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Various approaches to forecasting the solar cycle based on solar dynamo models are considered. The importance of separating predictions of catastrophic events such as the Maunder minimum, predictions of general trends in solar activity between Grand minima, and forecasts of the next cycle, based on current knowledge of previous cycles is noted. The role of fluctuations of dynamo drivers for the forecast is emphasized. The polar magnetic field in the current cycle is considered as a natural predictor of the amplitude of the following cycle. [ABSTRACT FROM AUTHOR]

Dynamo theory suggests that there are two types of solar dynamo, namely the conventional mean-field dynamo, which produces large- and small-scale magnetic fields involved in the activity cycle, and also the small-scale dynamo, which produces a cycle independent smallscale magnetic field. The relative contribution of the two mechanisms to solar magnetism remains a matter of scientific debate, which includes the opinion that the contribution of the small-scale dynamo is negligible. Here, we consider several tracers of magnetic activity that separate cycle-dependent contributions to the background solar magnetic field from those that are independent of the cycle. We call background fields the magnetic fields outside active regions and give further development of this concept. The main message of our paper is that background fields include two relative separate populations. The background fields with a strength up to 100 Mx cm-2 are very poorly correlated with the sunspot numbers and vary little with the phase of the cycle. In contrast, stronger magnetic fields demonstrate pronounced cyclic behaviour.We discuss how this result can be included in the above-mentioned concepts of solar dynamo studies. [ABSTRACT FROM AUTHOR]

The paper by Popova et al. presents an oversimplified mathematical model of solar activity with a claim of predicting/postdicting it for several millennia ahead/backwards. The work contains several flaws devaluating the results: (1) the method is unreliable from the point of view of signal processing (it is impossible to make harmonic predictions for thousands of years based on only 35 years of data) and lacks quality control; (2) the result of post-diction apparently contradicts the observational data. (3) theoretical speculations make little sense. To summarize, a multi-harmonic mathematical model, hardly related to full solar dynamo theory, is presented, which is not applicable to realistic solar conditions because of the significant chaotic/stochastic intrinsic component and strong non-stationarity of solar activity. The obtained result is apparently inconsistent with the data in the past and thus cannot be trusted for the future predictions. [ABSTRACT FROM AUTHOR]

Solar activity slowly and irregularly decreases from the first spotless day (FSD) in the declining phase of the old sunspot cycle and systematically, but also in an irregular way, increases to the new cycle maximum after the last spotless day (LSD). The time interval between the first and the last spotless day can be called the passive interval (PI), while the time interval from the last spotless day to the first one after the new cycle maximum is the related active interval (AI). Minima of solar cycles are inside PIs, while maxima are inside AIs. In this article, we study the properties of passive and active intervals to determine the relation between them. We have found that some properties of PIs, and related AIs, differ significantly between two group of solar cycles; this has allowed us to classify Cycles 8 - 15 as passive cycles, and Cycles 17 - 23 as active ones. We conclude that the solar activity in the PI declining phase (a descending phase of the previous cycle) determines the strength of the approaching maximum in the case of active cycles, while the activity of the PI rising phase (a phase of the ongoing cycle early growth) determines the strength of passive cycles. This can have implications for solar dynamo models. Our approach indicates the important role of solar activity during the declining and the rising phases of the solar-cycle minimum. [ABSTRACT FROM AUTHOR]

Context. The large-scale magnetic field in the Sun varies with a period of approximately 22 years, although the amplitude of the cycle is subject to long-term modulation with recurrent phases of significantly reduced magnetic activity. It is believed that a hydromagnetic dynamo is responsible for producing this large-scale field, although this dynamo process is not well understood. Aims. Within the framework of mean-field dynamo theory, our aim is to investigate how competing mechanisms for poloidal field regeneration (namely a time-delayed Babcock-Leighton surface α-effect and an interface-type α-effect), can lead to the modulation of magnetic activity in a deep-seated solar dynamo model. Methods. We solve the standard αΩ dynamo equations in one spatial dimension, including source terms corresponding to both of the competing α-effects in the evolution equation for the poloidal field. This system is solved using two different methods. In addition to solving the one-dimensional partial differential equations directly, using numerical techniques, we also use a local approximation to reduce the governing equations to a set of coupled ordinary differential equations (ODEs), which are studied using a combination of analytical and numerical methods. Results. In the ODE model, it is straightforward to find parameters such that a series of bifurcations can be identified as the time delay is increased, with the dynamo transitioning from periodic states to chaotic states via multiply periodic solutions. Similar transitions can be observed in the full model, with the chaotically modulated solutions exhibiting solar-like behaviour. Conclusions. Competing α-effects could explain the observed modulation in the solar cycle. [ABSTRACT FROM AUTHOR]

A solar-type dynamo model in a spherical shell is developed with allowance for random dependence of the poloidal field generation mechanism on time and latitude. The model shows repeatable epochs of a strongly decreased amplitude of magnetic cycles similar to the Maunder minimum of solar activity. Random dependence of dynamo parameters on latitude breaks the equatorial symmetry of generated fields. The model shows the correlation of the occurrence of grand minima with deviations in the dynamo field from dipolar parity. An increased north-south asymmetry of magnetic activity can, therefore, be an indicator of transitions to grand minima. Qualitative interpretation of this correlation is suggested. Statistics of grand minima in the model are close to the Poisson random process, indicating that the onset of a grand minimum is statistically independent of preceding minima. [ABSTRACT FROM AUTHOR]

Abstract: This review provides an introduction to the generation and evolution of the Sun’s magnetic field, summarising both observational evidence and theoretical models. The eleven year solar cycle, which is well known from a variety of observed quantities, strongly supports the idea of a large-scale solar dynamo. Current theoretical ideas on the location and mechanism of this dynamo are presented. The solar cycle influences the behaviour of the global coronal magnetic field and it is the eruptions of this field that can impact on the Earth’s environment. These global coronal variations can be modelled to a surprising degree of accuracy. Recent high resolution observations of the Sun’s magnetic field in quiet regions, away from sunspots, show that there is a continual evolution of a small-scale magnetic field, presumably produced by small-scale dynamo action in the solar interior. Sunspots, a natural consequence of the large-scale dynamo, emerge, evolve and disperse over a period of several days. Numerical simulations can help to determine the physical processes governing the emergence of sunspots. We discuss the interaction of these emerging fields with the pre-existing coronal field, resulting in a variety of dynamic phenomena. [Copyright &y& Elsevier]

We have developed a variational data assimilation technique for the Sun using a toy αΩ dynamo model. The purpose of this work is to apply modern data assimilation techniques to solar data using a physically based model. This work represents the first step toward a complete variational model of solar magnetism. We derive the adjoint αΩ dynamo code and use a minimization procedure to invert the spatial dependence of key physical ingredients of the model. We find that the variational technique is very powerful and leads to encouraging results that will be applied to a more realistic model of the solar dynamo. [ABSTRACT FROM AUTHOR]

Abstract: The correlation between geomagnetic activity and the sunspot number in the 11-year solar cycle exhibits long-term variations due to the varying time lag between the sunspot-related and non-sunspot related geomagnetic activity, and the varying relative amplitude of the respective geomagnetic activity peaks. As the sunspot-related and non-sunspot related geomagnetic activity peaks are caused by different solar agents, related to the solar toroidal and poloidal fields, respectively, we use their variations to derive the parameters of the solar dynamo transforming the poloidal field into toroidal field and back. We find that in the last 12 cycles the solar surface meridional circulation varied between 5 and 20m/s (averaged over latitude and over the sunspot cycle), the deep circulation varied between 2.5 and 5.5m/s, and the diffusivity in the whole of the convection zone was ∼108 m2/s. In the last 12 cycles solar dynamo has been operating in moderately diffusion dominated regime in the bulk of the convection zone. This means that a part of the poloidal field generated at the surface is advected by the meridional circulation all the way to the poles, down to the tachocline and equatorward to sunspot latitudes, while another part is diffused directly to the tachocline at midlatitudes, “short-circuiting” the meridional circulation. The sunspot maximum is the superposition of the two surges of toroidal field generated by these two parts of the poloidal field, which is the explanation of the double peaks and the Gnevyshev gap in sunspot maximum. Near the tachocline, dynamo has been operating in diffusion dominated regime in which diffusion is more important than advection, so with increasing speed of the deep circulation the time for diffusive decay of the poloidal field decreases, and more toroidal field is generated leading to a higher sunspot maximum. During the Maunder minimum the dynamo was operating in advection dominated regime near the tachocline, with the transition from diffusion dominated to advection dominated regime caused by a sharp drop in the surface meridional circulation which is in general the most important factor modulating the amplitude of the sunspot cycle. [Copyright &y& Elsevier]

Abstract: In this work we use a low order dynamo model and study under which conditions can it reproduce solar grand minima. We begin by building the phase space of a proxy for the toroidal component of the solar magnetic field and we develop a model, derived from mean field dynamo theory, that gives the time evolution of the toroidal field. This model is characterized by a non-linear oscillator whose coefficients retain most of the physics behind dynamo theory. In the derivation of the model we also include stochastic oscillations in the effect. We found evidences that stochastic fluctuations in effect can trigger grand minima episodes in this model under some considerations. We also explore other ways of creating grand minima by looking into the physical mechanisms that compose the coefficients of the oscillator. The balance between meridional circulation and magnetic diffusivity as well as the field intensification by buoyancy driven instabilities, might have a crucial role in inducing grand minima. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the dynamo underpinning of solar cycle precursor schemes based on direct or indirect measures of the solar surface magnetic field. We do so for various types of mean-field-like kinematic axisymmetric dynamo models, where amplitude fluctuations are driven by zero-mean stochastic forcing of the dynamo number controlling the strength of the poloidal source term. In all stochastically forced models considered, the surface poloidal magnetic field is found to have precursor value only if it feeds back into the dynamo loop, which suggests that accurate determination of the magnetic flux budget of the solar polar fields may hold the key to dynamo model-based cycle forecasting. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research. [ABSTRACT FROM AUTHOR]

A comparison between the two tracers of magnetic field mirror asymmetry in solar active regions – twist and current helicity – is presented. It is shown that for individual active regions these tracers do not possess visible similarity but averaging by time over the solar cycle, or by latitude, reveals similarities in their behavior. The main property of the data set is antisymmetry over the solar equator. Considering the evolution of helical properties over the solar cycle we find signatures of a possible sign change at the beginning of the cycle, though more systematic observational data are required for a definite confirmation. We discuss the role of both tracers in the context of solar dynamo theory. [ABSTRACT FROM AUTHOR]

Abstract: It is well accepted that the solar cycle originates from a magnetohydrodynamics dynamo deep inside the Sun. Many dynamo models have long been proposed based on a lot of observational constraints. In this paper, using 342 NSO/Kitt Peak solar synoptic charts we study the solar cycle phases in different solar latitudinal zones to set further constraints. Our results can be summarized as follows: (1) The variability of solar polar regions’ area has a correlation with total unsigned magnetic flux in advance of 5years. (2) The high-latitude region mainly appears unipolar in the whole solar cycle and its flux peak time lags sunspot cycle for 3years. (3) For the activity belt, it is not surprised that its phase be the same as sunspot’s. (4) The flux peak time of the low-latitude region shifts forward with an average gradient of 32.2day/deg. These typical characteristics may provide some hints for constructing an actual solar dynamo. [Copyright &y& Elsevier]

Abstract: The Solar Magnetic Field Telescope (SMFT) at the Huairou Solar Observing Station of the National Astronomical Observatory has been obtaining photospheric vector magnetograms on a daily basis for more than 20years. In this paper we first introduce our magnetograph and our data reduction routine. Then we focus on what we can learn from these vector magnetic field measurements about the magnetic non-potentiality of active regions. Derived physical quantities, such as shear angle, α value and current helicity, are good indicators of magnetic helicity. By studying values and evolutions of these physical quantities, we get a glimpse of the dynamo process in the solar interior. By examining the evolution of these quantities we can also learn what are the favorable conditions for coronal eruptions such as flares and coronal mass ejections. [Copyright &y& Elsevier]

More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric dynamo model is derived to explore the characteristics of the axisymmetric and the first non-axisymmetric modes and to provide a theoretical basis with which to explain the ‘active longitude’, ‘flip-flop’ and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the and the models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented. [ABSTRACT FROM AUTHOR]

We describe the properties of the Sun, those of its Active Regions (Centres of Activity, ARs or CAs) and the 11 and 22-year cycles as observed via the variable numbers of sunspots. We describe the variations with time of the solar irradiance and of the flux of ejected magnetised plasma. We discuss the probable cause of solar variability. Planetary influences are ruled out; the variability is intrinsic and is described by the solar dynamo. The dynamo is characterised by internal toroidal and more superficial poloidal fields, interchanging and alternating in a 22-year periodicity. From these two components in the solar magnetic fields emanate two possible scenarios for the Sun-climate interaction. Solar irradiance variations are related to those in the solar toroidal magnetic fields. The fraction of the solar irradiance that reaches the Earth's ground level and low troposphere is emitted by the solar photosphere. That fraction does not significantly vary since the quiet photosphere does not significantly vary during the cycle. The variable part of the solar radiation flux is mainly emitted by the chromospheric parts of the CAs. That radiation component does not reach the Earth's troposphere since it is absorbed in the higher, stratospheric terrestrial layers. Tropospheric solar-driven variations should therefore be due to stratosphere–troposphere coupling. The Group Sunspot number R Gs is a proxy for the variable irradiance component and for the toroidal field variations. Ejected solar plasma clouds such as the Coronal Mass Ejections (CMEs) and plasma ejected from Ephemeral Solar Regions and from the polar facular regions are related to variations in the poloidal magnetic fields. On the average they have their maximum intensity about a year after the maximum number of spots: we call this interval the Energetic Emissions Delay. These gas clouds fill the heliosphere with magnetised plasma. Thus, by emitting magnetised plasma, the Sun influences the Earth's atmosphere indirectly, by heliospheric modulation of the component of the galactic cosmic radiation (CR) that reaches tropospheric levels. Modulation is only important for cosmic ray particles with energies below about 50 GeV. Cosmic ray ionisation plays a minor role at ground level but it is the predominant ionising agent in higher atmospheric layers, already above a few kilometres. The amplitudes of the CR variations depend on those of the solar cycle. The atmospheric rate of ionisation varies with CR-intensity. A current hypothesis is that the variable ionisation may affect the degree of cloudiness. Cosmogenic radionuclides such as 10Be are proxies for this influence and for the poloidal field variations. The R G and cosmogenic radionuclide proxies, although loosely correlated, refer to the two different aspects of the solar dynamo with their different terrestrial effects; they do not reach maximum intensity simultaneously and should therefore neither be confused nor be interchanged. Cases have occurred in which the one varied strongly while the other did hardly or not at all. The explanation must be intrinsic in dynamo theory. There is a significant solar signal in the troposphere; it depends on latitude and longitude. A physical investigation of the cause of the Sun-climate relationship based on one unique Δ T(time)-curve, assumed valid for the whole Earth's surface, is therefore basically incorrect. Never during the past 10,000 years has the Sun been as active in ejecting magnetised plasma as during the past few decades. Estimates suggest that the level of solar activity may recently have passed its maximum and that it may decrease in coming decades. Solar activity is variable with six well-determined quasi-periodicities. Attempts to theoretically describe the solar dynamo have so far succeeded only in explaining the qualitative aspects. They fail in a numerical description and notably in one that would permit one to forecast solar activity with acceptable precision. This is so because the solar dynamo is a non-linear system that occasionally shows phase catastrophes. It is a quasi-periodic engine with the properties of deterministic chaos. “The future of such a chaotic system is intrinsically unpredictable”. [ABSTRACT FROM AUTHOR]

Small‐scale dynamo action is often held responsible for the generation of quiet Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small‐scale dynamos in nonrotating turbulent convection at low magnetic Prandtl numbers. We use high‐resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small‐scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers, such as the Sun. As a function of the magnetic Reynolds number (Rm), the growth rate of the dynamo is consistent with an Rm1/2 scaling. No evidence for a logarithmic increase of the growth rate with Rm is found. [ABSTRACT FROM AUTHOR]

At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha dynamos as the magnetic Reynolds number Rm is increased. Using Floquet theory, we are able to precisely quantify mean-field effects like the alpha and beta effect (i) by rigorously distinguishing dynamo modes that involve large-scale components from the ones that only involve small scales, and by (ii) providing a way to investigate arbitrary large-scale separations with minimal computational cost. We apply this framework to helical and nonhelical flows as well as to random flows with short correlation time. Our results determine that the alpha description is valid for Rm smaller than a critical value Rmc at which small-scale dynamo instability starts. When Rm is above Rmc, the dynamo ceases to follow the mean-field description and the growth rate of the large-scale modes becomes independent of the scale separation, while the energy in the large-scale modes is inversely proportional to the square of the scale separation. The results in this second regime do not depend on the presence of helicity. Thus, alpha-type modeling for solar and stellar models needs to be reevaluated and new directions for mean-field modeling are proposed. [ABSTRACT FROM AUTHOR]

The article discusses how numerical simulations are changing astronomers' views on the dynamo process underlying the solar magnetic activity cycle. Topics include the evolution of the Sun's magnetic field, an overview of dynamos, which are self-sustained amplifications of magnetic fields through the action of fluid motions, and the impact of parallel advances in raw computing and numerical algorithms on the ability of astronomers to produce and investigate magnetic cycles in Sun-like spheres with a thermally convecting magnetized fluid. A discussion of magnetohydrodynamics (MHD) and three images of a magnetohydrodynamical numerical simulation of solar convection via the multiscale flow simulation model EULAG are presented.

We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R⊙ has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number Rm. In the range of Rm = 104–106 the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process. [ABSTRACT FROM AUTHOR]

We present a series of radiative MHD simulations addressing the origin and distribution of the mixed polarity magnetic field in the solar photosphere. To this end, we consider numerical simulations that cover the uppermost 2-6 Mm of the solar convection zone and we explore scales ranging from 2 km to 25 Mm. We study how the strength and distribution of the magnetic field in the photosphere and subsurface layers depend on resolution, domain size, and boundary conditions. We find that 50% of the magnetic energy at the τ = 1 level comes from fields with the less than 500 G strength and that 50% of the energy resides on scales smaller than about 100 km. While the probability distribution functions are essentially independent of resolution, properly describing the spectral energy distribution requires grid spacings of 8 km or smaller. The formation of flux concentrations in the photosphere exceeding 1 kG requires a mean vertical field strength greater than 30-40 G at τ = 1. The filling factor of kG flux concentrations increases with overall domain size as the magnetic field becomes organized by larger, longer-lived flow structures. A solution with a mean vertical field strength of around 85 G at τ = 1 requires a subsurface rms field strength increasing with depth at the same rate as the equipartition field strength. We consider this an upper limit for the quiet Sun field strength, which implies that most of the convection zone is magnetized close to the equipartition. We discuss these findings in view of recent high-resolution spectropolarimetric observations of quiet Sun magnetism. [ABSTRACT FROM AUTHOR]

The variable magnetic field of the solar photosphere exhibits periodic reversals as a result of dynamo activity occurring within the solar interior. We decompose the surface field as observed by both the Wilcox Solar Observatory and the Michelson Doppler Imager into its harmonic constituents, and present the time evolution of the mode coefficients for the past three sunspot cycles. The interplay between the various modes is then interpreted from the perspective of general dynamo theory, where the coupling between the primary and secondary families of modes is found to correlate with large-scale polarity reversals for many examples of cyclic dynamos. Mean-field dynamos based on the solar parameter regime are then used to explore how such couplings may result in the various long-term trends in the surface magnetic field observed to occur in the solar case. [ABSTRACT FROM AUTHOR]