Thermal Equilibrium Curves and Turbulent Mixing in Keplerian Accretion Disks
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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 (AGN). We
propose a modified, anisotropic form of mixing-length theory, which 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 $\alpha$ suggested by the exponential
decay of the X-ray luminosity in SXTs. We have also included equilibrium curves
for DNe using an $\alpha$ which is constant down to a small magnetic Reynolds
number ($\sim 10^4$). Our models indicate that weak convection is usually
eliminated by turbulent radial mixing. The substitution of turbulent heat
transport for convection is more important on the unstable branches of thermal
equilibrium S-curves when $\alpha$ is larger. The low temperature turnover
points $\Sigma_{max}$ on the equilibrium S-curves are significantly reduced by
turbulent mixing in DNe 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 $\alpha$, since these disks are very thin at the relevant
radii. In accordance with previous work, we find that constant $\alpha$ models
give almost vertical S-curves in the $\Sigma-T$ plane and consequently imply
very slow, possibly oscillating, cooling waves.
