三维旋涡星系的动力学研究

A DYNAMIC STUDY OF THREE DIMENSIONAL SPIRAL GALAXIES

在三维对数螺线型密度扰动的引力Poisson方程严格解基础上 ,导出了对称平面(z=0 )上三维混合盘密度波的色散关系 ,并以此讨论了对于不同类型扰动盘的局域稳定性 ,同时还计算了盘面上密度波的群速度 .数值计算表明 :对数螺线型密度扰动 ,能比较好地满足扰动密度与扰动势反相位的关系 ;厚度和旋臂数目的增加有利于盘的稳定 ,而气体成分将导致盘不稳定 ;考虑厚度效应 ,银河系密度波传播的动力学时标与Toomre估计的数值相比将大大延长 ,至少需要 4.1 7× 1 0 9年 ,约占宇宙年龄的三分之一 ,从而可使以往密度波理论中得出的群速度太大的问题得到缓解 .

Based on the rigorous solution of the three dimensional (3D) Poisson's equation for logarithmic density disturbance, a more reasonable dispersion relation of 3D mixed disk on the symmetric plane is derived. Both the local gravitational stability of the disk and the group velocity of the density waves are discussed and calculated with a numerical method. Toomre's local stability criterion is generalized to more realistic 3D galaxy models. The numerical results show that the increase of the thickness and number of spiral arms are of benefit for the local stability, and increase of gas content will lead to instability. For our Galaxy, the dynamic time scale of the 3D density waves is 4.17×10 9 years, almost equal to one third of cosmic age and much longer than that given by Toomre. So the authors took into account the effect of thickness, and the group velocity problem in density wave theory can be eased up effectively.