Accretion discs models with the β-viscosity prescription derived from laboratory experiments

Abstract

We examine under which conditions one may apply, to steady state Keplerian accretion discs, the β-viscosity prescription which has been derived from rotating shear flow experiments (v = βΩR2, where Ω is the angular velocity at radius R and β is a constant of order 10-5; Richard & Zahn 1999). Using a vertically averaged model, we show that this law may be suitable for all three families of known systems: in young stellar objects, evolved binary stars and Active Galactic Nuclei discs (except in their outer gas pressure dominated regions where turbulence becomes hypersonic). According to the standard criterion for viscous stability, β-discs are always stable throughout. Using realistic opacities and equation of state, we demonstrate that these discs are thermally unstable in the temperature domain where hydrogen recombines, when they are optically thick, and this could lead to limit cycle behavior. Radiation pressure dominated regions are thermally stable, in contrast with α-discs. This results in a fully stable solution for the innermost parts of AGN discs.