Physical Manifestations of Chaos and Regularity Around Galaxies

宇宙中的一切都在运动：行星围绕恒星运行，恒星围绕星系运行，星系相互运行。我们对这些轨道应该如何运行抱有期望。行星围绕恒星运行的轨道是椭圆的。多年来，它们重复着同样的道路数百万次甚至数十亿次，每一次革命都需要相同的时间，即所谓的“周期”。当恒星穿过银河系时，它们本身遵循的轨道形成了“玫瑰花”图案。这些轨道可能需要数亿年的时间才能绕地球一周。花环轨道可以用两个周期来描述：“方位周期”概括了恒星绕银河系运行需要多长时间；“径向周期”描述了恒星在其轨道上离银河系中心最近和最远的点之间往返需要多长时间。恒星轨道的性质是由影响它们的物质的分布决定的。行星围绕着集中在中心恒星中的物质运动。银河系中的恒星在恒星、气体和暗物质的综合分布中运动。椭圆轨道和花环轨道都被称为“规则”轨道，因为它们的路径是可预测的和重复的。然而，人们也预计，宇宙中的一些轨道是“混乱的”。这些轨道没有明确定义的周期重复的模式，因此无法预测。而且-就像椭圆轨道和玫瑰花环轨道的性质由物质分布决定一样-混沌的重要性也是如此。如果可见物质和暗物质的分布很复杂，轨道更有可能是混乱的。研究人员还将继续她对科学中代表性较低的群体的工作。她寻求促进制度结构，以从多样化的劳动力中获益；减少不同群体之间做出决策的挑战；为在学术界担任领导角色的少数族裔提供支持；并随着学术机构的发展简化过渡。虽然在人类有生之年可以观察到围绕恒星运行的行星轨道的性质，但巨大的星系意味着绕恒星运行一圈需要数百万年。这项拟议的工作将探索一种新的数学方法来推断星系周围恒星轨道的性质，无论它们是规则的还是混沌的。在过去的20年里，在我们的银河系周围观察到了类似轨道的恒星流。在以前的工作中，提出者已经证明了这些流的形态对混沌的存在(或不存在)是敏感的。只有在非常规则的轨道上，这些流才能保持连贯。混沌的存在可以告诉我们星系周围难以捉摸的暗物质是如何分布的。对动力系统(星系只是一个例子)中轨道的性质-规则的或混沌的--的理论研究对于建立对轨道所支持的全球结构的深入理解至关重要。在最近的工作中，研究人员发现，在我们银河系周围的结构中可以观察到轨道性质的特征，这些结构是由卫星系统破坏形成的。他们发现了一个与球状星团Palomar 5有关的恒星流，它又长又细，结构简单。蛇夫座的另一颗恒星被截断了。研究人员将(I)更广泛地探索恒星碎片中规律性和混沌的物理表现，(Ii)开发使用这些特征绘制星系轨道性质地图的方法。该项目将非线性动力学经典研究中的工具和技术与数值实验相结合，这些实验跟踪从相空间中紧密聚集的初始条件开始的轨道系综的演变。他们将把他们的研究扩展到两个新的领域：短时间尺度(几十个轨道)上混沌轨道的演化，以及这种演化在整个轨道系综相空间结构中的可观测特征。他们还将探索规则和混乱的轨道如何支持恒星结构，而不是传统的自洽星系组成部分的研究，包括非束缚恒星关联。

Everything in the Universe is in motion: planets orbit stars, stars orbit within galaxies, and galaxies orbit each other. We have expectations for how these orbits should behave. Planets follow elliptical orbits around stars. They repeat the same path millions or even billions of times over the years with each revolution taking the same amount of time, known as the 'period'. The stars themselves follow orbits that form 'rosette' patterns as they move through a galaxy. These orbits can take hundreds of millions of years to go even once around. Rosette orbits can be described with two periods: the 'azimuthal period' encapsulates how long it takes for the star to go around the galaxy; the 'radial period' describes how long it take for the star to get between the points along its orbit that are closest to and farthest from the galaxy's center and back again. The nature of stellar orbits is set by the distribution of matter that influences them. Planets move around matter that is concentrated in the central stars. Stars in the galaxy are moving within the combined distribution of stars, gas, and dark matter. Both elliptical and rosette orbits are known as 'regular' orbits since their paths are predictable and repeating. However, it is also expected that some orbits in the Universe are 'chaotic.' These orbits do not have patterns that repeat with well-defined periods and hence are not predictable. And---just as the nature of elliptical and rosette orbits is set by the matter distribution---so is the importance of chaos. Orbits are more likely to be chaotic if the visible and dark matter distributions are complex.The investigator will also continue her work with underrepresented groups in the sciences. She seeks to facilitate institutional structures to gain benefits from a diverse workforce; reduce the challenges of making decisions among diverse groups; provide support for minorities in leadership roles in academia; and ease the transition as academic institutions evolve.While the nature of planetary orbits around stars can be observed within human lifetimes, the vast sizes of galaxies means that orbits of stars take millions of years. The proposed work will explore a new mathematical approach to deducing the nature of stellar orbits around galaxies, whether they are regular or chaotic. Over the last 20 years, streams of stars on similar orbits have been observed around our Galaxy. In prior work, the proposers have shown that the morphologies of these streams are sensitive to the presence (or absence) of chaos. Only on very regular orbits can these streams remain coherent. And the presence of chaos can tell us about how the elusive dark matter around galaxies is distributed.Theoretical studies of the nature of orbits---regular or chaotic---in dynamical systems (galaxies being just one example) are essential to building a deep understanding of the global structures that the orbits support. In recent work the investigator has discovered that signatures of the nature of orbits can be observed in structures around our own Galaxy, formed from the disruption of satellite systems. They found one stellar stream associated with globular cluster Palomar 5 that is long and thin with a simple structure. Another stream of stars in the constellation Ophiucus is extraordinarily truncated. The investigator will (i) explore the physical manifestations of regularity and chaos in stellar debris more generally and (ii) develop methods for making maps of the nature of orbits around galaxies using these signatures. The project combines tools and techniques from the classical study of non-linear dynamics with numerical experiments that follow the evolution of ensembles of orbits starting from initial conditions closely clustered in phase-space. They will extend their study to two new regimes: the evolution of chaotic orbits over short timescales (tens of orbits) and the observable signatures of this evolution in the full phase-space structure of ensembles of orbits. They will also explore how regular and chaotic orbits can support stellar structures beyond the traditional study of self-consistent galactic components, including unbound stellar associations.