Coupled macro-spin model with two variables for polarity reversals in the Earth and the Sun

Abstract Geomagnetism is extremely complex and straightforward magnetohydrodynamics simulations are still unable to reveal all its dynamics. Recently, a simple macro-spin model for geomagnetism has been suggested. This model is based on the idea that geomagnetism can be described by interactions with many local dynamo elements (macro-spins). This model can reproduce some complex features of geomagnetism by solving a simple set of ordinary differential equations with a minimal number of variables. In this paper, we complete this macro-spin model by considering the full set of variables in three dimensions. Utilizing this model, we can address several basic features of geomagnetism which could not be described in the previous minimal model: migration of the north and south magnetic poles, a precise comparison of the detailed surface distribution of magnetic fields with the observed data, etc. Moreover, by applying this model to solar magnetism, we can reproduce the periodic polarity reversals and the power index of the power spectrum from this complete spin model. Finally, we elucidate the statistical properties of pole migration.