Multi-dimensional Treatment of Photon Emission from Accretion Disks around Black Holes

Abstract

We consider photon emission from a supercritical accretion disk in which photons in the inner regions are trapped and advected in towards the center. Such disks are believed to be present in failed supernovae and gamma-ray bursts, and possibly also in ultra-luminous X-ray sources. We show that the luminosity from a supercritical accretion disk is proportional to the logarithm of the mass accretion rate when the vertical profile of the matter density is exponential. We obtain analytical results also for other density profiles, but the dependence of the luminosity on the accretion rate is no longer logarithmic.