Can We Probe the Lorentz Factor of Gamma-ray Bursts from Gev-tev Spectra Integrated over Internal Shocks?

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 cutoff should be drastically modified to a steepened 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 LAT 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. Observing the steepening energy (so-called ”pair-break energy”) is crucial to diagnose the Lorentz factor and/or the emission site in the future observations. Subject headings: gamma rays: bursts — gamma rays: theory — plasmas