Where is a Marginally Stable Last Circular Orbit in Super-Critical Accretion Flow?

Abstract

Impressed by the widespread misunderstanding of the issue, we return to the old question of the location of the inner edge of accretion disk around black hole. We recall the fundamental results obtained in the 1970's and 1980's by Warsaw and Kyoto research groups that proved, in particular, that the inner edge does not coincide with the location of the innermost stable Keplerian circular orbit. We give some novel illustrations of this particular point and of some other fundamental results obtained by Warsaw and Kyoto groups. To investigate the flow dynamics of the inner edge of accretion disk, we carefully solve the structure of the transonic flow and plot the effective potential profile based on the angular-momentum distribution calculated numerically. We show that the flow does not have a potential minimum for accretion rates, {\dot M} > 10 L_E/c^2 (with L_E being the Eddington luminosity and $c$ being the speed of light). This property is realized even in relatively small viscosity parameters (i.e., \alpha ~ 0.01), because of the effect of pressure gradient. In conclusion, the argument based on the last circular orbit of a test particle cannot give a correct inner boundary of the super-critical flow and the inner edge should be determined in connection with radiation efficiency. The same argument can apply to optically thin ADAF. The interpretation of the observed QPO frequencies should be re-considered, since the assumption of Kepler rotation velocity can grossly over- or underestimate the disk rotation velocity, depending on the magnitude of viscosity.