TURBULENT CONVECTION IN THIN ACCRETION DISKS

A self-consistent solution for a thin accretion disk with turbulent convection is presented. The turbulent convection plays a double role: it provides the disk viscosity and takes part in the vertical transport of the released energy. Rather than assuming arbitrary phenomenological parameterizations for the disk viscosity, the latter is derived from a physical model for turbulence. Employing this model, we express the turbulent viscosity and the vertically averaged convective flux in terms of the local physical conditions of the disk which, in turn, are controlled by the former two. The resulting self-consistent disk structure, and the ratio between the convective and total fluxes are obtained for radiation and gas pressure dominated regions, and for electron scattering and free-free absorption opacities. In the gas pressure region, two distinct solutions are obtained. In one, the convective flux is much larger than the radiative flux and the blackbody region extends over the entire gas pressure region and could also extend down to the inner boundary of the disk. In this solution the temperature profile is close to adiabatic. In the other solution, the convective flux is about a third of the total flux, the dimensionless superadiabatic temperature gradient is similar to 0.6 and there exist the gas pressure blackbody and electron scattering regions as well as an inner radiation pressure region. In the radiation pressure region, the temperature profile is very close to adiabatic, and the disk is geometrically thin and optically thick even for super Eddington accretion rates. The fraction of the convective flux, out of the total flux, increases with the accretion rate, and for accretion rates comparable to the Eddington limit is close to 1. This variation stabilizes the radiation pressure region so that all the disk solutions are secularily stable. The values of the effective or-parameter are rather small: less than or similar to 5 x 10(-4), similar to 1 x 10(-3), and similar to 5 x 10(-3) for radiation pressure region and for the two solutions in the gas pressure region, respectively.