Modeling the solar cycles 12-20 with a Babcock-Leighton flux transport dynamo

AbstractWe use a Babcock-Leighton-type of dynamo with the poloidal source based as closely as possible on the observations to model the solar cycle irregularities during the cycles 12-20. The nonlinearities in the poloidal field generation, i.e., the cycle dependence of the sunspot group tilt angles and the latitudes are included. The convective pumping dominates the transport of the surface poloidal field to the tachocline. Our results show that the modeled polar fields have a good correlation with the observed next cycle strength and the build-up of the toroidal flux at the tachocline is strongly correlated with the observed cycle strength as well. Both correlation coefficients are above 0.8. The success of the model indicates that they are the nonlinearities in the poloidal field generation which cause the solar cycle irregularities.

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Does the mean-field α effect have any impact on the memory of the solar cycle?

Astronomy and Astrophysics ◽

10.1051/0004-6361/201937287 ◽

2020 ◽

Vol 642 ◽

pp. A51

Author(s):

Soumitra Hazra ◽

Allan Sacha Brun ◽

Dibyendu Nandy

Keyword(s):

Solar Cycle ◽

Mean Field ◽

Solar Dynamo ◽

Dynamo Model ◽

Solar Cycles ◽

Poloidal Field ◽

Flux Transport ◽

Solar Convection ◽

The Mean ◽

And Diffusion

Context. Predictions of solar cycle 24 obtained from advection-dominated and diffusion-dominated kinematic dynamo models are different if the Babcock–Leighton mechanism is the only source of the poloidal field. Some previous studies argue that the discrepancy arises due to different memories of the solar dynamo for advection- and diffusion-dominated solar convection zones. Aims. We aim to investigate the differences in solar cycle memory obtained from advection-dominated and diffusion-dominated kinematic solar dynamo models. Specifically, we explore whether inclusion of Parker’s mean-field α effect, in addition to the Babcock–Leighton mechanism, has any impact on the memory of the solar cycle. Methods. We used a kinematic flux transport solar dynamo model where poloidal field generation takes place due to both the Babcock–Leighton mechanism and the mean-field α effect. We additionally considered stochastic fluctuations in this model and explored cycle-to-cycle correlations between the polar field at minima and toroidal field at cycle maxima. Results. Solar dynamo memory is always limited to only one cycle in diffusion-dominated dynamo regimes while in advection-dominated regimes the memory is distributed over a few solar cycles. However, the addition of a mean-field α effect reduces the memory of the solar dynamo to within one cycle in the advection-dominated dynamo regime when there are no fluctuations in the mean-field α effect. When fluctuations are introduced in the mean-field poloidal source a more complex scenario is evident, with very weak but significant correlations emerging across a few cycles. Conclusions. Our results imply that inclusion of a mean-field α effect in the framework of a flux transport Babcock–Leighton dynamo model leads to additional complexities that may impact memory and predictability of predictive dynamo models of the solar cycle.

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Flux-transport and mean-field dynamo theories of solar cycles

Proceedings of the International Astronomical Union ◽

10.1017/s1743921313002184 ◽

2012 ◽

Vol 8 (S294) ◽

pp. 37-47

Author(s):

Arnab Rai Choudhuri

Keyword(s):

Solar Cycle ◽

Meridional Circulation ◽

Mean Field ◽

Dynamo Model ◽

Solar Cycles ◽

Poloidal Field ◽

Flux Transport ◽

Mean Field Model ◽

Mean Field Models ◽

Mean Field Dynamo

AbstractWe point out the difficulties in carrying out direct numerical simulation of the solar dynamo problem and argue that kinematic mean-field models are our best theoretical tools at present for explaining various aspects of the solar cycle in detail. The most promising kinematic mean-field model is the flux transport dynamo model, in which the toroidal field is produced by differential rotation in the tachocline, the poloidal field is produced by the Babcock–Leighton mechanism at the solar surface and the meridional circulation plays a crucial role. Depending on whether the diffusivity is high or low, either the diffusivity or the meridional circulation provides the main transport mechanism for the poloidal field to reach the bottom of the convection zone from the top. We point out that the high-diffusivity flux transport dynamo model is consistent with various aspects of observational data. The irregularities of the solar cycle are primarily produced by fluctuations in the Babcock–Leighton mechanism and in the meridional circulation. We summarize recent work on the fluctuations of meridional circulation in the flux transport dynamo, leading to explanations of such things as the Waldmeier effect.

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Origin of solar magnetism

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311014967 ◽

2010 ◽

Vol 6 (S273) ◽

pp. 28-36 ◽

Cited By ~ 1

Author(s):

Arnab Rai Choudhuri

Keyword(s):

Solar Cycle ◽

Differential Rotation ◽

Convection Zone ◽

Meridional Circulation ◽

Solar Surface ◽

Dynamo Model ◽

Solar Cycles ◽

Poloidal Field ◽

Flux Transport ◽

Solar Magnetism

AbstractThe most promising model for explaining the origin of solar magnetism is the flux transport dynamo model, in which the toroidal field is produced by differential rotation in the tachocline, the poloidal field is produced by the Babcock–Leighton mechanism at the solar surface and the meridional circulation plays a crucial role. After discussing how this model explains the regular periodic features of the solar cycle, we come to the questions of what causes irregularities of solar cycles and whether we can predict future cycles. Only if the diffusivity within the convection zone is sufficiently high, the polar field at the sunspot minimum is correlated with strength of the next cycle. This is in conformity with the limited available observational data.

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Hemispheric injection of magnetic helicity by surface flux transport

Astronomy and Astrophysics ◽

10.1051/0004-6361/201936475 ◽

2019 ◽

Vol 631 ◽

pp. A138 ◽

Cited By ~ 3

Author(s):

G. Hawkes ◽

A. R. Yeates

Keyword(s):

Magnetic Field ◽

Solar Cycle ◽

Solar Rotation ◽

Surface Flux ◽

Magnetic Helicity ◽

Solar Cycles ◽

Flux Transport ◽

Transport Models ◽

Radial Magnetic Field ◽

Helicity Injection

Aims. We estimate the injection of relative magnetic helicity into the solar atmosphere by surface flux transport over 27 solar cycles (1700–2009). Methods. We determine the radial magnetic field evolution using two separate surface flux transport models: one driven by magnetogram inputs and another by statistical active region insertion guided by the sunspot number record. The injection of relative magnetic helicity is then computed from this radial magnetic field together with the known electric field in the flux transport models. Results. Neglecting flux emergence, solar rotation is the dominant contributor to the helicity injection. At high latitudes, the injection is always negative/positive in the northern/southern hemisphere, while at low latitudes the injection tends to have the opposite sign when integrated over the full solar cycle. The overall helicity injection in a given solar cycle depends on the balance between these two contributions. This net injected helicity correlates well with the end-of-cycle axial dipole moment.

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Solar cycle prediction

Living Reviews in Solar Physics ◽

10.1007/s41116-020-0022-z ◽

2020 ◽

Vol 17 (1) ◽

Cited By ~ 11

Author(s):

Kristóf Petrovay

Keyword(s):

Solar Activity ◽

Solar Cycle ◽

Solar Maximum ◽

Prediction Methods ◽

Implicit Assumption ◽

Solar Cycles ◽

Extrapolation Methods ◽

Dynamo Theory ◽

Flux Transport ◽

Model Based

AbstractA review of solar cycle prediction methods and their performance is given, including early forecasts for Cycle 25. The review focuses on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is further restricted to the issue of predicting the amplitude (and optionally the epoch) of an upcoming solar maximum no later than right after the start of the given cycle. Prediction methods form three main groups. Precursor methods rely on the value of some measure of solar activity or magnetism at a specified time to predict the amplitude of the following solar maximum. The choice of a good precursor often implies considerable physical insight: indeed, it has become increasingly clear that the transition from purely empirical precursors to model-based methods is continuous. Model-based approaches can be further divided into two groups: predictions based on surface flux transport models and on consistent dynamo models. The implicit assumption of precursor methods is that each numbered solar cycle is a consistent unit in itself, while solar activity seems to consist of a series of much less tightly intercorrelated individual cycles. Extrapolation methods, in contrast, are based on the premise that the physical process giving rise to the sunspot number record is statistically homogeneous, i.e., the mathematical regularities underlying its variations are the same at any point of time, and therefore it lends itself to analysis and forecasting by time series methods. In their overall performance during the course of the last few solar cycles, precursor methods have clearly been superior to extrapolation methods. One method that has yielded predictions consistently in the right range during the past few solar cycles is the polar field precursor. Nevertheless, some extrapolation methods may still be worth further study. Model based forecasts are quickly coming into their own, and, despite not having a long proven record, their predictions are received with increasing confidence by the community.

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Number of Sunspot Groups and Individual Sunspots Recorded by Tevel for the Period 1816–1836 in the Dalton Minimum

The Astrophysical Journal ◽

10.3847/1538-4357/ac24a5 ◽

2021 ◽

Vol 922 (1) ◽

pp. 58

Author(s):

V. M. S. Carrasco

Keyword(s):

Solar Cycle ◽

Sunspot Number ◽

Sunspot Group ◽

Maunder Minimum ◽

The Other ◽

Solar Cycles ◽

Group Number ◽

The One ◽

Dalton Minimum ◽

Sunspot Groups

Abstract Cornelis Tevel made sunspot observations during the period 1816–1836, including the Dalton Minimum. In this work, the first revision of these observations since Wolf incorporated them into his database is presented. On the one hand, the number of individual sunspots from Tevel’s drawings was counted. This is of special interest for the sunspot number reconstruction because this kind of information is not as common in historical sunspot records as the number of groups. Thus, Tevel could be considered for the future reconstruction of the sunspot number index. On the other hand, the number of groups counted according to modern sunspot group classifications finding significant misinterpretations with the number of groups assigned to Tevel in the existing databases. Tevel was a relevant sunspot observer in the Dalton Minimum. In fact, he was the observer with the highest number of groups observed in Solar Cycles 6 and 7 according to the existing sunspot group number databases. According to the raw group number recount in this work, the maximum amplitudes for Solar Cycles 6 and 7 are, respectively, 27% and 7% lower than those previously determined. Moreover, Solar Cycle 6 is the weakest solar cycle since the Maunder Minimum after applying these new counts. Group counts from Tevel’s observations were compared with those from relevant contemporary astronomers, demonstrating that Schwabe and Tevel systematically recorded a higher number of groups than Flaugergues and Derfflinger. In addition, sunspot areas and positions recorded by Tevel should be used with caution for scientific purposes.

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Changes in the Near-surface Shear Layer of the Sun

The Astrophysical Journal ◽

10.3847/1538-4357/ac32c3 ◽

2022 ◽

Vol 924 (1) ◽

pp. 19

Author(s):

H. M. Antia ◽

Sarbani Basu

Keyword(s):

Solar Cycle ◽

Shear Layer ◽

Solar Rotation ◽

High Latitudes ◽

Solar Cycles ◽

Surface Shear ◽

Near Surface ◽

Radial Gradient ◽

Cycle Dependence ◽

Solar Rotation Rate

Abstract We use helioseismic data obtained over two solar cycles to determine whether there are changes in the near-surface shear layer (NSSL). We examine this by determining the radial gradient of the solar rotation rate. The radial gradient itself shows a solar-cycle dependence, and the changes are more pronounced in the active latitudes than at adjoining higher latitudes; results at the highest latitudes (≳70°) are unreliable. The pattern changes with depth, even within the NSSL. We find that the near-surface shear layer is deeper at lower latitudes than at high latitudes and that the extent of the layer also shows a small solar-cycle-related change.

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Modelling variability of solar activity cycles

Astronomy and Astrophysics ◽

10.1051/0004-6361/201732549 ◽

2018 ◽

Vol 615 ◽

pp. A38 ◽

Cited By ~ 9

Author(s):

L. L. Kitchatinov ◽

A. V. Mordvinov ◽

A. A. Nepomnyashchikh

Keyword(s):

Solar Activity ◽

Solar Cycle ◽

Transport Model ◽

Magnetic Energy ◽

Solar Rotation ◽

Rotation Period ◽

Poloidal Field ◽

Flux Transport ◽

Activity Cycles ◽

Solar Activity Cycles

Context. Solar activity cycles vary in amplitude and duration. The variations can be at least partly explained by fluctuations in dynamo parameters. Aims. We want to restrict uncertainty in fluctuating dynamo parameters and find out which properties of the fluctuations control the amplitudes of the magnetic field and energy in variable dynamo cycles. Methods. A flux-transport model for the solar dynamo with fluctuations of the Babcock–Leighton type α-effect was applied to generate statistics of magnetic cycles for our purposes. The statistics were compared with data on solar cycle periods to restrict the correlation time of dynamo fluctuations. Results. A characteristic time of fluctuations in the α-effect is estimated to be close to the solar rotation period. The fluctuations produce asymmetry between the times of rise and descent of dynamo cycles, the rise time being on average shorter. The affect of the fluctuations on cycle amplitudes depends on the phase of the cycle in which the fluctuations occur. Negative fluctuations (decrease in α) in the rise phase delay decay of poloidal field and increase the cycle amplitude in toroidal field and magnetic energy. Negative fluctuation in the decline phase reduces the polar field at the end of a cycle and the amplitude of the next cycle. The low amplitude of the 24th solar cycle compared to the preceding 23rd cycle can be explained by this effect. Positive fluctuations in the descent phase enhance the magnetic energy of the next cycle by increasing the seed poloidal field for the next cycle. The statistics of the computed energies of the cycles suggest that superflares of ≥1034 erg are not possible on the Sun.

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On the Prediction of Solar Cycles

Solar Physics ◽

10.1007/s11207-020-01760-7 ◽

2021 ◽

Vol 296 (1) ◽

Author(s):

V. Courtillot ◽

F. Lopes ◽

J. L. Le Mouël

Keyword(s):

Solar Activity ◽

Solar Cycle ◽

Transfer Function ◽

Singular Spectrum Analysis ◽

Activity Cycle ◽

Solar Activity Cycle ◽

Planetary Motion ◽

Data Sets ◽

Solar Cycles ◽

Jovian Planets

AbstractThis article deals with the prediction of the upcoming solar activity cycle, Solar Cycle 25. We propose that astronomical ephemeris, specifically taken from the catalogs of aphelia of the four Jovian planets, could be drivers of variations in solar activity, represented by the series of sunspot numbers (SSN) from 1749 to 2020. We use singular spectrum analysis (SSA) to associate components with similar periods in the ephemeris and SSN. We determine the transfer function between the two data sets. We improve the match in successive steps: first with Jupiter only, then with the four Jovian planets and finally including commensurable periods of pairs and pairs of pairs of the Jovian planets (following Mörth and Schlamminger in Planetary Motion, Sunspots and Climate, Solar-Terrestrial Influences on Weather and Climate, 193, 1979). The transfer function can be applied to the ephemeris to predict future cycles. We test this with success using the “hindcast prediction” of Solar Cycles 21 to 24, using only data preceding these cycles, and by analyzing separately two 130 and 140 year-long halves of the original series. We conclude with a prediction of Solar Cycle 25 that can be compared to a dozen predictions by other authors: the maximum would occur in 2026.2 (± 1 yr) and reach an amplitude of 97.6 (± 7.8), similar to that of Solar Cycle 24, therefore sketching a new “Modern minimum”, following the Dalton and Gleissberg minima.

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