Solar magnetic fields and the dynamo theory

Unlike Earth’s dipolar magnetic fields, solar magnetic fields consist of wide ranges of length-scales and strengths, and interestingly, they evolve in a cyclic fashion with a 22-year periodicity. A magnetohydrodynamic dynamo operating in the Sun is most likely responsible for producing the solar magnetic activity cycle. While the first solar dynamo models were built half a century ago, recent views differ significantly from those models. According to widely accepted present concepts, the large-scale solar dynamo is of flux-transport type, which involves three basic processes: (i) generation of toroidal fields by shearing the pre-existing poloidal fields by differential rotation (the Ω-effect); (ii) re-generation of poloidal fields by lifting and twisting the toroidal fluxtubes (the α-effect); (iii) flux transport by meridional circulation. This class of dynamos has been successful in explaining many large-scale solar cycle features, including a particularly difficult one – the correct phase relationship between the equatorward-migrating sunspot belt and the poleward drifting large-scale, diffuse fields. The dynamo cycle period in such models is primarily governed by the meridional flow speed near the bottom of the convection zone. After briefly reviewing the historical background, we will present the successes of flux-transport dynamos, including their predictive capability. For example, we will demonstrate how the meridional circulation plays a key role in governing the Sun’s memory about its own magnetic field, and how a flux-transport dynamo-based predictive tool can explain the cause of the very slow polar reversal in the so-called “peculiar” cycle 23 compared to those in cycles 20, 21 and 22. We will close by presenting explanations for certain long-term variability using these models, such as, what may have maintained the observed cyclic variation in slow solar wind flow during Maunder minima, in the presence of near zero solar activity.     

Solar and late-type dwarfs

The Einstein Observatory and the IUE satellite have provided the observational basis for a major restructuring in theories of coronal formation for late-type stars. For the first time, coronal and transition region emission from a large sample of low mass (1 M_o) dwarf stars has been directly observed, with the unexpected result that essentially all such stars are x-ray emitters. The Sun, which was previously assumed to be typical, is now known to be at the low end of the x-ray luminosity function for solar-type stars. K- and M-dwarfs are observed to have nearly the same luminosity distributions as G-dwarfs and all of these spectral types have a large spread in x-ray luminosity.Observationally, there is a strong correlation between the strength of coronal emission in stars with outer convective zones and the rotation rates of these stars. At the present time we have only the beginnings of a satisfactory theoretical explanation for this correlation; although we are beginning to understand the connection between coronal emission strength and the magnetic field, we do not yet understand the stellar dynamo which generates the magnetic field. Studies of the coronal emission of stars may lead to a better understanding of stellar dynamos.     

The dynamics of the solar radiative zone

The picture of the solar radiative zone is evolving quickly. This review is separated in two parts. We first recall how the two powerful probes of the solar interior, namely the neutrinos and helioseismology have scrutinized the microscopic properties of the solar radiative plasma. Recent observations stimulate today complementary activities beyond the standard stellar model through theoretical modeling of angular momentum transport by rotation, internal waves or (and) by magnetic fields to get access to the dynamical motions of this important region of the Sun. So in the second part, we summarize the first impact of such processes on the radiative zone.     

太阳发电机理论研究

太阳活动主要是由磁场产生的, 因此, 对太阳磁场性质和起源的研究具有重要意义. 太阳发电机理论主要研究的是太阳上观测到的与太阳活动相关的磁场起源、磁场特征、各种活动现象之间的相关性及其变化规律. 其是太阳物理学中有待解决的最基本、最重要的问题. 根据太阳黑子及太阳周期的相关观测, 介绍了构成发电机的基本要素, 具体描述了各种典型发电机模型, 并对其分别进行评述, 进而探讨了目前存在的问题及发展方向.      

Einstein observations of cool stars

Observations of cool stars with the $\text{Einstein}$ Observatory (HEAO-2) have brought about a fundamental change in our knowledge and understanding of stellar coronae. The existence of X-ray emission from stars throughout the H-R diagram, the wide range of X-ray luminosity within a given spectral and luminosity class, and the strong correlation of X-ray luminosity with stellar age and rotation are among the more significant $\text{Einstein}$ results. These results are strong evidence for the influence of stellar dynamo action on the formation and heating of stellar coronae. A discussion of relevant consortium and guest observations will be given. The Hyades cluster, in particular, will serve as an example to demonstrate the usefulness of X-ray observations in the study of stellar activity and coronal evolution.     

Influence of Fast Global Variations of Solar Magnetic Fields on Space Weather in Cycle 23

It is established that the large-scale and global magnetic fields in the Sun's atmosphere do not change smoothly, and long-lasting periods of gradual variations are superseded by fast structural changes of the global magnetic field. Periods of fast global changes on the Sun are accompanied by anomalous manifestations in the interplanetary space and in the geomagnetic field. There is a regular recurrence of these periods in each cycle of solar activity, and the periods are characterized by enhanced flaring activity that reflects fast changes in magnetic structures. Is demonstrated, that the fast changes have essential influencing on a condition of space weather, as most strong geophysical disturbances are connected to sporadic phenomena on the Sun. An explanation has been offered for the origin of anomalous geomagnetic disturbances that are unidentifiable in traditionally used solar activity indices. Is shown, main physical mechanism that leads to fast variations of the magnetic fields in the Sun's atmosphere is the reconnection process.     

Chromospheric dynamics

This review focuses on dynamics of the solar chromosphere, which serves as a good proxy for understanding processes in stellar chromospheres as well. In the quiet chromosphere it is useful to distinguish between the magnetic network on the boundaries of supergranulation cells, where strong magnetic fields are organized in mainly vertical magnetic flux tubes, and internetwork regions in the cell interior, where magnetic fields are weaker and dynamically less important. Recently, some progress has been made in understanding the physics of the non-magnetic chromosphere. On the other hand, the physical processes that heat the magnetic network have not been fully identified. Is the network heated by wave dissipation and if so, what are their physical characteristics? These and other aspects relating to the dynamics and energy transport mechanisms will be discussed in detail. In addition, some of the outstanding problems in the field such the driving mechanism for spicules and the nature of internetwork magnetic fields will also be highlighted. Furthermore, a critical assessment will be made on the challenges facing theory and the direction for future investigations, particularly in the light of the new space experiments, will be highlighted.     

Local-area helioseismology as a diagnostic tool for solar variability

Dynamical and thermal variations of the internal structure of the Sun can affect the energy flow and result in variations in irradiance at the surface. Studying variations in the interior is crucial for understanding the mechanisms of the irradiance variations. “Global” helioseismology based on analysis of normal mode frequencies, has helped to reveal radial and latitudinal variations of the solar structure and dynamics associated with the solar cycle in the deep interior. A new technique, - “local-area” helioseismology or heliotomography, offers additional potentially important diagnostics by providing three-dimensional maps of the sound speed and flows in the upper convection zone. These diagnostics are based on inversion of travel times of acoustic waves which propagate between different points on the solar surface through the interior. The most significant variations in the thermodynamic structure found by this method are associated with sunspots and complexes of solar activity. The inversion results provide evidence for areas of higher sound speed beneath sunspot regions located at depths of 4–20 Mm, which may be due to accumulated heat or magnetic field concentrations. However, the physics of these structures is not yet understood. Heliotomography also provides information about large-scale stable longitudinal structures in the solar interior, which can be used in irradiance models. This new diagnostic tool for solar variability is currently under development. It will require both a substantial theoretical and modeling effort and high-resolution data to develop new capabilities for understanding mechanisms of solar variability.     

Seismological studies of the sun and other stars

Observations of a large number of different oscillation frequencies in the Sun provide an opportunity for detailed testing of the theory of stellar structure and evolution. At present highly significant discrepancies remain between observed and computed frequencies, and so our models of the solar interior have to be modified. With further improvements in the observations it might become possible to make a direct empirical determination of the density structure throughout the Sun.Similar oscillations have so far not been detected in other stars, but attempts to do so are under way. Theoretical estimates indicate that amplitudes somewhat greater than for the Sun might be expected for early F stars on the main sequence, and that the amplitude increases rapidly with decreasing gravity. Observation of such oscillations would enable investigations of the structure of these stars, and would in addition provide valuable information about the excitation mechanism of the oscillations.     

Investigation of the differential rotation of the large-scale magnetic elements for the solar activity cycles 20 and 21

The differential rotation of the patterns of the large-scale solar magnetic field during solar activity cycles 20 and 21 is investigated. Compact magnetic elements with the polarity of the general solar magnetic field have larger speed of rotation than the elements with the opposite polarity. The surface of the Sun was divided by 10°-zones. In all of them the average rotation rate of the magnetic elements with negative polarity is little higher than that of the magnetic elements with positive polarity, except for 50°-zone of the south hemisphere and at the 10° latitude of the north hemisphere.

The rates of differential rotation for large-scale magnetic elements with negative and positive polarities have similar behavior for both cycles of the solar activity.

The rotation rate varies at polarity reversal of the circumpolar magnetic fields. For the cycle No 20 in 1969–1970 the threefold reversal took place in the northern hemisphere and variations of rotation rate can be noticed for magnetic elements both with positive and negative polarity for each 10°-zone in the same hemisphere.     

Formation of relativistic jets by collapsing stars to black holes

Formation of relativistic jets in the magnetosphere of collapsing stars is considered. These jets will be formed in the polar caps of magnetosphere of collapsing star, where the stellar magnetic field increases during the collapse and the charged particles are accelerated. The jets will generate non-thermal radiation. The analysis of dynamics and emission of particles in the stellar magnetosphere under collapse shows that collapsing stars can be powerful sources of relativistic jets.     

Active stars and systems

The most notable manifestations of stellar activity are reviewed with particular emphasis on the merging picture of solar-type activity in physical conditions different from those in the Sun. Evidence for starspots, plages and high-level coronal emissions is presented from observations covering a wide range of spectral bands: from X-ray to radio wavelengths. The main physical parameters of the active areas in the active stars, when compared with solar values, indicate that the basic requirement for activity phenomena to develop is the presence of observationally elusive localized magnetic fields on and above the stellar surface. The importance of coordinated programs involving simultaneous observations from the ground and from space - aiming at empirical and theoretical modeling of activity phenomena - is stressed.     

α–ω Effect and peculiarities of the 27-day variations of the galactic cosmic rays intensity,solar wind and solar activity parameters

We show that the amplitudes of the 27-day variations of galactic cosmic ray (GCR) intensity, solar wind and solar activity parameters have a periodicity with duration of three to four Carrington rotation periods (3–4 CRP). We assume that the general reason for this phenomenon may be related to similar cyclicity of topological structure of the solar magnetic field lines created owing to the asymmetry of turbulent solar dynamo and solar differential rotation transforming the Sun’s poloidal magnetic field to the toroidal (α–ω effect), and vice versa.     

Solar cycles: A tutorial

The Sun is the nearest stellar and astrophysical laboratory, available for detailed studies in several fields of physics and astronomy. It is a sphere of hot gas with a complex and highly variable magnetic field which plays a very important role. The Sun shows an unprecedented wealth of phenomena that can be studied extensively and to the greatest detail, in a way we will never be in a position to study in other stars. Humans have studied the Sun for millennia and after the discovery of the telescope they realized that the Sun varies with time, i.e., solar activity is highly variable, in tune scales of millennia to seconds. The study of these variabilities helps us to understand how the Sun works and how it affects the interplanetary medium, Earth and the other planets. Solar power varies substantially and greatly affects the Earth and humans. Solar activity has several important periodicities, and quasi-periodicities. Knowledge of these periodicities helps us to forecast, to an extent, solar events that affect our planet. The most prominent periodicity of solar activity is the one of 11 years. The actual period is in fact 22 years because the magnetic field polarity of the Sun has to be taken into account. The Sun can be considered as a non-linear RLC electric circuit with a period of 22 years. The RLC equivalent circuit of the Sun is a van der Pol oscillator and such a model can explain many solar phenomena, including the variability of solar energy with time. Other quasi-periodicities such as the ones of 154 days, the 1.3, 1.7 to 2 years, etc., some of which might be harmonics of the 22 year cycle are also present in solar activity, and their study is very interesting and important since they affect the Earth and human activities. The period of 27 days related to solar rotation plays also a very important role in geophysical phenomena. It is noticeable that almost all periodicities are highly variable with time as wavelet analysis reveals. It is very important for humans to be in a position to forecast solar activity during the next hour, day, year, decade and century, because solar phenomena affect life on Earth and such predictions will help politicians and policy makers to better serve their countries and our planet.     

Recent progress in time–distance helioseismology

Time–distance helioseismology is one of the local helioseismology techniques that are used to derive the interior properties of the Sun. It has been used to study the structures and flow fields beneath sunspots on local scales, as well as used to derive interior rotational rates and meridional flow velocities on global scales. In addition to the efforts in improving time–distance measurements and inversions, theoretical modeling is also carried out to enhance the accuracy of sensitivity kernels. Recently, by use of realistic numerical simulation on solar convection, we have also started to investigate the validity of time–distance studies.     

Magnetic flux expulsion as an acceleration mechanism for stellar winds

Observations of the Sun show that magnetic flux is emerging through the surface in small scales in rather copious amounts. In order to maintain a steady state field strength, this flux must either be locally dissipated or explelled or both. We believe that magnetic reconnection and subsequent flux explusion is the most effective manner in which to achieve this. If new flux emerges into an already preexisting coronal magnetic field, the ambient field must be pushed aside to allow room for the new flux. If the ambient field strength decreases outward with radial distance as is expected for all stars, it may pinch off the emerging flux through magnetic reconnection and expell it outward. The net force on an isolated diamagnetic plasmoid produced by this process is shown to assume a particularly simple form, depending only on the plasmoid's mass, its temperature, and the radial gradient of the logarithm of the undisturbed magnetic pressure. If a sufficient number of these magnetic elements are produced per unit time, this process translates to a net outward magnetic force on the coronal plasma which can be greater that the gas pressure force. Thus, a stellar wind can be produced by magnetic forces alone without the need for a high coronal gas pressure — a mechanism which could be effective in explaining why stars, such as the late-type giants, which possess cool coronae nevertheless exhibit vigorous coronal expansions.     

Heating rates in X-ray flares: From solar microflares to stellar events

Soft X-ray solar and stellar flares appear in the coronae of solar-like stars due to abrupt release of energy accumulated in magnetic fields. To build a quantitatively correct model of a flare we need to know how much energy is released in flares of different sizes and strengths. Here we estimate and compare the energy release rate in flares as different as microflares occurring over the quiet Sun and strong stellar events in RS CVn systems. We find one simple scaling law which describes flares differing one from another by 10 orders of magnitude in the amount of emission measure.     

27-day variation in solar-terrestrial parameters: Global characteristics and an origin based approach of the signals

The Earth and the near interplanetary medium are affected by the Sun in different ways. Those processes generated in the Sun that induce perturbations into the Magnetosphere-Ionosphere system are called geoeffective processes and show a wide range of temporal variations, like the 11-year solar cycle (long term variations), the variation of ～27?days (recurrent variations), solar storms enduring for some days, particle acceleration events lasting for some hours, etc.In this article, the periodicity of ～27?days associated with the solar synodic rotation period is investigated. The work is mainly focused on studying the resulting 27-day periodic signal in the magnetic activity, by the analysis of the horizontal component of the magnetic field registered on a set of 103 magnetic observatories distributed around the world. For this a new method to isolate the periodicity of interest has been developed consisting of two main steps: the first one consists of removing the linear trend corresponding to every calendar year from the data series, and the second one of removing from the resulting series a smoothed version of it obtained by applying a 30-day moving average. The result at the end of this process is a data series in which all the signal with periods larger than 30?days are canceled.The most important characteristics observed in the resulting signals are two main amplitude modulations: the first and most prominent related to the 11-year solar cycle and the second one with a semiannual pattern. In addition, the amplitude of the signal shows a dependence on the geomagnetic latitude of the observatory with a significant discontinuity at approx. ±60°.The processing scheme was also applied to other parameters that are widely used to characterize the energy transfer from the Sun to the Earth: F10.7 and Mg II indices and the ionospheric vertical total electron content (vTEC) were considered for radiative interactions; and the solar wind velocity for the non-radiative interactions between the solar wind and the magnetosphere. The 27-day signal obtained in the magnetic activity was compared with the signals found in the other parameters resulting in a series of cross-correlations curves with maximum correlation between 3 and 5?days of delays for the radiative and between 0 and 1?days of delay for the non-radiative parameters. This result supports the idea that the physical process responsible for the 27-day signal in the magnetic activity is related to the solar wind and not to the solar electromagnetic radiation.     

A 22-year cycle in sunspot activity

We study the recently presented group sunspot number series and show that a persistent 22-year periodicity exists in sunspot activity throughout the entire period of about 400 years of direct sunspot observations. The amplitude of this periodicity in total cycle intensity is about 20% of the present intensity level. A 22-year periodicity in sunspot activity is naturally produced by the 22-year magnetic dynamo cycle in the presence of a relic magnetic field. Accordingly, a persistent 22-year periodicity in sunspot activity gives strong evidence for the existence of such a relic magnetic field in the Sun. The stable phase and the roughly constant amplitude of this periodicity during times of very different sunspot activity level strongly support this interpretation.