The current dynamo paradigm for the Sun and sun-like stars places the generation site for strong toroidal magnetic structures deep in the solar interior. Sunspots and star-spots on sun-like stars are believed to arise when sections of these magnetic structures become buoyantly unstable and rise from the deep interior to the photosphere. Here we present the first 3-D global magnetohydrodynamic (MHD) simulation in which turbulent convection, stratification, and rotation combine to yield a dynamo that self-consistently generates buoyant magnetic loops. We simulate stellar convection and dynamo action in a spherical shell with solar stratification, but rotating three times faster than the current solar rate. Strong wreaths of toroidal magnetic field are realized by dynamo action in the convection zone. By turning to a dynamic Smagorinsky model for subgrid-scale turbulence, we here attain considerably reduced diffusion in our simulation. This permits the regions of strongest magnetic field in these wreaths to rise toward the top of the convection zone via a combination of magnetic buoyancy instabilities and advection by convective giant cells. Such a global simulation yielding buoyant loops represents a significant step forward in combining numerical models of dynamo action and flux emergence.
Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much larger values than is possible through laminar proc…
Our Sun exhibits strong convective dynamo action which results in magnetic flux bundles emerging through the stellar surface as magnetic spots. Global-scale dynamo action is believed to generate large-scale magnetic structures in the deep solar interior through the interplay of convection, rotation, and shear. Portions of these large-scale magnetic structures are then believed to rise through the convective layer, forming magnetic loops which then pierce the photosphere as sunspot pairs. Previous global simulations of 3D MHD convection in rotating spherical shells have demonstrated mechanisms …
A hypothesis for sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges through the whole convection zone. We follow the evolution of a random seed magnetic field with the aim of study under what conditions it is possible to excite the dynamo instability and whether the dynamo generated magnetic field becomes buoyantly unstable and emerges to the surface as expected in the flux-tube context. We perform numerical simulations …
We study the influence of a dynamo magnetic field on the buoyant rise and emergence of twisted magnetic flux-ropes, and their influence on the global external magnetic field. We ran 3D MHD numerical simulations using the ASH code and analysed the dynamical evolution of such buoyant flux-ropes from the bottom of the convection zone until the post-emergence phases. The global nature of this model represents very crudely and inaccurately the local dynamics of the buoyant rise, but allows to study the influence of global effects such as self-consistently generated differential rotation, meridional…
We investigate the relations between tachocline-based dynamos and the surface flux transport mechanisms in stars with outer convection zones. Using our combined models of flux generation and transport, we demonstrate the importance of the buoyant rise of magnetic flux, which physically determines the emergence latitudes and tilt angles of bipolar magnetic regions. The combined effects of the dynamo strength, flux rise, and surface transport lead to various cyclic and non-cyclic time series of total unsigned surface magnetic flux.
Supergranulation is characterized by horizontally divergent flows with typical length scales of 32 Mm in the solar photosphere. Unlike granulation, the size of which is comparable to both the thickness of the radiative boundary layer and local scale height of the plasma in the photosphere, supergranulation does not reflect any obvious length scale of the solar convection zone. Early suggestions that the depth of second helium ionization is important are not supported by numerical simulations. Thus the origin of the solar supergranulation remains largely a mystery. Moreover, observations of flo…
The sunspot cycle is the magnetic cycle of the Sun produced by the dynamo process. A central idea of the solar dynamo is that the toroidal and the poloidal magnetic fields of the Sun sustain each other. We discuss the relevant observational data both for sunspots (which are manifestations of the toroidal field) and for the poloidal field of the Sun. We point out how the differential rotation of the Sun stretches out the poloidal field to produce the toroidal field primarily at the bottom of the convection zone, from where parts of this toroidal field may rise due to magnetic buoyancy to produc…
The Babcock-Leighton (BL) flux-transport model is a widely-accepted dynamo model of the Sun. This dynamo model has been extensively studied in a two-dimensional (2D) mean-field framework in both kinematic and non-kinematic regimes. Recent three-dimensional (3D) models have been restricted to the kinematic regime. In these models, the surface poloidal flux is produced by the emergence of bipolar magnetic regions (BMRs) that are tilted according to Joy's law. We investigate the prescription for emergence of a BMR in 3D non-kinematic simulations. We also report initial results of cyclic BL 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…
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 …
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…
Cool main-sequence stars, such as the Sun, have magnetic fields which are generated by an internal dynamo mechanism. In the Sun, the dynamo mechanism produces a balance between the amounts of magnetic flux generated and lost over the Sun's 11-year activity cycle and it is visible in the Sun's different atmospheric layers using multi-wavelength observations. We used the same observational diagnostics, spanning several decades, to probe the emergence of magnetic flux on the two close by, active- and low-mass K dwarfs: 61 Cygni A and Epsilon Eridani. Our results show that 61 Cygni A follows the S…
Neural Differential Equations for the Solar Dynamo
Moscow State University（莫斯科大学）；Institute of Continuous Media Mechanics（连续介质力学研究所）；Perm National Research Polytechnic University（彼尔姆国立研究波利亚技术大学）；IZMIRAN（地球磁场、电离层和无线电波传播研究所）
Contex: Solar magnetic activity exhibits variations with periods between 1.5--4 years, the so-called quasi-biennial oscillations (QBOs), in addition to the well-known 11-year Schwabe cycles. Solar dynamo is thought to be the responsible mechanism for generation of the QBOs. Aims: In this work, we analyse sunspot areas to investigate the spatial and temporal behaviour of the QBO signal and study the responsible physical mechanisms using simulations from fully nonlinear mean-field flux-transport dynamos. Methods: We investigated the behaviour of the QBOs in the sunspot area data in full disk, an…
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 …
We assess the global-scale dynamo action achieved in a simulation of a sun-like star rotating at three times the solar rate. The 3-D MHD Anelastic Spherical Harmonic code, using slope-limited diffusion, is employed to capture convection and dynamo processes in such a young sun. The simulation is carried out in a spherical shell that encompasses 3.8 density scale heights of the solar convection zone. We find that dynamo action with a high degree of time variation occurs, with many periodic polarity reversals every 6.2 years. The magnetic energy also rises and falls with a regular period, with t…
We explore effects of random non-axisymmetric perturbations of kinetic helicity (the $α$ effect) and diffusive decay of bipolar magnetic regions on generation and evolution of large-scale non-axisymmetric magnetic fields on the Sun. Using a reduced 2D nonlinear mean-field dynamo model and assuming that bipolar regions emerge due to magnetic buoyancy in situ of the large-scale dynamo action, we show that fluctuations of the $α$ effect can maintain the non-axisymmetric magnetic fields through a solar-type $α^{2}Ω$ dynamo process. It is found that diffusive decay of bipolar active regions is like…
The paper presents a study of a solar dynamo model operating in the bulk of the convection zone with the toroidal magnetic field flux concentrated in the subsurface rotational shear layer. We explore how this type of dynamo may depend on spatial variations of turbulent parameters and on the differential rotation near the surface. The mean-field dynamo model takes into account the evolution of magnetic helicity and describes its nonlinear feedback on the generation of large-scale magnetic field by the $α$-effect. We compare the magnetic cycle characteristics predicted by the model, including th…
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 release of energy. 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 mo…
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…
In the quiet Sun, magnetic fields are usually observed as small-scale magnetic elements, `salt and pepper', covering the entire solar surface. By using 3D radiative MHD numerical simulations we demonstrate that these fields are a result of local dynamo action in the top layers of the convection zone, where extremely weak `seed' magnetic fields can locally grow above the mean equipartition field (e.g., from a $10^{-6}$ G `seed' field to more than 1000 G magnetic structures). We find that the local dynamo action takes place only in a shallow, about 500 km deep, subsurface layer, from which the g…
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, …
We obtain information about the magnetic flux present in the quiet Sun by comparing radiative MHD simulations with Hinode/SP observations, with particular emphasis on the role of surface dynamo action. Simulation runs with different magnetic Reynolds numbers (Rm) are used together with observations at different heliocentric angles with different levels of noise. The results show that simulations with an imposed mixed-polarity field and Rm below the threshold for dynamo action reproduce the observed vertical flux density, but do not display a sufficiently high horizontal flux density. Surface d…
In this work, we have studied the variability and frequency of occurrence of the grand minima using kinematic dynamo models of one solar mass star with different rotation rates and depths of convection zones. We specify the large-scale flows (differential rotations and meridional circulations) from corresponding hydrodynamic models. We include stochastic fluctuations in the Babcock-Leighton source for the poloidal field to produce variable stellar cycles. We observe that the rapidly rotating stars produce highly irregular cycles with strong magnetic fields and rarely produce Maunder-like grand…
The Sun shows a wide range of temporal variations, from a few seconds to decades and even centuries, broadly classified into two classes short-term and Long-term. The solar dynamo mechanism is believed to be responsible for these global changes happening in the Sun. Hence, many dynamo models have been proposed to explain the observed behaviour of the Sun. This thesis is primarily focused on studying the \lt\ variation of the Sun and provides various inputs to the solar dynamo models. With a renewed interest in the subject, several automatic techniques have been developed for extensive data ana…
In this review, we explain recent progress made in the Babcock-Leighton dynamo models for the Sun, which have been most successful to explain various properties of the solar cycle. In general, these models are 2D axisymmetric and the mean-field dynamo equations are solved in the meriodional plane of the Sun. Various physical processes (e.g., magnetic buoyancy and Babcock-Leighton mechanism) involved in these models are inherently 3D process and could not be modeled properly in a 2D framework. After pointing out limitations of 2D models (e.g., Mean-field Babcock-Leighton dynamo models and Surfa…
Magnetic fields are usually observed in the quiet Sun as small-scale elements that cover the entire solar surface (the `salt and pepper' patterns in line-of-sight magnetograms). By using 3D radiative MHD numerical simulations we find that these fields result from a local dynamo action in the top layers of the convection zone, where extremely weak 'seed' magnetic fields (e.g., from a $10^{-6}$ G) can locally grow above the mean equipartition field, to a stronger than 2000~G field localized in magnetic structures. Our results reveal that the magnetic flux is predominantly generated in regions of…
Global dynamo simulations solving the equations of magnetohydrodynamics (MHD) have been a tool of astrophysicists who try to understand the magnetism of the Sun for several decades now. During recent years many fundamental issues in dynamo theory have been studied in detail by means of local numerical simulations that simplify the problem and allow the study of physical effects in isolation. Global simulations, however, continue to suffer from the age-old problem of too low spatial resolution, leading to much lower Reynolds numbers and scale separation than in the Sun. Reproducing the internal…
We analyze the X-ray emission and chromospheric activity of Sun-like stars of F, G and K spectral classes (late-type stars) studied in the framework of the HK project. More powerful coronas are possessed by stars displaying irregular variations of their chromospheric emission, while stars with regular cyclic activity are characterized by comparatively modest X-ray luminosities and ratios of the X-ray to bolometric luminosity. This indicates that the nature of processes associated with magnetic-field amplification on the convective envelope changes appreciably in the transition from small to la…
Observations of long-term north-south asymmetry in solar activity demand the equator-symmetric (quadrupolar) mode be present in the solar magnetic field in line with the dominant antisymmetric (dipolar) mode. This paper proposes treating the sunspot area as a proxy for subsurface toroidal magnetic flux to infer the quadrupolar mode of the solar dynamo from sunspot data. Toroidal pseudo-fluxes (PF) in the northern and southern hemispheres are defined as a signed sunspot area with plus or minus sign prescribed to them in accord with the Hale's sunspot polarity rules. Statistical correlation anal…
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…
We present a realistic numerical model of sunspot and active region formation based on the emergence of flux bundles generated in a solar convective dynamo. To this end we use the magnetic and velocity fields in a horizontal layer near the top boundary of the solar convective dynamo simulation to drive realistic radiative-magnetohydrodynamic simulations of the upper most layers of the convection zone. The main results are: (1) The emerging flux bundles rise with the mean speed of convective upflows, and fragment into small-scale magnetic elements that further rise to the photosphere, where bip…
In this paper, we explore the evolution of sunspot latitude distribution and explore its relations with the cycle strength. With the progress of the solar cycle, the distributions in two hemispheres from mid-latitudes propagate toward the equator and then (before the usual solar minimum) these two distributions touch each other. By visualizing the evolution of the distributions in two hemispheres, we separate the solar cycles by excluding this hemispheric overlap. From these isolated solar cycles in two hemispheres, we generate latitude distributions for each cycle, starting from cycle 8 to cy…
The activity of the Sun as a result of cyclic changes of the global magnetic field is studied. As a consequence of the analysis of magnetic activity of solar-type stars the following power dependencies were found: the dependence between the rotation periods and the effective temperatures, the dependence between the duration of the "11-year" cycles of activity and the effective temperatures, and the dependence between the duration of quasi-biennial cycles and the effective temperatures. It is shown that the physical nature of these dependencies associated with the observed properties of solar-t…
In this work we take advantage of eleven different sunspot group, sunspot, and active region databases to characterize the area and flux distributions of photospheric magnetic structures. We find that, when taken separately, different databases are better fitted by different distributions (as has been reported previously in the literature). However, we find that all our databases can be reconciled by the simple application of a proportionality constant, and that, in reality, different databases are sampling different parts of a composite distribution. This composite distribution is made up by …
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 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 …
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 …
Regions of quiet Sun generally exhibit a complex distribution of small-scale magnetic field structures, which interact with the near-surface turbulent convective motions. Furthermore, it is probable that some of these magnetic fields are generated locally by a convective dynamo mechanism. In addition to the well-known granular and supergranular convective scales, various observations have indicated that there is an intermediate scale of convection, known as mesogranulation, with vertical magnetic flux concentrations accumulating preferentially at mesogranular boundaries. Our aim is to investig…
The calling card of solar magnetism is the sunspot cycle, during which sunspots regularly reverse their polarity sense every 11 years. However, a number of more complicated time-dependent behaviors have also been identified. In particular, there are temporal modulations associated with active longitudes and hemispheric asymmetry, when sunspots appear at certain solar longitudes or else in one hemisphere preferentially. So far, a direct link between between this asymmetric temporal behavior and the underlying solar dynamo has remained elusive. In this work, we present results from global, 3D ma…
Prediction of the Sun's magnetic activity is important because of its effect on space environment and climate. However, recent efforts to predict the amplitude of the solar cycle have resulted in diverging forecasts with no consensus. Yeates et al. (2008) have shown that the dynamical memory of the solar dynamo mechanism governs predictability and this memory is different for advection- and diffusion-dominated solar convection zones. By utilizing stochastically forced, kinematic dynamo simulations, we demonstrate that the inclusion of downward turbulent pumping of magnetic flux reduces the mem…
We present a three-dimensional numerical model for the generation and evolution of the magnetic field in the solar convection zone, in which sunspots are produced and contribute to the cyclic reversal of the large-scale magnetic field. We then assess the impact of this dynamo-generated field on the structure of the solar corona and solar wind. This model solves the induction equation in which the velocity field is prescribed. This velocity field is a combination of a solar-like differential rotation and meridional circulation. We develop an algorithm that enables the magnetic flux produced in …
Magnetohydrodynamic interactions between plasma flows and magnetic fields is fundamental to the origin and sustenance of the 11-year sunspot cycle. These processes are intrinsically three-dimensional (3D) in nature. Our goal is to construct a 3D solar dynamo model that on the one hand captures the buoyant emergence of tilted bipolar sunspot pairs, and on the other hand produces cyclic large-scale field reversals mediated via surface flux-transport processes -- that is, the Babcock-Leighton mechanism. We perform kinematic dynamo simulations where the prescribed velocity field is a combination o…
Computational heliophysics has shed light on the fundamental physical processes inside the Sun, such as the differential rotation, meridional circulation, and dynamo-generation of magnetic fields. However, despite the substantial advances, the current results of 3D MHD simulations are still far from reproducing helioseismic inferences and surface observations. The reason is the multi-scale nature of the solar dynamics, covering a vast range of scales, which cannot be solved with the current computational resources. In such a situation, significant progress has been achieved by the mean-field a…
In 1844 Schwabe discovered that the number of sunspots increased and decreased over a period of about 11 years, that variation became known as the sunspot cycle. Almost eighty years later, Hale described the nature of the Sun's magnetic field, identifying that it takes about 22 years for the Sun's magnetic polarity to cycle. It was also identified that the latitudinal distribution of sunspots resembles the wings of a butterfly showing migration of sunspots in each hemisphere that abruptly start at mid-latitudes towards the Sun's equator over the next 11 years. These sunspot patterns were shown…
One important ingredient of flux transport dynamo models is the rise of the toroidal magnetic field through the convection zone due to magnetic buoyancy to produce bipolar sunspots and then the generation of the poloidal magnetic field from these bipolar sunspots due to the Babcock-Leighton mechanism. Over the years, two methods of treating magnetic buoyancy, a local method and a non-local method have been used widely by different groups in constructing 2D kinematic models of the flux transport dynamo. We review both these methods and conclude that neither of them is fully satisfactory, presum…
Sunspots are cool areas caused by strong surface magnetic fields inhibiting convection. Moreover, strong magnetic fields can alter the average atmospheric structure, degrading our ability to measure stellar masses and ages. Stars more active than the Sun have more and stronger dark spots than in the solar case, including on the rotational pole itself. Doppler imaging, which has so far produced the most detailed images of surface structures on other stars than the Sun, cannot always distinguish the hemisphere in which the starspots are located, especially in the equatorial region and if the dat…
We obtain the latitude-time distribution of the averaged tilt angle of solar bipoles. For large bipoles, which are mainly bipolar sunspot groups, the spatially averaged tilt angle is positive in the Northern solar hemisphere and negative in the Southern, with modest variations during course of the solar cycle. We consider the averaged tilt angle to be a tracer for a crucial element of the solar dynamo, i.e. the regeneration rate of poloidal large-scale magnetic field from toroidal. The value of the tilt obtained crudely corresponds to a regeneration factor corresponding to about 10% of r.m.s. …
The Hinode mission has revealed copious amounts of horizontal flux covering the quiet Sun. Local dynamo action has been proposed to explain the presence of this flux. We sought to test whether the quiet Sun flux detected by Hinode is due to a local or the global dynamo by studying long-term variations in the polarisation signals detectable at the disc centre of the quiet Sun between November 2006 and May 2012, with particular emphasis on weak signals in the internetwork. The investigation focusses on line-integrated circular polarisation V_tot and linear polarisation LP_tot profiles obtained f…
When our Sun was young it rotated much more rapidly than now. Observations of young, rapidly rotating stars indicate that many possess substantial magnetic activity and strong axisymmetric magnetic fields. We conduct simulations of dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code to explore the complex coupling between rotation, convection and magnetism. Here we study dynamo action realized in the bulk of the convection zone for a system rotating at three times the current solar rotation rate. We find that substantial organized global-scale magnet…
When stars like our Sun are young they rotate rapidly and are very magnetically active. We explore dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic fields built in these dynamos are organized on global-scales into wreath-like structures that span the convection zone. Wreath-building dynamos can undergo quasi-cyclic reversals of polarity and such behavior is common in the parameter space we have been able to explore. These dynamos do not appear to require tachoclines to achieve their spatial or temporal organization. Wreath-building d…
Recent observations reveal the surprising breakdown of stellar gyrochronology relations at about the Sun's age hinting that middle-aged, solar-like stars transition to a magnetically inactive future. We provide a theoretical basis for these intriguing observations inspired by simulations with a mathematical dynamo model that can explore long-term solar cycle fluctuations. We reproduce the observed bimodal distribution of sunspot numbers, but only for subcritical dynamos. Based on a bifurcation analysis, we argue that ageing of solar-like stars makes the magnetically-weak dynamo regime readily …
The magnetic cycle of the Sun, as manifested in the cyclic appearance of sunspots, significantly influences our space environment and space-based technologies by generating what is now termed as space weather. Long-term variation in the Sun's magnetic output also influences planetary atmospheres and climate through modulation of solar irradiance. Here, I summarize the current state of understanding of this magnetic cycle, highlighting important observational constraints, detailing the kinematic dynamo modeling approach and commenting on future prospects.
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…
The Stellar Imager mission concept is a space-based UV/Optical interferometer designed to resolve surface magnetic activity and subsurface structure and flows of a population of Sun-like stars, in order to accelerate the development and validation of a predictive dynamo model for the Sun and enable accurate long-term forecasting of solar/stellar magnetic activity.
We develop a three-dimensional kinematic self-sustaining model of the solar dynamo in which the poloidal field generation is from tilted bipolar sunspot pairs placed on the solar surface above regions of strong toroidal field by using the SpotMaker algorithm, and then the transport of this poloidal field to the tachocline is primarily caused by turbulent diffusion. We obtain a dipolar solution within a certain range of parameters. We use this model to study the build-up of the polar magnetic field and show that some insights obtained from surface flux transport (SFT) models have to be revised.…
Fluctuations in the Sun's magnetic activity, including episodes of grand minima such as the Maunder minimum have important consequences for space and planetary environments. However, the underlying dynamics of such extreme fluctuations remain ill-understood. Here we use a novel mathematical model based on stochastically forced, non-linear delay differential equations to study solar cycle fluctuations, in which, time delays capture the physics of magnetic flux transport between spatially segregated dynamo source regions in the solar interior. Using this model we explicitly demonstrate that the …
When our Sun was young it rotated much more rapidly than now. Observations of young, rapidly rotating stars indicate that many possess substantial magnetic activity and strong axisymmetric magnetic fields. We conduct simulations of dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code to explore the complex coupling between rotation, convection and magnetism. Here we study dynamo action realized in the bulk of the convection zone for two systems, rotating at three and five times the current solar rate. We find that substantial organized global-scale ma…
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.
Twisted magnetic fields are frequently seen to emerge above the visible surface of the Sun. This emergence is usually associated with the rise of buoyant magnetic flux structures. Here we ask how magnetic fields from a turbulent large-scale dynamo appear above the surface if there is no magnetic buoyancy. The computational domain is split into two parts. In the lower part, which we refer to as the turbulence zone, the flow is driven by an assumed helical forcing function leading to dynamo action. Above this region, which we refer to as the exterior, a nearly force-free magnetic field is comput…
