The quasi-biennial cycle of solar activity and dynamo theory

We have investigated the behavior of dynamo waves within the framework of a nonlinear αω-dynamo by taking into account the thickness of the convective zone, turbulent diffusivity, and meridional circulation. We show that there exists a regime in the model where short and longer patterns are simultaneously observed in the butterfly diagrams for the magnetic field. This regime is similar to the mixed cycle of the Sun, when fast quasi-biennial oscillations are observed against the background of the 22-year cycle.     

A dynamo theory of solar flares

It is proposed that the solar flare phenomenon can be understood as a manifestation of the electrodynamic coupling process of the photosphere-chromosphere-corona system as a whole. The system is coupled by electric currents, flowing along (both upward and downward) and across the magnetic field lines, powered by the dynamo process driven by the neutral wind in the photosphere and the lower chromosphere. A self-consistent formulation of the proposed coupling system is given. It is shown in particular that the coupling system can generate and dissipate the power of 10²⁹ erg s^#X2212;1 and the total energy of 10³² erg during a typical life time (10³ s) of solar flares. The energy consumptions include Joule heat production, acceleration of current-carrying particles along field lines, magnetic energy storage and kinetic energy of plasma convection. The particle acceleration arises from the development of field-aligned potential drops of 10–150 kV due to the loss-cone constriction effect along the upward field-aligned currents, causing optical, X-ray and radio emissions. The total number of precipitating electrons during a flare is shown to be of order 10³⁷–10³⁸.     

Meridional circulation and the period of the solar dynamo cycle

We consider the conditions in the transition from the tachocline to the solar convective zone with changing diffusion coefficient. The topology of the magnetic fields involved in the solar dynamo is revised under the assumption that intermediate fields (of the order of 10 mT) have a dominant role in generating the fields in new cycle. The inclusion of meridional circulation is found to increase the dynamo wave period in comparison to the observed period. This suggests that the αΩ-effects are unimportant in calculating the solar cycle period but hold significance in determining the cycle amplitude.     

Some recent developments in solar dynamo theory

We discuss the current status of solar dynamo theory and describe the dynamo model developed by our group. The toroidal magnetic field is generated in the tachocline by the strong differential rotation and rises to the solar surface due to magnetic buoyancy to create active regions. The decay of these active regions at the surface gives rise to the poloidal magnetic field by the Babcock-Leighton mechanism. This poloidal field is advected by the meridional circulation first to high latitudes and then down below to the tachocline. Dynamo models based on these ideas match different aspects of observational data reasonably well.     

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.     

Amplitude and period of the dynamo wave and prediction of the solar cycle

The relation of the solar cycle period and its amplitude is a complex problem as there is no direct correlation between these two quantities. Nevertheless, the period of the cycle is of important influence to the Earth's climate, which has been noted by many authors. The present authors make an attempt to analyse the solar indices data taking into account recent developments of the asymptotic theory of the solar dynamo. The use of the WKB method enables us to estimate the amplitude and the period of the cycle versus dynamo wave parameters in the framework of the nonlinear development of the one-dimensional Parker migratory dynamo. These estimates link the period T and the amplitude a with dynamo number D and thickness of the generation layer of the solar convective zone h. As previous authors, we have not revealed any considerable correlation between the above quantities calculated in the usual way. However, we have found some similar dependences with good confidence using running cycle periods. We have noticed statistically significant dependences between the Wolf numbers and the running period of the magnetic cycle, as well as between maximum sunspot number and duration of the phase of growth of each sunspot cycle. The latter one supports asymptotic estimates of the nonlinear dynamo wave suggested earlier. These dependences may be useful for understanding the mechanism of the solar dynamo wave and prediction of the average maximum amplitude of solar cycles. Besides that, we have noted that the maximum amplitude of the cycle and the temporal derivative of the monthly Wolf numbers at the very beginning of the phase of growth of the cycle have high correlation coefficient of order 0.95. The link between Wolf number data and their derivative taken with a time shift enabled us to predict the dynamics of the sunspot activity. For the current cycle 23 this yields Wolf numbers of order 107±7.     

Magnetoconvection and the solar dynamo

We review current understanding of the interaction of magnetic fields with convective motions in stellar convection zones. Among the most exciting recent results is the discovery that magnetic fields need not primarily be confined to the stable layer below the convection zone; numerical simulations have shown that surprisingly, strong magnetic fields can be maintained in the interior of the convection zone.     

Configurations of dynamo waves in a two-layer medium and the 11-year solar cycle

The behavior of dynamo waves in a two-layer medium is investigated in terms of the Parker dynamo model. The solar cycle duration is shown to depend on the ratio of turbulent diffusivities in the layers. Meridional circulation has been incorporated into the Parker system. An increase in the intensity of meridional flows is shown to decelerate the propagation of dynamo waves. The minimum of solar magnetic activity can occur not only in the case of intense meridional circulation in both layers but also when a difference in physical characteristics arises between the layers and the meridional flows are moderate.     

The solar dynamo

The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling.Received: 5 May 2003, Published online: 15 July 2003     

The solar dynamo

The basic features of the solar activity mechanism are explained in terms of the dynamo theory of mean magnetic fields. The field generation sources are the differential rotation and the mean helicity of turbulent motions in the convective zone. A nonlinear effect of the magnetic field upon the mean helicity results in stabilizing the amplitude of the 22-year oscillations and forming a basic limiting cycle. When two magnetic modes (with dipole and quadrupole symmetry) are excited nonlinear beats appear, which may be related to the secular cycle modulation.The torsional waves observed may be explained as a result of the magnetic field effect upon rotation. The magnetic field evokes also meriodional flows.Adctual variations of the solar activity are nonperiodic since there are recurrent random periods of low activity of the Maunder minimum type. A regime of such a magnetic hydrodynamic chaos may be revealed even in rather simple nonlinear solar dynamo models.The solar dynamo gives rise also to three-dimensional, non-axisymmetric magnetic fields which may be related to a sector structure of the solar field.     

On the non-symmetric solar dynamo

The external field of the solar magnetohydrodynamic dynamo is expressed in terms of spherical harmonics and in powers of 1/r. The non-symmetric dynamo is stabilized by a -dependent rotational oscillation which interacts with the magnetic field, thus compensating for Ohmic loss. As a consequence, the axis of a dipole wave is found to move on a great circle, with revolution time equal to the magnetic cycle.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Mechanism of cyclically polarity reversing solar magnetic cycle as a cosmic dynamo

We briefly describe historical development of the concept of solar dynamo mechanism that generates electric current and magnetic field by plasma flows inside the solar convection zone. The dynamo is the driver of the cyclically polarity reversing solar magnetic cycle. The reversal process can easily and visually be understood in terms of magnetic field line stretching and twisting and folding in three-dimensional space by plasma flows of differential rotation and global convection under influence of Coriolis force. This process gives rise to formation of a series of huge magnetic flux tubes that propagate along iso-rotation surfaces inside the convection zone. Each of these flux tubes produces one solar cycle. We discuss general characteristics of any plasma flows that can generate magnetic field and reverse the polarity of the magnetic field in a rotating body in the Universe. We also mention a list of problems which are currently being disputed concerning the solar dynamo mechanism together with observational evidences that are to be constraints as well as verifications of any solar cycle dynamo theories of short and long term behaviors of the Sun, particularly time variations of its magnetic field, plasma flows, and luminosity.     

Evidence for a long-term variation of the dynamo action responsible for the solar magnetic cycle

By using the sunspot time series as a proxy, we have made a detailed analysis of the mean solar magnetic field over the last two and half centuries, by means of a reconstruction of its phase space. We find evidence of a long-term trend variation of some of the solar physical processes (over a few decades) that might be responsible for the apparent erratic behaviour of the solar magnetic cycle. The analysis is done by means of a careful study of the axisymmetric dynamo model equations, where we show that the temporal counterpart of the magnetic field can be described by a self-regulated two-dimensional dynamic system, usually known as a Van der Pol–Duffing oscillator. Our results suggest that during the last two and half centuries, the velocity of the meridional flow, v _p, and the efficiency of the α mechanism responsible for the conversion of toroidal magnetic field into poloidal magnetic field might have suffered variations that can explain the observed variability in the solar cycle.     

The solar dynamo and the convective rolls

The most sophisticated attempts to model the convection zone have yielded results in which the angular velocity increases outwards and the largest scales of convection take the form of banana cells aligned with the rotation axis. However, not only does the sign of the angular velocity gradient present problems for dynamo theory, but attempts to detect banana type cells have so far been unsuccessful. Although by no means conclusive, current tracer, spectropic, and radiative data all tend to support models of azimuthal rolls encircling the axis as the fundamental mode.It is shown here that convective upflows and downflows are preferentially generated along the rotation axis and thus initially the large-scale eddies may take the form of azimuthal rolls surrounding the poles. It is then shown that such a system may generate a progressive dynamo wave propagating from pole to equator. Since Parker has shown that an azimuthal magnetic toroid can generate a thermal shadow above it which suppresses its buoyancy, the corresponding temperature deficit so formed becomes the natural site for the downflow of the azimuthal rolls. Thus as the dynamo propagates towards the equator, so will the convective rolls. Finally the compatibility of the most recent helioseismology data with the azimuthal roll model is discussed.Solar Cycle Workshop Paper.     

On global solar dynamo simulations

Global dynamo simulations solving the equations of magnetohydrodynamics (MHD) have been a tool of astrophysicists who try to understand the magnetism of the Sun for several decades now. During recent years many fundamental issues in dynamo theory have been studied in detail by means of local numerical simulations that simplify the problem and allow the study of physical effects in isolation. Global simulations, however, continue to suffer from the age‐old problem of too low spatial resolution, leading to much lower Reynolds numbers and scale separation than in the Sun. Reproducing the internal rotation of the Sun, which plays a crucial role in the dynamo process, has also turned out to be a very difficult problem. In the present paper the current status of global dynamo simulations of the Sun is reviewed. Emphasis is put on efforts to understand how the large‐scale magnetic fields, i.e. whose length scale is greater than the scale of turbulence, are generated in the Sun. Some lessons from mean‐field theory and local simulations are reviewed and their possible implications to the global models are discussed. Possible remedies to some current issues of solar simulations are put forward (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The solar wind-magnetosphere dynamo and the magnetospheric substorm

In a quiet condition, the solar wind kinetic energy is converted into electrical energy. A small part of this energy is dissipated as heat energy in the polar ionosphere. We identify at least three types of magnetospheric disturbances which are not associated with an increase of the heat production and call them reversible disturbances, while the magnetospheric substorm is an irreversible disturbance which is associated with a large increase of the heat production.The magnetosphere appears to have an inherent internal instability by which a large amount of heat energy is sporadically produced in the polar upper atmosphere at the expense of the magnetic energy in the magnetotail. A positive feed-back process may be responsible for the growth of the instability and for the expansive phase, while the recovery phase sets in when some process begins to suppress the positive feed-back process.     

A nonlinear model of the solar dynamo

The role of nonlinearity is explored in a mean-field dynamo model. Magnetic fields are amplified by the combined action of the and-effects, and as the field's intensity increases the Lorentz force becomes important. Torsional oscillations and meridional circulations are driven by the Lorentz force, and the oscillations are consistent with those measured on the surface of the Sun. The torsional oscillations feedback in the induction equation and saturate the magnetic field's growth by quenching differential rotation. This model can also help us understand the processes responsible for the range of periods seen in the activity cycles of other stars like the Sun.     

Mathematical theory of the ionospheric dynamo

A mathematical theory of the three-dimensional ionospheric dynamo is described, which is exact within the context of the assumption that the magnetic field lines are perfectly conducting.Explicit formulae are obtained for the electric fields, and hence for the current systems, which are excited by the dynamo e.m.f. associated with an arbitrary given wind field.They can also be applied to determine the fields arising from an external source of e.m.f., originating for example in the magnetosphere.The convergence properties of the solution are investigated for a simple symmetric wind field; it is found that inclusion of spherical harmonics up to degree 80 is sufficient to yield the features of the electrojet region, now fully coupled to the global current system.     

Towards a model for the solar dynamo

We study a mean field model of the solar dynamo, in which the non-linearity is the action of the azimuthal component of the Lorentz force of the dynamo-generated magnetic field on the angular velocity. The underlying zero-order angular velocity is consistent with recent determinations of the solar rotation law, and the form of the alpha effect is chosen so as to give a plausible butterfly diagram. For small Prandtl numbers we find regular, intermittent and apparently chaotic behaviour, depending on the size of the alpha coefficient. For certain parameters, the intermittency displays some of the characteristics believed to be associated with the Maunder minimum. We thus believe that we are capturing some features of the solar dynamo.