Simon Wing, Applied Physics Laboratory, Johns Hopkins University; Jesse Snelling, Andrews University, Jake Willard, Andrews University
Complex systems such as the solar/stellar/magnetospheric environments often exhibit patterns of behavior that suggest underlying organizing principles. Causality is a key organizing principle that is particularly difficult to establish in strongly coupled systems, but essential for understanding and modeling the behavior of systems. While traditional methods of time-series analysis can identify correlations, they do not adequately quantify the distinction between causal and coincidental dependence. Entropy-based measures are useful to detect high order nonlinear dependence as well as to eliminate coincidental dependence between system variables. As examples, we consider the dynamics solar flares and geomagnetic substorms. Solar and stellar flares are powered by energy stored in magnetic fields, so their occurrence should depend on the evolution of the underlying magnetic field. As such, flare sequences contain information about the underlying dynamics of the stellar activity cycle, which can be seen in long-term variability of the flaring rate. However, the distribution of flares over shorter time scales appear to be random and are thought to be well described as a nonstationary Poisson process. The interpretation of the waiting time distribution is that flares may be produced by processes sufficiently complex to appear random, or the randomness may be a property of the evolution of the magnetic field configurations. We have found that in contrast to a Poisson process, there is significant mutual information between subsequent flares, suggesting that the dynamics is not well described as a nonstationary Poisson process. We also compare the solar waiting time distribution with that of other sun-like stars. While the underlying dynamics of magnetospheric substorms been described as a load and release process, there is considerable debate as to what triggers substorm onset. Several studies have suggested that substorm onset is controlled by an external driver, such as northward turning of the interplanetary magnetic field. Although this trigger is often found to be correlated with substorm onset, analysis based on conditional mutual information demonstrates that this relationship is coincidental rather than causal.
Mode of presentation: oral (Need to be confirmed by the SOC)