Instabilities, Modes, and Bifurcations of Orbits in Stellar Systems

9704615首席研究员亨特提议研究两类与星系动力学有关的现象。一个是不稳定和模式的问题，另一个是轨道分叉的问题。这项工作是分析性的，基于星系是无碰撞的恒星系统的近似值。这种近似是基于这样一种信念，即星系的大部分质量是以恒星和暗物质的形式存在的，这些恒星和暗物质在没有相互碰撞的轨道上运动，轨道的形状由星系的总重力场决定。对星系的N体模拟表明，确实存在不稳定性和大规模振荡模式，而且它们的发生取决于星系的轨道密度。当所有轨道以一致的方式脉动时，模式就会发生，而当轨道人口对扰动的集体反应是加强它并使它增长时，就会发生不稳定。首席调查员将寻求对这些可能性的详细描述，以帮助解释潜在的动态。他开发了一种新技术，用于准确定位和跟踪模式和不稳定性。要研究的分叉是轨道的形式和稳定性发生变化的那些分叉。轨道的性质对星系的结构至关重要。虽然这两类现象是分开调查的，但它们可能是相互关联的。星系之所以令人感兴趣，是因为它们是宇宙的基本组成部分。一个典型的星系由数千亿颗恒星组成，根据众所周知的物理动力学定律，每一颗恒星都在自己的单独轨道上运行。主要研究人员的主要兴趣是这些系统的稳定性，次要兴趣是轨道的性质和它们可以改变的方式。人们通过研究一个系统在被破坏时的反应来确定它是否稳定。这种反应可能是一种模式，在这种模式下，所有的轨道都设法有规律地一致地脉动。或者，当有稳定时，扰动消散和衰减，或者当有不稳定时，扰动加强和增长。每种类型的行为都在计算机实验中被观察到。这项工作寻求的是对潜在原因的理论理解。它将使用数学模型进行，由于要表示的恒星数量很多，这些模型必然是统计的，并结合了数学分析和计算。众所周知，星系的存在时间超过了宇宙年龄的很大一部分，因此应该没有所有的不稳定，除了最轻微的不稳定。因此，任何关于稳定性要求的发现，原则上都可以通过对当今星系动力结构的观察来检验。

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.