Luminosity limits for funnels in thick accretion discs

A narrow, highly luminous funnel in a thick accretion disc is a common feature of many models for active galactic nuclei. The constraints on the luminosity imposed by the effects of radiation forces on the funnel are examined. The treatment allows properly for the irradiation of any part of the funnel by the rest, an important effect for this problem. It is found that the maximum luminosity of a funnel of small semi-angle phi is reduced below the Eddington limit Lsub(E) by a factor phi2 if the funnel is to be in strict equilibrium. Even with allowance for flow induced viscous stresses, the luminosity cannot exceed of the order of Lsub(E)phi. In contrast, current models have luminosities of the order of Lsub(E)/phi. It is shown that the resulting large unbalanced forces at the funnel surface cause a significant outflow of matter which should be incorporated in the model for consistency. These results do not depend on the detailed angular momentum distribution over the disc surface but only on the funnel geometry. (author)