ar X iv : a st ro - p h / 98 03 14 1 v 1 1 2 M ar 1 99 8 Advection - Dominated Accretion around Black Holes †

Accretion processes around black holes almost inevitably involve rotating gas flows. Consequently, there is great interest in self–consistent solutions of the hydrodynamic equations of viscous differentially–rotating flows. Four solutions are currently known (see Chen et al. 1995 for a discussion). In these solutions viscosity transports angular momentum outward, allowing the accreting gas to spiral in toward the central mass. Viscosity also acts as a source of heat; some or all of this heat is radiated, leading to the observed spectrum. The most famous of the four solutions is the thin disk model developed by Shakura & Sunyaev (1973), Novikov & Thorne (1973), Lynden–Bell & Pringle (1974) and others (see Pringle 1981 and Frank et al. 1992 for reviews). The accreting gas forms a geometrically thin, optically thick disk, and produces a quasi–blackbody spectrum. The effective temperature of the radiation is in the range 10 − 10 K, depending on the black hole mass and the accretion rate (Teff ∝ M Ṁ). The thin disk solution has been used to model a large number of astrophysical systems. Shapiro, Lightman and Eardley (1976; hereafter SLE; see also Björnsson & Svensson 1991 and Luo & Liang 1994) discovered a second, much hotter self–consistent solution in which the accreting gas forms a two temperature plasma with the ion temperature greater than the electron temperature (Ti ∼ 10 K, Te ∼ 10 −10K). The gas is optically thin and produces a power–law spectrum at X–ray and soft γ–ray energies. The SLE solution is, however, thermally unstable (Piran 1978), and is therefore not considered viable for real flows. At super–Eddington accretion rates, a third solution is present (Katz 1977; Begelman 1978; Abramowicz et al. 1988; see also Begelman & Meier 1982; Eggum, Coroniti, & Katz 1988), in which the large optical depth of the inflowing gas traps most of the radiation and carries it inward, or “advects” it, into the central black hole. This solution is referred to as an optically thick advection–dominated accretion flow (optically thick ADAF). A full analysis of the dynamics of the solution was presented in an important paper by Abramowicz et al. (1988). A fourth solution is present in the opposite limit of low, sub–Eddington, accretion rates (Ichimaru 1977; Rees et al. 1982; Narayan & Yi 1994, 1995a, 1995b; Abramowicz