 2011 , The dynamo basis of solar cycle precursor schemes . Journal of Atmospheric and Solar-Terrestrial Physics 73 , 198 . https://doi.org/10.1016/j.jastp.2009.12.020 . 2011JASTP..73..198C . barticle
2011 doi
-
[17]
, Dikpati , M
barticle Charbonneau , P. , Dikpati , M. : 2000 , Stochastic Fluctuations in a Babcock-Leighton Model of the Solar Cycle . 543 , 1027 . https://doi.org/10.1086/317142 . 2000ApJ...543.1027C . barticle
2000 doi
-
[18]
, Blais-Laurier , G
barticle Charbonneau , P. , Blais-Laurier , G. , St-Jean , C. : 2004 , Intermittency and Phase Persistence in a Babcock-Leighton Model of the Solar Cycle . 616 , L183 . https://doi.org/10.1086/426897 . 2004ApJ...616L.183C . barticle
2004 doi
-
[19]
, St-Jean , C
barticle Charbonneau , P. , St-Jean , C. , Zacharias , P. : 2005 , Fluctuations in Babcock-Leighton Dynamos. I. Period Doubling and Transition to Chaos . 619 , 613 . https://doi.org/10.1086/426385 . 2005ApJ...619..613C . barticle
2005 doi
-
[20]
, Nandy , D
barticle Chatterjee , P. , Nandy , D. , Choudhuri , A.R. : 2004 , Full-sphere simulations of a circulation-dominated solar dynamo: Exploring the parity issue . 427 , 1019 . https://doi.org/10.1051/0004-6361:20041199 . 2004A\ barticle
2004 doi
-
[21]
, Hazra , G
barticle Choudhuri , A.R. , Hazra , G. : 2016 , The treatment of magnetic buoyancy in flux transport dynamo models . Advances in Space Research 58 , 1560 . https://doi.org/10.1016/j.asr.2016.03.015 . 2016AdSpR..58.1560C . barticle
2016 doi
-
[22]
, Karak , B.B
barticle Choudhuri , A.R. , Karak , B.B. : 2009 , A possible explanation of the Maunder minimum from a flux transport dynamo model . Res. Astron. Astrophys. 9 , 953 . https://doi.org/10.1088/1674-4527/9/9/001 . 2009RAA.....9..953C . barticle
2009 doi
-
[23]
, Karak , B.B
barticle Choudhuri , A.R. , Karak , B.B. : 2012 , Origin of Grand Minima in Sunspot Cycles . Phys. Rev. Lett. 109 , 171103 . barticle
2012
-
[24]
, Chatterjee , P
barticle Choudhuri , A.R. , Chatterjee , P. , Jiang , J. : 2007 , Predicting Solar Cycle 24 With a Solar Dynamo Model . Physical Review Letters 98 , 131103 . https://doi.org/10.1103/PhysRevLett.98.131103 . 2007PhRvL..98m1103C . barticle
2007 doi
-
[25]
, Nandy , D
barticle Choudhuri , A.R. , Nandy , D. , Chatterjee , P. : 2005 , Reply to the Comments of Dikpati et al. 437 , 703 . https://doi.org/10.1051/0004-6361:20052934 . 2005A&A...437..703C . barticle
2005 doi
-
[26]
, Sch\"ussler , M
barticle Choudhuri , A.R. , Sch\"ussler , M. , Dikpati , M. : 1995 , The solar dynamo with meridional circulation. 303 , L29 . 1995A\ barticle
1995
-
[27]
, Solanki , S.K
barticle Dasi-Espuig , M. , Solanki , S.K. , Krivova , N.A. , Cameron , R. , Pe \ n uela , T. : 2010 , Sunspot group tilt angles and the strength of the solar cycle . 518 , A7 . https://doi.org/10.1051/0004-6361/201014301 . 2010A\ barticle
2010 doi
-
[28]
, Charbonneau , P
barticle Dikpati , M. , Charbonneau , P. : 1999 , A Babcock-Leighton Flux Transport Dynamo with Solar-like Differential Rotation . 518 , 508 . https://doi.org/10.1086/307269 . 1999ApJ...518..508D . barticle
1999 doi
-
[29]
: 1976 , The Maunder Minimum
barticle Eddy , J.A. : 1976 , The Maunder Minimum . Science 192 , 1189 . https://doi.org/10.1126/science.192.4245.1189 . 1976Sci...192.1189E . barticle
1976
-
[30]
, Fang , F
barticle Fan , Y. , Fang , F. : 2014 , A Simulation of Convective Dynamo in the Solar Convective Envelope: Maintenance of the Solar-like Differential Rotation and Emerging Flux . 789 , 35 . https://doi.org/10.1088/0004-637X/789/1/35 . http://esoads.eso.org/abs/2014ApJ...789......
2014 doi
-
[31]
, Karak , B.B
botherref Garg , S. , Karak , B.B. , Egeland , R. , Soon , W. , Baliunas , S. : 2019, Waldmeier Effect in Stellar Cycles . arXiv e-prints, arXiv:1909.12148. 2019arXiv190912148G . botherref
2019 arXiv
-
[32]
, Kumar , P
barticle Ghosh , A. , Kumar , P. , Prasad , A. , Karak , B.B. : 2024 , Characterizing the Solar Cycle Variability Using Nonlinear Time Series Analysis at Different Amounts of Dynamo Supercriticality: Solar Dynamo is Not Highly Supercritical . 167 , 209 . https://doi.org/10.384...
2024 doi
-
[33]
: 2015 , The Solar Cycle
barticle Hathaway , D.H. : 2015 , The Solar Cycle . Living Reviews in Solar Physics 12 , 4 . https://doi.org/10.1007/lrsp-2015-4 . 2015LRSP...12....4H . barticle
2015 doi
-
[34]
, Choudhuri , A.R
barticle Hazra , G. , Choudhuri , A.R. : 2019 , A New Formula for Predicting Solar Cycles . 880 , 113 . https://doi.org/10.3847/1538-4357/ab2718 . 2019ApJ...880..113H . barticle
2019 doi
-
[35]
, Nandy , D
barticle Hazra , G. , Nandy , D. , Kitchatinov , L. , Choudhuri , A.R. : 2023 , Mean Field Models of Flux Transport Dynamo and Meridional Circulation in the Sun and Stars . 219 , 39 . https://doi.org/10.1007/s11214-023-00982-y . 2023SSRv..219...39H . barticle
2023 doi
-
[36]
, Passos , D
barticle Hazra , S. , Passos , D. , Nandy , D. : 2014 , A Stochastically Forced Time Delay Solar Dynamo Model: Self-consistent Recovery from a Maunder-like Grand Minimum Necessitates a Mean-field Alpha Effect . 789 , 5 . https://doi.org/10.1088/0004-637X/789/1/5 . 2014ApJ...78...
2014 doi
-
[37]
, Kusano , K
barticle Hotta , H. , Kusano , K. , Shimada , R. : 2022 , Generation of Solar-like Differential Rotation . 933 , 199 . https://doi.org/10.3847/1538-4357/ac7395 . 2022ApJ...933..199H . barticle
2022 doi
-
[38]
, Karak , B.B
barticle Jha , B.K. , Karak , B.B. , Mandal , S. , Banerjee , D. : 2020 , Magnetic Field Dependence of Bipolar Magnetic Region Tilts on the Sun: Indication of Tilt Quenching . 889 , L19 . https://doi.org/10.3847/2041-8213/ab665c . 2020ApJ...889L..19J . barticle
2020 doi
-
[39]
, Cameron , R.H
barticle Jiang , J. , Cameron , R.H. , Sch \"u ssler , M. : 2014 , Effects of the Scatter in Sunspot Group Tilt Angles on the Large-scale Magnetic Field at the Solar Surface . 791 , 5 . https://doi.org/10.1088/0004-637X/791/1/5 . 2014ApJ...791....5J . barticle
2014 doi
-
[40]
a pyl \"a , M.J. , K \
barticle K \"a pyl \"a , M.J. , K \"a pyl \"a , P.J. , Olspert , N. , Brandenburg , A. , Warnecke , J. , Karak , B.B. , Pelt , J. : 2016 , Multiple dynamo modes as a mechanism for long-term solar activity variations . 589 , A56 . https://doi.org/10.1051/0004-6361/201527002 . 2...
2016 doi
-
[41]
, Browning , M.K
barticle K \"a pyl \"a , P.J. , Browning , M.K. , Brun , A.S. , Guerrero , G. , Warnecke , J. : 2023 , Simulations of Solar and Stellar Dynamos and Their Theoretical Interpretation . 219 , 58 . https://doi.org/10.1007/s11214-023-01005-6 . 2023SSRv..219...58K . barticle
2023 doi
-
[42]
: 2010 , Importance of Meridional Circulation in Flux Transport Dynamo: The Possibility of a Maunder-like Grand Minimum
barticle Karak , B.B. : 2010 , Importance of Meridional Circulation in Flux Transport Dynamo: The Possibility of a Maunder-like Grand Minimum . 724 , 1021 . https://doi.org/10.1088/0004-637X/724/2/1021 . 2010ApJ...724.1021K . barticle
2010 doi
-
[43]
: 2023 , Models for the long-term variations of solar activity
barticle Karak , B.B. : 2023 , Models for the long-term variations of solar activity . Living Reviews in Solar Physics 20 , 3 . https://doi.org/10.1007/s41116-023-00037-y . 2023LRSP...20....3K . barticle
2023 doi
-
[44]
, Choudhuri , A.R
barticle Karak , B.B. , Choudhuri , A.R. : 2013 , Studies of grand minima in sunspot cycles by using a flux transport solar dynamo model . Res. Astron. Astrophys. 13 , 1339 . https://doi.org/10.1088/1674-4527/13/11/005 . 2013RAA....13.1339K . barticle
2013 doi
-
[45]
, Miesch , M
barticle Karak , B.B. , Miesch , M. : 2017 , Solar Cycle Variability Induced by Tilt Angle Scatter in a Babcock-Leighton Solar Dynamo Model . 847 , 69 . https://doi.org/10.3847/1538-4357/aa8636 . 2017ApJ...847...69K . barticle
2017 doi
-
[46]
, Miesch , M
barticle Karak , B.B. , Miesch , M. : 2018 , Recovery from Maunder-like Grand Minima in a Babcock--Leighton Solar Dynamo Model . 860 , L26 . https://doi.org/10.3847/2041-8213/aaca97 . 2018ApJ...860L..26K . barticle
2018 doi
-
[47]
, Kitchatinov , L.L
barticle Karak , B.B. , Kitchatinov , L.L. , Brandenburg , A. : 2015 , Hysteresis between Distinct Modes of Turbulent Dynamos . 803 , 95 . https://doi.org/10.1088/0004-637X/803/2/95 . http://esoads.eso.org/abs/2015ApJ...803...95K . barticle
2015 doi
-
[48]
, Mandal , S
barticle Karak , B.B. , Mandal , S. , Banerjee , D. : 2018 , Double Peaks of the Solar Cycle: An Explanation from a Dynamo Model . 866 , 17 . https://doi.org/10.3847/1538-4357/aada0d . 2018ApJ...866...17K . barticle
2018 doi
-
[49]
, Miesch , M
barticle Karak , B.B. , Miesch , M. , Bekki , Y. : 2018 , Consequences of high effective Prandtl number on solar differential rotation and convective velocity . Physics of Fluids 30 , 046602 . https://doi.org/10.1063/1.5022034 . 2018PhFl...30d6602K . barticle
2018 doi
-
[50]
, Jiang , J
barticle Karak , B.B. , Jiang , J. , Miesch , M.S. , Charbonneau , P. , Choudhuri , A.R. : 2014 , Flux Transport Dynamos: From Kinematics to Dynamics . 186 , 561 . https://doi.org/10.1007/s11214-014-0099-6 . 2014SSRv..186..561K . barticle
2014 doi
-
[51]
a pyl \"a , P.J. , K \
barticle Karak , B.B. , K \"a pyl \"a , P.J. , K \"a pyl \"a , M.J. , Brandenburg , A. , Olspert , N. , Pelt , J. : 2015 , Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles . 576 , A26 . https://doi.org/10.1051/0004-636...
2015 doi
-
[52]
, Nepomnyashchikh , A
barticle Kitchatinov , L. , Nepomnyashchikh , A. : 2017 , How supercritical are stellar dynamos, or why do old main-sequence dwarfs not obey gyrochronology? 470 , 3124 . https://doi.org/10.1093/mnras/stx1473 . 2017MNRAS.470.3124K . barticle
2017 doi
-
[53]
, Olemskoy , S.V
barticle Kitchatinov , L.L. , Olemskoy , S.V. : 2010 , Dynamo hysteresis and grand minima of solar activity . Astron. Lett. 36 , 292 . barticle
2010
-
[54]
, Olemskoy , S.V
barticle Kitchatinov , L.L. , Olemskoy , S.V. : 2011 , Does the Babcock-Leighton mechanism operate on the Sun? Astronomy Letters 37 , 656 . https://doi.org/10.1134/S0320010811080031 . 2011AstL...37..656K . barticle
2011 doi
-
[55]
, R \"a dler , K.H
bbook Krause , F. , R \"a dler , K.H. : 1980 , Mean-field magneto\-hydro\-dynamics and dynamo theory , Oxford: Pergamon Press . bbook
1980
-
[56]
, Biswas , A
barticle Kumar , P. , Biswas , A. , Karak , B.B. : 2022 , Physical link of the polar field buildup with the Waldmeier effect broadens the scope of early solar cycle prediction: Cycle 25 is likely to be slightly stronger than Cycle 24 . 513 , L112 . https://doi.org/10.1093/mnra...
2022 doi
-
[57]
, Karak , B.B
botherref Kumar , P. , Karak , B.B. , Sreedevi , A. : 2024, Variabilities in the polar field and solar cycle due to irregular properties of Bipolar Magnetic Regions . . https://doi.org/10.1093/mnras/stae1052 . 2024MNRAS.tmp.1058K . botherref
2024 doi
-
[58]
, Karak , B.B
barticle Kumar , P. , Karak , B.B. , Vashishth , V. : 2021 , Supercriticality of the Dynamo Limits the Memory of the Polar Field to One Cycle . 913 , 65 . https://doi.org/10.3847/1538-4357/abf0a1 . 2021ApJ...913...65K . barticle
2021 doi
-
[59]
, Nagy , M
barticle Kumar , P. , Nagy , M. , Lemerle , A. , Karak , B.B. , Petrovay , K. : 2021 , The Polar Precursor Method for Solar Cycle Prediction: Comparison of Predictors and Their Temporal Range . 909 , 87 . https://doi.org/10.3847/1538-4357/abdbb4 . 2021ApJ...909...87K . barticle
2021 doi
-
[60]
: 1969 , A Magneto-Kinematic Model of the Solar Cycle
barticle Leighton , R.B. : 1969 , A Magneto-Kinematic Model of the Solar Cycle . 156 , 1 . https://doi.org/10.1086/149943 . 1969ApJ...156....1L . barticle
1969 doi
-
[61]
, Egeland , R
barticle Metcalfe , T.S. , Egeland , R. , van Saders , J. : 2016 , Stellar Evidence That the Solar Dynamo May Be in Transition . 826 , L2 . https://doi.org/10.3847/2041-8205/826/1/L2 . 2016ApJ...826L...2M . barticle
2016 doi
-
[62]
: 1978 , Magnetic field generation in electrically conducting fluids
bbook Moffatt , H.K. : 1978 , Magnetic field generation in electrically conducting fluids . 1978mfge.book.....M . bbook
1978
-
[63]
, Karak , B.B
barticle Mordvinov , A.V. , Karak , B.B. , Banerjee , D. , Golubeva , E.M. , Khlystova , A.I. , Zhukova , A.V. , Kumar , P. : 2022 , Evolution of the Sun's activity and the poleward transport of remnant magnetic flux in Cycles 21-24 . 510 , 1331 . https://doi.org/10.1093/mnras...
2022 doi
-
[64]
, Dasi-Espuig , M
barticle Mu \ n oz-Jaramillo , A. , Dasi-Espuig , M. , Balmaceda , L.A. , DeLuca , E.E. : 2013 , Solar Cycle Propagation, Memory, and Prediction: Insights from a Century of Magnetic Proxies . 767 , L25 . https://doi.org/10.1088/2041-8205/767/2/L25 . 2013ApJ...767L..25M . barticle
2013 doi
-
[65]
, Hartmann , L.W
barticle Noyes , R.W. , Hartmann , L.W. , Baliunas , S.L. , Duncan , D.K. , Vaughan , A.H. : 1984 , Rotation, convection, and magnetic activity in lower main-sequence stars . 279 , 763 . https://doi.org/10.1086/161945 . 1984ApJ...279..763N . barticle
1984 doi
-
[66]
, Kitchatinov , L.L
barticle Olemskoy , S.V. , Kitchatinov , L.L. : 2013 , Grand Minima and North-South Asymmetry of Solar Activity . 777 , 71 . barticle
2013
-
[67]
, Choudhuri , A.R
barticle Olemskoy , S.V. , Choudhuri , A.R. , Kitchatinov , L.L. : 2013 , Fluctuations in the alpha-effect and grand solar minima . Astronomy Reports 57 , 458 . https://doi.org/10.1134/S1063772913050065 . 2013ARep...57..458O . barticle
2013 doi
-
[68]
: 1955 , Hydromagnetic Dynamo Models
barticle Parker , E.N. : 1955 , Hydromagnetic Dynamo Models. 122 , 293 . https://doi.org/10.1086/146087 . 1955ApJ...122..293P . barticle
1955 doi
-
[69]
, Nandy , D
barticle Passos , D. , Nandy , D. , Hazra , S. , Lopes , I. : 2014 , A solar dynamo model driven by mean-field alpha and Babcock-Leighton sources: fluctuations, grand-minima-maxima, and hemispheric asymmetry in sunspot cycles . 563 , A18 . https://doi.org/10.1051/0004-6361/201...
2014 doi
-
[70]
, Charbonneau , P
barticle Racine , \'E . , Charbonneau , P. , Ghizaru , M. , Bouchat , A. , Smolarkiewicz , P.K. : 2011 , On the Mode of Dynamo Action in a Global Large-eddy Simulation of Solar Convection . 735 , 46 . https://doi.org/10.1088/0004-637X/735/1/46 . 2011ApJ...735...46R . barticle
2011 doi
-
[71]
: 1984 , Age-rotation relationship for late-type main-sequence stars
barticle Rengarajan , T.N. : 1984 , Age-rotation relationship for late-type main-sequence stars . 283 , L63 . barticle
1984
-
[72]
, Nesme-Ribes , E
barticle Ribes , J.C. , Nesme-Ribes , E. : 1993 , The solar sunspot cycle in the Maunder minimum AD1645 to AD1715 . 276 , 549 . 1993A\ barticle
1993
-
[73]
, Scherrer , P.H
barticle Schatten , K.H. , Scherrer , P.H. , Svalgaard , L. , Wilcox , J.M. : 1978 , Using dynamo theory to predict the sunspot number during solar cycle 21 . 5 , 411 . https://doi.org/10.1029/GL005i005p00411 . 1978GeoRL...5..411S . barticle
1978 doi
-
[74]
, Wright , J.T
barticle Shah , S.P. , Wright , J.T. , Isaacson , H. , Howard , A.W. , Curtis , J.L. : 2018 , HD 4915: A Maunder Minimum Candidate . 863 , L26 . https://doi.org/10.3847/2041-8213/aad40c . 2018ApJ...863L..26S . barticle
2018 doi
-
[75]
: 1972 , Time Scales for CA II Emission Decay, Rotational Braking, and Lithium Depletion
barticle Skumanich , A. : 1972 , Time Scales for CA II Emission Decay, Rotational Braking, and Lithium Depletion . 171 , 565 . https://doi.org/10.1086/151310 . 1972ApJ...171..565S . barticle
1972 doi
-
[76]
, Jha , B.K
barticle Sreedevi , A. , Jha , B.K. , Karak , B.B. , Banerjee , D. : 2024 , Analysis of BMR Tilt from AutoTAB Catalog: Hinting toward the Thin Flux Tube Model? 966 , 112 . https://doi.org/10.3847/1538-4357/ad34b8 . 2024ApJ...966..112S . barticle
2024 doi
-
[77]
, Beaudoin , P
barticle Strugarek , A. , Beaudoin , P. , Charbonneau , P. , Brun , A.S. : 2018 , On the Sensitivity of Magnetic Cycles in Global Simulations of Solar-like Stars . 863 , 35 . https://doi.org/10.3847/1538-4357/aacf9e . 2018ApJ...863...35S . barticle
2018 doi
-
[78]
, Nandy , D
barticle Tripathi , B. , Nandy , D. , Banerjee , S. : 2021 , Stellar mid-life crisis: subcritical magnetic dynamos of solar-like stars and the breakdown of gyrochronology . 506 , L50 . https://doi.org/10.1093/mnrasl/slab035 . 2021MNRAS.506L..50T . barticle
2021 doi
-
[79]
: 2023 , A history of solar activity over millennia
barticle Usoskin , I.G. : 2023 , A history of solar activity over millennia . Living Reviews in Solar Physics 20 , 2 . https://doi.org/10.1007/s41116-023-00036-z . 2023LRSP...20....2U . barticle
2023 doi
-
[80]
, Solanki , S.K
barticle Usoskin , I.G. , Solanki , S.K. , Kovaltsov , G.A. : 2007 , Grand minima and maxima of solar activity: new observational constraints . 471 , 301 . barticle
2007
-
[81]
, Solanki , S.K
barticle Usoskin , I.G. , Solanki , S.K. , Krivova , N.A. , Hofer , B. , Kovaltsov , G.A. , Wacker , L. , Brehm , N. , Kromer , B. : 2021 , Solar cyclic activity over the last millennium reconstructed from annual ^ 14 C data . 649 , A141 . https://doi.org/10.1051/0004-6361/202...
2021 doi
-
[82]
, Solanki , S.K
barticle Usoskin , I.G. , Solanki , S.K. , Krivova , N. , Hofer , B. , Kovaltsov , G.A. , Wacker , L. , Brehm , N. , Kromer , B. : 2022 , Solar cyclic activity over the last millennium reconstructedfrom annual ^ 14 C data (Corrigendum) . 664 , C3 . https://doi.org/10.1051/0004...
2022 doi
-
[83]
, Karak , B.B
barticle Vashishth , V. , Karak , B.B. , Kitchatinov , L. : 2021 , Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model . Research in Astronomy and Astrophysics 21 , 266 . https://doi.org/10.1088/1674-4527/21/10/266 . 2021RAA....21..266V . barticle
2021 doi
-
[84]
, Karak , B.B
barticle Vashishth , V. , Karak , B.B. , Kitchatinov , L. : 2023 , Dynamo modelling for cycle variability and occurrence of grand minima in Sun-like stars: rotation rate dependence . 522 , 2601 . https://doi.org/10.1093/mnras/stad1105 . 2023MNRAS.522.2601V . barticle
2023 doi
-
[85]
, Gregory , S.G
barticle Vidotto , A.A. , Gregory , S.G. , Jardine , M. , Donati , J.F. , Petit , P. , Morin , J. , Folsom , C.P. , Bouvier , J. , Cameron , A.C. , Hussain , G. , Marsden , S. , Waite , I.A. , Fares , R. , Jeffers , S. , do Nascimento , J.D. : 2014 , Stellar magnetism: empiric...
2014 doi
-
[86]
, Nandy , D
barticle Wilmot-Smith , A.L. , Nandy , D. , Hornig , G. , Martens , P.C.H. : 2006 , A Time Delay Model for Solar and Stellar Dynamos . 652 , 696 . https://doi.org/10.1086/508013 . 2006ApJ...652..696W . barticle
2006 doi
-
[87]
: 2016, Stellar Magnetic Activity Cycles, and Hunting for Maunder Minimum-like Events among Sun-like Stars
botherref Wright , J.T. : 2016, Stellar Magnetic Activity Cycles, and Hunting for Maunder Minimum-like Events among Sun-like Stars . AGU Fall Meeting Abstracts, SH43D. 2016AGUFMSH43D2592W . botherref
2016
Reviewed August 10, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.