Analysis of Ground Level Enhancements (GLE): Extreme solar energetic   particle events have hard spectra
  Nearly 70 Ground Level Enhancements (GLEs) of cosmic rays have been recorded by the worldwide neutron monitor network since the 1950s depicting a big variety of energy spectra of solar energetic particles (SEP). Here we studied a statistical relation between the event-integrated intensity of GLEs (calculated as count-rate relative excess, averaged over all available polar neutron monitors, and expressed in percent-hours) and the hardness of the solar particle energy spectra. For each event the integral omnidirectional event-integrated fluences of particles with energy above 30 MeV ($F_{30}$) and above 200 MeV ($F_{200}$) were computed using the reconstructed spectra, and the ratio between the two fluences was considered as a simple index of the event's hardness. We also provided a justification of the spectrum estimate in the form of the Band-function, using direct PAMELA data for GLE 71 (17-May-2012). We found that, while there is no clear relation between the intensity and the hardness for weak events, all strong events with the intensity greater 100 \%*hr are characterized by a very hard spectrum. This implies that a hard spectrum can be securely assumed for all extreme GLE events, e.g., those studied using cosmogenic isotope data in the past. 
E. Asvestari, T. Willamo, A. Gil, I.G. Usoskin, G.A. Kovaltsov, V.V.   Mikhailov, A. Mayorov
physics.space-ph astro-ph.SR