Plasma-physical aspects of the solar cycle

Mass motions below the photosphere drive the solar cycle which is associated with variations in the magnetic field structure and accompanying phenomena. In addition to semi-empirical models, dynamo theories have been used to explain the solar cycle. The emergence of magnetic field generated by these mechanisms and its expansion into the corona involves many plasma physical processes. Magnetic buoyancy aids the expulsion of magnetic flux. The corona may respond dynamically or by continually adjusting to a quasi-static force-free or pressure-balanced equilibrium. The formation and disruption of current sheets is significant for the overall structure of the coronal magnetic field and the physics of quiescent prominences. The corona has a fine structure consisting of magnetic loops. The structure and stability of these are important as they are one of the underlying elements which make up the corona.     

The Solar Dynamo

Observations relevant to current models of the solar dynamo are presented, with emphasis on the history of solar magnetic activity and on the location and nature of the solar tachocline. The problems encountered when direct numerical simulation is used to analyse the solar cycle are discussed, and recent progress is reviewed. Mean field dynamo theory is still the basis of most theories of the solar dynamo, so a discussion of its fundamental principles and its underlying assumptions is given. The role of magnetic helicity is discussed. Some of the most popular models based on mean field theory are reviewed briefly. Dynamo models based on severe truncations of the full MHD equations are discussed.     

Physical Causes of Solar Activity

The magnetic fields that dominate the structure of the Sun's atmosphere are controlled by processes in the solar interior, which cannot be directly observed. Magnetic activity is found in all stars with deep convective envelopes: young and rapidly rotating stars are very active but cyclic activity only appears in slow rotators. The Sun's 11-year activity cycle corresponds to a 22-year magnetic cycle, since the sunspot fields (which are antisymmetric about the equator) reverse at each minimum. The record of magnetic activity is aperiodic and is interrupted by episodes of reduced activity, such as the Maunder Minimum in the seventeenth century, when sunspots almost completely disappeared. The proxy record from cosmogenic isotopes shows that similar grand minima recur at intervals of around 200 yr. The Sun's large-scale field is generated by dynamo action rather than by an oscillator. Systematic magnetic cycles are apparently produced by a dynamo located in a region of weak convective overshoot at the base of the convection zone, where there are strong radial gradients in the angular velocity . The crucial parameter (the dynamo number) increases with increasing and kinematic (linear) theory shows that dynamo action can set in at an oscillatory (Hopf) bifurcation that is probably subcritical. Although it has been demonstrated that the whole process works in a self-consistent model, most calculations have relied on mean-field dynamo theory. This approach is physically plausible but can only be justified under conditions that do not apply in the Sun. Still, mean-field dynamos do reproduce the butterfly diagram and other key features of the solar cycle. An alternative approach is to study generic behaviour in low-order models, which exhibit two forms of modulation, associated with symmetry-breaking and with reduced activity. Comparison with observed behaviour suggests that modulation of the solar cycle is indeed chaotic, i.e. deterministically rather than stochastically driven.     

The high latitude heliospheric magnetic field

As the Ulysses spacecraft approaches its first pass under the south pole of the sun, it is an appropriate time to review our current knowledge and predictions regarding the three dimensional behaviour of the heliospheric magnetic field, in particular at high heliographic latitudes. Optical techniques for measuring the photospheric magnetic field and observations of coronal brightness structures provide indications of the behaviour of the source of the heliospheric field in the corona. As the coronal fields are carried out into the heliosphere by the solar wind, from Parker's model we would expect that the spiral field observed in the equatorial plane should gradually unwind with latitude leading to open, approximately radial, field lines over the polar regions. Predictions of departures from, and models extending this simple picture are discussed. Both the Pioneer and Voyager spacecraft have spent brief periods in the regions above the maximum latitude of the heliospheric current sheet-relevant results from these missions are reviewed as well as results from the early stages of the out-of-ecliptic phase of the Ulysses mission. The configuration of the coronal magnetic field exhibits a strong dependence on the phase of the solar activity cycle. While the forthcoming Ulysses polar passes take place near to solar minimum, the different conditions which might be encountered on a second orbit of the sun at solar maximum are described.     

Modulation of Cosmic Rays in the Heliosphere From Solar Minimum to Maximum: a Theoretical Perspective

The modulation of galactic cosmic rays in the heliosphere seems to be dominated by four major mechanisms: convection, diffusion, drifts (gradient, curvature and current sheet), and adiabatic energy losses. In this regard the global structure of the solar wind, the heliospheric magnetic field (HMF), the current sheet (HCS), and that of the heliosphere itself play major roles. Individually, the four mechanisms are well understood, but in combination, the complexity increases significantly especially their evolvement with time - as a function of solar activity. The Ulysses observations contributed significantly during the past solar minimum modulation period to establish the relative importance of these major mechanisms, leading to renewed interest in developing more sophisticated numerical models, and in the underlying physics, e.g., what determines the diffusion tensor. With increased solar activity, the relative contributions of the mentioned mechanisms change, but how they change and what causes these changes over an 11-year solar cycle is not well understood. It can therefore be expected that present and forthcoming observations during solar maximum activity will again produce very important insights into the causes of long-term modulation. In this paper the basic theory of solar modulation is reviewed for galactic cosmic rays. The influence of the Ulysses observations on the development of the basic theory and numerical models are discussed, especially those that have challenged the theory and models. Model-based predictions are shown for what might be encountered during the next solar minimum. Lastly, modulation theory and modelling are discussed for periods of maximum solar activity when a global reorganization of the HMF, and the HCS, occurs. This revised version was published online in August 2006 with corrections to the Cover Date.     

Flux-Transport Solar Dynamos

Large-scale solar dynamo models were first built by Parker (1955). Over the past half a century these models have evolved significantly. We discuss here the development of a class of large-scale dynamo models which include, along with the α-effect and Ω-effect, an important third process, flux transport by meridional circulation. We present the properties of this ‘flux-transport’ dynamo, including the crucial role meridional circulation plays in giving this dynamo predictive power.     

Dynamo Models for Planets Other Than Earth

Observations from planetary spacecraft missions have demonstrated a spectrum of dynamo behaviour in planets. From currently active dynamos, to remanent crustal fields from past dynamo action, to no observed magnetization, the planets and moons in our solar system offer magnetic clues to their interior structure and evolution. Here we review numerical dynamo simulations for planets other than Earth. For the terrestrial planets and satellites, we discuss specific magnetic field oddities that dynamo models attempt to explain. For the giant planets, we discuss both non-magnetic and magnetic convection models and their ability to reproduce observations of surface zonal flows and magnetic field morphology. Future improvements to numerical models and new missions to collect planetary magnetic data will continue to improve our understanding of the magnetic field generation process inside planets.     

Solar Magnetism: The State of Our Knowledge and Ignorance

We review some longstanding scientific mysteries related to solar magnetism, with final attention to the mystery of the “turbulent diffusion” essential for the theoretical α ω-dynamo that is believed to be the source of the magnetic fields of the Sun. Fundamental difficulties with the concept of turbulent diffusion of magnetic fields suggest that the solar dynamo problem needs to be reformulated. An alternative dynamo model is proposed, but it remains to be shown that the model can provide the quantitative aspects of the cyclic magnetic fields of the Sun.     

Comparison of the Past Two Solar Minima from the Perspective of the Interior Dynamics and Dynamo of the Sun

Solar cycle 23 behaved differently than cycle 22 in many ways. Certain properties, namely the long minimum at the end of cycle 23, weakening of polar fields, shrinking of polar coronal holes, reduction in the terrestrial atmospheric neutral density layer, have been identified as unusual compared to several past cycles. The origin of these differences most likely lies in the ways the dynamo has operated that led to distinctly different generation and evolution of the large-scale magnetic fields in cycles 22 and 23. Certain differences in the properties of Galactic-Cosmic Rays during cycles 22 and 23 have recently been explained by the differences in evolutionary pattern of coronal holes, which are linked to the dynamo-generated large-scale magnetic fields. In this paper, I will discuss the differences in the solar interior dynamics, particularly the properties of flow fields and their influence in governing the evolution of dynamo-generated magnetic fields during cycles 22 and 23, respectively.     

Coronal Mass Ejections

This workshop summary tries to distill the key difficulties and questions in the art of (I)CME physics and strategies to address them. (I)CMEs are multi-dimensional, multi-parameter, and multi-scale phenomena related to the solar dynamo, corona, and heliosphere. This workshop illustrates the immense progress made in describing and modeling these spectacular energetic solar events, but also shows clear shortcomings in our understanding of them.     

Using Precise Solar Limb Shape Measurements to Study the Solar Cycle

Despite 20 years of total solar irradiance measurements from space, the lack of high precision spatially resolved observations limits definitive answers to even simple questions like ``Are the solar irradiance changes caused solely by magnetic fields perturbing the radiative flux at the photosphere?" More subtle questions like how the aspheric structure of the sun changes with the magnetic cycle are only now beginning to be addressed with new tools like p-mode helioseismology. Solar 5-min oscillation studies have yielded precise information on the mean radial interior solar structure and some knowledge about the rotational and thermal solar asphericity. Unfortunately this progress has not been enough to generate a self-consistent theory for why the solar irradiance and luminosity vary with the magnetic cycle. We need sharper tools to describe and understand the sun's global aspheric response to its internal dynamo, and we need to be able to measure the solar cycle manifestation of the magnetic cycle on entropy transport from the interior to the photosphere in much the same way that we study the fundamentally more complex problem of magnetic flux transport from the solar interior. A space experiment called the Solar Physics Explorer for Radius, Irradiance and Shape (SPHERIS) and in particular its Astrometric and Photometric Telescope (APT) component will accomplish these goals.

     

Theory and Modeling of Planetary Dynamos

Numerical dynamo models are increasingly successful in modeling many features of the geomagnetic field. Moreover, they have proven to be a useful tool for understanding how the observations connect to the dynamo mechanism. More recently, dynamo simulations have also ventured to explain the surprising diversity of planetary fields found in our solar system. Here, we describe the underlying model equations, concentrating on the Boussinesq approximations, briefly discuss the numerical methods, and give an overview of existing model variations. We explain how the solutions depend on the model parameters and introduce the primary dynamo regimes. Of particular interest is the dependence on the Ekman number which is many orders of magnitude too large in the models for numerical reasons. We show that a minor change in the solution seems to happen at $\mbox {E}=3\mbox {$\times 10^{-6}$}$ whose significance, however, needs to be explored in the future. We also review three topics that have been a focus of recent research: field reversal mechanisms, torsional oscillations, and the influence of Earth’s thermal mantle structure on the dynamo. Finally we discuss the possibility of tidally or precession driven planetary dynamos.     

The Solar Dynamo

It is generally accepted that the strong toroidal magnetic fields that emerge through the solar surface in sunspots and active regions are formed by the action of differential rotation on a poloidal field, and then stored in or near the tachocline at the base of the Sun’s convection zone. The problem is how to explain the generation of a reversed poloidal field from this toroidal flux—a process that can be parametrised in terms of an α-effect related to some form of turbulent helicity. Here we first outline the principal patterns that have to be explained: the 11-year activity cycle, the 22-year magnetic cycle and the longer term modulation of cyclic activity, associated with grand maxima and minima. Then we summarise what has been learnt from helioseismology about the Sun’s internal structure and rotation that may be relevant to our subject. The ingredients of mean-field dynamo models are differential rotation, meridional circulation, turbulent diffusion, flux pumping and the α-effect: in various combinations they can reproduce the principal features that are observed. To proceed further, it is necessary to rely on large-scale computation and we summarise the current state of play.     

Global Solar Wind Structure from Solar Minimum to Solar Maximum: Sources and Evolution

During the past few years, significant progress has been made in identifying the coronal sources of structures observed in the solar wind. This recent work has been facilitated by the relative simplicity and stability of structures during solar minimum. The challenge now is to continue to use coordinated coronal/solar wind observations to study the far more complicated and time-evolving structures of solar maximum. In this paper I will review analyses that use a wide range of observations to map out the global heliosphere and connect the corona to the solar wind. In particular, I will review some of the solar minimum studies done for the first Whole Sun Month campaign (WSM1), and briefly consider work in progress modeling the ascending phase time period of the second Whole Sun Fortnight campaign (WSF) and SPARTAN 201-05 observations, and the solar maximum third Whole Sun Month campaign (WSM3). In so doing I hope to demonstrate the increase in complexity of the connections between corona and heliosphere with solar cycle, and highlight the issues that need to be addressed in modeling solar maximum connections. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon Observations

Muon observations are complementary to neutron monitor observations but there are some important differences in the two techniques. Unlike neutron monitors, muon telescope systems use coincidence techniques to obtain directional information about the arriving particle. Neutron monitor observations require simple corrections for pressure variations to compensate for the varying mass of atmospheric absorber over a site. In contrast, muon observations require additional corrections for the positive and negative temperature effects. Muon observations commenced many years before neutron monitors were constructed. Thus, muon data over a larger number of solar cycles is available to study solar modulation on anisotropies and other cosmic ray variations. The solar diurnal and semi-diurnal variations have been studied for many years. Using the techniques of Bieber and Chen it has been possible to derive the radial gradient, parallel mean-free path and symmetric latitude gradient of cosmic rays for rigidities <200 GV. The radial gradient varies with the 11-year solar activity cycle whereas the parallel mean-free path appears to vary with the 22-year solar magnetic cycle. The symmetric latitudinal gradient reverses at each solar polarity reversal. These results are in general agreement with predictions from modulation models. In undertaking these analyses the ratio of the parallel to perpendicular mean-free path must be assumed. There is strong contention in the literature about the correct value to employ but the results are sufficiently robust for this to be, at most, a minor problem. An asymmetric latitude gradient of highly variable nature has been found. These observations do not support current modulation models. Our view of the sidereal variation has undergone a revolution in recent times. Nagashima, Fujimoto and Jacklyn proposed a narrow Tail-In source anisotropy and separate Loss-Cone anisotropy as being responsible for the observed variations. A new analysis technique, more amenable to such structures, was developed by Japanese and Australian researchers. They confirmed the existence of the two anisotropies. However, they found that the Tail-In anisotropy is asymmetric and that both anisotropies had different positions from the prediction. Most 27-day modulations are observed at neutron monitor rigidities but not so readily at higher rigidities. An exception to this is the Isotropic Intensity Wave modulation observed in the early 1980s and again in 1991. This modulation is very strongly related to the heliospheric sector structure and implies a significantly different cosmic ray density on either side of the neutral sheet. The interpretation of most cosmic ray modulation phenomena requires good latitude coverage in both hemispheres. The closure of many muon observatories is a matter of concern. In the northern hemisphere a few new instruments are being constructed and spatial coverage is barely adequate. In the southern hemisphere the situation is far worse with the possibility that within a decade only the Mawson observatory in Antarctica will still be in operation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Planetary Dynamos from a Solar Perspective

Direct numerical simulations of the geodynamo and other planetary dynamos have been successful in reproducing the observed magnetic fields. We first give an overview on the fundamental properties of planetary magnetism. We review the concepts and main results of planetary dynamo modeling, contrasting them with the solar dynamo. In planetary dynamos the density stratification plays no major role and the magnetic Reynolds number is low enough to allow a direct simulation of the magnetic induction process using microscopic values of the magnetic diffusivity. The small-scale turbulence of the flow cannot be resolved and is suppressed by assuming a viscosity far in excess of the microscopic value. Systematic parameter studies lead to scaling laws for the magnetic field strength or the flow velocity that are independent of viscosity, indicating that the models are in the same dynamical regime as the flow in planetary cores. Helical flow in convection columns that are aligned with the rotation axis play an important role for magnetic field generation and forms the basis for a macroscopic α-effect. Depending on the importance of inertial forces relative to rotational forces, either dynamos with a dominant axial dipole or with a small-scale multipolar magnetic field are found. Earth is predicted to lie close to the transition point between both classes, which may explain why the dipole undergoes reversals. Some models fit the properties of the geomagnetic field in terms of spatial power spectra, magnetic field morphology and details of the reversal behavior remarkably well. Magnetic field strength in the dipolar dynamo regime is controlled by the available power and found to be independent of rotation rate. Predictions for the dipole moment agree well with the observed field strength of Earth and Jupiter and moderately well for other planets. Dedicated dynamo models for Mercury, Saturn, Uranus and Neptune, which assume stably stratified layers above or below the dynamo region, can explain some of the unusual field properties of these planets.     

Anomalous and Galactic Cosmic Rays at 1 AU During the Cycle 23/24 Solar Minimum

Anomalous cosmic ray (ACR) intensities at 1 AU at solar minimum generally track galactic cosmic ray (GCR) intensities such as those measured by neutron monitors, albeit with differences between solar polarity cycles. The unusual cycle 23/24 solar minimum was long-lasting with very low sunspot numbers and significantly reduced interplanetary magnetic field strength and solar wind dynamic pressure and turbulence, but also featured a heliospheric current sheet tilt that remained high for an extended period. Peak ACR intensities did not recover to the maximum values reached during the last two A>0 solar minima and just barely reached the last A<0 levels. However, GCR intensities in 2009 (neutron monitor rates and also at ～200 MeV/nucleon) were the highest recorded during the last 50 years, indicating their intensities were not as heavily modulated during their transport from the outer heliosphere. This unexpected difference in the behavior of ACRs and GCRs remains unexplained, but suggests that either the ACR source intensity may have weakened since the last A<0 epoch, or perhaps that ACR intensities at 1 AU in the ecliptic may be more sensitive than GCRs to the higher tilt angle. This seems plausible if the ACR source intensity is greater at low latitudes during A<0 cycles, while the GCR distribution at the heliospheric boundary is more uniform in latitude. Shortly after an abrupt increase in the current sheet tilt angle in late 2009, both ACR and GCR intensities showed dramatic decreases, marking the end of solar minimum modulation conditions for this cycle.     

Signature of the 11-Year Cycle in the Upper Atmosphere

In the last 45 years I have studied the thermal structure of the atmosphere from the thermosphere down to the stratosphere, and found evidence of its variability in relationship with the change of solar irradiation during the 11-year solar cycle. I would review, in the light of recent model results, the measurements which I had made since the 1960s and which, for some of them, did not find any explanation at the time of their publication. The data were obtained by two different techniques, rockets and lidars and correspond to different regions of the atmosphere from the upper thermosphere to the stratosphere. The expectation was until recently that the atmosphere should be warmed by an increase of solar flux in the course of the solar cycle due to the increase of UV flux. It has been shown to be the case in the tropical stratosphere and at all latitudes in the upper thermosphere. But, at high and mid latitudes and at other altitudes, the reverse situation was found to exist and, until recently, this cooling observed in parts of the atmosphere with increasing solar flux had never been simulated by models. In addition to reviewing our own data, the paper will present recent results using other dataset which support our observations. It is only recently that we succeeded with a model able to tune the forcing by planetary waves at the tropopause level and thus reproduce such behaviour.     

Large Scale Flows in the Solar Convection Zone

We discuss the current theoretical understanding of the large scale flows observed in the solar convection zone, namely the differential rotation and meridional circulation. Based on multi-D numerical simulations we describe which physical processes are at the origin of these large scale flows, how they are maintained and what sets their unique profiles. We also discuss how dynamo generated magnetic field may influence such a delicate dynamical balance and lead to a temporal modulation of the amplitude and profiles of the solar large scale flows.