Accretion disk boundary layers.

Abstract

We examine the nature of the boundary layer in α-viscous accretion disks. The boundary layer is the interface between the disk and the accreting central star or black hole. We develop two models for the boundary layer by expanding and generalizing the standard disk equations, and then solving our new set of equations numerically using a relaxation method. First, we use a model which includes a polytropic equation of state to examine the disk dynamics. This allows us to ignore the energetics and radiative transfer and simplifies the problem considerably. We find two types of boundary layer solutions with this model, depending on the rotation rate of the accreting star. One of these is a new type of solutions in which the angular momentum accretion rate can be small or negative. These solutions allow accretion to continue even after the star spins up to breakup speed. We apply a causally-limited viscosity prescription to our solutions, and find that it prevents the radial velocities from becoming supersonic in the boundary layer, thus preserving causality. We apply the same prescription to a model for disks around black holes, and find that it allows us to calculate solutions for reasonable values of α, where none existed before. We develop a more complete model, which includes the energetics and radiative transfer of the boundary layer, for comparison with observations. We apply this model to cataclysmic variables, and find that the nature of the boundary layer in these systems depends strongly on the optical depth, which in turn depends largely on the mass accretion rate and the rotation rate of the accreting star. The dependence of our results on the accretion rate agrees well with X-ray observations of these systems. We also apply the model to accretion disks in pre-main sequence stars, such as T Tauri and FU Orionis stars, and find that the temperatures and radial widths of the boundary layer in our solutions agree well with those inferred from observations.