Dual scaling for self-organized critical models of the magnetosphere

The central plasma sheet is a complex magnetized plasma structure located in the equatorial plane of the magnetotail from where substorms are believed to originate. Dynamically, it may behave like a self-organized critical (SOC) system, driven by the slow energy input of the solar wind. The power law distributions for the sizes, energies, and durations of substorms that are reflected in observations can be reproduced using such SOC models. However, the expected scale invariance does not seem to hold for all scale ranges and observables. Recent observations of all-sky auroras have suggested a dual regime, where small and large events scale as different power laws, the smaller events having a steeper slope. On the other hand, scale-dependent substorm behavior can materialize as a consequence of an energy loading-unloading cycle. Accordingly, we designed a 2-D SOC model subject to global deterministic driving and a nonconservative redistribution law. This model can reproduce the coexistence of two scaling regimes, with the second regime appearing as a consequence of the enhanced spatial development of avalanches caused by a higher spatial intermittency in the energy gradients. Thresholded interevent waiting time statistics showed a well-defined peak with an exponential tail, consistent with observations and the expected dynamics of a loading-unloading cycle. Finally, we show that the coherency index extracted from the simulations decreases prior to large avalanches, as is in fact observed in auroral arcs. This suggests that the coherency index may be a useful substorm predictor.