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

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