Comptonization modifications to the gamma-ray spectrum of active galactic nuclei

Pair cascade models predict the appearance of 512 keV pair annihilation lines above the gamma-ray continuum. The moderate optical depths associated with pair cascades suggests Comptonization of the line will contribute to the hard X-ray continuum. Here numerical calculations of the Comptonization of the line and analytic approximations to this are presented for mildly relativistic plasmas. Earlier calculations in the Thomson limit are inappropriate and here the time-independent solution of the photon kinetic equation yields a ghost line at about 170 keV due to Compton backscattering. This feature has been predicted for the Galactic Centre. A cold plasma assumption is employed in order to develop the analytic technique for approximating the spectrum.