The authors determine the steady state particle and photon distributions under the assumption of continuous injection of relativistic electrons and low-energy photons throughout a spherical volume. Through inverse Compton scattering, the primary electrons produce γ-rays, which then produce electron-positron pairs. The pairs constitute a secondary electron injection, and the process continues, with each generation of pairs cooling down to subrelativistic energies before thermalizing and annihilating. The authors compute detailed emergent spectra for a wide range of parameters, and compare the results to the data from active galactic nuclei.
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Lightman et al. (1987) studied this question.