The vertical eddy-heat flux as a stabilizer of cold accretion disks

The time-dependent vertical structure of cold accretion disks and their thermal stability have been studied with turbulent heat transfer being included. A strong turbulent heat transport enforces a nearly adiabatic stratification and the disk evolves quasi-homologously, although homology is broken by the outer boundary condition. The radiative energy loss scales with the disk’s optical depth τ like Q− ∝ T 4 c /τ with Tc the midplane temperature. The disk is only stable if the resulting m fulfills the stability criterion 3 + m (n/2 − q) > 0, with n and q taken from the opacity law κ ∝ ρT . For rather cool disks with n = 1/3 and q = 10 the vertical structure proves to be thermally unstable unless the turbulent Prandtl number (the ratio between the eddy viscosity and turbulent heat conductivity) is less than, say, 0.1. For weaker temperature power-laws of the opacity (smaller q) the disks become more and more stable even without the stabilizing support of the eddy-heat flux. Numerical simulations confirm the quasi-analytically derived stability criterion.