The fluctuating α-effect and Waldmeier relations in the nonlinear dynamo models

Abstract

We study the possibility to reproduce the statistical relations of the sunspot activity cycle, like the so-called Waldmeier relations, the cycle period - amplitude and the cycle rise rate - amplitude relations, by means of the mean field dynamo models with the fluctuating α-effect. The dynamo model includes the long-term fluctuations of the α-effect and two types of the nonlinear feedback of the mean-field on the α-effect including the algebraic quenching and the dynamic quenching due to the magnetic helicity generation. We found that the models are able to reproduce qualitatively and quantitatively the inclination and dispersion across the Waldmeier relations with the 20% fluctuations of the α-effect. The models with the dynamic quenching are in a better agreement with observations than the models with the algebraic α-quenching. We compare the statistical distributions of the modeled parameters, like the amplitude, period, the rise and decay rates of the sunspot cycles, with observations.

revision, (add comment about effect of nonlinear diffusivity): 18 pages, 7 Figures, submitted to Physica Scripta

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• The origin of the helicity hemispheric sign rule reversals in the mean-field solar-type dynamo
• Dependence of stellar magnetic activity cycles on rotational period in nonlinear solar-type dynamo
• Does nonaxisymmetric dynamo operate in the Sun?
• Helicity-vorticity turbulent pumping of magnetic fields in solar convection zone
• Waldmeier relations and the solar cycle dynamics by the mean-field dynamos
• Advances in mean-field dynamo theories