Coupled spin models for magnetic variation of planets and stars




Geomagnetism is characterized by intermittent polarity reversals and rapid fluctuations. We have recently proposed a coupled macro-spin model to describe these dynamics based on the idea that the whole dynamo mechanism is described by the coherent interactions of many local elements. In this paper, we further develop this idea and construct the minimal model for magnetic variations. This simple model naturally yields many of the observed features of geomagnetism: its time evolution, the power spectrum, the frequency distribution of stable polarity periods etc. This model is characterized by two coexisting phases of spins: i.e. the cluster phase which determines the global dipole magnetic moment, and the expanded phase which gives random perpetual perturbations that yield the intermittent polarity flip of the dipole moment. This model can also describe the synchronization of the spin oscillations. This corresponds to the case of our Sun and the model well describes the quasi-regular cycles of the solar magnetism. Furthermore, by analysing the relevant terms of magnetohydrodynamic equations based on our model, we have obtained a scaling relation for the magnetism for planets, satellites and the Sun. Comparing it with various observations, we can estimate the relevant scale of the macro-spins.