Efficiency and Spectrum of Internal Gamma‐Ray Burst Shocks

We present an analysis of the Internal Shock Model of GRBs, where gamma-raysare produced by internal shocks within a relativistic wind. We show thatobserved GRB characteristics impose stringent constraints on wind and sourceparameters. We find that a significant fraction, of order 20 %, of the windkinetic energy can be converted to radiation, provided the distribution ofLorentz factors within the wind has a large variance and provided the minimumLorentz factor is higher than 10^(2.5)L_(52)^(2/9), where L=10^(52)L_(52)erg/sis the wind luminosity. For a high, >10 %, efficiency wind, spectral energybreaks in the 0.1 to 1 MeV range are obtained for sources with dynamical timeR/c < 1 ms, suggesting a possible explanation for the observed clustering ofspectral break energies in this range. The lower limit to wind Lorenz factorand the upper limit, around (R/10^7 cm)^(-5/6) MeV to observed break energiesare set by Thomson optical depth due to electron positron pairs produced bysynchrotron photons. Natural consequences of the model are absence of burstswith peak emission energy significantly exceeding 1 MeV, and existence of lowluminosity bursts with low, 1 keV to 10 keV, break energies.Comment: 10 pages, 5 ps-figures. Expanded discussion of magnetic field and electron energy fraction. Accepted for publication in Astrophysical Journa