Potential energy stored by planets and grand minima events

Recently, Wolff & Patrone (2010), have developed a simple but very interesting model by which the movement of the Sun around the barycentre of the Solar system could create potential energy that could be released by flows pre-existing inside the Sun. The authors claim that it is the first mechanism showing how planetary movements can modify internal structure in the Sun that can be related to solar cycle. In this work we point out limitations of mentioned mechanism (which is based on interchange arguments), which could be inapplicable to a real star. Then, we calculate the temporal evolution of potential energy stored in zones of Sun's interior in which the potential energy could be most efficiently stored taking into account detailed barycentric Sun dynamics. We show strong variations of potential energy related to Maunder Minimum, Dalton Minimum and the maximum of Cycle 22, around 1990. We discuss briefly possible implications of this putative mechanism to solar cycle specially Grand Minima events.