(N. Omodei, Z.L. Uhm, J. Racusin. J. McEnery)
The standard Gamma-Ray Burst (GRB) model predicts the evolution of the spectral (beta) and temporal (alpha) indices during the GRB afterglow for a variety of different environmental conditions. We study the relationship between alpha and beta, the so-called "closure relation", with GRBs detected by Fermi Large Area Telescope from August 2008 to August 2018. From the analyses of the > 100 MeV temporally extended emission, we calculate the spectral index and the exponent of the temporal decay. We test a set of closure relations, which are determined by several conditions such as electron spectral index, the electron cooling regime and the surrounding environment, and classify Fermi-LAT GRBs into the best-matched relation. From the test and classification, we can infer the GRB environment such as the density profile, an electron distribution, and the electron cooling regime. We find several interesting features from this work.