A REVISED LIMIT OF THE LORENTZ FACTORS OF GAMMA-RAY BURSTs WITH TWO EMITTING REGIONS

摘要

Fermi observations of GeV emission from gamma-ray bursts (GRBs) have suggested that the Lorentz factor of some GRBs is around a thousand or even higher. At the same time, the same Fermi observations have shown an extended GeV emission indicating that this higher energy emission might be a part of the afterglow and it does not come from the same region as the lower energy prompt emission. If this interpretation is correct then we may have to reconsider the opacity limits on the Lorentz factor which are based on a one-zone model. We describe here a two-zone model in which the GeV photons are emitted in a larger radius than the MeV photons and we calculate the optical depth for pair creation of a GeV photon passing the lower energy photons shell. We find that, as expected, the new two-zone limits on the Lorentz factor are significantly lower. When applied to Fermi bursts the corresponding limits are lower by a factor of five compared to the one-zone model. It is possible that both the MeV and GeV regions have relatively modest Lorentz factors (-200-400). This two-zone limit is significantly softer than the one-zone limit.