The solar cycle from data on the large-scale surface magnetic field and solar-dynamo theory

Latitude-time (butterfly) diagrams of the large-scale solar magnetic field differ appreciably from the butterfly diagrams for sunspots. Tilted features corresponding to waves propagating from the middle latitudes to the equator are virtually absent from the diagrams for the large-scale magnetic field. The latitude-time diagram of the 22-year solar cycle based on data for the large-scale surface field appears as a checkerboard pattern rather than a traveling wave. Solutions describing similar behavior for the poloidal magnetic field are found for Parker’s solar-dynamo equations. These solutions agree with observations especially well if meridional circulation is added to the two sources generating the magnetic-field in this dynamo-differential rotation and mirror-asymmetric convection.     

Magnetohydrodynamic model of the solar tachocline

The tachocline is a thin layer providing the transition from differential to uniform rotation in the upper region of the solar radiative zone, which can be explained as an effect of the magnetic field if the magnetic field lines are closed inside the radiative zone. It is shown that the confined field structure that is necessary for the tachocline formation can arise due to the penetration of meridional flow from the convective envelope to the radiative zone. The time for the distortion of the magnetic field by the penetrating flow is short compared to the time for diffusion to the penetration depth. The most long-lived mode of the poloidal field has a confined geometry, and the Ohmic lifetime of this mode exceeds the age of the Sun. The calculated distribution of the angular velocity in the radiative zone taking into account such a field shows a thin tachocline.     

The effect of meridional circulation on dynamo waves approaching the solar poles

Dynamo waves approaching the solar poles are analyzed in the Parker approximation taking into account meridional circulation. Asymptotic solutions of the equations describing the generation of the magnetic field are constructed. It is shown in which cases the effect of meridional circulation results in traveling dynamo waves both incident on and reflected from the pole, or in a superposition of standing dynamo waves.     

Formation of complex rotational structures in convective and isothermal magnetized zones

We study the development of a complex rotation law in the magnetized convective and isothermal zones of stars and planetary atmospheres through the decomposition of vector quantities in terms of orthogonal vector spherical harmonics. In the case of a solar-type extended convective zone, it is assumed that (a) the transformation of thermal into magnetic energy is favorable from the viewpoint of energy balance, (b) the state that is supported with minimum energy loss is realized, and (c) the condition of minimum entropy production consistent with the two previous requirements is satisfied. To find the rotation law of a zone, weak interaction between variations in the rotation and magnetic-field distributions is assumed. Two possible zones of generation of the solar magnetic field are considered. The first is located in the lower half of the solar convective zone and possesses a latitude dependence of the rotational velocity similar to that observed. The second zone is located just below the surface, and has a rotational velocity that decreases sharply with height and depends only weakly on latitude. We also study simple equilibrium structures, in particular, those describing the super-rotation of the medium in a convective or isothermal zone. Realization of such super-rotation in an isothermal zone is associated with the outflow of matter and fields toward upper layers.     

The solar dynamo and integrated irradiance variations in the course of the 11-year cycle

Abstractthe effect of the large-scale magnetic fields generated by the solar dynamo on the radiation flux issuing from the convection zone is studied. A governing equation describing convective heat transfer is obtained in the framework of mean-field magnetohydrodynamics, with account for the influence of magnetic fields and differential rotation on the energy budget of the convection zone. The principal effects are illustrated using a one-dimensional numerical model. Calculations indicate that the influence of large-scale magnetic fields can modulate the solar irradiance with a relative amplitude of ～0.07%.     

Coherent structures in the dynamics of the large-scale solar magnetic field

Variations in the mean solar magnetic field (MSMF) are studied in both the frequency-time and longitude-time domains. A wavelet analysis of the MSMF clearly demonstrates that variations in the mean field are not stationary. Combined with longitude-time diagrams for the background solar magnetic field (BSMF), the analysis reveals the emergence of the background field, which occurs discretely at intervals of 1.5–2 years. Based on an analysis of the fine structure in MSMF variations, we develop a numerical technique to study timedependent heliographic-longitude distribution of the large-scale magnetic field. A detailed picture of the rotation of the large-scale magnetic field is derived for activity cycles 20–23. Coherent structures are detected in longitude-time diagrams obtained by deconvolving the MSMF series. These structures are related to discrete rigid-rotation modes of the large-scale magnetic fields. Various rotational modes coexist and replace one another. During the phase of activity growth, modes with periods of 27.8–28.5 days dominate, whereas a mode with a rotational period of about 27 days dominates during the decline phase. Occasionally, modes with periods of 29–30 days appear. Most structures in the longitude-time MSMF distribution correspond to similar structures in the BSMF distribution for the northern or southern hemisphere. Chronologically, the emergence of the BSMF has frequently been accompanied by changes in the solar rotational regime and has been correlated with variations in the polarity asymmetry in the course of the 11-year activity cycle.     

The generation of magnetic field via convective motions in the photosphere,Alvén waves,and the origin of chromospheric spicules

The basis is laid out for a theory relating various phenomena in the solar atmosphere, including localized concentrations of magnetic field at the bases of coronal magnetic arches, chromospheric spicules, twisted coronal magnetic flux tubes, and flows of energy carried by Alfvén waves propagating upward into the corona. The structure of photospheric currents localized in the vicinity of supergranule boundaries and excited by convective motions is studied. These currents exist primarily in a “dynamo layer” of sharply enhanced transverse conductivity, which forms in the weakly ionized thermal photospheric plasma located in the solar gravitational field. The motions of the electrons and ions in this layer have appreciably different characters: the ions are collisionly driven by the flows of neutral atoms, while the electrons drift in the crossed electric and magnetic fields. The electric field supporting the current arises due to the polarization of the electrons and ions. This field also gives rise to Alfvén perturbations that propagate upward into the corona, together with their associated longitudinal currents. The character of this “loading” makes the system of fields and currents uniquely defined. Moreover, the momentum flux carried by these Alfvén waves should be transferred to the cool chromospheric gas, facilitating the vertical ejection of this gas in the form of spicules, as was first proposed in 1992 by Haerendel.     

Parity fluctuations in stellar dynamos

Observations of the solar butterfly diagram from sunspot records suggest persistent fluctuations in parity, away from the overall, approximately dipolar pattern. A simple mean-field dynamo model is used with a solar-like rotation law and perturbed α effect. The parity of the magnetic field relative to the rotational equator can demonstrate can be described as resonance behavior, while the magnetic energy behaves in a more or less expected way. Possible applications of this effect are discussed in the context of various deviations of the solar magnetic field from dipolar symmetry, as reported from analyses of archival sunspot data. The model produces fluctuations in field parity, and hence in the butterfly diagram, that are consistent with observed fluctuaions in solar behavior.     

Stability of toroidal magnetic fields in the radiation zone of a star

The stability of a toroidal magnetic field in the rotating radiation zone of a star is analyzed to estimate the maximum possible magnitude of relic fields. Equations for small perturbations are obtained taking into account the finite diffusivity and the stabilizing effect of the subadiabatic stratification. The numerical solution of the eigenvalue problem indicates that the threshold field strength for the onset of instability in the radiation zone of the Sun is about 600 G. This figure sets an upper bound for the strength of the relic field. The assumption that magnetic instabilities are present in the solar radiation zone disagrees with the observed abundance of lithium. Our analysis of joint stability of toroidal field and nonuniform rotation shows that two-dimensional MHD solutions for the solar tachocline are stable against three-dimensional perturbations.     

Generation of solar magnetic fields by the αδΘ dynamo

We consider a solar dynamo mechanism that generates large-scale magnetic fields due to the combined action of cyclonic flows (the α effect), differential rotation (the Θ effect), and the non-uniformity of large-scale magnetic fields (the Θ × J effect). Our results are based on numerical model which takes into account currently available data on the differential rotation of the convection zone and the intensity of convective flows in the solar interior. A reasonable choice of parameters characterizing the intensity of magnetic-field generation by the α and Θ × J mechanisms can account for an oscillatory dynamo regime with properties similar to the 22-year magnetic-activity cycle of the Sun. We analyze the nonlinear saturation of the generation effects in the large-scale magnetic field, due to either magnetic stresses or the conservation of magnetic helicity. Allowance for the helicity of the small-scale magnetic fields is of crucial importance in limiting the energy of the generated large-scale magnetic field.     

The effect of acoustic waves on spectral-line profiles in the solar atmosphere: Observations and theory

The fine structure of the FeI λ 532.4185-nm line of neutral iron is studied with high spatial (0.5″) and temporal (9.3 s) resolution using observations of a quiet region at the center of the solar disk. The character of the line asymmetry depends strongly on the nature of the velocity field, i.e., on whether it is due to convective or wave motions. The magnitude of the asymmetry due to acoustic waves is comparable to that due to convective motions. The propagation of acoustic waves in moving granules and intergranular lanes is studied by solving a system of hydrodynamical equations in a three-dimensional model for the solar atmosphere. The temporal variations in the bisector of the line synthesized in a non-LTE approximation agree well with the observational data.     

Impulse-like behavior of the sunspot activity

Gnevyshev’s hypothesis of time space organization of sunspot activity over the solar surface like impulses is considered. Using numerical simulation it was shown that complex solar cycle shape can be explained by distribution of impulses in the northern and southern hemispheres. For long solar cycles, impulses at higher latitudes breaking Sp?rer’s law were found. Comparison of the time-latitude diagrams of solar magnetic fields and impulses has shown that each wave of new polarity to the poles is accompanied by impulse of sunspot activity.     

Butterfly diagram for starspots on LQ Hya

Information on the latitude distribution of starspots and changes in this distribution from year to year is very important for our understanding of the nature of stellar activity and for developing dynamo theory. The concept of butterfly diagrams is introduced for highly spotted stars of late spectral types, by analogy to the Maunder diagrams for the Sun. Our approach is based on the zonal spottedness models constructed by Alekseev and Gershberg. A detailed analysis is given for the single active star LQ Hya, and a comparison is made to similar analyses for several stars with two well-separated spot belts—EK Dra, VY Ari, V775 Her, and V833 Tau. The lower boundary of the butterfly diagram drifts toward the equator during the activity-rise phase, i.e., during years when the relative spotted area increases. This effect is clearly expressed for LQ Hya and other stars whose orientation enables observation of both hemispheres and virtually vanishes for V833 Tau, which is viewed nearly pole-on. The upper boundary of the diagram is virtually unchanged for all the considered spotted stars except V775 Her, for which it moves toward the pole. The drift rate of the lower boundary is ?1 to ?2 deg/yr, a factor of two to three smaller in magnitude than the corresponding solar value. Our analysis provides an independent confirmation of the occurrence of high-latitude spots on stars that are younger than the Sun and whose activity is high but less regular than the solar activity; it also enables the identification of the starting times of stellar cycles.     

Convective mechanism for the formation of photospheric magnetic fields

The well-known model that attributes the formation of a bipolar sunspot group to the emergence of a flux tube disagrees sharply with the usual observed pattern of phenomena. At the same time, the observed patterns can be accounted for quite convincingly in terms of local magnetic-field amplification due to cellular convective motions of the solar plasma. In this study, magnetoconvection in a plane horizontal fluid layer is simulated numerically in the framework of the fully nonlinear, three-dimensional problem. A weak horizontal magnetic field and weak cellular flow are assumed to be present initially. Convection is shown to be capable of producing bipolar magnetic configurations of the strongly amplified magnetic field. Indications of magnetic freezing of the flow in the cell are found. The action of the amplification mechanism under study may be controlled by the large-scale toroidal magnetic field of the Sun.     

Rotational and magnetic corrections to the g-mode frequencies in a one-dimensional MHD model

The central magnetic field and rotation of the solar radiative zone are responsible for corrections to the g-mode frequencies. Magnetogravitational spectra are calculated analytically in a simple one-dimensional MHD model that goes beyond the WKB approximation and avoid any cusp resonances that trap the wave within the radiative zone in the presence of a weak magnetic background. The calculations are compared with spacecraft observations of the 1% frequency shifts for candidate g-modes found in the SOHO GOLF experiment. The magnetic correction is the main contribution for a strong magnetic field satisfying the approximation used. It is shown that a constant magnetic field of 700 kG in the radiative zone provides the required frequency shift for the n = ?10 g-mode. The rotational correction, which is due to the Coriolis force in the one-dimensional model used, is much less than a percent (α_Ω ≤ 0.003).     

Helioseismic models of the sun with a low heavy element abundance

Helioseismology and neutrino experiments probing the internal structure of the Sun have yieldedmuch information, such as the adiabatic elasticity index, density, and sound speed in the convective and radiative zones, the depth of the convective zone, and the flux of neutrinos from the core. The standard model of the Sun does not adequately reproduce these characteristics, with models with low heavy element contents (mass fraction of metals Z = 0.013 in the convective zone) deviating from the helioseismic data appreciably more strongly than models with high heavy element contents (Z = 0.018). However, a spectroscopic low Z value is supported by studies reconstructing the Γ ₁ profile in the adiabatic part of the convective zone based on the oscillation frequencies. Models of the convective zone show a good agreement precisely for low Z values. This study attempts to construct a model for the Sun with low Z that satisfies the helioseismic constraints. This model requires changes in the p + p reaction cross section and the opacities in the radiative zone. In our view, the helioseismic result for the mass concentrated in the convective zone testifies that the p + p reaction cross section or the electron-screening coefficient in the solar core must be increased by several percent over the current values. This requires a comparatively small correction to the opacities (by less than 5%), in order to obtain a solar model with low Z that is in agreement with the results of helioseismology and the observed solar neutrino fluxes.     

Can Superflares Occur on the Sun? A View from Dynamo Theory

Recent data from the Kepler mission has revealed the occurrence of superflares in Sun-like stars which exceed by far any observed solar flares in released energy. Radionuclide data do not provide evidence for occurrence of superflares on the Sun over the past eleven millennia. Stellar data for a subgroup of superflaring Kepler stars are analysed in an attempt to find possible progenitors of their abnormal magnetic activity. A natural idea is that the dynamo mechanism in superflaring stars differs in some respect from that in the Sun. We search for a difference in the dynamo-related parameters between superflaring stars and the Sun to suggest a dynamo mechanism as close as possible to the conventional solar/stellar dynamo but capable of providing much higher magnetic energy. Dynamo based on joint action of differential rotation and mirror asymmetric motions can in principle result in excitation of two types of magnetic fields. First of all, it is well-known in solar physics dynamo waves. The point is that another magnetic configuration with initial growth and further stabilisation can also be excited. For comparable conditions, magnetic field of second configuration is much stronger than that of the first one just because dynamo does not spend its energy for periodic magnetic field inversions but uses it for magnetic field growth. We analysed available data from the Kepler mission concerning the superflaring stars in order to find tracers of anomalous magnetic activity. As suggested in a recent paper [1], we find that anti-solar differential rotation or anti-solar sign of the mirror-asymmetry of stellar convection can provide the desired strong magnetic field in dynamo models. We confirm this concept by numerical models of stellar dynamos with corresponding governing parameters. We conclude that the proposed mechanism can plausibly explain the superflaring events at least for some cool stars, including binaries, subgiants and, possibly, low-mass stars and young rapid rotators.     

Form of the latitude distribution of sunspot activity

The spatial (latitude) distribution of sunspots is studied, including its dependence on solar activity. It is shown that the latitude distributions of sunspots for a given year can be approximately described by the normal law, with its variance being a linear function of the current level of solar activity. Thus, an increase in activity is accompanied by an expansion of the zone of solar activity, in good agreement with earlier results. As the solar activity increases, the width of the zone of sunspot generation and the latitude maximum of the sunspot density grow somewhat more slowly than the number of sunspots, in agreement with observations. The results obtained can be used to reconstruct the spatial distributions of sunspots in the past, interpret the magnetic activity of stars, and address the requirements of the dynamo theory in the form of constraints imposed on models of cyclicity.     

Restructuring of the Solar Magnetic Fields and Flare Activity Centers in Cycle 24

The development of the solar magnetic activity in cycle 24 has been analyzed. It has been shown that the significant north–south asymmetry of magnetic activity was accompanied by the asynchronous reorganization of solar magnetic fields in the northern and southern hemispheres. The formation of unipolar magnetic regions after the decay of activity centers has been studied. The meridional transport of unipolar magnetic regions leading to changes in the zonal structure of the solar magnetic field has been shown. Long-lived centers of flare activity have been found to exist during the periods of magnetic field restructuring. The spatiotemporal analysis of the flare ensemble making it possible to diagnose non-stationary processes in the solar atmosphere has been shown.     

Dynamics of the photospheric magnetic field in the vicinity of the solar equator

SOHO-MDI daily magnetic field synoptic data (a 14-year series of daily maps of the solar magnetic field intensity B available at the site ) have been used to analyze the dynamics of the photospheric magnetic field in the vicinity of the solar equator. The standard deviation s _B of the field B calculated over areas of tens of square degrees on the solar disk was taken as a basic index. An 11-year variation similar to that observed at higher latitudes is observed in the vicinity of the equator, and is similar for weak and strong fields; i.e., the solar cycle exists in the sunspot-free zone. New qualitative data support the idea that the weak background magnetic field increases toward the solar limb. This angular dependence suggests the existence of a transverse component of the background field. The magnetic fields in the vicinity of the equator were significantly different in the initial phases of Cycles 23 and 24. Annual variations of s _B were observed near the center of the solar disk. These variations are due to two factors: the annual variation of the distance from the equator to the disk center and the increase of s _B with with distance from the equator. Reliable detection of these variations is an evidence of high accuracy of the s _B estimates.