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

Abstract

We study the possibility of reproducing the statistical relations of the sunspot activity cycle, such as 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 fluctuating α-effect. The dynamo model takes into account the long-term fluctuations of the α-effect and two types of nonlinear feedback of the mean field on the α-effect, namely, 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 20% fluctuations of the α-effect. The models with dynamic quenching are in better agreement with observations than the models with algebraic α-quenching. We compare the statistical distributions of the modelled parameters, such as the amplitude, period, and the rise and decay rates of the sunspot cycles with observations.