Tidally synchronized Tayler-Spruit and Babcock-Leighton type dynamos

The usual explanation of the Hale cycle of the solar magnetic field builds on intrinsic features of the solar dynamo, comprising the turbulent resistivity and the intensities of the alpha effect, the Omega effect and the meridional circulation. However, the dissimilarity of the sequence of solar cycles with a random walk in phase, and their remarkable synchronization with the 11.07 years period of the alignment of the tidally dominant planets Venus, Earth and Jupiter has not remained unobserved.
Asking for a viable physical mechanism that could link the very weak planetary forces with solar dynamo action, we focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability that is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations can be resonantly excited by m=2 perturbations that reflect tidal oscillations. Specifically, we speculate that the 11.07 years tidal oscillation may lead to a 1:1 resonant excitation of the oscillation of the associated alpha effect. In the framework of simple dynamo model of the Tayler-Spruit type, we recover the 22.14-year cycle of the solar dynamo. Interestingly, slight parameter changes of this model lead to transitions between oscillatory and pulsatory behaviour with maintained phase coherence, which might serve as an analogue of the behaviour during grand minima.
We have also tested similar dynamo models of the Babcock-Leighton type, for which we have pursued two ideas on how such a synchronization could work. The first one bears on the concept of a sensitive flux storage capacity of the tachocline, which might be easily influenced by minor perturbations as provoked by tidal forces, the second one on periodic changes of the Omega effect. In either case, and in contrast to this easy and robust synchronizability of Tayler-Spruit type dynamos, the model proved rather rather stubborn to synchronization.