Variations of the solar cycle profile in a solar dynamo with fluctuating dynamo governing parameters

Abstract

Solar cycles vary in their amplitude and shape. There are several empirical relations between various parameters linking cycle's shape and amplitude, in particular the Waldmeier relations. As solar cycle is believed to be a result of the solar dynamo action, these relations require explanation in the framework of this theory.Here we aim to present a possible explanation of such kind. We relate the cycle-to-cycle variability of solar activity to fluctuations of solar dynamo drivers and primarily to fluctuations in the parameter responsible for recovery of the poloidal magnetic field from the toroidal one. To be specific, we develop such a model in the framework of the mean-field dynamo based on the differential rotation and $\alpha$-effect. We demonstrate that the mean-field dynamo based on a realistic rotation curve and nonlinearity associated with the magnetic helicity balance reproduces both qualitatively and quantitatively the Waldmeier relations observed in sunspot data since 1750 (SIDC data). The model also reproduces more or less successfully other relations between the parameters under discussion, in particular, the link between odd and even cycles (Gnevyshev-Ohl rule). We conclude that the contemporary solar dynamo theory provides a way to explain the cycle-to-cycle variability of solar activity as recorded in sunspots. We discuss the importance of the model for stellar activity cycles which, as known from the data of HK project, demonstrate the cycle-to-cycle variability similar to solar cycles.

12 pages, 9 figures, to appear in A&A

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Cited by in corpus (24)

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• Evidence for distinct modes of solar activity
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• Evolution of solar and stellar dynamo theory
• Fluctuations in the Alpha-Effect and Grand Solar Minima
• The mean-field solar dynamo with double cell meridional circulation pattern
• On the Origin of Solar Torsional Oscillations and Extended Solar Cycle
• Nonlinear Rossby wave-wave and wave-mean flow theory for long term Solar cycle modulations
• Helicity conservation in nonlinear mean-field solar dynamo
• The origin of the helicity hemispheric sign rule reversals in the mean-field solar-type dynamo
• Effects of large-scale non-axisymmetric perturbations in the mean-field solar dynamo
• The dynamics of Wolf numbers based on nonlinear dynamo with magnetic helicity: comparisons with observations
• Dependence of magnetic cycle parameters on period of rotation in nonlinear solar-type dynamos
• Effects of anisotropy of turbulent convection in mean-field solar dynamo models
• Does nonaxisymmetric dynamo operate in the Sun?
• Nonkinematic solar dynamo models with double-cell meridional circulation
• Dependence of stellar magnetic activity cycles on rotational period in nonlinear solar-type dynamo
• The Extended Solar Cycle and Asymmetry of the Large-Scale Magnetic Field
• The Dependence of Stellar Activity Cycles on Effective Temperature
• Zonal harmonics of solar magnetic field for solar cycle forecast
• Forecasting the solar cycle using variational data assimilation: validation on cycles 22 to 25
• The origin and effect of hemispheric helicity imbalance in solar dynamo
• Waldmeier relations and the solar cycle dynamics by the mean-field dynamos
• Evolution of proto-neutron stars to pulsars, magnetars and central compact objects