Relativistic winds from compact gamma-ray sources. I. Radiative acceleration in the Klein-Nishina regime

We consider the radiative acceleration to relativistic bulk velocities of a cold, optically thin plasma which is exposed to an external source of γ-rays. The flow is driven by radiative momentum input to the gas, the accelerating force being due to Compton scattering in the relativistic Klein-Nishina limit. The bulk Lorentz factor of the plasma, Γ, derived as a function of distance from the radiating source, is compared with the corresponding result in the Thomson limit. Depending on the geometry and spectrum of the radiation field, we find that particles are accelerated to the asymptotic Lorentz factor at infinity much more rapidly in the relativistic regime and the radiation drag is reduced as blueshifted, aberrated photons experience a decreased relativistic cross section and scatter preferentially in the forward direction. The random energy imparted to the plasma by γ-rays can be converted into bulk motion if the hot particles execute many Larmor orbits before cooling. This "Compton afterburn" may be a supplementary source of momentum if energetic leptons are injected by pair creation but can be neglected in the case of pure Klein-Nishina scattering. Compton drag by side-scattered radiation is shown to be more important in limiting the bulk Lorentz factor than the finite inertia of the accelerating medium. The processes discussed here may be relevant to a variety of astrophysical situations where luminous compact sources of hard X-ray and γ-ray photons are observed, including active galactic nuclei, galactic black hole candidates, and γ-ray bursts.