A hint to the origin of the extended emission in LAT GRBs: the relation between LAT luminosity and prompt energetics

Abstract

We consider the 0.1-10 GeV rest frame light curves of 10 GRBs detected by LAT and with known redshift. In all cases the emission persists after the prompt has faded away. This extended emission decays in time as a power-law. The decay slope is similar among different bursts, while the normalization spans more than 2 decades. However, when the LAT luminosity is normalized to the 1 keV-10 MeV energetics of the prompt emission E_iso all light curves become consistent with having the same normalization, i.e. they cluster. At each given time the ratio between the LAT luminosity and the prompt energetics is narrowly distributed. We argue that this result is expected in the external shock scenario and it strengthens the interpretation of the GeV emission in terms of radiation from external shocks. In this context, we derive limits on the distribution of epsilon_e (the fraction of the shock energy that goes into electrons) and eta (the efficiency of the mechanism producing the prompt).