Solar activity forecast with a dynamo model

Although systematic measurements of the Sun's polar magnetic field exist only from mid-1970s, other proxies can be used to infer the polar field at earlier times. The observational data indicate a strong correlation between the polar field at a sunspot minimum and the strength of the next cycle, although the strength of the cycle is not correlated well with the polar field produced at its end. This suggests that the Babcock–Leighton mechanism of poloidal field generation from decaying sunspots involves randomness, whereas the other aspects of the dynamo process must be reasonably ordered and deterministic. Only if the magnetic diffusivity within the convection zone is assumed to be high (of order  10¹² cm² s⁻¹  ), we can explain the correlation between the polar field at a minimum and the next cycle. We give several independent arguments that the diffusivity must be of this order. In a dynamo model with diffusivity like this, the poloidal field generated at the mid-latitudes is advected toward the poles by the meridional circulation and simultaneously diffuses towards the tachocline, where the toroidal field for the next cycle is produced. To model actual solar cycles with a dynamo model having such high diffusivity, we have to feed the observational data of the poloidal field at the minimum into the theoretical model. We develop a method of doing this in a systematic way. Our model predicts that cycle 24 will be a very weak cycle. Hemispheric asymmetry of solar activity is also calculated with our model and compared with observational data.     

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 co-efficient 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 ei-ther 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.     

Predicting solar ‘climate’ by assimilating magnetic data into a flux-transport dynamo

Observational and theoretical knowledge about global-scale solar dynamo ingredients have reached the stage that it is possible to calibrate a flux-transport dynamo for the Sun by adjusting only a few tunable parameters. The important ingredients in this class of model are differential rotation (Omega-effect), helical turbulence (alpha-effect), meridional circulation and turbulent diffusion. The meridional circulation works as a conveyor belt and governs the dynamo cycle period. Meridional circulation and magnetic diffusivity together govern the memory of the Sun's past magnetic fields. After describing the physical processes involved in a flux-transport dynamo, we will show that a predictive tool can be built from it to predict mean solar cycle features by assimilating magnetic field data from previous cycles. We will discuss the theoretical and observational connections among various predictors, such as dynamo-generated toroidal flux integral, cross-equatorial flux, polar fields and geomagnetic indices. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global solar dynamo models: Simulations and predictions

Flux-transport type solar dynamos have achieved considerable success in correctly simulating many solar cycle features, and are now being used for prediction of solar cycle timing and amplitude. We first define flux-transport dynamos and demonstrate how they work. The essential added ingredient in this class of models is meridional circulation, which governs the dynamo period and also plays a crucial role in determining the Sun’s memory about its past magnetic fields. We show that flux-transport dynamo models can explain many key features of solar cycles. Then we show that a predictive tool can be built from this class of dynamo that can be used to predict mean solar cycle features by assimilating magnetic field data from previous cycles.     

Solar Wind Sources in the Late Declining Phase of Cycle 23: Effects of the Weak Solar Polar Field on High Speed Streams

The declining phases of solar cycles are known for their high speed solar wind streams that dominate the geomagnetic responses during this period. Outstanding questions about these streams, which can provide the fastest winds of the solar cycle, concern their solar origins, persistence, and predictability. The declining phase of cycle 23 has lasted significantly longer than the corresponding phases of the previous two cycles. Solar magnetograph observations suggest that the solar polar magnetic field is also ～?2?–?3 times weaker. The launch of STEREO in late 2006 provided additional incentive to examine the origins of what is observed at 1 AU in the recent cycle, with the OMNI data base at the NSSDC available as an Earth/L1 baseline for comparisons. Here we focus on the year 2007 when the solar corona exhibited large, long-lived mid-to-low latitude coronal holes and polar hole extensions observed by both SOHO and STEREO imagers. STEREO provides in situ measurements consistent with rigidly corotating solar wind stream structure at up to ～?45° heliolongitude separation by late 2007. This stability justifies the use of magnetogram-based steady 3D solar wind models to map the observed high speed winds back to their coronal sources. We apply the WSA solar wind model currently running at the NOAA Space Weather Prediction Center with the expectation that it should perform its best at this quiet time. The model comparisons confirm the origins of the observed high speed streams expected from the solar images, but also reveal uncertainties in the solar wind source mapping associated with this cycle’s weaker solar polar fields. Overall, the results illustrate the importance of having accurate polar fields in synoptic maps used in solar wind forecast models. At the most fundamental level, they demonstrate the control of the solar polar fields over the high speed wind sources, and thus one specific connection between the solar dynamo and the solar wind character.     

Evolution of Active and Polar Photospheric Magnetic Fields During the Rise of Cycle 24 Compared to Previous Cycles

The evolution of the photospheric magnetic field during the declining phase and minimum of cycle 23 and the recent rise of cycle 24 are compared with the behavior during previous cycles. We used longitudinal full-disk magnetograms from the NSO??s three magnetographs at Kitt Peak, the Synoptic Optical Long-term Investigations of the Sun (SOLIS) vector spectro-magnetograph (VSM), the spectro-magnetograph and the 512-channel magnetograph instruments, and longitudinal full-disk magnetograms from the Mt. Wilson 150-foot tower. We analyzed 37 years of observations from these two observatories that have been observing daily, weather permitting, since 1974, offering an opportunity to study the evolving relationship between the active region and polar fields in some detail over several solar cycles. It is found that the annual averages of a proxy for the active region poloidal magnetic field strength, the magnetic field strength of the high-latitude poleward streams, and the time derivative of the polar field strength are all well correlated in each hemisphere. The active region net poloidal fields effectively disappeared in both hemispheres around 2004 and the polar fields have not become significantly stronger since this time. These results are based on statistically significant cyclical patterns in the active region fields and are consistent with the Babcock?CLeighton phenomenological model for the solar activity cycle. There was more hemispheric asymmetry in the total and maximum active region flux during late cycle 23 (after around 2004), when the southern hemisphere was more active, and the rise of cycle?24, when the northern hemisphere was more active, than at any other time since 1974. We see evidence that the process of cycle 24 field reversal has begun at both poles.     

The reversal of the solar polar magnetic fields

It is a basic feature of the Babcock-Leighton model of the solar cycle that the polar field reversal is due to the diffusive decay and poleward drift of the active region fields. The flux from follower regions moves preferentially polewards in each hemisphere, where it cancels with, and then replaces, the previously existing polar fields. A number of workers have attempted to model this process by numerical solutions of the flux transport equation, which include the surface effects of supergranule diffusion, differential rotation and meridional flow, with conflicting results.Here we describe recent changes in the polar fields using synoptic magnetic data provided by the Mount Wilson Observatory, and compare them with simulations using the flux transport equation and based on the observed fields for Carrington rotation 1815. These changes include a part-reversal of the north polar field. It is shown that the evolution of the polar fields cannot be reproduced accurately by simulations of the diffusion and poleward drift of the emerging active regions at sunspot latitudes.Histograms of the distribution of the field intensities derived from the daily magnetograms obtained at the Kitt Peak Station of the National Solar Observatory provide independent evidence that flux is emerging at high latitudes and that this flux makes a contribution to the evolution of these patterns. This implies the presence of some form of sub-surface dynamo action at high latitudes.On leave from the School of Mathematics, University of Sydney.     

Origin of the polar magnetic field reversals

The polar magnetic field on the Sun changes its sign during the maximum of solar cycles. It is known that the phenomenon of three-fold reversal of the polar magnetic field occurred in solar cycle 20. Using the magnetograph data of the Mount Wilson Observatory from 1967 to 1993, we confirm a previously suggested topological model of the three-fold magnetic-field reversal (Benevolenskaya, 1991). From the data set we have found that cycles with three-fold polar magnetic field reversals are characterized by a pronounced high-frequency component of the magnetic field compared with cycles with single polar magnetic-field reversals.     

Variations of helioseismic parameters due to magnetic field generated by a flux transport model

The change of sound speed has been found at the base of the convection during the solar cycles,which can be used to constrain the solar internal magnetic field.We aim to check whether the magnetic field generated by the solar dynamo can lead to the cyclic variation of the sound speed detected through helioseismology.The basic configuration of magnetic field in the solar interior was obtained by using a Babcock-Leighton(BL) type flux transport dynamo.We reconstructed one-dimensional solar models by assimilating magnetic field generated by an established dynamo and examined their influences on the structural variables.The results show that magnetic field generated by the dynamo is able to cause noticeable change of the sound speed profile at the base of the convective zone during a solar cycle.Detailed features of this theoretical prediction are also similar to those of the helioseismic results in solar cycle 23 by adjusting the free parameters of the dynamo model.     

An Exploration of Non-kinematic Effects in Flux Transport Dynamos

Recent global magnetohydrodynamical simulations of solar convection producing a large-scale magnetic field undergoing regular, solar-like polarity reversals also present related cyclic modulations of large-scale flows developing in the convecting layers. Examination of these simulations reveal that the meridional flow, a crucial element in flux transport dynamos, is driven at least in part by the Lorentz force associated with the cycling large-scale magnetic field. This suggests that the backreaction of the field onto the flow may have a pronounced influence on the long-term evolution of the dynamo. We explore some of the associated dynamics using a low-order dynamo model that includes this Lorentz force feedback. We identify several characteristic solutions which include single period cycles, period doubling and chaos. To emulate the role of turbulence in the backreaction process we subject the model to stochastic fluctuations in the parameter that controls the Lorentz force amplitude. We find that short term fluctuations produce long-term modulations of the solar cycle and, in some cases, grand minima episodes where the amplitude of the magnetic field decays to near zero. The chain of events that triggers these quiescent phases is identified. A subsequent analysis of the energy transfer between large-scale fields and flows in the global magnetohydrodynamical simulation of solar convection shows that the magnetic field extracts energy from the solar differential rotation and deposits part of that energy into the meridional flow. The potential consequences of this marked departure from the kinematic regime are discussed in the context of current solar cycle modeling efforts based on flux transport dynamos.     

“TOY” Dynamo to Describe the Long-Term Solar Activity Cycles

Secular variations of solar activity (Gleissberg and Suess cycles) have approximately 80 – 130 and 200 year periods. They are manifested in both observed and proxy data. Here, we show that the basic dynamic features of the Schwabe cycle (asymmetry of its growth and decay phases) and secular cycles (multi-frequency structure and irregular Grand-extremes), as well as a connection between them, can be described by parameter tuning of the electromechanical “toy” dynamo system which has been widely used to model the inversions of the geomagnetic field. An amplitude-frequency diagram for the model magnetic flux has the same shape as the directly observed and reconstructed sunspot area indices. An erratum to this article is available at .     

Dynamo model with a small number of modes and magnetic activity of T Tauri stars

We suggest a model based on the representation of the stellar magnetic field as a superposition of a finite number of poloidal and toroidal free decay modes to describe the dynamo action in fully convective stars. For the adopted law of stellar differential rotation, we determined the dynamo number in exceeding which the generation of a cyclically varying magnetic field is possible in stars without a radiative core and derived an expression for the period of the cycle. The dynamo cycles in fully convective stars and in stars with thin convective envelopes are shown to differ qualitatively: first, the distributions of spots in latitude during the cycle are different for these two types of stars and, second, the model predicts a great weakening of the spot formation in fully convective stars at certain phases of the cycle. To compare the theory with observations, we have analyzed the historical light curve for the weak-line T Tauri star V410 Tau and found that its long-term activity is not a well-defined cycle with a definite period—its activity is more likely quasi-cyclic with a characteristic time of ～4 yr and with a chaotic component superimposed. we have also concluded that a redistribution of spots in longitude is responsible for the secular brightness variations in the star. This does not allow the results of photometric observations to be directly compared with predictions of ourmodel, in which, for simplicity, we assumed a symmetry in longitude and investigated the temporal evolution of the spot distribution in latitude. Therefore, we discuss the questions of what and how observations can be compared with predictions of the dynamo theory.     

Solar Cycle Asymmetry as a Consequence of Fluctuations in Dynamo Parameters

The duration of activity growths in solar cycles is on average shorter than the duration of its declines. This asymmetry can result from fluctuations in dynamo parameters. A solar dynamo model with fluctuations in the α-effect shows the statistical asymmetry which increases with both fluctuation amplitude and coherence time. An interpretation for the asymmetry origin is suggested, which predicts a correlation between the asymmetry measure and delay of the polar field reversals relative to the activity maxima. Data on the twelve latest solar cycles confirm such a correlation.     

Solar torsional oscillations and the grand activity cycle

Some consequences of a nonlinear coupling between magnetic field and rotation are studied within a solar type 2D dynamo model for a spherical convective shell. The magnetic feedback on the rotation law produces two main effects. First, the torsional oscillations are excited. Second, a long-term amplitude modulation of the dynamo cycles is produced. The latter may be identified with the grand cycle of solar activity. The dynamo model seems to be in accord with the phase relations between the torsional and magnetic activity oscillations observed in the 11-year cycle as well as in the 55-year grand cycle. It, however, fails to reproduce the observationally suggested global decreasing trend in the equatorial rotation rate.     

An electric-current description of solar flares

The presently prevailing theories of solar flares rely on the hypothetical presence of magnetic flux tubes beneath the photosphere and the two subsequent hypotheses, their emergence above the photosphere and explosive magnetic reconnection, converting magnetic energy carried by the flux tubes to solar flare energy. In this paper, we discuss solar flares from an entirely different point of view, namely in terms of power supply by a dynamo process in the photosphere. By this process, electric currents flowing along the magnetic field lines are generated and the familiar ‘force-free’ fields or the ‘sheared’ magnetic fields are produced. Upward field-aligned currents thus generated are carried by downward streaming electrons; these electrons can excite hydrogen atoms in the chromosphere, causing the optical Hα flares or ‘low temperature flares’. It is thus argued that as the ‘force-free’ fields are being built up for the magnetic energy storage, a flare must already be in progress.     

THE CORRELATION BETWEEN SUNSPOT AND CORONAL HOLE CYCLES AND A FORECAST OF THE MAXIMUM OF SUNSPOT CYCLE 23

We have shown in previous papers that a close relationship exists between the evolution of polar coronal hole area, estimated from K-coronameter observations, and the Wolf sunspot number, with a time lag of about half a solar cycle. In this paper we study the same relationship, but with the total coronal hole area at the base of the corona as obtained from a potential field model of the coronal magnetic field, which provides a more complete series of about three solar cycles. We confirm the relationship for the two last cycles and find that the forward time shift in the coronal hole area for the best correlation with sunspot number is almost the same for cycles 21 and 22, and this shift is also the time between peaks in both series. We use this result to make an early prediction of the time and size of the sunspot maximum for solar cycle 23, and find that this should occur early in 2001 and have a magnitude of about 190, similar to that of the two previous sunspot cycles.     

Turbulent dynamo near tachocline and reconstruction of azimuthal magnetic field in the solar convection zone

In order to extend the abilities of the αΩ dynamo model to explain the observed regularities and anomalies of the solar magnetic activity, the negative buoyancy phenomenon and the magnetic quenching of the α effect were included in the model, as well as newest helioseismically determined inner rotation of the Sun were used. Magnetic buoyancy constrains the magnitude of toroidal field produced by the Ω effect near the bottom of the solar convection zone (SCZ). Therefore, we examined two “antibuoyancy” effects: i) macroscopic turbulent diamagnetism and ii) magnetic advection caused by vertical inhomogeneity of fluid density in the SCZ, which we call the ∇ρ effect. The Sun's rotation substantially modifies the ∇ρ effect. The reconstruction of the toroidal field was examined assuming the balance between mean‐field magnetic buoyancy, turbulent diamagnetism and the rotationally modified ∇ρ effect. It is shown that at high latitudes antibuoyancy effects block the magnetic fields in the deep layers of the SCZ, and so the most likely these deep‐rooted fields could not become apparent at the surface as sunspots. In the near‐equatorial region, however, the upward ∇ρ effect can facilitate magnetic fields of about 3000 – 4000 G to emerge through the surface at the sunspot belt. Allowance for the radial inhomogeneity of turbulent velocity in derivations of the helicity parameter resulted in a change of sign of the α effect from positive to negative in the northern hemisphere near the bottom of the SCZ. The change of sign is very important for direction of the Parker's dynamo‐waves propagation and for parity of excited magnetic fields. The period of the dynamo‐wave calculated with allowance for the magnetic quenching is about seven years, that agrees by order of magnitude with the observed mean duration of the sunspot cycles. Using the modern helioseismology data to define dynamo‐parameters, we conclude that north‐south asymmetry should exist in the meridional field. At low latitudes in deep layers of the SCZ, the αΩ dynamo excites most efficiency the dipolar mode of the meridional field. Meanwhile, in high‐latitude regions a quadrupolar mode dominates in the meridional field. The obtained configuration of the net meridional field is likely to explain the magnetic anomaly of polar fields (the apparent magnetic “monopole”) observed near the maxima of solar cycles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Axisymmetric field generation within an ambient axial field

The generation of magnetic field in a homogeneous, electrically conducting fluid – as required for the dynamo generation of the fields of many astrophysical bodies – is normally a threshold process; the dynamo mechanism, applicable to such bodies in unmagnetised environments, requires motions of sufficient strength to overcome the innate magnetic diffusion. In the presence of an ambient field, however, the critical nature of the field generation process is relaxed. Motions can distort and amplify the ambient field for all amplitudes of flow. For motions with appropriate geometries, an internal ‘dynamo‐like’ field of appreciable strength can be generated, even for relatively weak flows. At least a minority of planets, moons and other bodies exist within significant external astrophysical fields. For these bodies, the ambient field problem is more relevant than the classical dynamo problem, yet it remains relatively little studied. In this paper we consider the effect of an axial ambient field on a spherical mean‐field α ²ω dynamo model, through nonlinear calculations with α ‐quenching feedback. Ambient fields of varying strengths, and both stationary and oscillatory in time, are imposed. Particular focus is placed on the effects of these fields on the equatorial symmetry and the time dependence of the preferred solutions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anomalies in the evolution of global and large-scale solar magnetic fields as the precursors of several upcoming low solar cycles

Anomalies in the solar magnetic fields of various scales are studied. The polar magnetic field strength is shown to have decreased steadily during the last three solar cycles. This is because the increase in the dipole magnetic moment observed from 1915 to 1976 has changed into a decrease in the last three cycles. At the same time, the medium scale magnetic fields (like those of isolated coronal holes) have been unusually strong in the last cycle. As a result, the tilt of the heliospheric current sheet is still about 30°. The large effective contribution from the medium scale fields to the total energy of the large-scale fields is also confirmed by our calculations of the effective multipolarity index. The aa-index at the cycle minima is correlated with the height of the succeeding maxima. The set of data considered may be indicative of the possible approach of a sequence of low solar cycles.