Physics of the solar cycle

The theory of the solar/stellar activity cycles is presented, based on the mean-field concept in magnetohydrodynamics. A new approach to the formulation of the electromotive force and the theory of differential rotation and meridional circulation is described. Dynamo cycles in the overshoot layer and distributed dynamos are compared, with the latter including the influence of meridional flow. The overshoot layer dynamo reproduces the solar cycle periods and the butterfly diagram only if alpha=0 in the convection zone (CZ). The distributed dynamo including meridional flows shows the observed butterfly diagram even with a positive dynamo-alpha in CZ. The nonlinear feedback of strong magnetic fields on differential rotation leads to grand minima in the cyclic activity similar to those observed. Our 2D model contains the large- and small-scale feedback of magnetic fields on diff. rotation and induction in a mean-field formulation (Lambda-, alpha-quenching). Grand minima may also occur if a dynamo occasionally falls below its critical eigenvalue. We never found any indication that such an on-off dynamo collapses by this effect after being excited. The full quenching of turbulence by strong magnetic fields as reduced induction (alpha) and reduced turbulent diffusivity (eta_T) is studied in 1D. We find a stronger dependence of cycle period on dynamo number compared with a pure alpha-quenching model giving a very weak cycle period dependence. Also the temporal fluctuations of alpha and eta_T from a random-vortex simulation were applied to a dynamo. Then the low `quality' of the solar cycle can be explained with a small number of giant cells as dynamo-active turbulence. The transition from almost regular magnetic oscillations (many vortices) to a more or less chaotic time series (very few vortices) is shown.