Evolution of finite viscous disks with time-independent viscosity

Abstract

We find the Green's functions for the accretion disk with the fixed outer radius and time-independent viscosity. With the Green's functions, a viscous evolution of the disk with any initial conditions can be described. Two types of the 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 the disks around stars with the magnetosphere's boundary exceeding 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_rise ~ 0.15 r_out^2/nu_out and the e-folding time of the decay is t_exp ~ 0.45 r_out^2/nu_out. Comparison to non-stationary alpha-disks shows that both models with the same value of viscosity at the outer radius produce similar behaviour on the viscous time-scale. For six bursts in X-ray novae, which exhibit fast-rise-exponential-decay (FRED) and are fitted by the model, we find a way to restrict the turbulent parameter alpha.