Instabilities, Modes, and Bifurcations of Orbits in Stellar Systems

小行星9704615 首席研究员建议调查两类 与星系动力学有关的现象。一个是 不稳定性和模式，另一个是轨道的分叉。的 工作是分析性的，是基于近似星系是 无碰撞的恒星系统这种近似是基于这样一种信念， 星系的大部分质量是以恒星和暗物质的形式存在的， 移动，没有相互碰撞，在轨道上，其形式是由 银河系的重力场星系的N体模拟显示 不稳定性和大尺度振荡模式确实会发生， 它们的出现取决于银河系的轨道人口。模式 当所有轨道以连贯的方式脉动时，就会发生不稳定性， 当轨道人口的集体反应发生时， 干扰是为了加强它，使它成长。主要研究者 我将寻求这些可能性的详细描述，以帮助解释 潜在的动力学 他发明了一种新技术， 模式和不稳定性的定位和跟踪。分叉将是 研究的是轨道的形式和稳定性发生变化的那些。的 轨道的性质对星系的结构至关重要。尽管这两 如果要单独研究不同类别的现象， 相互关联 Galerkin之所以令人感兴趣，是因为它们是 宇宙一个典型的星系由数千亿颗恒星组成， 根据众所周知的 动力学的物理定律主要研究者的主要兴趣 是在这种系统的稳定性，和次要的利益是在性质， 轨道和它们的变化方式一个决定是否 通过研究一个系统在受到扰动时的反应来判断它是否稳定。 这种反应可能是所有轨道都在脉动的一种模式 有规律的一致。或者，扰动消散和衰减， 有稳定，有不稳定就壮大，每种类型 在计算机实验中观察到的行为。这是什么工作 寻求的是对根本原因的理论理解。它将被携带 使用数学模型，这是必要的统计，因为 大量的恒星被代表，以及 数学分析和计算。Galeries已知存在于 在宇宙年龄的很大一部分，因此应该是免费的 除了最轻微的不稳定性因此，任何关于 稳定性要求原则上可根据 现代星系的动力学结构。

9704615 Hunter The principal investigator is proposing to investigate two classes of phenomena that are relevant to the dynamics of galaxies. One is that of instabilities and modes, and the other is that of bifurcations of orbits. The work is analytical and is based on the approximation that galaxies are collisionless stellar systems. That approximation is based on the belief that most of the mass of galaxies is in the form of stars and dark matter, which move, without mutual collisions, on orbits whose form is determined by the total gravity field of the galaxy. N-body simulations of galaxies have shown that both instabilities and large-scale modes of oscillation do occur, and that their occurrence depends on the orbital population of the galaxy. Modes occur when all the orbits pulsate in a coherent manner, while instability occurs when the collective response of the orbital population to a disturbance is to reinforce it and make it grow. The principal investigator will seek detailed descriptions of these possibilities to help explain the underlying dynamics. He has developed a new technique for the accurate location and tracking of modes and instabilities. The bifurcations to be investigated are those at which the form and stability of orbits change. The nature of the orbits is crucial to the structure of a galaxy. Though the two classes of phenomena are to be investigated separately, they are likely interrelated. Galaxies are of interest because they are the fundamental building blocks of the Universe. 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. The primary interest of the principal investigator is in the stability of such systems, and a secondary interest is in the nature of the orbits and the ways in which they can change. One determines whether or not a system is stable by studying how it responds when it is pertur bed. The response may be a mode in which all the orbits manage to pulsate regularly in unison. Alternatively, disturbances dissipate and decay when there is stability, or reinforce and grow when there is instability. Each type of behavior has been observed in computer experiments. What this work seeks is theoretical understanding of underlying causes. It will be carried out using mathematical models, which are of necessity statistical because of the large number of stars to be represented, and a combination of mathematical analysis and computation. Galaxies are known to have existed over a large fraction of the age of the Universe, and hence should be free of all but the mildest instabilities. Hence any findings concerning the requirements for stability is in principle testable against observations of the present day dynamical structure of galaxies.