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 (AGN). 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, 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 α suggested by the exponential decay of the X-ray luminosity in SXTs. We have also included equilibrium curves for DNe using an α which is constant down to a small magnetic Reynolds number (∼ 10 4 ). 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 Σ 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 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.

Hydrogen-poor Disks in Compact X-Ray Binaries

“…We note, however, that Gu, Vishniac, & Cannizzo (2000) have argued for weak convection in thin accretion disks because of the action of shearing and turbulent radial mixing. T Շ 10 corresponds to the recombination of the last available free electron.…”

The global structure of thin, stratified α-discs and the reliability of the one layer approximation

“…Cox & Giuli 1968), the disc region mainly involved has a small size and convection does not drastically change the disc structure (Meyer & Meyer-Hofmeister 1982;Cannizzo 1993). Note that the weak effect of convection is sustained in the work by Gu et al (2000). Third, as explained below, we shall not analyze the region where the one layer has multiple solutions and which precisely encompasses the convectively unstable zone.…”

Cross-correlation-aided transport in stochastically driven accretion flows

“…While being unconventional in connection with turbulence that is generally associated with growing nonlinear instabilities, such a phenomenology is not altogether unknown, since equivalent predictions in the context of Taylor-Couette twist instability vortices were already made way back in the early nineties [7]. The new surge in interest though is in keeping with experimental projections in relation to the physics of hot accretion flows [8][9][10][11][12][13][14][17][18][19] where rotating shear flows in the Rayleigh stable regime have shown unmistakable signatures of transition to turbulence with a combination of angular momentum increase inspite of decreasing angular speed profiles. Often referred to as "subcritical turbulence", especially in the context of Keplerian accretion disks, the subject remained largely controversial since the emergence of such strong power-law driven instabilities leading to huge energy bursts (optimal transient energy ∼ Re 2/3 [3,19]) was difficult to explain on the basis of purely hydrodynamic mechanisms.…”