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The Fermi Large Area Telescope (Fermi-LAT) Collaboration reported the SecondGamma-ray Burst Catalog (2FLGC), which comprises a subset of 29 bursts withphoton energies above 10 GeV. Although the standard synchrotron forward-shockmodel has successfully explained the Gamma-ray burst (GRB) afterglowobservations, energetic photons higher than 10 GeV from these transient eventscan hardly be described in this scenario. We present the closure relations(CRs) of synchrotron self-Compton (SSC) afterglow model in the adiabatic andradiative scenario and when the central engine injects continuous energy intothe blastwave to study the evolution of the spectral and temporal indexes ofthose bursts reported in 2FLGC. We consider the SSC afterglow model evolving instellar-wind and interstellar medium, and the CRs as a function of theradiative parameter, the energy injection index, and the electron spectralindex for $1<p<2$ and $ 2\leq p$. We select all GRBs that have been modeledwith both a simple or a broken power law in the 2FLGC. We found that the CRs ofthe SSC model can satisfy a significant fraction of burst that cannot beinterpreted in the synchrotron scenario, even though those that require anintermediate density profile (e.g., GRB 130427A) or an atypical fraction oftotal energy given to amplify the magnetic field ($\varepsilon_B$). The valueof this parameter in the SSC model ranges ($\varepsilon_B\approx 10^{-5} -10^{-4}$) when the cooling spectral break corresponds to the Fermi-LAT band fortypical values of GRB afterglow. The analysis shows that ISM is preferred forthe scenario without energy injection and the stellar wind medium for an energyinjection scenario.

Synchrotron Self-Compton Afterglow Closure Relations and Fermi-LAT Detected Gamma-Ray Bursts