星系盘厚度效应的研究

在三维引力Poisson方程严格解基础上，探讨了有限厚星系盘基盘的动力学性质，并进一步讨论了盘的厚度效应对银河系所需晕质量的影响。研究了扰动盘的动力学性质，通过将扰动引力势Poisson方程的严格解与林家翘、徐遐生提出的自维持密度波理论相结合，建立了三维旋涡星系有限厚盘上密度波的色散关系。在此色散关系的基础上讨论了盘的局域稳定性，研究了旋涡星系旋臂的形态、三维盘状星系密度波的群速度。研究表明厚度是星系盘研究中不容忽略的重要参量。另外在有限厚盘星系密度波色散关系的基础上还探讨了一种确定星系厚度的新方法。

The Thickness Effect of Galactic Disk

Based on the limited solution of three-dimensional (3D) Poisson equation, the dynamical properties of finite-thickness galactic disk is studied first. Calculation shows that the thickness effect cannot be neglected. It is found that the more realistic Galaxy model needs only about half of the halo masses than that with an infinitesimal thin disk. For a steeply decreasing halo density model, the thickness effect is more obvious. In addition, the dynamical properties of disturbed disk are investigated. By using the solution of 3D Poisson equation with Lin-Shu self-maintained density wave theory, a dispersion relation of 3D-density wave is set up. The local stability of disk is discussed, and the Toomre's local stability criterion is extended to the more realistic galactic model. Then we study the form of spiral arm, and show that only two armed spiral galaxies can be self-consistent with the logarithmic density disturbance, which is consistent with the observation. The group velocity of density waves is discussed, and it is shown that the group velocity problem can be soften by introducing the effect of thickness to a certain extent. Anyhow, it is shown that the finite thickness effect is a very important parameter in density waves theory. At the same time we put forward a tentative method to determine the thickness of galaxies.