Critical luminosity of Super-Dddington accretion disks

Abstract

Slim disk is a kind of optically thick, advection dominated accretion flow, in which the disk height can be comparable with the disk radius. The Slim disk has been widely used to explain the observation phenomena of various Super Eddington accretion disks. Outflows are always present in the numerical simulations of Super Eddington accretion disks, which implies that only a small fraction of gas in the disk is finally swallowed by the black hole. In the study of the Slim disk, we adopt an explicit vertical gravitational force in the thermal equilibrium solutions. The results of our calculation show that there is a maximum for the gravitational force of a black hole in the vertical direction of the accretion disk, and there exists a maximally possible accretion rate for each radius in the outer region of the slim disk. The existence of a maximally possible accretion rate in the case of Super-Eddington accretion implies that only the inner region of these flows can possibly take the form of Slim disk, and strong outflows from the outer region are required to reduce the accretion rate in order for Slim disks to be realized. This result is in agreement with the numerical simulation result. Finally, we fit the curve of the disk luminosity L disk/ L Edd with the dimensionless accretion rate m ˙ , and derive an analytic relation between the total luminosity and the mass accretion rate.