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_± ≈ 10^2.5L^2/9₅₂, 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.