Off-axis Afterglow Closure Relations and Fermi-LAT Detected Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are one of the most promising transient events for studying multi-wavelength observations in extreme conditions. Observation of GeV photons from bursts would provide crucial information on GRB physics, including the off-axis emission. The Second Gamma-ray Burst Catalog (2FLGC) was announced by the Fermi Large Area Telescope (Fermi-LAT) Collaboration. This catalog includes 29 bursts with photon energy higher than 10 GeV. While the synchrotron forward-shock model has well explained the afterglow data of GRBs, photon energies greater than 10 GeV are very difficult to interpret within this framework. To study the spectral and temporal indices of those bursts described in 2FLGC, Fraija et al. (2022a) proposed the closure relations (CRs) of the synchrotron self-Compton (SSC) emitted from an on-axis jet which decelerates in stellar-wind and the constant-density medium. In this paper, we extend the CRs of the SSC afterglow from an on-axis scenario to an off-axis, including the synchrotron afterglow radiation that seems off-axis. In order to investigate the spectral and temporal index evolution of those bursts reported in 2FLGC, we consider the hydrodynamical evolution with energy injection in the adiabatic and radiative regime for an electron distribution with a spectral index of $1<p<2$ and $2 < p$. The results show that the most likely scenario for synchrotron emission corresponds to the stellar wind whether or not there is energy injection and that the most likely scenario for SSC emission corresponds to the constant density when there is no energy injection and to the stellar wind when there is energy injection.