Thermal Comptonization in Mildly Relativistic Pair Plasmas
  We use a Monte Carlo simulation to calculate the spectra of mildly relativistic thermal plasmas in pair balance. We use the exact integral expression for the electron-positron thermal annihilation spectrum, and provide accurate expressions for the Gaunt factors of electron-ion, electron-electron, and electron-positron thermal bremsstrahlung in the transrelativistic temperature regime. The particles are assumed to be uniformly distributed throughout a sphere, and the pair opacity is self-consistently calculated from the energy and angular distribution of scattered photons. The resultant photon spectra are compared with the nonrelativistic diffusion treatment of Sunyaev and Titarchuk, the bridging formulas of Zdziarski, and the relativistic corrections proposed by Titarchuk. We calculate allowed pair-balanced states of thermal plasmas with no pair escape which include bremsstrahlung and internal soft photons. The results are presented in the spectral index/compactness plane, and can be directly compared with observations of spectra from AGNs and Galactic black hole candidates. By comparing with X-ray spectral indices of Seyfert AGNs and compactnesses inferred from X-ray variability data, we find that the allowed solutions for pair equilibrium plasma imply that the temperatures of Seyfert galaxies are $\lesssim 300$ keV. This prediction can be tested with more sensitive gamma-ray observations of Seyfert galaxies. We find that if the X-ray variability time scale gives an accurate measure of the compactness, pair-dominated solutions are inconsistent with the data. 
J. G. Skibo, C. D. Dermer, R. Ramaty and J. M. McKinley