Stochastic and nonlinear fluctuations in a mean field dynamo.
Abstract
We study the effect of rapid stochastic fluctuations in the kinetic helicity in a plane parallel mean field dynamo model for the Sun. The αparameter has a fluctuating component δα=αα_0_, which is modelled as a random forcing term. The fluctuations give rise to variations in the amplitude and phase of the dynamo wave, such that shorter cycles have higher amplitudes, as is observed in the solar cycle. By making a second order expansion close to the unperturbed marginally stable dynamo wave we are able to go beyond the weak forcing limit studied by Hoyng. We show that with increasing strength of the forcing the effective dynamo frequency decreases. We introduce a simple nonlinearity to model αquenching and derive a set of linear equations for the mean field, valid in the weak forcing case. With αquenching, phase and amplitude fluctuations are bounded, but still correlated. The strength of the αquenching is measured by a parameter q=(T_e_/α_0_)(dα/dT)_T_e__, where T_e_ is the equilibrium value of the toroidal field. We make a comparison with sunspot data, and conclude that these are well explained by the model if δα/α_0_=~2.2 and q=~0.7. Finally we briefly consider the alternative possibility of fluctuations caused by nonlinear dynamics, without external forcing (δα=0). We show that the resulting phaseamplitude diagram does not agree with observations. Although this is no proof that the phaseamplitude correlation cannot be reproduced by nonlinear chaos, we conclude that stochastic noise provides a more natural explanation.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 September 1996
 Bibcode:
 1996A&A...313..959O
 Keywords:

 SUN: MAGNETIC FIELDS;
 SUNSPOTS;
 CONVECTION;
 TURBULENCE;
 MHD