6 v 1 2 0 Ju n 20 00 1 THREE - DIMENSIONAL STRUCTURE OF AN ALPHA ACCRETION DISK

An analytic solution is presented to the three-dimensional problem of steady axisymmetric fluid flow through an accretion disk. The solution has been obtained through a systematic expansion in the small parameter ǫ = ¯ H/ ¯ R (the ratio of disk thickness to its radial dimension) of the equations of viscous hydrodynamics. The equation of state was assumed to be polytropic. For all values α < 0.685 of the viscosity parameter, we find significant backflow in the midplane of the disk occuring at all radii larger than a certain value; however, in the inner regions of the disk the fluid always flows toward the accreting object. The region of backflow is separated from the region of inflow by a surface flaring outwards from a circular locus of stagnation points situated in the midplane of the disk.