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 Gamma (+/-) approximate to 10(2.5) L-52(2/9), 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 less than or similar to 1 ms, suggesting a possible explanation for the observed clustering of spectral break energies in this range. The lower limit Gamma (+/-) of wind Lorentz factor and the upper limit approximate to1(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 I MeV and the existence of low-luminosity bursts with low (1-10 keV) break energies.