Mathematical Sciences: Dynamics of Galaxies/Order and Chaos

本文将星系盘动力学作为非线性动力系统，采用模态方法进行研究。为了保证模态方法的真实性和可行性，将对选定星系的螺旋结构进行研究。因此，该理论将首先应用于M81星系和银河系，这些星系已经有了观测数据，并且已经进行了某些螺旋模式的初步研究。接下来，将考虑与双组分基本平衡状态（由恒星和星际气体组成）相关的轻度不稳定模式的非线性相互作用。这一过程预计将受到气体成分的强烈非线性响应的影响，气体成分的自引力和耗散特性将倾向于稳定螺旋结构。最后，在对各种物理过程进行数学处理后，将对这些物理过程进行分析研究。

This proposal will study the dynamics of galactic disks as nonlinear dynamical systems using the modal approach. To assure that the modal approach is realistic and viable, a study will be made of the spiral structure of selected galaxies. Thus, the theory will first be applied to the galaxy M81 and the Milky Way for which observational data are already available and certain preliminary studies of spiral modes have also been carried out. Next, the nonlinear interactions of the mildly unstable modes associated with a two-component basic equilibrium state (consisting of stars and interstellar gas) will be considered. This process is expected to be greatly influenced by the gaseous component whose strong nonlinear response, and self-gravitating and dissipative character would tend to stabilize the spiral structure. Finally analytical studies will be made of the various physical processes after these processes have been formulated for mathematical treatment.