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

TL;DR

This study demonstrates that nonlinear mean field dynamo models with fluctuating fect can reproduce key statistical relations of solar sunspot cycles, with dynamic quenching providing better agreement with observations.

Contribution

It introduces a dynamo model incorporating long-term fect fluctuations and nonlinear feedback, improving the reproduction of observed solar cycle relations.

Findings

Models with 20% fect fluctuations replicate Waldmeier relations.

Dynamic quenching aligns better with observed cycle statistics.

Modeled distributions match observed sunspot cycle parameters.

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 \alpha-effect. The dynamo model includes the long-term fluctuations of the \alpha-effect and two types of the nonlinear feedback of the mean-field on the \alpha-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 \alpha-effect. The models with the dynamic quenching are in a better agreement with observations than the models with the algebraic \alpha-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.