Efficiency and Spectrum of Internal Gamma‐Ray Burst Shocks

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Abstract
We present an analysis of the internal shock model of gamma-ray bursts (GRBs), where gamma-rays are produced by internal shocks within a relativistic wind. We show that observed GRB characteristics impose stringent constraints on wind and source parameters. We find that a significant fraction of the wind kinetic energy, on the order of 20%, can be converted to radiation, provided the distribution of Lorentz factors within the wind has a large variance and the minimum Lorentz factor is greater than Γ± ≈ 102.5L, where L = 1052L52 ergs s-1 is the wind luminosity. For a high-efficiency (>10%) wind, spectral energy breaks in the 0.1-1 MeV range are obtained for sources with dynamical time R/c 1 ms, suggesting a possible explanation for the observed clustering of spectral break energies in this range. The lower limit Γ± of wind Lorentz factor and the upper limit ≈1(R/107 cm)-5/6 MeV of observed break energies are set by Thomson optical depth because of e± pairs produced by synchrotron photons. Natural consequences of the model are the absence of bursts with peak emission energy significantly exceeding 1 MeV and the existence of low-luminosity bursts with low (1-10 keV) break energies.