Physics of the solar cycle

Abstract

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 as well as the theory of differential rotation and meridional circulation is described for use in dynamo theory. Activity cycles of dynamos in the overshoot layer (BL-dynamo) and distributed dynamos are compared, with the latter including the influence of meridional flow. The overshoot layer dynamo is able to reproduce the solar cycle periods and the butterfly diagram only if α = 0 in the convection zone. The problems of too many magnetic belts and too short cycle times emerge if the overshoot layer is too thin. The distributed dynamo including meridional flows with a magnetic Reynolds number Rm > ∼ 20 (low magnetic Prandtl number) reproduces the observed butterfly diagram even with a positive dynamo-α in the bulk of the convection zone. The nonlinear feedback of strong magnetic fields on differential rotation in the mean-field conservation law of angular momentum leads to grand minima in the cyclic activity similar to those observed. The 2D model described here contains the large-scale interactions as well as the small-scale feedback of magnetic fields on differential rotation and induction in terms of a mean-field formulation (Λ-quenching, α-quenching). Grand minima may also occur if a dynamo occasionally falls below its critical eigenvalue. We expressed this idea by an on-off α function which is non-zero only in a certain range of magnetic fields near the equipartition value. We never found any indication that the dynamo collapses by this effect after it had once been excited. The full quenching of turbulence by strong magnetic fields in terms of reduced induction (α) and reduced turbulent diffusivity (η T ) is studied with a 1D model. The full quenching results in a stronger dependence of cycle period on dynamo number compared with the model with α-quenching alone giving a very weak cycle period dependence. Also the temporal fluctuations of α and η T from a random-vortex simulation were applied to a dynamo model. Then the low 'quality' of the solar cycle can be explained with a relatively small number of giant cells acting as the dynamo-active turbulence. The simulation contains the transition from almost regular magnetic oscillations (many vortices) to a more or less chaotic time series (very few vortices).

Dynamo Models of the Solar Cycle

“…The series of review articles published in Proctor and Gilbert (1994) and Ferriz-Mas and Núñez (2003) are also essential reading for more in-depth reviews of some of the topics covered here. Among the most recent reviews, Petrovay (2000); Tobias (2002); Rüdiger and Arlt (2003); Usoskin and Mursula (2003), and Ossendrijver (2003) offer (in my opinion) particularly noteworthy alternate and/or complementary viewpoints to those expressed here.…”

“…While this approach usually displaces the ad hoc assumptions away from the α-effect and into the turbulence model, it has the definite advantage of offering an internally consistent approach to the calculation of turbulent diffusivities and large-scale flows. Rüdiger and Brandenburg (1995) remain a good example of the current state-of-the-art in this area; see also Rüdiger and Arlt (2003), and references therein.…”

Dynamo Models of the Solar Cycle

“…The series of review articles published in Proctor and Gilbert (1994) and are also essential reading for more in-depth reviews of some of the topics covered here. Among the most recent reviews, Petrovay (2000); Tobias (2002); Rüdiger and Arlt (2003); Usoskin and Mursula (2003); Ossendrijver (2003), and Brandenburg and Subramanian (2005) offer (in my opinion) particularly noteworthy alternate and/or complementary viewpoints to those expressed here.…”

“…While this approach usually displaces the ad hoc assumptions into the turbulence model, it has the definite merit of offering an internally consistent approach to the calculation of turbulent diffusivities and large-scale flows. Rüdiger and Brandenburg (1995) remain a good example of the current state-of-the-art in this area; see also Rüdiger and Arlt (2003), and references therein.…”

Circulation-dominated solar shell dynamo models with positive alpha-effect

“…with s = r sin θ (see Rüdiger & Arlt 2000). The unusual form of the eddy diffusivity term is used to include the turbulent diamagnetism, which occurs in case of spatially inhomogeneous turbulence intensity and is a strong effect for low-η T dynamos.…”