Spectroscopic diagnostic of halos and elves detected from space-based photometers.

In this work, we develop two spectroscopic diagnostic methods to derive the peak reduced electric field in Transient Luminous Events (TLEs) from their optical signals. These methods could be used to analyze the optical signature of TLEs reported by spacecraft such as ASIM (ESA) and the future TARANIS (CNES). As a first validation of these methods, we apply them to the predicted (synthetic) optical signatures of halos and elves, two type of TLEs, obtained from electrodynamical models. This procedure allows us to compare the inferred value of the peak reduced electric field with the value computed by halo and elve models. Afterward, we apply both methods to the analysis of optical signatures of elves and halos reported by GLIMS (JAXA) and ISUAL (NSPO) spacecraft, respectively. We conclude that the best emission ratios to estimate the maximum reduced electric field in halos and elves are the ratio of the Second Positive System (SPS) of N$_2$ to First Negative System (FNS) of N$_2^+$, the First Positive System (FPS) of N$_2$ to FNS of N$_2^+$ and the Lyman-Birge-Hopfield (LBH) band of N$_2$ to FNS of N$_2^+$. In the case of reduced electric fields below 150~Td, we found that the ratio of the SPS of N$_2$ to FPS of N$_2$ can also be used to reasonably estimate the value of the field. Finally, we show that the reported optical signals from elves can be treated following an inversion method in order to estimate some of the characteristics of the parent lightning.