Efficiency and Spectrum of Internal Gamma‐Ray Burst Shocks

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 ± ≈ 10 2.5 L , where L = 10 52 L 52 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 /10 7 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.