A relation between the energy deposition by electron precipitation and geomagnetic indices during substorms

[1] Observations from the Polar Ionospheric X-ray Imaging Experiment (PIXIE) and the Ultraviolet Imager (UVI) on board the Polar satellite have been used to derive the total energy dissipation (U-A) in the Northern Hemisphere by electron precipitation in the energy range from 100 eV to 100 keV. Comparing with geomagnetic indices, we find that during substorms, U-A is linearly related to the quick look AE(QL)(1/2) and AL(QL)(1/2) indices. The best correlation (0.86) is found between the energy flux above 10 keV and the AL(QL) index, which reflects that the energetic electron precipitation modulates the westward electrojet intensity by affecting the Hall conductance. The AU(QL) index which reflects the eastward electrojet intensity shows poor correlation with U-A, either for soft or energetic electrons. This is consistent with an electric field dominance in the dusk sector and a minor role for auroral conductance in the eastward electrojet. On the basis of ionospheric electrodynamics, we argue that a nonlinear relation between U-A and AE (and AL) is more appropriate than a linear relation. We show that the linear relations reported by others do not fit our data set and that they provide U-A values which are too low. For the total electron energy flux (0.1-100 keV) we find the best fit to be U-A[GW] = 4.4 AL(QL)(1/2)-7.6, with a correlation coefficient of 0.83, which is slightly better than that for the AE(QL) index (0.77). By time-integrating the U-A derived from AL(QL), we obtain estimates of the total deposited energy during substorms within +/-20% of the time-integrated U-A derived from UV and X rays.