Schwabe, Gleissberg, Suess-de Vries: A simple model for synchronizing solar cycles by planetary forces

Aiming at a simple and consistent planetary synchronization model of both short-term and long-term solar cycles we analyze Schove's data of the cycle minima and maxima. Their residuals from the average cycle duration of 11.07 years show a high degree of regularity, comprising a dominant period of 200 years (Suess-de Vries cycle), and a few periods around 90 years (Gleissberg cycle). Based on Dicke's ratio between the mean square of the residuals to the mean square of the difference of two consecutive residuals, we conjecture that the Schwabe cycle is synchronized, very likely via a helicity-mediated parametric resonance, by the 11.07 years alignment cycle of the tidally dominant planets Venus, Earth and Jupiter. In an attempt to explain the rather regular long-term behaviour, we enhance our Parker-type solar dynamo model by a modulation of the field-storage capacity of the tachocline with the 19.86 years periodicity of the movement of the sun around the barycenter of the solar system, which results basically from the Jupiter-Saturn synodes. Not surprisingly, this modulation leads to a 193-year beat period of dynamo activity which is indeed close to the observed 200 years Suess-de Vries cycle. In cases, the model produces also additional peaks at typical Gleissberg frequencies, which might be interpreted as beat periods of the Schwabe cycle with the Jupiter-Uranus (13.81-year) or the Jupiter-Neptune (12.78-year) synodes.