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Using different proxies of solar activity, we have studied the following features of the solar cycle: i) The linear correlation between the amplitude of cycle and its decay rate, ii) the linear correlation between the amplitude of cycle $n$ and the decay rate of cycle $(n - 1)$, and iii) the anti-correlation between the amplitude of cycle $n$ and the period of cycle $(n - 1)$. Features ii) and iii) are very useful because they provide precursors for future cycles. We have reproduced these features using a flux-transport dynamo model with stochastic fluctuations in the Babcock-Leighton $\alpha$ effect and in the meridional circulation. Only when we introduce fluctuations in meridional circulation, are we able to reproduce different observed features of the solar cycle. We discuss the possible reasons for these correlations. [ABSTRACT FROM AUTHOR]

We construct a series of kinematic axisymmetric mean-field dynamo models operating in the αΩ, α²Ω and α² regimes, all using the full α-tensor extracted from a global magnetohydrodynamical simulation of solar convection producing large-scale magnetic fields undergoing solar-like cyclic polarity reversals. We also include an internal differential rotation profile produced in a purely hydrodynamical parent simulation of solar convection, and a simple meridional flow profile described by a single cell per meridional quadrant. An α²Ω mean-field model, presumably closest to the mode of dynamo action characterizing the MHD simulation, produces a spatiotemporal evolution of magnetic fields that share some striking similarities with the zonally-averaged toroidal component extracted from the simulation. Comparison with α² and αΩ mean-field models operating in the same parameter regimes indicates that much of the complexity observed in the spatiotemporal evolution of the large-scale magnetic field in the simulation can be traced to the turbulent electromotive force. Oscillating α²solutions are readily produced, and show some similarities with the observed solar cycle, including a deep-seated toroidal component concentrated at low latitudes and migrating equatorward in the course of the solar cycle. Various numerical experiments performed using the mean-field models reveal that turbulent pumping plays an important role in setting the global characteristics of the magnetic cycles. [ABSTRACT FROM AUTHOR]

ABSTRACT We develop and subsequently explore the solution space of a simple flux transport dynamo model that incorporates a time-dependent large-scale meridional circulation. Based on recent observations, we prescribed an analytical form for the amplitude of this circulation and study its impact in the evolution of the magnetic field. We find that cyclic variations in the amplitude and frequency of the meridional flow affect the strength of the solar cycle. Variations in the amplitude of the fluctuations influence the shape of the solar cycle but are only relevant to the cycle's strength variations when they occur at a frequency different from or out of phase of the solar cycle's. [ABSTRACT FROM AUTHOR]

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]

Two systems of Lorenz-type equations modelling solar magnetic activity are studied: Firstly a low order dynamic system in which the toroidal and poloidal fields are represented by x- and y-coordinates respectively, and the hydrodynamical information is given by the z coordinate. Secondly a complex generalization of the three ordinary differential equations studied by Lorenz. By studying the Poincaré map we give numerical evidence that the flow has an attractor with fractal structure. The period is defined as the time needed for a point on a hyperplane to return to the hyperplane again. The periods are distributed in an interval. For large values of the Dynamo number there is a long tail toward long periods and other interesting comet-like features. These general relations found for periods can further be physically interpreted with improved helioseismic estimates of the parameters used by the dynamical systems. Solar Dynamic Observatory is expected to offer such improved measurements. [ABSTRACT FROM AUTHOR]

We discuss the current status of solar dynamo theory and describe the dynamo model developed by our group. The toroidal magnetic field is generated in the tachocline by the strong differential rotation and rises to the solar surface due to magnetic buoyancy to create active regions. The decay of these active regions at the surface gives rise to the poloidal magnetic field by the Babcock-Leighton mechanism. This poloidal field is advected by the meridional circulation first to high latitudes and then down below to the tachocline. Dynamo models based on these ideas match different aspects of observational data reasonably well. [ABSTRACT FROM AUTHOR]

The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the α effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the α effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling. [ABSTRACT FROM AUTHOR]

Measurements of the general magnetic field of the Sun seen as a star were performed over last 45 years by the CrAO and five other observatories (1968–2012, nearly 23 thousand daily strengths B ). Analysis of the B time series showed that the most substantial long-term period of the field variation is the Hale’s cycle 22 years, which cannot be explained by dynamo theory. It reveals a saw-edged profile, indicating perhaps a cosmic origin of the cycle. [ABSTRACT FROM AUTHOR]