Zhe Chang, Hai-Nan Lin, Yunguo Jiang
Recent observations by Fermi-LAT showed that there are delayed arrival of GeV photons relative to the onset of MeV photons in some GRBs. In order to avoid a large optical depth, minimum values of Lorentz factor have been estimated to be higher than 1000 in some brightest bursts. In this paper, we present a detailed calculation of the time delay between the MeV and GeV photons in the framework of the magnetic-dominated jet model. We find that the time delay strongly depends on the terminal bulk Lorentz factor of the jet. Inspired by this fact, we use this model to calculate the Lorentz factors of four Fermi bursts. The results show that the Lorentz factors are much lower than that obtained from ``single-zone" scenario. The short GRB 090510 has a minimal Lorentz factor 385, while the three long GRBs have almost the same Lorentz factors, with an average value near 260. Another interesting feature is that, for long GRBs, GeV photons are emitted after the Lorentz factor saturates. For short GRBs, however, MeV and GeV photons are emitted at the same phase, i.e, either at the expansion phase or at the coast phase.
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http://arxiv.org/abs/1205.3572
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