Spectra of the two official GLEs of solar cycle 24

Based on ground-level data and on satellite data we determine in this work the observational spectrum of both, the Ground Level Enhancement of May 17, (2012) the so-called GLE71 and the Ground Level Enhancement of September 10, 2017 (GLE 72). We describe a simplified method to obtain the experimental spectrum at ground level. Data of the GLE71 and GLE72 indicate the presence of two different populations, each one with a different energy spectrum. On the other hand, we explore the kind of phenomena that take place at the source in these two particular events. In contrast with other methods based on the temporal synchronization between electromagnetic emissions of flares and coronal mass ejections (CME), here we develop an alternative option based on the study of the accelerated particles, by adjusting our theoretical spectra to the observational spectra. The main results of this work are the derivation of the source and acceleration parameters involved in the generation process. These results lead us to construct possible scenarios of particle generation in the source for each one of the two studied GLEs.