Poloidal Field Generation Research Articles

The mean solar butterfly diagram and poloidal field generation rate at the surface of the Sun

The difference between individual solar cycles in the magnetic butterfly diagram can mostly be ascribed to the stochasticity of the emergence process. We aim to obtain the expectation value of the butterfly diagram from observations of four cycles. This allows us to further determine the generation rate of the surface radial magnetic field. We used data from Wilcox Solar Observatory to generate time-latitude diagrams of the surface radial and toroidal magnetic fields spanning cycles 21 to 24. We symmetrized them across the equator and cycle-averaged them. From the mean butterfly diagram and surface toroidal field, we then inferred the mean poloidal field generation rate at the surface of the Sun. The averaging procedure removes realization noise from individual cycles. The amount of emerging flux required to account for the evolution of the surface radial field is found to match that provided by the observed surface toroidal field and Joy's law. Cycle-averaging butterfly diagrams removes realization noise and artefacts due to imperfect scale separation and corresponds to an ensemble average that can be interpreted in the mean-field framework. The result can then be directly compared to $ dynamo models. The Babcock-Leighton alpha -effect is consistent with observations, a result that can be appreciated only if the observational data are averaged in some way.

Shear-driven magnetic buoyancy in the solar tachocline: the mean electromotive force due to rotation

ABSTRACT The leading theoretical paradigm for the Sun’s magnetic cycle is an αω-dynamo process, in which a combination of differential rotation and turbulent, helical flows produces a large-scale magnetic field that reverses every 11 yr. Most αω solar dynamo models rely on differential rotation in the solar tachocline to generate a strong toroidal field. The most problematic part of such models is then the production of the large-scale poloidal field, via a process known as the α-effect. Whilst this is usually attributed to small-scale convective motions under the influence of rotation, the efficiency of this regenerative process has been called into question by some numerical simulations. Motivated by likely conditions within the tachocline, the aim of this paper is to investigate an alternative mechanism for the poloidal field regeneration, namely the magnetic buoyancy instability in a shear-generated, rotating magnetic layer. We use a local, fully compressible model in which an imposed vertical shear winds up an initially vertical magnetic field. The field ultimately becomes buoyantly unstable, and we measure the resulting mean electromotive force (EMF). For sufficiently rapid rotation, we find that a significant component of the mean EMF is aligned with the direction of the mean magnetic field, which is the characteristic feature of the classical αω-dynamo model. Our results therefore suggest that magnetic buoyancy could contribute directly to the generation of large-scale poloidal field in the Sun.

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.

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.

A THEORETICAL STUDY OF THE BUILD-UP OF THE SUN’S POLAR MAGNETIC FIELD BY USING A 3D KINEMATIC DYNAMO MODEL

ABSTRACT We develop a three-dimensional kinematic self-sustaining model of the solar dynamo in which the poloidal field generation is from tilted bipolar sunspot pairs placed on the solar surface above regions of strong toroidal field by using the SpotMaker algorithm, and then the transport of this poloidal field to the tachocline is primarily caused by turbulent diffusion. We obtain a dipolar solution within a certain range of parameters. We use this model to study the build-up of the polar magnetic field and show that some insights obtained from surface flux transport models have to be revised. We present results obtained by putting a single bipolar sunspot pair in a hemisphere and two symmetrical sunspot pairs in two hemispheres. We find that the polar fields produced by them disappear due to the upward advection of poloidal flux at low latitudes, which emerges as oppositely signed radial flux and which is then advected poleward by the meridional flow. We also study the effect that a large sunspot pair, violating Hale’s polarity law, would have on the polar field. We find that there would be some effect—especially if the anti-Hale pair appears at high latitudes in the mid-phase of the cycle—though the effect is not very dramatic.

Inflows towards active regions and the modulation of the solar cycle: A parameter study

Aims: We aim to investigate how converging flows towards active regions affect the surface transport of magnetic flux, as well as their impact on the generation of the Sun's poloidal field. The inflows constitute a potential non-linear mechanism for the saturation of the global dynamo and may contribute to the modulation of the solar cycle in the Babcock-Leighton framework. Methods: We build a surface flux transport code incorporating a parametrized model of the inflows and run simulations spanning several cycles. We carry out a parameter study to assess how the strength and extension of the inflows affect the build-up of the global dipole field. We also perform simulations with different levels of activity to investigate the potential role of the inflows in the saturation of the global dynamo. Results: We find that the interaction of neighbouring active regions can lead to the occasional formation of single-polarity magnetic flux clumps inconsistent with observations. We propose the darkening caused by pores in areas of high magnetic field strength as a plausible mechanism preventing this flux-clumping. We find that inflows decrease the amplitude of the axial dipole moment by a $\sim30\,\%$, relative to a no-inflows scenario. Stronger (weaker) inflows lead to larger (smaller) reductions of the axial dipole moment. The relative amplitude of the generated axial dipole is about $9\%$ larger after very weak cycles than after very strong cycles. This supports the inflows as a non-linear mechanism capable of saturating the global dynamo and contributing to the modulation of the solar cycle within the Babcock-Leighton framework.

BABCOCK–LEIGHTON SOLAR DYNAMO: THE ROLE OF DOWNWARD PUMPING AND THE EQUATORWARD PROPAGATION OF ACTIVITY

ABSTRACT The key elements of the Babcock–Leighton dynamos are the generation of poloidal field through decay and the dispersal of tilted bipolar active regions and the generation of toroidal field through the observed differential rotation. These models are traditionally known as flux transport dynamo models as the equatorward propagations of the butterfly wings in these models are produced due to an equatorward flow at the bottom of the convection zone. Here we investigate the role of downward magnetic pumping near the surface using a kinematic Babcock–Leighton model. We find that the pumping causes the poloidal field to become predominately radial in the near-surface shear layer, which allows the negative radial shear to effectively act on the radial field to produce a toroidal field. We observe a clear equatorward migration of the toroidal field at low latitudes as a consequence of the dynamo wave even when there is no meridional flow in the deep convection zone. Both the dynamo wave and the flux transport type solutions are thus able to reproduce some of the observed features of the solar cycle including the 11-year periodicity. The main difference between the two types of solutions is the strength of the Babcock–Leighton source required to produce the dynamo action. A second consequence of the magnetic pumping is that it suppresses the diffusion of fields through the surface, which helps to allow an 11-year cycle at (moderately) larger values of magnetic diffusivity than have previously been used.

What drives the solar magnetic cycle?

Solar magnetic activities show an about 11-year cycle period with the variations of the amplitudes. The increasing technological advancement induces the stronger influence of the solar magnetic cycle on humans. The magnetic cycle is believed to be caused by a magnetohydrodynamic (MHD) dynamo process in the solar interior, where the flows and the magnetic fields interact in the strongly turbulent convective zone. The intrinsic features of the solar interior, e.g., the stratification, the turbulence and the nonlinearities, make the global MHD simulations of solar convection with the realistic parameters of the Sun extremely hard. The past substantial progress in understanding the solar magnetic cycle benefitted from the simplified models, e.g., the axisymmetric kinematic ones. The mean field electrodynamics and the helioseismology laid the foundation of the progress. Under the effects of the large-scale flows, the poloidal and the toroidal components of the magnetic field sustain each other, which persists the cycle variations of the solar magnetic field. The key ingredients in the dynamo process include the mechanism and the location of the toroidal field generation, the mechanism and the location of the poloidal field generation, the rising of toroidal field to form the sunspots with tilts and the mechanism for the equatorward migration of the sunspots. So far, only the generation of the toroidal field by differential rotations is less controversial. The current dynamo models usually do not include the toroidal flux tube emergence, which was investigated as a separated topic. As the workhorse to understand the solar cycle during the past decade, the Babcock-Leighton (BL) type flux transport dynamos is a popular paradigm for explaining the cyclic nature of solar magnetic activity. They were even used to predict future solar cycles by assimilating observed surface flows and fields into the models. Recently the flux transport dynamos faces some challenges, such as the depth variation of the equatorward flow, the strong turbulent diffusivity, and so on. But the BL mechanism which is due to the decay of the tilt sunspot groups on the solar surface to regenerate the poloidal field, is most probably at the heart of the solar cycle. The further understanding of the solar magnetic cycle will benefit from the constraints of the solar historical data, the helioseismology, the different magnetic cycles of different types of stars, and the global MHD numerical simulations. These fields will be developed in parallel with the kinematic dynamo and fertilize each other. The three dimensional Babcock-Leighton type dynamo models coupled with the toroidal flux tube emergence is expected to be the workhorse of the next generation of solar dynamo.

The role of the alpha effect of Babcock–Leighton in the generation of poloidal magnetic field of the Sun

The role of the alpha effect of Babcock–Leighton in the generation of poloidal magnetic field of the Sun

North-South asymmetry of solar dynamo in the current activity cycle

An explanation is suggested for the north-south asymmetry of the polar magnetic field reversal in the current cycle of solar activity. The contribution of the Babcock-Leighton mechanism to the poloidal field generation is estimated using sunspot data for the current activity cycle. Estimations are performed separately for the northern and southern hemispheres. The contribution of the northern hemisphere exceeded considerably that of the southern hemisphere during the initial stage of the cycle. This is the probable reason for the earlier reversal of the northern polar field. The estimated contributions of the Babcock-Leighton mechanism are considerably smaller than similar estimations for the previous activity cycles. A relatively weak (<1 G) large-scale polar field can be expected for the next activity minimum.

The irregularities of the sunspot cycle and their theoretical modelling

The 11-year sunspot cycle has many irregularities, the most promi- nent amongst them being the grand minima when sunspots may not be seen for several cycles. After summarizing the relevant observational data about the irregularities, we introduce the flux transport dynamo model, the currently most successful theoretical model for explaining the 11-year sunspot cycle. Then we analyze the respective roles of nonlinearities and random fluctuations in creating the irregularities. We also discuss how it has recently been realized that the fluctuations in meridional circula- tion also can be a source of irregularities. We end by pointing out that fluctuations in the poloidal field generation and fluctuations in meridional circulation together can explain the occurrences of grand minima.

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.

Studies of grand minima in sunspot cycles by using a flux transport solar dynamo model

We propose that grand minima in solar activity are caused by simultaneous fluctuations in the meridional circulation and the Babcock—Leighton mechanism for the poloidal field generation in the flux transport dynamo model. We present the following results: (a) fluctuations in the meridional circulation are more effective in producing grand minima; (b) both sudden and gradual initiations of grand minima are possible; (c) distributions of durations and waiting times between grand minima seem to be exponential; (d) the coherence time of the meridional circulation has an effect on the number and the average duration of grand minima, with a coherence time of about 30 yr being consistent with observational data. We also study the occurrence of grand maxima and find that the distributions of durations and waiting times between grand maxima are also exponential, like the grand minima. Finally we address the question of whether the Babcock—Leighton mechanism can be operative during grand minima when there are no sunspots. We show that an α-effect restricted to the upper portions of the convection zone can pull the dynamo out of the grand minima and can match various observational requirements if the amplitude of this α-effect is suitably fine-tuned.

GRAND MINIMA AND NORTH-SOUTH ASYMMETRY OF SOLAR ACTIVITY

A solar-type dynamo model in a spherical shell is developed with allowance for random dependence of the poloidal field generation mechanism on time and latitude. The model shows repeatable epochs of strongly decreased amplitude of magnetic cycles similar to the Maunder minimum of solar activity. Random dependence of dynamo-parameters on latitude brakes the equatorial symmetry of generated fields. The model shows the correlation of the occurrence of grand minima with deviations in the dynamo-field from dipolar parity. An increased north-south asymmetry of magnetic activity can, therefore, be an indicator of transitions to grand minima. Qualitative interpretation of this correlation is suggested. Statistics of grand minima in the model are close to the Poisson random process indicating that the onset of a grand minimum is statistically independent of preceding minima.

SOLAR CYCLE PROPAGATION, MEMORY, AND PREDICTION: INSIGHTS FROM A CENTURY OF MAGNETIC PROXIES

The solar cycle and its associated magnetic activity are the main drivers behind changes in the interplanetary environment and the Earth's upper atmosphere (commonly referred to as space weather). These changes have a direct impact on the lifetime of space-based assets and can create hazards to astronauts in space. In recent years there has been an effort to develop accurate solar cycle predictions (with aims at predicting the long-term evolution of space weather), leading to nearly a hundred widely spread predictions for the amplitude of solar cycle 24. A major contributor to the disagreement is the lack of direct long-term databases covering different components of the solar magnetic field (toroidal vs.\ poloidal). Here we use sunspot area and polar faculae measurements spanning a full century (as our toroidal and poloidal field proxies), to study solar cycle propagation, memory, and prediction. Our results substantiate predictions based on the polar magnetic fields, whereas we find sunspot area to be uncorrelated to cycle amplitude unless multiplied by area-weighted average tilt. This suggests that the joint assimilation of tilt and sunspot area is a better choice (with aims to cycle prediction) than sunspot area alone, and adds to the evidence in favor of active region emergence and decay as the main mechanism of poloidal field generation (i.e. the Babcock-Leighton mechanism). Finally, by looking at the correlation between our poloidal and toroidal proxies across multiple cycles, we find solar cycle memory to be limited to only one cycle.

Origin of Grand Minima in Sunspot Cycles

One of the most striking aspects of the 11-year sunspot cycle is that there have been times in the past when some cycles went missing, a most well-known example of this being the Maunder minimum during 1645-1715. Analyses of cosmogenic isotopes ((14)C and (10)Be) indicated that there were about 27 grand minima in the last 11,000 yrs, implying that about 2.7% of the solar cycles had conditions appropriate for forcing the Sun into grand minima. We address the question of how grand minima are produced and specifically calculate the frequency of occurrence of grand minima from a theoretical dynamo model. We assume that fluctuations in the poloidal field generation mechanism and in the meridional circulation produce irregularities of sunspot cycles. Taking these fluctuations to be Gaussian and estimating the values of important parameters from the data of the last 28 solar cycles, we show from our flux transport dynamo model that about 1-4% of the sunspot cycles may have conditions suitable for inducing grand minima.

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.

Dynamo models of grand minima

AbstractSince a universally accepted dynamo model of grand minima does not exist at the present time, we concentrate on the physical processes which may be behind the grand minima. After summarizing the relevant observational data, we make the point that, while the usual sources of irregularities of solar cycles may be sufficient to cause a grand minimum, the solar dynamo has to operate somewhat differently from the normal to bring the Sun out of the grand minimum. We then consider three possible sources of irregularities in the solar dynamo: (i) nonlinear effects; (ii) fluctuations in the poloidal field generation process; (iii) fluctuations in the meridional circulation. We conclude that (i) is unlikely to be the cause behind grand minima, but a combination of (ii) and (iii) may cause them. If fluctuations make the poloidal field fall much below the average or make the meridional circulation significantly weaker, then the Sun may be pushed into a grand minimum.

The Waldmeier effect and the flux transport solar dynamo

We confirm that the evidence for the Waldmeier effect WE1 (the anti-correlation between rise times of sunspot cycles and their strengths) and the related effect WE2 (the correlation between rise rates of cycles and their strengths) is found in different kinds of sunspot data. We explore whether these effects can be explained theoretically on the basis of the flux transport dynamo models of sunspot cycles. Two sources of irregularities of sunspot cycles are included in our model: fluctuations in the poloidal field generation process and fluctuations in the meridional circulation. We find WE2 to be a robust result which is produced in different kinds of theoretical models for different sources of irregularities. The Waldmeier effect WE1, on the other hand, arises from fluctuations in the meridional circulation and is found only in the theoretical models with reasonably high turbulent diffusivity which ensures that the diffusion time is not more than a few years.

The hemispheric asymmetry of solar activity during the last century and the solar dynamo

We believe the Babcock–Leighton process of poloidal field generation to be the main source of irregularity in the solar cycle. The random nature of this process may make the poloidal field in one hemisphere stronger than that in the other hemisphere at the end of a cycle. We expect this to induce an asymmetry in the next sunspot cycle. We look for evidence of this in the observational data and then model it theoretically with our dynamo code. Since actual polar field measurements exist only from the 1970s, we use the polar faculae number data recorded by Sheeley (1991, 2008) as a proxy of the polar field and estimate the hemispheric asymmetry of the polar field in different solar minima during the major part of the twentieth century. This asymmetry is found to have a reasonable correlation with the asymmetry of the next cycle. We then run our dynamo code by feeding information about this asymmetry at the successive minima and compare the results with observational data. We find that the theoretically computed asymmetries of different cycles compare favorably with the observational data, with the correlation coefficient being 0.73. Due to the coupling between the two hemispheres, any hemispheric asymmetry tends to get attenuated with time. The hemispheric asymmetry of a cycle either from observational data or from theoretical calculations statistically tends to be less than the asymmetry in the polar field (as inferred from the faculae data) in the preceding minimum. This reduction factor turns out to be 0.43 and 0.51 respectively in observational data and theoretical simulations.