窄吸积环动力学不稳定性的数值解

NUMERICAL SOLUTION OF DYNAMICAL INSTABILITY IN A SLENDER ACCRETION TORUS

本文在细环近似和共转半径位移不为零的条件下，考虑吸积环中非轴对称动力学不稳定性的线性扰动过程，采用数值计算方法求得不稳定性的线性增长率和共转半径位移随波数的变化关系，发现线性增长率受共转半径不为零的影响较小，而共转半径位移项随波数变化的色散关系与线性ＫｄＶ方程的色散关系相同，说明窄吸收环在动力学不稳定性数值模拟中出现的“行星状解”很可能是类似于ＫｄＶ方程中的孤子解。

In this paper, we consider the linear perturbation process of a nonaxisymmetric dynamical instability in an accretion disk with the approximation of slender torus and non-vanishing shift of corotation radius. By means of numerical calculation,we obtain the growth rate of instability and the co-rotation radius shift in the different wave numbers. From these numerical results we find that the non-vanishing corotation radius shift affects the growth rate slightly, but a non-linear term appears in the dispersion relation between the shift of corotation radius and the wave number. This dispersion relation is similar to that of the linear KdV equation under specific conditions. It shows that the 'planet-like' solution in the numerical simulation of dynamical instability of a slender accretion torus is much probably similar to the solitons solution of KdV equation.