Can we probe the Lorentz factor of gamma-ray bursts from GeV-TeV spectra integrated over internal shocks?

Understand

We revisit the high-energy spectral cutoff originating from the electron-positron pair creation in the prompt phase of gamma-ray bursts (GRBs) with numerical and analytical calculations.

• We show that the conventional exponential and/or broken power law cutoff should be drastically modified to a shallower broken power-law in practical observations that integrate emissions from different internal shocks.
• Since the steepening is tiny for observations, this "smearing" effect can generally reduce the previous estimates of the Lorentz factor of the GRB outflows.
• We apply our formulation to GRB 080916C, recently detected by the Large Area Telescope detector on the Fermi satellite, and find that the minimum Lorentz factor can be ~600 (or even smaller values), which is below but consistent with the previous result of ~900.