粘性与时间无关的有限粘性圆盘的演化
Evolution of finite viscous disks with time-independent viscosity
摘要：
我们发现格林函数的吸积盘具有固定的外径和时间无关的粘度。用格林函数可以描述任意初始条件下圆盘的粘性演化。考虑了两类内边界条件：零应力张量和零吸积率。也可以包括外半径处的可变质量流入。众所周知的吸积速率的指数下降是具有内部零应力张量的解的一部分。中心吸积率为零的解适用于磁层边界超过共转半径的恒星周围的盘。利用该解，可以研究某些二元系统中圆盘的粘性演化。我们将零内应力张量的解应用于短周期X射线瞬态在峰值附近的时间内的爆发。发现对于Kramers不透明度和初始表面密度与半径成正比的情况，到达峰值的上升时间为t_rise ~ 0.15 r_out^2/nu_out，衰减的e折叠时间为t_exp ~ 0.45 r_out^2/nu_out。与非平稳α-磁盘的比较表明，这两种模型具有相同的粘度值在外径产生类似的行为上的粘性时间尺度。对于六个X射线新星爆发，这表现出快速上升指数衰减（FRED）和模型拟合，我们找到了一种方法来限制湍流参数α。
英文摘要：
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.
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