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 variety of solutions, with different symmetries, over the course of millennia.
An update is given on the current status of solar and stellar dynamos. At present, it is still unclear why stellar cycle frequencies increase with rotation frequency in such a way that their ratio increases with stellar activity. The small-scale dynamo is expected to operate in spite of a small value of the magnetic Prandtl number in stars. Whether or not the global magnetic activity in stars is a shallow or deeply rooted phenomenon is another open question. Progress in demonstrating the presence and importance of magnetic helicity fluxes in dynamos is briefly reviewed, and finally the role of…
We perform spectral simulations of dynamo for magnetic Prandtl number of one with Taylor-Green forcing. We observe dynamo transition through a supercritical pitchfork bifurcation. Beyond the transition, the numerical simulations reveal complex dynamo states with windows of constant, periodic, quasiperiodic, and chaotic magnetic field configurations. For some forcing amplitudes, multiple attractors were obtained for different initial conditions. We show that one of the chaotic windows follows the period-doubling route to chaos.
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. 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 alpha-effect and an interface-type alpha-ef…
Using a summary curve of two eigen vectors of solar magnetic field oscillations derived with Principal Components Analysis (PCA) from synoptic maps for solar cycles 21-24 as a proxy of solar activity, we extrapolate this curve backwards three millennia revealing 9 grand cycles lasting 350-400 years each. The summary curve shows a remarkable resemblance to the past sunspot and terrestrial activity: grand minima - Maunder Minimum (1645-1715 AD), Wolf minimum (1280-1350 AD), Oort minimum (1010-1050 AD) and Homer minimum (800-900 BC); grand maxima - modern warm period (1990-2015), medieval warm pe…
The dynamo mechanism, responsible for the solar magnetic activity, is still an open problem in astrophysics. Different theories proposed to explain such phenomena have failed in reproducing the observational properties of the solar magnetism. Thus, ab-initio computational modeling of the convective dynamo in a spherical shell turns out as the best alternative to tackle this problem. In this work we review the efforts performed in global simulations over the past decades. Regarding the development and sustain of mean-flows, as well as mean magnetic field, we discuss the points of agreement and …
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…
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,…
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 consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and demonstrate how complicated interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle. For some parameters, Type 1 modulation occurs by the transfer of energy between modes of different symmetries with little change in the overall amplitude, for other parameters, the modulation is of Type 2, where the ampl…
Solar activity cycle varies in amplitude. The last Cycle 24 is the weakest in the past century. Sun's activity dominates Earth's space environment. The frequency and intensity of the Sun's activity are accordant with the solar cycle. Hence there are practical needs to know the amplitude of the upcoming Cycle 25. The dynamo-based solar cycle predictions not only provide predictions, but also offer an effective way to evaluate our understanding of the solar cycle. In this article we apply the method of the first successful dynamo-based prediction developed for Cycle 24 to the prediction of Cycle…
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-scal…
Numerical MHD simulations play increasingly important role for understanding mechanisms of stellar magnetism. We present simulations of convection and dynamos in density-stratified rotating spherical fluid shells. We employ a new 3D simulation code for the solution of a physically consistent anelastic model of the process with a minimum number of parameters. The reported dynamo simulations extend into a "buoyancy-dominated" regime where the buoyancy forcing is dominant while the Coriolis force is no longer balanced by pressure gradients and strong anti-solar differential rotation develops as a…
Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）；University of Chinese Academy of Sciences（中国科学院大学）；State Key Laboratory of Solar Activity and Space Weather, National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台太阳活动与空间天气国家重点实验室）；Yunnan Key Laboratory of Solar Physics and Space Science（云南省太阳物理与空间科学重点实验室）
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 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…
The sunspot number data during the past 400 years indicates that both the profile and the amplitude of the solar cycle have large variations. Some precursors of the solar cycle were identified aiming to predict the solar cycle. The polar field and the geomagnetic index are two precursors which are received the most attention. The geomagnetic variations during the solar minima are potentially caused by the solar polar field by the connection of the solar open flux. The robust prediction skill of the polar field indicates that the memory of the dynamo process is less than 11 yrs within the frame…
Observations of the solar magnetic cycle showed that the amplitude of the cycle did not grow all the time in the past. Thus, there must be a mechanism to halt the growth of the magnetic field in the Sun. We demonstrate a recently proposed mechanism for this under the Babcock--Leighton dynamo framework, which is believed to be the most promising paradigm for the generation of the solar magnetic field at present. This mechanism is based on the observational fact that the stronger solar cycles produce bipolar magnetic regions (BMRs) at higher latitudes and thus have higher mean latitudes than the…
The level of solar magnetic activity, as exemplified by the number of sunspots and by energetic events in the corona, varies on a wide range of time scales. Most prominent is the 11-year solar cycle, which is significantly modulated on longer time scales. Drawing from dynamo theory together with empirical results of past solar activity and of similar phenomena on solar-like stars, we show that the variability of the solar cycle can be essentially understood in terms of a weakly nonlinear limit cycle affected by random noise. In contrast to ad-hoc `toy models' for the solar cycle, this leads to…
Long-term forcing of Sun's coronal field, open flux and cosmic ray modulation potential during grand minima, maxima and regular activity phases by the solar dynamo mechanism
Although sunspots have been systematically observed on the Sun's surface over the last four centuries, their magnetic properties have been revealed and documented only since the early 1900s. Sunspots typically appear in pairs of opposite magnetic polarities which have a systematic orientation. This polarity orientation is opposite across the equator -- a trend that has persisted over the last century over which magnetic field observations exist. Taken together with the configuration of the global poloidal field of the Sun -- that governs the heliospheric open flux and cosmic ray flux at Earth …
Direct observations over the past four centuries show that the number of sunspots observed on the Sun's surface vary periodically, going through successive maxima and minima. Following sunspot cycle 23, the Sun went into a prolonged minimum characterized by a very weak polar magnetic field and an unusually large number of days without sunspots. Sunspots are strongly magnetized regions and are generated by a dynamo mechanism which recreates the solar polar field mediated via plasma flows. Here we report results from kinematic dynamo simulations which demonstrate that a fast meridional flow in t…
Over the past decade, Boozer has argued that three-dimensional (3D) magnetic reconnection fundamentally differs from two-dimensional (2D) reconnection due to the fact that the separation between any pair of neighboring field lines almost always increases exponentially over distance in a 3D magnetic field. According to Boozer, this feature makes 3D field-line mapping chaotic and exponentially sensitive to small non-ideal effects; consequently, 3D reconnection can occur without intense current sheets. We test Boozer's theory via ideal and resistive reduced magnetohydrodynamic simulations of the …
