Using mutual information to investigate non-linear correlation between AE index, ULF Pc5 wave activity and electron precipitation

In this study, we use mutual information from information theory to investigate non-linear correlation between geomagnetic activity indicated by auroral electrojet (AE) index with both the global ultra low frequency (ULF) Pc5 wave power and medium energy (≥30 keV) electron precipitation at the central outer radiation belt. To investigate the energy and magnetic local time (MLT) dependence of the non-linearity, we calculate the mutual information and Pearson correlation coefficient separately for three different energy ranges (30–100 keV, 100–300 keV and ≥300 keV) and four different MLT sectors (0–6, 6–12, 12–18, 18–24). We compare results from 2 years 2004 and 2007 representing geomagnetically more active and less active years, respectively. The correlation analysis between the AE index and electron precipitation shows a clear MLT and energy dependence in both active and quiet conditions. In the two lowest energy ranges of the medium energy electrons (30–100 keV and 100–300 keV) both non-linear correlation and Pearson correlation indicate strong dependence with the AE index in the dawn sector. The linear dependence indicated by the Pearson correlation coefficient decreases from dawn to dusk while the change in the non-linear correlation is smaller indicating an increase in the non-linearity from dawn to dusk. The non-linearity between the AE index and electron precipitation is larger at all MLT sectors except MLTs 6–12 during geomagnetically more active year when larger amount of the activity is driven by interplanetary coronal mass ejections (ICMEs) compared to lower activity year with high speed stream (HSS) and stream interaction region (SIR) driven activity. These results indicate that the processes leading to electron precipitation become more non-linear in the dusk and during geomagnetically more active times when the activity is driven by ICMEs. The non-linearity between the AE index and global ULF Pc5 activity is relatively low and seems not to be affected by the difference in the geomagnetic activity during the 2 years studied.