The Evolution of Vicosity Over Time in Viscous Disks

EVOLUTION OF FINITE VISCOUS DISKS WITH TIME-INDEPENDENT VISCOSITY

Author:

Lipunova

Abstract:

We find Green functions for the accretion disk with fixed outer radius and time-independent viscosity. With the Green functions, a viscous evolution of the disk with any initial conditions can be described. Two types of inner boundary conditions are considered: the zero stress tensor and the zero accretion rate. The variable mass inflow at the outer radius can also be included. The well-known exponential decline of the accretion rate is a part of the solution with the inner zero stress tensor. The solution with the zero central accretion rate is applicable to disks around stars whose magnetosphere's boundary exceeds the corotation radius. Using the solution, the viscous evolution of disks in some binary systems can be studied. We apply the solution with zero inner stress tensor to outbursts of short-period X-ray transients during the time around the peak. It is found that for the Kramers' regime of opacity and the initial surface density proportional to the radius, the rise time to the peak is ${{t}_{{\rm rise}}}\approx 0.15\;r_{{\rm out}}^{2}/{{\nu }_{{\rm out}}}$ and the e-folding time of the decay is ${{t}_{{\rm exp} }}\approx 0.45\;r_{{\rm out}}^{2}/{{\nu }_{{\rm out}}}$. Comparison to non-stationary α-disks shows that both models with the same value of viscosity at the outer radius produce similar behavior on the viscous time-scale. For six bursts in X-ray novae, which exhibit fast-rise–exponential-decay and are fitted by the model, we find a way to restrict the turbulent parameter α.