Babcock-Leighton Dynamo Models Research Articles

Discriminating between Babcock–Leighton-type Solar Dynamo Models by Torsional Oscillations

The details of the dynamo process in the Sun are an important aspect of research in solar-terrestrial physics and astrophysics. The surface part of the dynamo can be constrained by direct observations, but the subsurface part lacks direct observational constraints. The torsional oscillations, a small periodic variation of the Sun's rotation with the solar cycle, are thought to result from the Lorentz force of the cyclic magnetic field generated by the dynamo. In this study, we aim to discriminate between three Babcock–Leighton dynamo models by comparing the zonal acceleration of the three models with the observed one. The property that the poleward and equatorward branches of the torsional oscillations originate from about ±55° latitudes with their own migration time periods serves as an effective discriminator that could constrain the configuration of the magnetic field in the convection zone. The toroidal field, comprising poleward and equatorward branches separated at about ±55° latitudes, can generate the two branches of the torsional oscillations. The alternating acceleration and deceleration bands in time are the other property of the torsional oscillations that discriminates between the dynamo models. To reproduce this property, the phase difference between the radial (B r ) and toroidal (B ϕ ) components of the magnetic field near the surface should be about π/2.

A Babcock-Leighton dynamo model of the Sun incorporating toroidal flux loss and the helioseismically inferred meridional flow

Context. Key elements of the Babcock-Leighton model for the solar dynamo are increasingly constrained by observations. Aims. We investigate whether the Babcock-Leighton flux-transport dynamo model remains in agreement with observations if the meridional flow profile is taken from helioseismic inversions. Additionally, we investigate the effect of the loss of toroidal flux through the solar surface. Methods. We employ the two-dimensional flux-transport Babcock-Leighton dynamo framework. We use the helioseismically inferred meridional flow profile, and include toroidal flux loss in a way that is consistent with the amount of poloidal flux generated by Joy’s law. Our model does not impose a preference for emergences at low latitudes; however, we do require that the model produces such a preference. Results. We can find solutions that are in general agreement with observations, including the latitudinal migration of the butterfly wings and the 11 year period of the cycle. The most important free parameters in the model are the depth to which the radial turbulent pumping extends and the turbulent diffusivity in the lower half of the convection zone. We find that the pumping needs to extend to depths of about 0.80 R⊙ and that the bulk turbulent diffusivity needs to be around 10 km2 s−1 or less. We find that the emergences are restricted to low latitudes without the need to impose such a preference. Conclusions. The flux-transport Babcock-Leighton model, incorporating the helioseismically inferred meridional flow and toroidal field loss term, is compatible with the properties of the observed butterfly diagram and with the observed toroidal loss rate. Reasonably tight constraints are placed on the remaining free parameters. The pumping needs to be just below the depth corresponding to the location where the meridional flow changes direction, and where numerical simulations suggest the convection zone becomes marginally subadiabatic. However, our linear model does not reproduce the observed ‘rush to the poles’ of the diffuse surface radial field resulting from the decay of sunspots; reproducing this might require the imposition of a preference for flux to emerge near the equator.

Evolution of the Sun’s activity and the poleward transport of remnant magnetic flux in Cycles 21–24

ABSTRACT Detailed study of the solar magnetic field is crucial to understand its generation, transport, and reversals. The timing of the reversals may have implications on space weather and thus identification of the temporal behaviour of the critical surges that lead to the polar field reversals is important. We analyse the evolution of solar activity and magnetic flux transport in Cycles 21–24. We identify critical surges of remnant flux that reach the Sun’s poles and lead to the polar field reversals. We reexamine the polar field build-up and reversals in their causal relation to the Sun’s low-latitude activity. We further identify the major remnant flux surges and their sources in the time-latitude aspect. We find that special characteristics of individual 11-yr cycles are generally determined by the spatiotemporal organization of emergent magnetic flux and its unusual properties. We find a complicated restructuring of high-latitude magnetic fields in Cycle 21. The global rearrangements of solar magnetic fields were caused by surges of trailing and leading polarities that occurred near the activity maximum. The decay of non-Joy and anti-Hale active regions resulted in the remnant flux surges that disturbed the usual order in magnetic flux transport. We finally show that the leading-polarity surges during cycle minima sometimes link the following cycle and a collective effect of these surges may lead to secular changes in the solar activity. The magnetic field from a Babcock–Leighton dynamo model generally agrees with these observations.

Recent advances in the 3D kinematic Babcock–Leighton solar dynamo modeling

In this review, we explain recent progress made in the Babcock-Leighton dynamo models for the Sun, which have been most successful to explain various properties of the solar cycle. In general, these models are 2D axisymmetric and the mean-field dynamo equations are solved in the meriodional plane of the Sun. Various physical processes (e.g., magnetic buoyancy and Babcock-Leighton mechanism) involved in these models are inherently 3D process and could not be modeled properly in a 2D framework. After pointing out limitations of 2D models (e.g., Mean-field Babcock-Leighton dynamo models and Surface Flux Transport models), we describe recently developed next-generation 3D dynamo models that implement more sophisticated flux emergence algorithm of buoyant flux tube rise through the convection zone and capture Babcock-Leighton process more realistically than previous 2D models. The detailed results from these 3D dynamo models including surface flux transport counterpart are presented. We explain the cycle irregularities that are reproduced in 3D dynamo models by introducing scattering around the tilt angle only. Some results by assimilating observed photospheric convective velocity fields into the 3D models are also discussed, pointing out the wide opportunity that these 3D models hold to deliver.

Does the mean-fieldαeffect have any impact on the memory of the solar cycle?

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-fieldαeffect, 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-fieldαeffect. 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-fieldαeffect 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-fieldαeffect. 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-fieldαeffect 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.

Average motion of emerging solar active region polarities: II. Joy's law.

Context.The tilt of solar active regions described by Joy’s law is essential for converting a toroidal field to a poloidal field in Babcock-Leighton dynamo models. In thin flux tube models the Coriolis force causes what we observe as Joy’s law, acting on east-west flows as they rise towards the surface.Aims.Our goal is to measure the evolution of the average tilt angle of hundreds of active regions as they emerge, so that we can constrain the origins of Joy’s law.Methods.We measured the tilt angle of the primary bipoles in 153 emerging active regions (EARs) in the Solar Dynamics Observatory Helioseismic Emerging Active Region survey. We used line-of-sight magnetic field measurements averaged over 6 h to define the polarities and measure the tilt angle up to four days after emergence.Results.We find that at the time of emergence the polarities are on average aligned east-west, and that neither the separation nor the tilt depends on latitude. We do find, however, that EARs at higher latitudes have a faster north-south separation speed than those closer to the equator at the emergence time. After emergence, the tilt angle increases and Joy’s law is evident about two days later. The scatter in the tilt angle is independent of flux until about one day after emergence, when we find that higher-flux regions have a smaller scatter in tilt angle than lower-flux regions.Conclusions.Our finding that active regions emerge with an east-west alignment is consistent with earlier observations, but is still surprising since thin flux tube models predict that tilt angles of rising flux tubes are generated below the surface. Previously reported tilt angle relaxation of deeply anchored flux tubes can be largely explained by the change in east-west separation. We conclude that Joy’s law is caused by an inherent north-south separation speed present when the flux first reaches the surface, and that the scatter in the tilt angle is consistent with buffeting of the polarities by supergranulation.

Delayed Babcock-Leighton dynamos in the diffusion-dominated regime

Context. Solar dynamo models of Babcock-Leighton type typically assume the rise of magnetic flux tubes to be instantaneous. The periods of solutions with high magnetic diffusivity are too short, and their active belts do not migrate correctly. Only the low-diffusivity regime with advective meridional flows is usually considered.Aims. We here discuss these assumptions and apply a time delay in the source term of the azimuthally averaged induction equation. This delay is set to be the rise time of magnetic flux tubes, which are assumed to form at the tachocline. We study the effect of the delay, which adds a nonlinear temporal to the spacial nonlocality in the advective but particularly in the diffusive regime.Methods. We have previously obtained the rise time as a function of rotation and the magnetic field strength at the bottom of the convection zone. These results allowed us to constrain the delay in the mean-field model we used in a parameter study.Results. We identify an unknown family of solutions. These solutions show self-quenching and exhibit longer periods than their nondelayed counterparts. Additionally, we demonstrate that the nonlinear delay is responsible for the recovery of the equatorward migration of the active belts at high turbulent diffusivities.Conclusions. By introducing a nonlinear temporal nonlocality (the delay) in a Babcock-Leighton dynamo model, we were able to obtain solutions that are quantitatively comparable to the solar butterfly diagram in the diffusion-dominated regime.

Double Peaks of the Solar Cycle: An Explanation from a Dynamo Model

Abstract One peculiar feature of the solar cycle that is yet to be understood properly is the frequent occurrence of double peaks (also known as the Gnevyshev peaks). The double peaks, and also multiple peaks and spikes, are often observed in any phase of the cycle. We propose that these peaks and spikes are generated due to fluctuations in the Babcock–Leighton process (the poloidal field generation from tilted bipolar magnetic regions). When the polar field develops, large negative fluctuations in the Babcock–Leighton process can reduce the net polar field abruptly. As these fluctuations in the polar field are propagated to the new toroidal field, these can promote double peaks in the next solar cycle. When fluctuations in the polar field occur outside the solar maximum, we observe their effects as spikes or dips in the following sunspot cycle. Using an axisymmetric Babcock–Leighton dynamo model, we first demonstrate this idea. Later, we perform a long simulation by including random scatter in the poloidal field generation process and successfully reproduce the double-peaked solar cycles. These results are robust under reasonable changes in the model parameters, as long as the diffusivity is not too much larger than 1012 cm2 s−1. Finally, we analyze the observed polar field data to show a close connection between the short-term fluctuations in the polar field and the double peaks/spikes in the next cycle. Thereby, this supports our theoretical idea that the fluctuations in the Babcock–Leighton process can be responsible for the double peaks/spikes in the observed solar cycle.

Incorporating Surface Convection into a 3D Babcock–Leighton Solar Dynamo Model

Abstract The convective flows observed on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock–Leighton (BL) process to generate large-scale polar fields from sunspot fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields are modeled as an effective turbulent diffusion. Recent SFT models have incorporated explicit, realistic convective flows in order to improve the fidelity of convective transport but, to our knowledge, this has not yet been implemented in previous BL models. We present the first kinematic 3D Flux-Transport/BL model to explicitly incorporate realistic convective flows based on solar observations. Though we describe a means to generalize these flows to 3D, we find that the kinematic small-scale dynamo action they produce disrupts the operation of the cyclic dynamo. The cyclic solution is found by limiting the convective flow to act only on the vertical radial component of the magnetic field. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective models that have a turbulent diffusivity of the order of 3 × 1012 cm2 s−1 (300 km2 s−1). However, we find that the use of a turbulent diffusivity underestimates the dynamo efficiency, producing weaker mean fields and a shorter cycle than in the convective models. Also, the convective models exhibit bands of mixed polarity in the polar regions that have no counterpart in solar observations, and the poleward migration speed of poloidal flux is determined mainly by the meridional flow and the vertical diffusion.

A Three dimensional Babcock-Leighton Solar Dynamo Model with Non-axisymmetric Convective Flows

AbstractThe observed convective flows on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock-Leighton (BL) process to generate large scale polar fields from sunspots fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields is modeled as an effective turbulent diffusion. We present the first kinematic 3D FT/BL model to explicitly incorporate realistic convective flows based on solar observations. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective models that have a turbulent diffusivity on the order of 3 × 1012 cm2 s−1 (300 km2 s−1). However, we find that the use of a turbulent diffusivity underestimates the dynamo efficiency, producing weaker mean fields and shorter cycle.

Long-term variability of the solar cycle in the Babcock-Leighton dynamo framework

AbstractWe explore the cause of the solar cycle variabilities using a novel 3D Babcock–Leighton dynamo model. In this model, based on the toroidal flux at the base of the convection zone, bipolar magnetic regions (BMRs) are produced with statistical properties obtained from observed distributions. We find that a little quenching in BMR tilt is sufficient to stabilize the dynamo growth. The randomness and nonlinearity in the BMR emergences make the poloidal field unequal and cause some variability in the solar cycle. However, when observed scatter of BMR tilts around Joy’s law with a standard deviation of 15°, is considered, our model produces a variation in the solar cycle, including north-south asymmetry comparable to the observations. The morphology of magnetic fields closely resembles observations, in particular the surface radial field possesses a more mixed polarity field. Observed scatter also produces grand minima. In 11,650 years of simulation, 17 grand minima are detected and 11% of its time the model remained in these grand minima. When we double the tilt scatter, the model produces correct statistics of grand minima. Importantly, the dynamo continues even during grand minima with only a few BMRs, without requiring any additional alpha effect. The reason for this is the downward magnetic pumping which suppresses the diffusion of the magnetic flux across the surface. The magnetic pumping also helps to achieve 11-year magnetic cycle using the observed BMR flux distribution, even at the high diffusivity.

Observing and modeling the poloidal and toroidal fields of the solar dynamo

Context. The solar dynamo consists of a process that converts poloidal magnetic field to toroidal magnetic field followed by a process that creates new poloidal field from the toroidal field. Aims. Our aim is to observe the poloidal and toroidal fields relevant to the global solar dynamo and to see if their evolution is captured by a Babcock-Leighton dynamo. Methods. We used synoptic maps of the surface radial field from the KPNSO/VT and SOLIS observatories, to construct the poloidal field as a function of time and latitude; we also used full disk images from Wilcox Solar Observatory and SOHO/MDI to infer the longitudinally averaged surface azimuthal field. We show that the latter is consistent with an estimate of the longitudinally averaged surface azimuthal field due to flux emergence and therefore is closely related to the subsurface toroidal field. Results. We present maps of the poloidal and toroidal magnetic fields of the global solar dynamo. The longitude-averaged azimuthal field observed at the surface results from flux emergence. At high latitudes this component follows the radial component of the polar fields with a short time lag of between 1−3 years. The lag increases at lower latitudes. The observed evolution of the poloidal and toroidal magnetic fields is described by the (updated) Babcock-Leighton dynamo model.

3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension

Context: Long-term variability in solar cycles represents a challenging constraint for theoretical models. Mean-field Babcock-Leighton dynamos that consider non-instantaneous rising flux tubes have been shown to exhibit long-term variability in their magnetic cycle. However a relation that parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of stellar parameters is still missing. Aims: We aim to find a general parameterization of the rise-time of magnetic flux tubes for solar-like stars. Methods: By considering the influence of magnetic tension on the rise of non-axisymmetric flux tubes, we predict the existence of a control parameter referred as $\Gamma_{\alpha_1}^{\alpha_2}$. This parameter is a measure of the balance between rotational effects and magnetic effects (buoyancy and tension) acting on the magnetic flux tube. We carry out two series of numerical experiments (one for axisymmetric rise and one for non-axisymmetric rise) and demonstrate that $\Gamma_{\alpha_1}^{\alpha_2}$ indeed controls the rise-time of magnetic flux tubes. Results: We find that the rise-time follows a power law of $\Gamma_{\alpha_1}^{\alpha_2}$ with an exponent that depends on the azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In the case of non-axisymmetric rise, the tension force modifies the force balance acting on the magnetic flux tube. We identified the three independent parameters required to predict the rise-time of magnetic flux tubes, that is, the stellar rotation rate, the magnetic flux density of the flux tube, and its azimuthal wavenumber. We combined these into one single relation that is valid for any solar-like star. We suggest using this generalized relation to constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo models.

A PROPOSED PARADIGM FOR SOLAR CYCLE DYNAMICS MEDIATED VIA TURBULENT PUMPING OF MAGNETIC FLUX IN BABCOCK–LEIGHTON-TYPE SOLAR DYNAMOS

ABSTRACT At present, the Babcock–Leighton flux transport solar dynamo models appear to be the most promising models for explaining diverse observational aspects of the sunspot cycle. The success of these flux transport dynamo models is largely dependent upon a single-cell meridional circulation with a deep equatorward component at the base of the Sun’s convection zone. However, recent observations suggest that the meridional flow may in fact be very shallow (confined to the top 10% of the Sun) and more complex than previously thought. Taken together, these observations raise serious concerns on the validity of the flux transport paradigm. By accounting for the turbulent pumping of magnetic flux, as evidenced in magnetohydrodynamic simulations of solar convection, we demonstrate that flux transport dynamo models can generate solar-like magnetic cycles even if the meridional flow is shallow. Solar-like periodic reversals are recovered even when meridional circulation is altogether absent. However, in this case, the solar surface magnetic field dynamics does not extend all the way to the polar regions. Very importantly, our results demonstrate that the Parker–Yoshimura sign rule for dynamo wave propagation can be circumvented in Babcock–Leighton dynamo models by the latitudinal component of turbulent pumping, which can generate equatorward propagating sunspot belts in the absence of a deep, equatorward meridional flow. We also show that variations in turbulent pumping coefficients can modulate the solar cycle amplitude and periodicity. Our results suggest the viability of an alternate magnetic flux transport paradigm—mediated via turbulent pumping—for sustaining solar-stellar dynamo action.

Role of response time of a Babcock-Leighton solar dynamo model in meridional flow-speed reconstruction by EnKF data assimilation

Ensemble Kalman Filter in the framework of Data Assimilation Research Testbed (DART) has been successfully implemented into a 2D kinematic flux-transport dynamo model by Dikpati and colleagues in order to do a parameter estimation, the parameter being the meridional flow-speed as function of time. They performed several ‘Observing System Simulation Experiments’ (OSSEs), and showed that an optimal reconstruction of time-series of meridional flow-speed can be obtained by using 16 ensemble members and only one surface magnetic observation with 30% observational error. Error in reconstruction can be reduced by increasing the ensemble size and number of observations. However, this parameter reconstruction has been found to be sensitive to locations from where observational data are taken. While assimilation of low-latitudes’ surface poloidal magnetic field data can produce good reconstruction, medium-frequency oscillations appear in time-series of reconstructed flow-speed if tachocline toroidal field data are assimilated. These oscillations occur primarily because tachocline toroidal fields change very little during an assimilation interval taken to be 15days, due to changes in meridional flow. A Babcock-Leighton dynamo model’s response time to changes in meridional flow-speed is a few months. We show here that rms error in reconstruction can be significantly reduced if model’s response time is taken into consideration in assimilation of tachocline toroidal field data.

COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY

ABSTRACT The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.

EFFECTS OF THE SCATTER IN SUNSPOT GROUP TILT ANGLES ON THE LARGE-SCALE MAGNETIC FIELD AT THE SOLAR SURFACE

The tilt angles of sunspot groups represent the poloidal field source in Babcock-Leighton-type models of the solar dynamo and are crucial for the build-up and reversals of the polar fields in Surface Flux Transport (SFT) simulations. The evolution of the polar field is a consequence of Hale's polarity rules, together with the tilt angle distribution which has a systematic component (Joy's law) and a random component (tilt-angle scatter). We determine the scatter using the observed tilt angle data and study the effects of this scatter on the evolution of the solar surface field using SFT simulations with flux input based upon the recorded sunspot groups. The tilt angle scatter is described in our simulations by a random component according to the observed distributions for different ranges of sunspot group size (total umbral area). By performing simulations with a number of different realizations of the scatter we study the effect of the tilt angle scatter on the global magnetic field, especially on the evolution of the axial dipole moment. The average axial dipole moment at the end of cycle 17 (a medium-amplitude cycle) from our simulations was 2.73G. The tilt angle scatter leads to an uncertainty of 0.78 G (standard deviation). We also considered cycle 14 (a weak cycle) and cycle 19 (a strong cycle) and show that the standard deviation of the axial dipole moment is similar for all three cycles. The uncertainty mainly results from the big sunspot groups which emerge near the equator. In the framework of Babcock-Leighton dynamo models, the tilt angle scatter therefore constitutes a significant random factor in the cycle-to-cycle amplitude variability, which strongly limits the predictability of solar activity.

A THREE-DIMENSIONAL BABCOCK-LEIGHTON SOLAR DYNAMO MODEL

We present a 3D kinematic solar dynamo model in which poloidal field is generated by the emergence and dispersal of tilted sunspot pairs (more generally Bipolar Magnetic Regions, or BMRs). The axisymmetric component of this model functions similarly to previous 2D Babcock-Leighton (BL) dynamo models that employ a double-ring prescription for poloidal field generation but we generalize this prescription into a 3D flux emergence algorithm that places BMRs on the surface in response to the dynamo-generated toroidal field. In this way, the model can be regarded as a unification of BL dynamo models (2D in radius/latitude) and surface flux transport models (2D in latitude/longitude) into a more self-consistent framework that captures the full 3D structure of the evolving magnetic field. The model reproduces some basic features of the solar cycle including an 11-yr periodicity, equatorward migration of toroidal flux in the deep convection zone, and poleward propagation of poloidal flux at the surface. The poleward-propagating surface flux originates as trailing flux in BMRs, migrates poleward in multiple non-axisymmetric streams (made axisymmetric by differential rotation and turbulent diffusion), and eventually reverses the polar field, thus sustaining the dynamo. In this letter we briefly describe the model, initial results, and future plans.

Buoyancy-induced time delays in Babcock-Leighton flux-transport dynamo models

The Sun is a magnetic star whose cyclic activity is thought to be linked to internal dynamo mechanisms. A combination of numerical modelling with various levels of complexity is an efficient and accurate tool to investigate such intricate dynamical processes. We investigate the role of the magnetic buoyancy process in 2D Babcock-Leighton dynamo models, by modelling more accurately the surface source term for poloidal field. Methods. To do so, we reintroduce in mean-field models the results of full 3D MHD calculations of the non-linear evolution of a rising flux tube in a convective shell. More specifically, the Babcock-Leighton source term is modified to take into account the delay introduced by the rise time of the toroidal structures from the base of the convection zone to the solar surface. We find that the time delays introduced in the equations produce large temporal modulation of the cycle amplitude even when strong and thus rapidly rising flux tubes are considered. Aperiodic modulations of the solar cycle appear after a sequence of period doubling bifurcations typical of non-linear systems. The strong effects introduced even by small delays is found to be due to the dependence of the delays on the magnetic field strength at the base of the convection zone, the modulation being much less when time delays remain constant. We do not find any significant influence on the cycle period except when the delays are made artificially strong. A possible new origin of the solar cycle variability is here revealed. This modulated activity and the resulting butterfly diagram are then more compatible with observations than what the standard Babcock-Leighton model produces.

Turbulent effects in flux-transport solar dynamos

AbstractThe effects of turbulent pumping and η-quenching on Babcock-Leighton dynamo models are explored separately. Turbulent pumping seems to be important to solve several reported problems in these dynamo models related to the magnetic flux transport and to the parity. On the other hand, the suppression of the magnetic diffusivity, η, could help in the formation of long-lived, small and intense structures of toroidal magnetic field.