The Closure Relations in High-Energy Gamma-ray Bursts Detected by Fermi-LAT

Gamma-ray bursts (GRBs) are brief, intense pulses of high-energy emission associated with extreme astrophysical phenomena, e.g. the death of massive stars or the coalescence of compact objects. They have been observed at high energies by the Fermi Large Area Telescope (LAT), which detects GRBs in the 20 MeV–300 GeV energy range. The Fermi-LAT Second GRB Catalog (2FLGC) presents information on 186 GRBs observed from 2008 to 2018. We consider the GRBs that have been fitted in the 2FLGC with a broken (21 GRBs) or simple power law (65 GRBs), compiling a total sample of 86 GRBs. We analyze the relationship between the spectral and temporal indices using closure relations according to the synchrotron forward-shock model evolving in stratified environments ($n\propto r^{-k}$). We find that the model without energy injection is preferred over the one with energy injection. There is a clear preference for the cooling conditions $\nu >$ max{${\nu }_c,{\nu }_m$} and ${\nu }_m<\nu <{\nu }_c$ (where ${\nu }_c$ and ${\nu }_m$ are the cooling and characteristic frequencies, namely the frequency at the spectral break). Within these cooling conditions, density profiles $r^{-k}$ with values of $k=1.5$ and 2 generally have a higher rate of occurrence when considering relations with and without energy injection.