Using Mutual Information to Investigate Non-Linear Dependence Between AE index, ULF Pc5 Wave Activity and Electron Precipitation

The Earth's outer radiation belt is occupied by energetic electrons trapped by the geomagnetic field. The response of the radiation belt electrons to the variations of the solar wind have been found to depend on different solar wind structures, i.e., whether the geomagnetic activity is driven, for example, by coronal mass ejections (CMEs) or high-speed streams (HSS). An anisotropic electron population injected from the magnetotail during substorms drives the very low frequency whistler mode chorus waves in the outer radiation belt. Chorus waves can accelerate the electrons as well as cause them to precipitate into the upper atmosphere. The ultra-low frequency (ULF) waves in the Pc5 range that can be driven internally or by the solar wind-magnetosphere interactions have been found to modulate the chorus waves and affect the radiation belt electron population. Using mutual information from information theory, we investigate the nonlinear dependence between the substorm activity indicated by the AE index, global Pc5 ULF wave activity, and electron precipitation at three different energy ranges between L shells from 5 to 7 within the outer radiation belt. We find that both the Pearson correlation and mutual information are highest between the AE index and precipitation of 30-300 keV energy electrons in the dawn MLT sectors 0-12, where the electrons are usually precipitated by the chorus waves. We compare results from geomagnetically more and less active years and the results indicate that linear Pearson correlation between AE index and electron precipitation is weaker i.e., the dependency is more non-linear during the more active year especially in the dusk. This suggest that during quieter magnetospheric conditions driven mostly by HSSs and stream interaction regions the processes leading to electron precipitation are more linear than during CME driven geomagnetic activity.