Two-dimensional viscous accretion disk models. I - On meridional circulations in radiative regions

It has been suggested that thin Keplerian disks, like rotating stars, cannot attain hydrostatic and thermal equilibrium simultaneously if the angular velocity is a function of radius only. To address the problem of vertical structure and stability of thin accretion disks, we performed 2D axisymmetric calculations by solving the set of fully nonlinear hydrodynamic equations, including radiation transport. The results indicate that the variation of the rotational velocity with height is too small to sustain hydrostatic equilibrium. Instead, the variation of the radial (inflow) velocity with height suffices to establish a stationary state. In particular, we find that for low values of the viscosity parameter alpha, there is mass outflow in the central parts of the disk close to the equatorial plane, and inflow only near the surface. Only for modestly high values of alpha, the flow throughout the disk is directed inward. Thus, the flow within the disk is the result of viscous radial inflow plus a circulatory flow directed outward in the midplane and inward near the surface.