Relativistic winds from compact gamma-ray sources. II. Pair loading and radiative acceleration in gamma-ray bursts

We consider the effects of rapid pair creation by an intense pulse of γ-rays propagating ahead of a relativistic shock. Sidescattered photons colliding with the main γ-ray beam amplify the density of scattering charges. The acceleration rate of the pair-loaded medium is calculated and its limiting bulk Lorentz factor related to the spectrum and compactness of the photon source. One obtains, as a result, a definite prediction for the relative inertia in baryons and pairs. The deceleration of a relativistic shock in the moving medium and the resulting synchrotron emissivity are compared with existing results for a static medium. The radiative efficiency is increased dramatically by pair loading. When the initial ambient density exceeds a critical value, the scattering depth traversed by the main γ-ray pulse rises above unity and the pulse is broadened. This sets an upper limit to the preburst mass-loss rate of ∼10-5 M⊙ per year and places significant constraints on γ-ray burst progenitors. An anisotropic γ-ray flux (on an angular scale Γ-1 or larger) drives a large velocity shear that greatly increases the energy in the seed magnetic field forward of the propagating shock.