A comparison of one- And two-dimensional models of transonic accretion discs around collapsed objects

Abstract

We construct models of the inner part of a transonic adiabatic accretion disc, assuming constant specific angular momentum and taking the vertical structure fully into account. For comparison purposes, we construct the corresponding onedimensional viscous-disc models derived under vertical-averaging assumptions. The conditions for which a unique location for the critical/sonic point is obtained, given an appropriate set of exterior boundary conditions for these models, are also discussed. The location of this point is not unique if the standard 'α'-prescription with viscous stress proportional to the angular velocity gradient is used. We use a simple model to discuss the possible limitations on the form of the viscous stress that arise from the requirement that viscous information must travel at a finite speed. Contrary to results in the existing literature, the viscous stress tends to be increased rather than reduced for the type of flow we consider, in which the angular momentum and angular velocity gradients have opposite signs. Finite propagation effects may, however, result in a unique location for the sonic point. We find good agreement between the radial flow and specific angular momentum profiles in the inner regions of the one-dimensional models and those in the equatorial plane for corresponding two-dimensional models which may be matched to the former for a range of α between 0.1 and 10-4