TURBULENT CONVECTION IN THIN ACCRETION DISKS

A self-consistent solution for a thin accretion disk with turbulent co nvection is presented. The turbulent convection plays a double role: i t provides the disk viscosity and takes part in the vertical transport of the released energy. Rather than assuming arbitrary phenomenologic al parameterizations for the disk viscosity, the latter is derived fro m a physical model for turbulence. Employing this model, we express th e turbulent viscosity and the vertically averaged convective flux in t erms of the local physical conditions of the disk which, in turn, are controlled by the former two. The resulting self-consistent disk struc ture, and the ratio between the convective and total fluxes are obtain ed for radiation and gas pressure dominated regions, and for electron scattering and free-free absorption opacities. In the gas pressure reg ion, two distinct solutions are obtained. In one, the convective flux is much larger than the radiative flux and the blackbody region extend s over the entire gas pressure region and could also extend down to th e 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 temp erature gradient is similar to 0.6 and there exist the gas pressure bl ackbody and electron scattering regions as well as an inner radiation pressure region. In the radiation pressure region, the temperature pro file is very close to adiabatic, and the disk is geometrically thin an d optically thick even for super Eddington accretion rates. The fracti on of the convective flux, out of the total flux, increases with the a ccretion rate, and for accretion rates comparable to the Eddington lim it is close to 1. This variation stabilizes the radiation pressure reg ion so that all the disk solutions are secularily stable. The values o f 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 radi ation pressure region and for the two solutions in the gas pressure re gion, respectively.