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We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution ofWolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behaviour of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 yr ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 per cent correlation over all intervals of observation (about 270 yr). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependences are in good agreement with observations. [ABSTRACT FROM AUTHOR]

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 compared to the amplitude of the cyclic dynamo. Sufficiently large and durable fluctuations reversing the sign of the alpha-effect during the growth phase of a magnetic cycle can, therefore, cause a transient change to a steady dynamo with considerably increased magnetic energy. This qualitative scenario for grand activity maxima is supported by computations of the dynamo model with a fluctuating alpha-effect. The computed statistics of several thousand magnetic cycles gives examples of cycles with very high magnetic energy. Our preliminary estimations, however, suggest that the probability of solar superflares is extremely low. [ABSTRACT FROM AUTHOR]

Aims. The Sun shows strong variability in its magnetic activity, from Grand minima to Grand maxima, but the nature of the variability is not fully understood, mostly because of the insufficient length of the directly observed solar activity records and of uncertainties related to long-term reconstructions. Here we present a new adjustment-free reconstruction of solar activity over three millennia and study its different modes. Methods. We present a new adjustment-free, physical reconstruction of solar activity over the past three millennia, using the latest verified carbon cycle, 14C production, and archeomagnetic field models. This great improvement allowed us to study different modes of solar activity at an unprecedented level of details. Results. The distribution of solar activity is clearly bi-modal, implying the existence of distinct modes of activity. The main regular activity mode corresponds to moderate activity that varies in a relatively narrow band between sunspot numbers 20 and 67. The existence of a separate Grand minimum mode with reduced solar activity, which cannot be explained by random fluctuations of the regular mode, is confirmed at a high confidence level. The possible existence of a separate Grand maximum mode is also suggested, but the statistics is too low to reach a confident conclusion. Conclusions. The Sun is shown to operate in distinct modes - a main general mode, a Grand minimum mode corresponding to an inactive Sun, and a possible Grand maximum mode corresponding to an unusually active Sun. These results provide important constraints for both dynamo models of Sun-like stars and investigations of possible solar influence on Earth's climate. [ABSTRACT FROM AUTHOR]

Aims. We use observations of solar activity to constrain parameters relating to the α effect in stochastic nonlinear dynamo models. Methods. This is achieved through performing a comprehensive statistical comparison by computing probability distribution functions (PDFs) of solar activity from observations and from our simulation of α - Ω mean field dynamo model. The observational data that are used are the time history of solar activity inferred for C14 data in the past 11 000 years on a long time scale and direct observations of the sun spot numbers obtained in recent years 1795-1995 on a short time scale. Monte Carlo simulations are performed on these data to obtain probability distribution functions (PDFs) of the solar activity on both long and short time scales. These PDFs are then compared with predicted PDFs from numerical simulation of our α - Ω dynamo model, where α is assumed to have both mean α0 and fluctuating α' parts. Results. By varying the correlation time τα of fluctuating α', the ratio of the amplitude of the fluctuating to mean alpha αR = √α'2≺/α20 (where angular brackets ≺ ≻ denote ensemble average), and the ratio of poloidal to toroidal magnetic fields, we show that the results from our stochastic dynamo model can match the PDFs of solar activity when τα ϵ [22, 44] years with αR ϵ [0.21, 0.24]. [ABSTRACT FROM AUTHOR]

Photospheric ephemeral regions (EPRs) cover the Sun like a magnetic carpet. From this, we update the Babcock – Leighton solar dynamo. Rather than sunspot fields appearing in the photosphere de novo from eruptions originating in the deep interior, we consider that sunspots form directly in the photosphere by a rapid accumulation of like-sign field from EPRs. This would only occur during special circumstances: locations and times when the temperature structure is highly superadiabatic and contains a large subsurface horizontal magnetic field (only present in the Sun’s lower latitudes). When these conditions are met, superadiabatic percolation occurs, wherein an inflow and downflow of gas scours the surface of EPRs to form active regions. When these conditions are not met, magnetic elements undergo normal percolation, wherein magnetic elements move about the photosphere in Brownian-type motions. Cellular automata (CA) models are developed that allow these processes to be calculated and thereby both small-scale and large-scale models of magnetic motions can be obtained. The small-scale model is compared with active region development and Hinode observations. The large-scale CA model offers a solar dynamo, which suggests that fields from decaying bipolar magnetic regions (BMRs) drift on the photosphere driven by subsurface magnetic forces. These models are related to observations and are shown to support Waldmeier’s findings of an inverse relationship between solar cycle length and cycle size. Evidence for significant amounts of deep magnetic activity could disprove the model presented here, but recent helioseismic observations of “butterfly patterns” at depth are likely just a reflection of surface activity. Their existence seems to support the contention made here that the field and flow separate, allowing cool, relatively field-free downdrafts to descend with little field into the nether worlds of the solar interior. There they heat by compression to form a hot solar-type Santa Ana wind deep below active regions. [ABSTRACT FROM AUTHOR]

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]