Advances in mean-field dynamo theories

We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.Comment: Revision2, replaced two figures by color version, 12 pages, IAU 294 Proceeding

Magnetic helicity in non-axisymmetric mean-field solar dynamo

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 transient phase. Also our simulations shows that the non-axisymmetric distributions of magnetic helicity tend to follows the regions of the Hale polarity rule.Comment: 8 pages, 4 figures, to appear in Magnehydrodynamics, "Russian Magnetohydrodynamics 2015", Perm', June, 201

Helicity-vorticity turbulent pumping of magnetic fields in solar convection zone

We study the effect of turbulent drift of a large-scale magnetic field that results from the interaction of helical convective motions and differential rotation in the solar convection zone. The principal direction of the drift corresponds to the direction of the large-scale vorticity vector. Thus, the effect produces a latitudinal transport of the large-scale magnetic field in the convective zone wherever the angular velocity has a strong radial gradient. The direction of the drift depends on the sign of helicity and it is defined by the Parker-Yoshimura rule. The analytic calculations are done within the framework of mean-field magnetohydrodynamics using the minimal \tau-approximation. We estimate the magnitude of the drift velocity and find that it can be several m/s near the base of the solar convection zone. The implications of this effect for the solar dynamo are illustrated on the basis of an axisymmetric mean-field dynamo model with a subsurface shear layer. We find that the helicity--vorticity pumping effect can have an influence on the features of the sunspot time--latitude diagram, producing a fast drift of the sunspot activity maximum at the rise phase of the cycle and a slow drift at the decay phase of the cycle.Comment: 19 pages, 8 figures, submitted to GAF

The shear-induced alpha-effect and long-term variations in solar dynamo

The consequences of the shear-induced alpha effect to the long-term modulation of magnetic activity are examined with the help of the axisymmetric numerical dynamo model that includes the self-consistent description of the angular momentum balance, heat transport and magnetic field generation in the spherical shell. We find that the shear contributions to alpha effect can complicate the long-term behaviour of the large-scale magnetic activity and differential rotation in nonlinear dynamo. Additionally we consider the impact secular magnetic activity variations to the secular modulations of the solar luminosity and radius.Comment: AOGS 2nd Annual Meeting 200

Helicity--vorticity turbulent pumping of magnetic fields in the solar dynamo

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.Comment: 2 pages, IAU 294 Proceeding

Benchmarking the solar dynamo with Maxima

Recently, Jouve et al(A&A, 2008) published the paper that presents the numerical benchmark for the solar dynamo models. Here, I would like to show a way how to get it with help of computer algebra system Maxima. This way was used in our paper (Pipin & Seehafer, A&A 2008, in print) to test some new ideas in the large-scale stellar dynamos. In the present paper I complement the dynamo benchmark with the standard test that address the problem of the free-decay modes in the sphere which is submerged in vacuum.Comment: 8 pages, 1 figur

On the turbulent sources of the solar dynamo

We revisit the possible turbulent sources of the solar dynamo. Studying axisymmetric mean-field dynamo models, we find that the large-scale poloidal magnetic field could be generated not only by the famous alpha effect, but also by the Omega x J and shear-current effects. The inclusion of these additional turbulent sources alleviates several of the known problems of solar mean-field dynamo models.Comment: 7th Int. PAMIR Conf. on Fundamental and Applied MHD (Giens, France, 2008

Large-scale magnetic fields and anomalies of chemical composition of stellar coronae

We present evidences that anomalies in abundance of the chemical minor elements with the low first ionization potential (FIP) in the low corona of the late-type stars can be related with topology of the large-scale magnetic field. The solar observations show the increased abundances of the low FIP elements in compare to the abundances of the high FIP elements above the active regions and in the closed magnetic configurations of the low corona. Observational data of Ulysses and the Stanford Solar Observatory show high correlations between FIP effect of the solar wind, amount of the unsigned open magnetic flux, and the ratio between strength of the large-scale toroidal and poloidal magnetic field on the surface. The solar-type stars show the increase abundance of the low FIP elements relative to elements with the high FIP with the decrease of the large-scale poloidal magnetic field (and increase the toroidal component of the magnetic field). The branch of the fully convective stars demonstrates inversion of the FIP-effect. This inversion can be result from strong coronal activity, which is followed to the strong poloidal magnetic on these stars.Comment: 24 pages, 5 figures, accepted for publication on March 21, 2018 in Journal of Atmospheric and Solar-Terrestrial Physics (JASTP

Does nonaxisymmetric dynamo operate in the Sun?

We explore effects of random non-axisymmetric perturbations of kinetic helicity (the $\alpha$ 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 $\alpha$ effect can maintain the non-axisymmetric magnetic fields through a solar-type $\alpha^{2}\Omega$ dynamo process. It is found that diffusive decay of bipolar active regions is likely to be the primary source of the non-axisymmetric magnetic fields observed on the Sun. Our results show that the non-axisymmetric dynamo model with stochastic perturbations of the $\alpha$ effect can explain periods of extremely high activity (`super-cycle' events) as well as periods of deep decline of magnetic activity. We compare the models with synoptic observations of solar magnetic fields for the last four activity cycles, and discuss implications of our results for interpretation of observations of stellar magnetic activity.Comment: 15 pages, 11 figures, accepted in Ap

The mean-field solar dynamo with double cell meridional circulation pattern

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 helicity. Contrary to previous flux-transport dynamo models, it is found that the dynamo model can robustly reproduce the basic properties of the solar magnetic cycles for a wide range of model parameters and the circulation speed. The best agreement with observations is achieved when the surface speed of meridional circulation is about 12 m/s. For this circulation speed the simulated sunspot activity shows good synchronization with the polar magnetic fields. Such synchronization was indeed observed during the past sunspot cycles 21 and 22. We compare theoretical and observed phase diagrams of the sunspot number and the polar field strength and discuss the peculiar properties of Cycle 23.Comment: 19 pages, 7 figures, revise