Self-similar solution of optically thick advection-dominated flows

The photons released by the viscosity process in a disk with accretion rate exceeding the Eddington critical value will be trapped and restored as entropy in the accreting gas rather than being radiated from the disk surface, since the advection cooling dominates the diffusion cooling in such a flow. In this paper a self-similar solution of optically thick advection-dominated flow has been obtained. This kind of flow shows some interesting characteristics that differ from both the optically thin advection-dominated disk and the standard disk. Such a how is thermally stable. The Bernoulli number is not positive in a wide range of parameters unless the viscosity alpha is extremely small. The shape always stays slim and is independent of the accretion rate (H/r approximate to 1/root 5). The gas rotates with sub-Keplerian angular velocity Omega approximate to Omega(K)/root 5 (for smaller viscosity). The luminosity of the disk weakly depends on the accretion rate, and the maximum luminosity is about 4.0 x 10(37) (ergs s(-1)) (M/M.) (less than the Eddington luminosity), although the accretion rate is super-Eddington. This provides a method for estimating the mass of a black hole. The validity of this solution has been tested and found to be suitable in most of the accretion disk (within the photon trapping radius). Its potential applications to the saturated accreting systems are pointed out.