Beta Viscose Prescription in Self-Gravitating Disks

TL;DR

This paper applies the beta-viscosity prescription to self-gravitating accretion disks around young stars, revealing differences from standard alpha disks and suggesting broader astrophysical applications.

Contribution

It demonstrates the use of beta-viscosity in modeling self-gravitating disks, showing stability and potential for diverse astrophysical environments.

Findings

Beta disks are viscously stable.

Outer disk regions differ from alpha disk models.

Toomre parameter exceeds unity everywhere.

Abstract

Duschl et al. (2000) have shown that the standard model for geometrically thin accretion disks ($\alpha$-disks) leads to inconsistency if self-gravity play a role. This problem arise from parametrization of viscosity in terms of local sound velocity and vertical disks scale hight. The $\beta$-viscosity prescription was introduced by Duschl et al. (2000), which has been derived from rotating shear flow experiment ($\nu=\beta \Omega R^2$). Following the Duschl et al. (2000) suggestion for a $\beta$-prescription for viscosity, we apply this model for a thin self-gravitating disk around newborn stars. Our result is quite different with standard alpha disks in the outer part of the disks where the self-gravity becomes important. In the inner part of the disks, our solution converged to the standard $\alpha$ disks. It has been presented that for beta model, Toomre parameter is more than unity everywhere which means that gravitational fragmentation can be occur everywhere. We suggest that the kind of hydrodynamically driven viscosity, $\beta$-model, can be used for modeling of accretion disks from proto-stellar disks to AGN and galactic disks. It would be interest to investigate ADAF-type solution for follow any effects by $\beta$-viscosity model. An important property of the $\beta$-disk is that they are viscously stable.