2011ApJ...733..112J

To study the outflows from accretion disks, we solve the set of hydrodynamic equations for accretion disks in spherical coordinates (rθφ) to obtain the explicit structure along the θ-direction. Using self-similar assumptions in the radial direction, we change the equations to a set of ordinary differential equations about the θ-coordinate, which are then solved with symmetrical boundary conditions in the equatorial plane; the velocity field is then obtained. The α viscosity prescription is applied and an advective factor f is used to simplify the energy equation. The results display thinner, quasi-Keplerian disks for Shakura-Sunyaev disks; thicker, sub-Keplerian disks for advection-dominated accretion flows; and slim disks which are consistent with previous popular analytical models. However, an inflow region and an outflow region always exist, except when the viscosity parameter α is too large, which supports the results of some recent numerical simulation works. Our results indicate that the outflows should be common in various accretion disks and may be stronger in slim disks, where both advection and radiation pressure are dominant. We also present the structure's dependence on the input parameters and discuss their physical meanings. The caveats of this work and possible improvements for the future are discussed.