2011ApJ...726...89Z

The Lorentz factor (LF) of gamma-ray burst (GRB) ejecta may be constrained by observations of high-energy (HE) spectral attenuation. The recent Fermi-LAT observations of prompt GeV emission from several bright GRBs have led to conclusions of unexpectedly large LFs, Γ>10³. Here we revisit this problem with two main concerns. (1) With a one-zone assumption where all photons are assumed to be generated in the same region (radius) and time, we self-consistently calculate the γγ optical depth by adopting a target photon spectrum with an HE cutoff. We find that this might be important when the GRB LF is below a few hundreds. (2) Recent Fermi-LAT observations suggest that the bulk MeV-range and HE ( ≳ 100 MeV) emission may arise from different regions. We then consider a two-zone case where HE emission is generated in much larger radii than that of the MeV-range emission. We find that the HE emission may mainly be attenuated by the MeV-range emission and that the attenuated HE spectrum does not show an exponential spectral cutoff but a slight steepening. This suggests that there may be no abrupt cutoff due to γγ attenuation if relaxing the one-zone assumption. By studying the spectra of three bright Fermi-LAT GRBs, 080916C, 090510, and 090902B, we show that bulk LFs of Γ ∼ 600 can be consistent with observations in the two-zone case. Even lower LFs can be obtained in the multi-zone case.