Flux enhancement in the inner region of a geometrically and optically thick accretion disk

The surface flux (and the corresponding observed flux) of a geometrically thick funnel'' shaped disk is computed taking into account the radiation impinging on the surface from other parts of the disk. It is found that the ratio of the maximum apparent luminosity to the real luminosity of the disk is only a factor $\approx 5$ even when the opening angle of the disk is small ($\approx 15^o$). Thus, geometrically beamed emission from funnel’’ shaped sub-Eddington disks around stellar mass black holes, cannot explain the Ultra-Luminous X-ray sources detected in nearby galaxies.