The existence of a turbulent small-scale solar surface dynamo is likely, considering existing numerical and laboratory experiments, as well as comparisons of a small-scale dynamo in MURaM simulations with Hinode observations. We find the observed peaked probability distribution function (PDF) from Stokes-V magnetograms is consistent with a monotonic PDF of the actual vertical field strength. The cancellation function of the vertical flux density from a Hinode SP observation is found to follow a self-similar power law over two decades in length scales down to the ~200 km resolution limit. This provides observational evidence that the scales of magnetic structuring in the photosphere extend at least down to 20 km. From the power law, we determine a lower bound for the true quiet-Sun mean vertical unsigned flux density of ~43 G, consistent with our numerically-based estimates that 80% or more of the vertical unsigned flux should be invisible to Stokes-V observations at a resolution of 200 km owing to cancellation. Our estimates significantly reduce the order-of-magnitude discrepancy between Zeeman- and Hanle-based estimates.
The interaction of helical convective motions and differential rotation in the solar convection zone results in turbulent drift of a large-scale magnetic field. We discuss the pumping mechanism and its impact on the solar dynamo.
Solar cycles vary in their amplitude and shape. There are several empirical relations between various parameters linking cycle's shape and amplitude, in particular the Waldmeier relations. As solar cycle is believed to be a result of the solar dynamo action, these relations require explanation in the framework of this theory.Here we aim to present a possible explanation of such kind. We relate the cycle-to-cycle variability of solar activity to fluctuations of solar dynamo drivers and primarily to fluctuations in the parameter responsible for recovery of the poloidal magnetic field from the to…
We compare spectra of the zonal harmonics of the large-scale magnetic field of the Sun using observation results and solar dynamo models. The main solar activity cycle as recorded in these tracers is a much more complicated phenomenon than the eigen solution of solar dynamo equations with the growth saturated by a back reaction of the dynamo-driven magnetic field on solar hydrodynamics. The nominal 11(22)-year cycle as recorded in each mode has a specific phase shift varying from cycle to cycle; the actual length of the cycle varies from one cycle to another and from tracer to tracer. Both the…
The duration of activity growths in solar cycles is on average shorter than the duration of its declines. This asymmetry can result from fluctuations in dynamo parameters. A solar dynamo model with fluctuations in the $α$-effect shows the statistical asymmetry which increases with both fluctuation amplitude and coherence time. An interpretation for the asymmetry origin is suggested, which predicts a correlation between the asymmetry measure and delay of the polar field reversals relative to the activity maxima. Data on the twelve latest solar cycles confirm such a correlation.
Global and semi-global convective dynamo simulations of solar-like stars are known to show a transition from an anti-solar (fast poles, slow equator) to solar-like (fast equator, slow poles) differential rotation (DR) for increasing rotation rate. The dynamo solutions in the latter regime can exhibit regular cyclic modes, whereas in the former one, only stationary or temporally irregular solutions have been obtained so far. In this paper we present a semi-global dynamo simulation in the transition region, exhibiting two coexisting dynamo modes, a cyclic and a stationary one, both being dynamic…
We study turbulent generation of large-scale magnetic fields using nonlinear dynamo models for solar-type stars in the range of rotational periods from 14 to 30 days. Our models take into account non-linear effects of dynamical quenching of magnetic helicity, and escape of magnetic field from the dynamo region due to magnetic buoyancy. The results show that the observed correlation between the period of rotation and the duration of activity cycles can be explained in the framework of a distributed dynamo model with a dynamical magnetic feedback acting on the turbulent generation either from ma…
While obviously having a common root, solar and planetary dynamo theory have taken increasingly divergent routes in the last two or three decades, and there are probably few experts now who can claim to be equally versed in both. Characteristically, even in the fine and comprehensive book "The magnetic Universe" (Rudiger & Hollerbach 2004), the chapters on planets and on the Sun were written by different authors. Separate reviews written on the two topics include Petrovay (2000}, Charbonneau (2005), Choudhuri (2008) on the solar dynamo and Glatzmaier (2002), Stevenson (2003) on the planetary d…
Recent data on superflares on sun-like stars and radiocarbon data on solar activity in the past are both indicative of transient epochs of unusually high magnetic activity. We propose an explanation for the grand activity maxima in the framework of a solar dynamo model with fluctuating parameters. Solar-type dynamos are oscillatory because of the combination of the solar-type differential rotation with positive (in the Northern hemisphere) alpha-effect. An artificial reversal of the sign in the alpha-effect changes the dynamo to a steady regime with hundreds of times larger magnetic energy com…
We propose a solar dynamo model distributed in the bulk of the convection zone with the toroidal magnetic field the flux concentrated in the near-surface layer. We show that if the boundary conditions at the top of the dynamo region allow the large-scale toroidal magnetic fields to penetrate closer to the surface, then the pattern of the modeled butterfly diagram for the toroidal magnetic fields in the upper part of the convection zone is formed by the surface rotational shear layer. The model is in agreement with observed properties of the magnetic solar cycle.
The record of solar activity is reviewed here with emphasis on peculiarities. Since sunspot positions tell us a lot more about the solar dynamo than the various global sunspot numbers, we first focus on the records of telescopic observations of sunspots leading to positional information. Then we turn to the proxy record from cosmogenic isotope abundances, which shows recurrent grand minima over the last 9500 years. The apparent distinction between episodes of strong modulation, and intervening episodes with milder modulation and weaker overall activity, hints at the solar dynamo following a va…
The paper address the effects of magnetic helicity conservation in a non-linear nonaxisymmetric mean-field solar dynamo model. We study the evolution of the shallow non-axisymmetric magnetic field perturbation with the strength about 10G in the solar convection zone. The dynamo evolves from the pure axisymmetric stage through the short (about 2 years) transient phase when the non-axisymmetric m=1 dynamo mode is dominant to the final stage where the axisymmetry of the dynamo is almost restored. It is found that magnetic helicity is transferred forth and back over the spectral space during the t…
Thermal convection is commonly believed to be the energy source of stellar or planetary dynamo. In this short paper we provide another possibility, namely large-scale tidal flow. In close binary stars, say, solar-like stars with orbital period at 2 or 3 days, large-scale tidal flow is comparable to or even stronger than convective flow, and it can induce magnetic dynamo action. Based on dynamo equation and tidal theory we estimate the magnetic energy induced by large-scale tidal flow, which is proportional to the cube of orbital frequency. Our estimation can be tested by the future spectropola…
The solar surface dynamo has become an active area of research in an attempt to understand the origin of a variety of magnetic field structures on the sun. The major modification that needs to be incorporated in the standard dynamo process is the inclusion of the partial ionization of the gas in the layers underlying and overlaying the photosphere along with the effects associated with the multifluid nature of the system. This not only changes the inertia carrying species but also substantially modifies the temporal and spatial evolution of the magnetic induction. The energy equation also carr…
In order to clarify a possible role of small-scale dynamo in formation of solar magnetic field, we suggest an observational test for small-scale dynamo action based on statistics of anti-Hale sunspot groups. As we have shown, according to theoretical expectations the small-scale dynamo action has to provide a population of sunspot groups which do not follow the Hale polarity law, and the density of such groups on the time-latitude diagram is expected to be independent on the phase of the solar cycle. Correspondingly, a percentage of the anti-Hale groups is expected to reach its maximum values …
In this review, we discuss whether the present solar dynamo models can be extrapolated to explain various aspects of stellar activity. We begin with a summary of the following kinds of data for solar-like stars: (i) data pertaining to stellar cycles from Ca H/K emission over many years; (ii) X-ray data indicating hot coronal activity; (iii) starspot data (especially about giant polar spots); and (iv) data pertaining to stellar superflares. Then we describe the current status of solar dynamo modelling---giving an introduction to the flux transport dynamo model, the currently favoured model for …
We explore the nature of the small-scale solar dynamo by tracking magnetic features. We investigate two previously-explored categories of the small-scale solar dynamo: shallow and deep. Recent modeling work on the shallow dynamo has produced a number of scenarios for how a strong network concentration can influence the formation and polarity of nearby small-scale magnetic features. These scenarios have measurable signatures, which we test for here using magnetograms from the Narrowband Filter Imager (NFI) on Hinode. We find no statistical tendency for newly-formed magnetic features to cluster …
At present, Babcock-Leighton flux transport solar dynamo models appear as the most promising model for explaining diverse observational aspects of the sunspot cycle. The success of these flux transport dynamo models is largely dependent upon a single-cell meridional circulation with a deep equatorward component at the base of the Sun's convection zone. However, recent observations suggest that the meridional flow may in fact be very shallow (confined to the top 10 % of the Sun) and more complex than previously thought. Taken together these observations raise serious concerns on the validity of…
We carry out a magneto-hydrodynamic (MHD) simulation of convective dynamo in the rotating solar convective envelope driven by the solar radiative diffusive heat flux. The simulation is similar to that reported in Fan & Fang (2014) but with further reduced viscosity and magnetic diffusion. The resulting convective dynamo produces a large scale mean field that exhibits similar irregular cyclic behavior and polarity reversals, and self-consistently maintains a solar-like differential rotation. The main driver for the solar-like differential rotation (with faster rotating equator) is a net outward…
The magnetic activity of solar-type stars generally increases with stellar rotation rate. The increase, however, saturates for fast rotation. The Babcock-Leighton mechanism of stellar dynamos saturates as well when the mean tilt-angle of active regions approaches ninety degrees. Saturation of magnetic activity may be a consequence of this property of the Babcock-Leighton mechanism. Stellar dynamo models with a tilt-angle proportional to the rotation rate are constructed to probe this idea. Two versions of the model - treating the tilt-angles globally and using Joy's law for its latitude depend…
New developments in surface flux transport modeling and theory of flux transport dynamos have given rise to the notion that certain large active regions with anomalous properties (location, tilt angle and/or Hale/non-Hale character) may have a major impact on the course of solar activity in subsequent years, impacting also on the amplitude of the following solar cycles. Here we discuss our current understanding of the role of such "rogue" active regions in cycle-to-cycle variations of solar activity.
We report the results of a magneto-hydrodynamic (MHD) simulation of a convective dynamo in a model solar convective envelope driven by the solar radiative diffusive heat flux. The convective dynamo produces a large-scale mean magnetic field that exhibits irregular cyclic behavior with oscillation time scales ranging from about 5 to 15 years and undergoes irregular polarity reversals. The mean axisymmetric toroidal magnetic field is of opposite signs in the two hemispheres and is concentrated at the bottom of the convection zone. The presence of the magnetic fields is found to play an important…
Observations of proxies of the magnetic helicity in the Sun over the past two solar cycles revealed reversals of the helicity hemispheric sign rule (negative in the North and positive in the South hemispheres). We apply the mean-field solar dynamo model to study the reversals of the magnetic helicity sign for the dynamo operating in the bulk of the solar convection zone. The evolution of the magnetic helicity is governed by the conservation law. We found that the reversal of the sign of the small-scale magnetic helicity follows the dynamo wave propagating inside the convection zone. Therefore,…
It is often claimed that there is not only one, but two different types of solar dynamos: the one that is responsible for the appearance of sunspots and the 11-yr cycle, frequently referred to as the "global dynamo", and a statistically time-invariant dynamo, generally referred to as the "local dynamo", which is supposed to be responsible for the ubiquitous magnetic structuring observed at small scales. Here we examine the relative contributions of these two qualitatively different dynamos to the small-scale magnetic flux, with the following conclusion: The local dynamo does not play a signifi…
Generation and diffusion of the magnetic field on the Sun is a key mechanism responsible for solar activity on all spatial and temporal scales - from the solar cycle down to the evolution of small-scale magnetic elements in the quiet Sun. The solar dynamo operates as a non-linear dynamical process and is thought to be manifest in two types: as a global dynamo responsible for the solar cycle periodicity, and as a small-scale turbulent dynamo responsible for the formation of magnetic carpet in the quiet Sun. Numerous MHD simulations of the solar turbulence did not yet reach a consensus as to the…
In solar-type stars (with radiative cores and convective envelopes), the magnetic field powers star spots, flares and other solar phenomena, as well as chromospheric and coronal emission at ultraviolet to X-ray wavelengths. The dynamo responsible for generating the field depends on the shearing of internal magnetic fields by differential rotation. The shearing has long been thought to take place in a boundary layer known as the tachocline between the radiative core and the convective envelope. Fully convective stars do not have a tachocline and their dynamo mechanism is expected to be very dif…
A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly reviewed. The main open questions that remain are concerned with the subsurface dynamics, including why sunspots emerge at preferred latitudes as seen in the familiar butterfly wings, why the cycle is about 11 years long, and why the sunspot groups emerge tilted with respect to the equator (Joy's law). Next, we turn to magnetic helicity, whose conservation property …
For more than thirty years, the dynamical maintenance of the thin solar tachocline has remained one of the central outstanding problems of stellar astrophysics. Three main theories have been developed to explain the tachocline's thinness, but so far none of them has been shown to work convincingly in the extreme parameter regime of the solar interior. Here, we present a rotating, 3D, spherical-shell simulation of a combined solar-like convection zone and radiative zone that achieves a tachocline built and maintained by convective dynamo action. Because of numerical constraints, the dynamo prev…
Context: Most solar and stellar dynamo models use the alpha-Omega scenario where the magnetic field is generated by the interplay between differential rotation (the Omega effect) and a mean electromotive force due to helical turbulent convection flows (the alpha effect). There are, however, turbulent dynamo mechnisms that may complement the alpha effect or may be an alternative to it. Aims: We investigate models of solar-type dynamos where the alpha effect is completely replaced by two other turbulent dynamo mechanisms, namely the Omega x J effect and the shear-current effect, which both resul…
We investigate to what extent the current helicity distribution observed in solar active regions is compatible with solar dynamo models. We use an advanced 2D mean-field dynamo model with dynamo action largely concentrated near the bottom of the convective zone, and dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtain butterfly diagrams for both the small-scale current helicity and the large-scale magnet…
It can be shown on observational grounds that two basic effects of dynamo theory for solar activity - production of the toroidal field from the poloidal one by differential rotation and reverse conversion of the toroidal field to the poloidal configuration by helical motions - are operating in the Sun. These two effects, however, do not suffice for constructing a realistic model for the solar dynamo. Only when a non-local version of the alpha-effect is applied, is downward diamagnetic pumping included and field advection by the equatorward meridional flow near the base of the convection zone a…
Parameters of magnetic activity on the solar type stars depend on the properties of the dynamo processes operating in stellar convection zones. We apply nonlinear mean-field axisymmetric $α^2Ω$ dynamo models to calculate of the magnetic cycle parameters, such as the dynamo cycle period, the total magnetic flux and the Poynting magnetic energy flux on the surface of solar analogs with the rotation periods from 15 to 30 days. The models take into account the principal nonlinear mechanisms of the large-scale dynamo, such as the magnetic helicity conservation, magnetic buoyancy, and effects of mag…
A number of observational and theoretical aspects of solar magnetoconvection are considered in this review. We discuss recent developments in our understanding of the small-scale structure of the magnetic field on the solar surface and its interaction with convective flows, which is at the centre of current research. Topics range from plage areas in active regions over the magnetic network shaped by supergranulation to the ubiquituous `turbulent' internetwork fields. On the theoretical side, we focus upon magnetic field generation by small-scale dynamo action.
We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. This dynamo model takes into account the algebraic and dynamic nonlinearities of the alpha effect, where the equation for the dynamic nonlinearity is derived from the conservation law for the magnetic helicity. The budget equation for the evolution of the Wolf number is based on a formation mechanism of sunspots related to the negative effective magnetic pressure instability. This instability redistributes the magnetic flux produced by the mean-field dynamo.…
Torsional oscillations represent bands of fast and slow zonal flows around the Sun, which extend deep into the convection zone and migrate during solar cycles towards the equator following the sunspot butterfly diagram. Analysis of helioseismology data obtained in 1996-2018 for almost two solar cycles reveals zones of deceleration of the torsional oscillations inside the Sun due to dynamo-generated magnetic field. The zonal deceleration originates near the bottom of the convection zone at high latitudes, and migrates to the surface revealing patterns of magnetic dynamo waves predicted by the P…
Predictions of solar cycle 24 obtained from advection-dominated and diffusion-dominated kinematic dynamo models are different if the Babcock-Leighton mechanism is the only source of the poloidal field. Yeates et al. (2008) argue that the discrepancy arises due to different memories of the solar dynamo for advection- and diffusion-dominated solar convection zones. We aim to investigate the differences in solar cycle memory obtained from advection-dominated and diffusion-dominated kinematic solar dynamo models. Specifically, we explore whether the inclusion of Parker's mean-field $α$ effect, in …
Context. The solar dynamo consists of a process that converts poloidal field to toroidal field followed by a process which creates new poloidal field from the toroidal field. Aims. Our aim is to observe the poloidal and toroidal fields relevant to the global solar dynamo and see if their evolution is captured by a Babcock-Leighton dynamo. Methods. We use synoptic maps of the surface radial field from the KPNSO/VT and SOLIS observatories to construct the poloidal field as a function of time and latitude, and Wilcox Solar Observatory and SOHO/MDI full disk images to infer the longitudinally aver…
Helioseismology provides important constraints for the solar dynamo problem. However, the basic properties and even the depth of the dynamo process, which operates also in other stars, are unknown. Most of the dynamo models suggest that the toroidal magnetic field that emerges on the surface and forms sunspots is generated near the bottom of the convection zone, in the tachocline. However, there is a number of theoretical and observational problems with justifying the deep-seated dynamo models. This leads to the idea that the subsurface angular velocity shear may play an important role in the …
Our understanding of stellar dynamos has largely been driven by the phenomena we have observed of our own Sun. Yet, as we amass longer-term datasets for an increasing number of stars, it is clear that there is a wide variety of stellar behavior. Here we briefly review observed trends that place key constraints on the fundamental dynamo operation of solar-type stars to fully convective M dwarfs, including: starspot and sunspot patterns, various magnetism-rotation correlations, and mean field flows such as differential rotation and meridional circulation. We also comment on the current insight t…
A two-wave dynamo model was recently proposed by Zharkova et al. (2015, Zh15 henceforth), which aims at long-term predictions of solar activity for millennia ahead and backwards. Here we confront the backward model predictions for the last 800 years with known variability of solar activity, using both direct sunspot observations since 1610 and reconstructions based on cosmogenic radionuclide data. We show that the Zh15 model fails to reproduce the well-established features of the solar activity evolution during the last millennium. This means that the predictive part for the future is not reli…
Obtaining observational evidence of the turbulent component of solar dynamo operating in the convective zone is a challenging problem because the dynamo action is hidden below the photosphere. Here we present results of a statistical study of flaring active regions (ARs) that produced strong solar flares of an X-ray class X1.0 and higher during a time period that covered solar cycles 23 and 24. We introduced a magneto-morphological classification (MMC) of ARs, which allowed us to estimate possible contribution of the turbulent component of the dynamo into the structure of an AR. We found that …
The meridional circulation plays an essential role in determining the basic mechanism of the dynamo action in case the of a low eddy diffusivity. Flux-transport dynamos with strong return flow and a deep stagnation point are discussed in the case of a positive $α$-effect located in the overshoot layer and a rotation law consistent with helioseismology. By means of a linear dynamo model, it will be shown that the migration of the toroidal belts at lower latitudes and the periods of the activity cycles are consistent with the observations. Moreover, at variance with previous investigations, the …
Recent findings of helioseismology as well as advances in direct numerical simulations of global dynamics of the Sun have indicated that in each solar hemisphere the meridional circulation forms the two cells along the in the convection zone. We investigate properties of a mean-field solar dynamo with such double-cell meridional circulation. The dynamo model also includes the realistic profile of solar differential rotation (including the tachocline and subsurface shear layer), and takes into account effects of turbulent pumping, anisotropic turbulent diffusivity, and conservation of magnetic …
We begin with a review of the predictions for cycle~24 before its onset. After summarizing the basics of the flux transport dynamo model, we discuss how this model had been used to make a successful prediction of cycle~24, on the assumption that the irregularities of the solar cycle arise due to the fluctuations in the Babcock--Leighton mechanism. We point out that fluctuations in the meridional circulation can be another cause of irregularities in the cycle.
We explore a reduced Babcock-Leighton (BL) dynamo model based on delay differential equations using numerical bifurcation analysis. This model reveals hysteresis, seen in the recent mean-field dynamo model and the direct numerical simulations of turbulent dynamos. The BL model with 'magnetic noise' as an additional weak-source of the poloidal field recovers the solar cycle every time from grand minima, which BL source alone cannot do. The noise-incorporated model exhibits a bimodal distribution of toroidal field energy confirming two modes of solar activity. It also shows intermittency and rep…
The magnetic activity of the Sun, as manifested in the sunspot cycle, originates deep within its convection zone through a dynamo mechanism which involves non-trivial interactions between the plasma and magnetic field in the solar interior. Recent advances in magnetohydrodynamic dynamo theory have led us closer towards a better understanding of the physics of the solar magnetic cycle. In conjunction, helioseismic observations of large-scale flows in the solar interior has now made it possible to constrain some of the parameters used in models of the solar cycle. In the first part of this revie…
The long-term variability of the sunspot cycle, as recorded by the Wolf numbers, are imprinted in different kinds of statistical relations which relate the cycle amplitudes, duration and shapes. This subject always gets a special attention because it is important for the solar activity forecast. We discuss statistical properties of the mean-field dynamo model with the fluctuating α-effect. Also, we estimate dynamical properties of the model for the long and short time-scale and compare it with the dynamics of the sunspot numbers data sets.
Since the discovery of solar cycle related with magnetic field in 1908, deep seated oscillatory dynamo has been studied extensively. However, there are still open questions on the solar dynamo, e.g., asymmetric conversion between large-scale poloidal and toroidal field as well as physics underlying the butterfly pattern of sunspots. Here we report a new generation of large-scale magnetic field and process of energy release. The inductive action of fluid motions pervading the solar interior is represented by a RLC circuit in which the toroidal field built up through twisting of poloidal field, …
A major outstanding problem in solar physics is the confinement of the solar tachocline, the thin shear layer that separates nearly solid-body rotation in the radiative interior from strong differential rotation in the convection zone. Here, we present the first 3-D, global solar simulation in which a tachocline is confined by a self-excited dynamo. The non-axisymmetric magnetism is initially built in the convection zone and then diffusively imprints downward. Additionally, the field is locally amplified throughout the radiative interior by vigorous horizontal motions that arise from equatoria…
Context: The Sun's polar fields and open flux around the time of activity minima have been considered to be strongly correlated with the strength of the subsequent maximum of solar activity. Aims: We aim to investigate the behavior of a Babcock-Leighton dynamo with a source poloidal term that is based on the observed sunspot areas and tilts. In particular, we investigate whether the toroidal fields at the base of convection zone from the model are correlated with the observed solar cycle activity maxima. Methods: We used a flux transport dynamo model that includes convective pumping and a polo…
The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates …
We present the assessment of a diffusion-dominated mean field axisymmetric dynamo model in reproducing historical solar activity and forecast for solar cycle 25. Previous studies point to the Sun's polar magnetic field as an important proxy for solar activity prediction. Extended research using this proxy has been impeded by reduced observational data record only available from 1976. However, there is a recognised need for a solar dynamo model with ample verification over various activity scenarios to improve theoretical standards. The present study aims to explore the use of helioseismology d…
The hemispheric asymmetry of sunspot activity observed possesses a regular component varying on a time scale of several solar cycles whose origin and properties are currently debated. This paper addresses the question of whether the long-term hemispheric asymmetry can result from random variations of solar dynamo parameters in time and latitude. Scatter in the observed tilt angles of sunspot groups is estimated to infer constraints on fluctuations in the dynamo mechanism for poloidal field regeneration. A dynamo model with fluctuations in the Babcock-Leighton type $α$-effect is designed in acc…
