The effect of cooling processes on the tail of a relativistic thermal pair distribution

Abstract

The maintenance of the population in the Maxwellian tail of a relativistic thermal pair plasma by binary collisions is investigated, and the effect of perturbations on the tail of the distribution due to cooling by bremsstrahlung, inverse Compton scattering of soft photons, synchrotron emission, and pair annihilation is considered. A comparison is made between the spectral time-scales for two-body thermalization and cooling at different pair energies, and it is found that the formation of the thermal tail is suppressed under certain conditions that are established, and that correspond to very efficient cooling. The loss of the tail would then lead to the loss of the higher energy component of X-ray and γ-ray emission in thermal models for compact objects such as γ-ray burst sources and active galactic nuclei. This spectral approach to the problem of thermalization complements previous treatments that consider time-scales averaged over all pair energies.