The early high-energy afterglow emission from Short GRBs

We calculate the high energy afterglow emission from short Gamma-Ray Bursts (SGRBs) in the external shock model. There are two possible components contributing to the high energy afterglow: the electron synchrotron emission and the synchrotron self-Compton (SSC) emission. We find that for typical parameter values of SGRBs, the early high-energy afterglow emission in 10 MeV-10 GeV is dominated by the synchrotron emission. For a burst occurring at redshift z =0.1, the high-energy emission can be detectable by Fermi LAT if the blast wave has an energy E>=10^51 ergs and the fraction of energy in electrons is \epsilon_e>=0.1 . This provides a possible explanation for the high energy tail of SGRB 081024B.