Thermal Equilibrium Curves and Turbulent Mixing in Keplerian Accretion Disks

We consider vertical heat transport in Keplerian accretion disks, includingthe effects of radiation, convection, and turbulent mixing driven by theBalbus-Hawley instability, in astronomical systems ranging from dwarf novae(DNe), and soft X-ray transients (SXTs), to active galactic nuclei (AGN). Wepropose a modified, anisotropic form of mixing-length theory, which includesradiative and turbulent damping. We also include turbulent heat transport,which acts everywhere within disks, regardless of whether or not they arestably stratified, and can move entropy in either direction. We have generateda series of vertical structure models and thermal equilibrium curves using thescaling law for the viscosity parameter $\alpha$ suggested by the exponentialdecay of the X-ray luminosity in SXTs. We have also included equilibrium curvesfor DNe using an $\alpha$ which is constant down to a small magnetic Reynoldsnumber ($\sim 10^4$). Our models indicate that weak convection is usuallyeliminated by turbulent radial mixing. The substitution of turbulent heattransport for convection is more important on the unstable branches of thermalequilibrium S-curves when $\alpha$ is larger. The low temperature turnoverpoints $\Sigma_{max}$ on the equilibrium S-curves are significantly reduced byturbulent mixing in DNe and SXT disks. However, in AGN disks the standardmixing-length theory for convection is still a useful approximation when we usethe scaling law for $\alpha$, since these disks are very thin at the relevantradii. In accordance with previous work, we find that constant $\alpha$ modelsgive almost vertical S-curves in the $\Sigma-T$ plane and consequently implyvery slow, possibly oscillating, cooling waves.Comment: 43 pages, 12 figures, 6 tables, to be published in Ap