Structure of thermal pair clouds around gamma-ray-emitting black holes
Using certain simplifying assumptions, the general structure of a quasi-spherical thermal pair-balanced cloud surrounding an accreting black hole is derived from first principles. Pair-dominated hot solutions exist only for a restricted range of the viscosity parameter. These results are applied as examples to the 1979 HEAO 3 gamma-ray data of Cygnus X-1 and the Galactic center. Values are obtained for the viscosity parameter lying in the range of about 0.1-0.01. Since the lack of synchrotron soft photons requires the magnetic field to be typically less than 1 percent of the equipartition value, a magnetic field cannot be the main contributor to the viscous stress of the inner accretion flow, at least during the high gamma-ray states.