Klein-Nishina effects on the high-energy gamma-ray emission of gamma-ray bursts

Prompt and long-lived high-energy (> 100 MeV) gamma-ray emission has been detected by Fermi Large Area Telescope (LAT) recently from more than ten gamma-ray bursts. It has been suggested that such emission is produced by synchrotron radiation of electrons accelerated in internal and external shocks. Here we show that, during both the prompt and early afterglow phase, inverse-Compton (IC) scattering of these electrons with synchrotron photons are typically in the Klein-Nishina (KN) regime. For the prompt emission, the KN effect may strongly suppress the IC component, which is consistent with one single spectral component seen in some strong bursts, such as in GRB080916C and GRB090217. The KN inverse-Compton cooling may also affect the low-energy electron number distribution and hence results in a low-energy synchrotron photon spectrum harder than the standard fast-cooling spectrum n(V) proportional to V-3/2. During the early afterglow, KN effect leads to a low Compton-Y parameter, which is generally less than a few in the first tens of seconds for a wide range of parameter space. Furthermore, we suggest that the KN effect can explain the somewhat faster than expected decay of the early-time high-energy emission observed in some GRBs.