Thick accretion disks: Self-similar, supercritical models

We generate self-similar models for geometrically thick, supercritical accretion disks, and study their structure and stability. By assumption, our models are characterized by near-equilibrium between gravity, centrifugal force, and radiation pressure. Slow nonazimuthal currents are driven by the viscous transport of angular momentum, which also dissipates binding energy. In contrast with thin disks, which are able to cool efficiently, the energy dissipated in a thick disk is partially trapped, resulting in large pressure gradients, sub-Keplerian angular velocities, and a shear stress which is no longer unidirectional. The assumption that hydrodynamic quantities scale as power laws in radius enables us to compute the disk structure as a function of angle from the rotation axis, given a model for the viscosity law. The structure of the interior of the disk is sensitive to the viscosity law, as well as to the degree of pressure support on the equator. Virtually all models possess a ''surface'' at which the pressure drops sharply to zero. The behavior of other hydrodynamic quantities near the surface depend on the viscosity law, but not on the degree of pressure support on the equator. All models appear to be unstable to local axisymmetric perturbations at sufficiently high latitudes. Adiabatic and inviscid interchanges of fluid elements lead to convection which brings the disk to marginal stability in a dynamical time. Short-wavelength instabilities, driven in part by viscosity, tend to make the disk barytropic, but are too slow to reorganize the disk structure on a viscous time scale. Future models of thick accretion disks should take into account their convective nature, as well as the dependence of their structure on the viscosity law