The problem of stationary, spherical accretion onto a Schwarzschild hole is here reinvestigated by the construction of a self-consistent model which incorporates all relevant physical processes taking place in an astrophysical plasma, apart from the presence of magnetic fields and dissipative processes. In particular, transfer of radiation through the accreting gas is treated in full generality using a completely relativistic formalism. A careful analysis of critical points and boundary conditions for radiation hydrodynamics equations is performed. The complete topology of solutions in the accretion rate-luminosity plane is obtained, showing the existence of two distinct branches of models with very different emission properties: stationary accretion reveals, therefore, a bimodal behavior. By means of a self-consistent study of the effects of Compton heating, both the upper and the lower bounds for the existence of high-luminosity solutions were derived. The stability of the two possible accretion regimes is also briefly discussed.
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Nobili et al. (1991) studied this question.