Mathematical Sciences: The Dynamical Structure and Stabilityof Galaxies

首席研究员提议对星系动力学的某些方面进行理论研究。本研究的目标之一是建立椭圆星系的自洽平衡恒星动力学模型，特别强调存在多个基本族轨道的星系。为了实现自一致性，在动态上可能存在的不同轨道必须以这样一种方式填充，即产生的引力场恰好是将星系聚集在一起所需要的。这项工作的第二个目的是了解恒星动力学模型的运动学特性，并将它们与观测联系起来。真实星系的运动特性在天空平面上的投影是可以观察到的，并且只能提供间接的信息来确定真正的内在运动。这项工作的第三个目的是研究盘状星系的振荡和稳定性。一个典型的星系是由数千亿颗恒星组成的，每一颗恒星都按照众所周知的动力学物理定律在自己的轨道上运行。星系也是复杂系统的有趣例子，它们的行为来自于更简单的组成部分的综合效应。该项目旨在建立数学模型，结合真实星系的基本特征，尽可能地匹配观测结果，这并不简单，因为只有真正的三维星系的平面图片才被观测到。这项工作将结合数学分析和计算来阐明当前星系的动态结构，其中应该包含有关它们过去历史的重要信息，包括它们的形成过程。

The principal investigator is proposing theoretical studies into some aspects of the dynamics of galaxies. One objective of this research is to build self-consistent equilibrium stellar dynamic models of elliptical galaxies, with special emphasis on galaxies in which orbits of more than one basic family are present. For self-consistency, the different orbits that are dynamically possible must be populated in such a way that the resulting gravitational field is exactly that needed to hold the galaxy together. The second aim of the work is to understand the kinematic properties of the stellar dynamic models, and to relate them to observations. Projections of the kinematic properties of real galaxies on the plane of the sky can be observed, and provide only indirect information from which to determine the true intrinsic motions. A third aim of the work is to study the oscillations and stability of disk-like galaxies. A typical galaxy is composed of hundreds of billions of stars, each of which moves on its own individual orbit according to well-known physical laws of dynamics. Galaxies are also interesting examples of complex systems, whose behavior comes from the combined effects of much simpler components. This project aims to build mathematical models that incorporate the basic characteristics of real galaxies, matching observations as far as possible, which is not simple because only flat pictures of the truly three-dimensional galaxies are ever observed. The work will use a combination of both mathematical analysis and computation to elucidate the present day dynamical structure of galaxies, which should contain significant information about their past history, including that of their formation.