Hot accretion discs with thermal Comptonization and advection in luminous black hole sources

We solve for the structure of a hot accretion disc with unsaturated thermal Comptonization of soft photons and with advection, generalizing the classical model of Shapiro et al. The upper limit on the accretion rate due to advection constrains the luminosity to less than or equal to 0.15y(3/5)alpha(7/5) Of th, Eddington Limit, where y and alpha are the Compton and viscosity parameters, respectively. The characteristic electron temperature and Thomson optical depth of the inner how at accretion rates within an order of magnitude of that upper limit are similar to 10(9) K and similar to 1, respectively. The resulting spectra are then in close agreement with the X-ray and soft gamma-ray spectra from black hole binaries in the hard state and Seyferts. At low accretion rates, bremsstrahlung becomes the dominant radiative process.