Asymptotic models of meridional flows in thin viscous accretion disks

Abstract

We present the results of numerical integrations yielding the structure of and meridional flow in axisymmetric thin viscous accretion disk models. The solutions are obtained by simplifying and approximating first the equations, using systematic asymptotic expansions in the small parameter $ε$, measuring the relative disk thickness. The vertical structure is solved including radiative transfer in the diffusion approximation. Carrying out the expansion to second order in $ε$ we obtain, for low enough values of the viscosity parameter $α$, solutions containing {\em backflows}. These solutions are similar to the results first found by Urpin (1984), who used approximations that are only valid for large radii and the asymptotic analytical solutions of Kluźniak & Kita (1997), valid only for polytropic disks. Our results may be important for several outstanding issues in accretion disk theory.