Stochastic excitation and memory of the solar dynamo

We consider a simple axisymmetric mean field dynamo model for the Sun in the alpha Omega-limit and study the effect of rapid, latitude dependent stochastic fluctuations in alpha. The fluctuations excite overtones of the fundamental mode of the mean magnetic field. We decompose the mean field into eigenmodes and derive an equation for the mode coefficients. Transient mode excitation gives rise to a mean field with spatial and temporal variability, and may provide an explanation for grand minima, the observed phase-amplitude correlation, North-South asymmetries and, close to the equator, reverse polarity regions in the solar butterfly diagram. We find that the North-South asymmetry often peaks near the activity minimum, in agreement with the observations. The most likely candidate for the origin of the fluctuations are giant cells. Sunspot data are well reproduced if alpha, defined as an azimuthal average, has fluctuations delta alpha of the order delta alpha/alpha(0) approximate to 3 at colatitude theta = 60 degrees, assuming that there are 20 giant cells from pole to pole, with a coherence time of 1 month. The model predicts that the resulting phase and amplitude fluctuations of the fundamental mode are correlated for about 90 dynamo periods.