Can planetary tides synchronize the solar dynamo?

While the traditional explanation of the Hale cycle of the solar magnetic field relies on intrinsic features of the solar dynamo, we presently witness an increased interest in the question of whether gravitational forces of planets could influence the length and intensity of the cycle. Although tidal forces are usually considered as much too weak to play any role, one should note the large gravitational acceleration at the tachocline that amounts to 500 m/s². This translates the apparently tiny tidal heights of the order of 1 mm to equivalent velocities of 1 m/s. Such velocities, when allowed to coherently develop in the quiet regions of the tachocline, might indeed be relevant for the dynamo.
In our quest for a viable physical mechanism that could link the weak planetary force 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 induced by the tidally dominant Venus--Earth--Jupiter system may lead to a 1:1 resonant excitation of the oscillation of the associated alpha-effect. In the framework of a reduced, zero-dimensional alpha-Omega dynamo model, including a weak non-oscillatory and a resonantly excited oscillatory part of alpha, we recover the 22.14-year cycle of the solar dynamo. We finally show that the synchronization model can produce the correct orientation of the butterfly diagram even in case that the product of the non-oscillatory part of alpha with Omega is positive.