Prospects for GeV-TeV detection of short gamma-ray bursts with extended emission

We discuss the GeV to TeV photon emission of gamma-ray bursts (GRBs) within the refreshed shock and the continuous injection scenarios, motivated by the observation of extended emission in a substantial fraction of short GRBs. In the first model we assume that the central engine emits promptly material with a range of Lorentz factors. When the fastest shell starts to decelerate, it drives a forward shock into the ambient medium and a reverse shock in the ejecta. These shocks are reenergized by the slower and later arriving material. In the second model we assume that there is a continued ejection of material over an extended time, and the continuously arriving new material keeps reenergizing the shocks formed by the preceding shells of ejecta. We calculate the synchrotron and synchrotron self-Compton radiation components for the forward and reverse shocks and find that prospective and current GeV to TeV range instruments such as CTA, HAWC, VERITAS, MAGIC and HESS have a good chance to detect afterglows of short bursts with extended emission, assuming a reasonable response time.