Thermal Equilibrium Curves and Turbulent Mixing in Keplerian Accretion Disks

Abstract

We consider vertical heat transport in Keplerian accretion disks, including the effects of radiation, convection, and turbulent mixing driven by the Balbus-Hawley instability, in astronomical systems ranging from dwarf novae (DNe) and soft X-ray transients (SXTs) to active galactic nuclei (AGNs). In order to account for the interplay between convective and turbulent energy transport in a shearing environment, we propose a modified, anisotropic form of mixing-length theory that includes radiative and turbulent damping. We also include turbulent heat transport, which acts everywhere within disks, regardless of whether or not they are stably stratified and can move entropy in either direction. We have generated a series of vertical structure models and thermal equilibrium curves using the scaling law for the viscosity parameter α suggested by the exponential decay of the X-ray luminosity in SXTs. We have also included equilibrium curves for DNe using an α that is constant down to a small magnetic Reynolds number (~104). Our models indicate that weak convection is usually eliminated by turbulent radial mixing, even when mixing length estimates of convective vertical heat transport are much larger than turbulent heat transport. The substitution of turbulent heat transport for convection is more important on the unstable branches of thermal equilibrium S curves when α is larger. The low temperature turnover points Σmax on the equilibrium S curves are significantly reduced by turbulent mixing in DN and SXT disks. However, in AGN disks the standard mixing-length theory for convection is still a useful approximation when we use the scaling law for α since these disks are very thin at the relevant radii. In accordance with previous work, we find that constant α models give almost vertical S curves in the Σ-T plane and consequently imply very slow, possibly oscillating, cooling waves.