Transition from axi- to nonaxisymmetric dynamo modes in spherical convection models of solar-like stars

Context. Both dynamo theory and observations of stellar large-scale magnetic fields suggest a change from nearly axisymmetric configurations at solar rotation rates to nonaxisymmetric configurations for rapid rotation. Aims. We seek to understand this transition using numerical simulations. Methods. We use three-dimensional simulations of turbulent magnetohydrodynamic convection in spherical shell wedges and considered rotation rates between 1 and 31 times the solar value. Results. We find a transition from axi- to nonaxisymmetric solutions at around 1.8 times the solar rotation rate. This transition coincides with a change in the rotation profile from antisolar- to solar-like differential rotation with a faster equator and slow poles. In the solar-like rotation regime, the field configuration consists of an axisymmetric oscillatory field accompanied by an m = 1 azimuthal mode (two active longitudes), which also shows temporal variability. At slow (rapid) rotation, the axisymmetric (nonaxisymmetric) mode dominates. The axisymmetric mode produces latitudinal dynamo waves with polarity reversals, while the nonaxisymmetric mode often exhibits a slow drift in the rotating reference frame and the strength of the active longitudes changes cyclically over time between the different hemispheres. In the majority of cases we find retrograde waves, while prograde waves are more often found from observations. Most of the obtained dynamo solutions exhibit cyclic variability either caused by latitudinal or azimuthal dynamo waves. In an activity-period diagram, the cycle lengths normalized by the rotation period form two different populations as a function of rotation rate or magnetic activity level. The slowly rotating axisymmetric population lies close to what in observations is called the inactive branch, where the stars are believed to have solar-like differential rotation, while the rapidly rotating models are close to the superactive branch with a declining cycle to rotation frequency ratio and an increasing rotation rate. Conclusions. We can successfully reproduce the transition from axi- to nonaxisymmetric dynamo solutions for high rotation rates, but high-resolution simulations are required to limit the effect of rotational quenching of convection at rotation rates above 20 times the solar value.

Probing latitudinal variations of the solar magnetic field in cycles 21–23 by Parker's Two-Layer Dynamo Model with meridional circulation

Principle component analysis (PCA) of the solar background magnetic field (SBMF) measured from Wilcox Solar Observatory (WSO) magnetograms revealed the following principal components (PCs) in latitudes: two main symmetric components, which are the same for all cycles 21–23, and three pairs of asymmetric components, which are unique for each cycle. These SBMF variations are assumed to be those of poloidal magnetic field travelling slightly off-phase from pole to pole while crossing the equator. They are assumed to be caused by a joint action of dipole and quadruple magnetic sources in the Sun. In the current paper, we make the first attempt to interpret these latitudinal variations in the surface magnetic field with Parker's two-layer dynamo model. The latitudinal distributions of such waves are simulated for cycles 21–23 by the modified Parker's dynamo model taking into account both α and ω effects operating simultaneously in the two (upper and lower) layers of the solar convective zone (SCZ) and having opposite directions of meridional circulation. The simulations are carried out for both dipole and quadruple magnetic sources with the dynamo parameters specifically selected to provide the curves fitting closely the PCs derived from SBMF variations in cycles 21–23. The simulations are optimised for matching the positions of maximums in latitude, the number of equator crossings and the phase difference between the two dynamo waves operating in the two layers. The dominant pair of PCs present in each cycle is found to be fully asymmetric with respect to the magnetic poles and produced by a magnetic dipole. This pair is found to account for the two main dynamo waves operating between the two magnetic poles. There are also three further pairs of waves unique to each cycle and associated with multiple magnetic sources in the Sun. For the odd cycle 21 the simulated poloidal field fits the observed PCs, only if they are produced by magnetic sources with a quadruple symmetry in both layers, while for the even cycle 22 the fit to the observed PCs is achieved only in the case of quadruple magnetic sources in the upper layer and dipole sources in the inner layer. For the other odd cycle 23 the fit to observation is obtained for the quadruple magnetic sources in the inner layer and the dipole sources in the upper layer. The magnitudes of dynamo numbers D defining the conditions (depth and latitude) of a magnetic flux formation and the numbers N of zeros (equator crossings by the waves) are found to increase and the meridional circulation speed to decrease with a cycle number increase (D = −700, N = 3 for cycle 21 and D = −104, N = 9 for cycle 23). The phase delays between the waves in each unique pairs are also found to increase with the cycle number from ~9° in cycle 21 to ~13° in cycle 23.

Mechanisms of planetary and stellar dynamos

We review some of the recent progress on modeling planetary and stellar dynamos. Particular attention is given to the dynamo mechanisms and the resulting properties of the field. We present direct numerical simulations using a simple Boussinesq model. These simulations are interpreted using the classical mean-field formalism. We investigate the transition from steady dipolar to multipolar dynamo waves solutions varying different control parameters, and discuss the relevance to stellar magnetic fields. We show that owing to the role of the strong zonal flow, this transition is hysteretic. In the presence of stress-free boundary conditions, the bistability extends over a wide range of parameters.