Does the circularization radius exist or not for low-angular-momentum accretion?

If the specific angular momentum of accretion gas at large radius is small compared to the local Keplerian value, one usually believes that there exists a 'circularization radius' beyond which the angular momentum of accretion flow is almost a constant while within which a disc is formed and the angular momentum roughly follows the Keplerian distribution. In this paper, we perform numerical simulations to study whether the picture above is correct in the context of hot accretion flow. We find that for a steady accretion flow, the 'circularization radius' does not exist and the angular momentum profile will be smooth throughout the flow. However, for transient accretion systems, such as the tidal disruption of a star by a black hole, a 'turning point' should exist in the radial profile of the angular momentum, which is conceptually similar to the 'circularization radius'. At this radius, the viscous time-scale equals the lifetime of the accretion event. The specific angular momentum is close to Keplerian within this radius, while beyond this radius the angular momentum is roughly constant.