On Thermal Comptonization in e+- Pair Plasmas
  We study $e^{\pm}$ pair plasmas in pair equilibrium, which emit high energy radiation by thermal Comptonization of soft photons. We find that the maximum luminosity to size ratio of the source (i.e. the compactness) depends not only on the hot plasma temperature, but also on the spectral index of the resulting Comptonized spectrum. In the observationally interesting range, sources of same compactness can be hotter if their spectrum is steeper. Instruments observing in the 50--500 keV energy range, such as OSSE on board CGRO, and especially the future SAX satellite, can be more successful in detecting sources moderately steep, the flattest sources being characterized by an high energy cut--off at too low frequencies. For any given pair of values of spectral index and temperature, Comptonization theory alone fixes the $ratio$ of the compactnesses in hard and soft photons. However, if the source is pair dominated, the absolute values of the two compactnesses are fixed. Therefore there is a a one--to--one correspondence between the physical parameters of the source (the compactnesses in soft and hard photons) and the observable quantities (spectral index and temperature). This correspondence can be extremely useful in interpreting the physical behaviour of the sources, especially during variations, and can help discriminating between different models for the high energy emission of compact sources. 
Gabriele Ghisellini and Francesco Haardt