Luminosity limit for alpha-viscosity accretion disks

The existence of a luminosity limit for alpha-viscosity physically thin accretion disks around black holes is established, using a new formulation of the radiation equation bridging optically thick and thin regimes. For alpha close to unity, this limit can be lower than the Eddington limit. Physically, this limit is due to the combined effects of gas and radiation pressure which become too large to satisfy vertical hydrostatic balance at intermediate optical depths for sufficiently high luminosities. This effect was overlooked in previous treatments using only the optically thin or thick limits of the radiative equation.