Physical Manifestations of Chaos and Regularity Around Galaxies

宇宙中的一切都在运动：行星绕恒星运行，恒星在星系中运行，星系相互绕轨道运行。 我们对这些轨道的行为有期望。 行星沿着椭圆轨道绕恒星运行。 它们多年来重复相同的路径数百万甚至数十亿次，每次革命都花费相同的时间，称为“周期”。 恒星在星系中运行时，它们自身的轨道形成了“玫瑰花结”图案。 这些轨道可能需要数亿年才能走一圈。玫瑰轨道可以用两个周期来描述：“方位周期”概括了星星绕星系一周所需的时间;“径向周期”描述了星星从沿着其轨道的最接近和最远离星系中心的点之间返回所需的时间。恒星轨道的性质是由影响它们的物质分布决定的。 行星围绕着集中在中心恒星的物质运动。 星系中的恒星在恒星、气体和暗物质的组合分布中运动。 椭圆形和玫瑰形轨道都被称为“规则”轨道，因为它们的路径是可预测的和重复的。 然而，也有人认为宇宙中的某些轨道是“混沌的”。“这些轨道没有以明确的周期重复的模式，因此无法预测。 正如椭圆轨道和玫瑰轨道的性质是由物质分布决定的一样，混沌的重要性也是如此。 如果可见光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在科学界代表性不足的群体的工作。 她致力于促进制度结构，以从多元化的劳动力中获益;减少在不同群体中做出决策的挑战;为学术界领导角色中的少数群体提供支持;并随着学术机构的发展而简化过渡。虽然行星围绕恒星的轨道的性质可以在人类有生之年观察到，但星系的巨大尺寸意味着恒星的轨道需要数百万年。 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乱的。 在过去的20年里，在我们的银河系周围观察到了类似轨道上的恒星流。 在先前的工作中，提议者已经表明，这些流的形态对混沌的存在（或不存在）很敏感。 只有在非常规则的轨道上，这些流才能保持相干。 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）中轨道性质（规则或混沌）的理论研究对于深入理解轨道所支持的全球结构至关重要。 在最近的工作中，研究人员发现，轨道性质的特征可以在我们银河系周围的结构中观察到，这些结构是由卫星系统的破坏形成的。 他们发现了一个与球状星团Palomar 5相关的恒星流，它又长又细，结构简单。 蛇夫座的另一个恒星流被非常截断。 研究人员将（一）更普遍地探索恒星碎片中规律性和混乱的物理表现，（二）开发利用这些特征绘制星系周围轨道性质图的方法。 该项目将非线性动力学经典研究的工具和技术与数值实验相结合，数值实验跟踪从相空间中紧密聚集的初始条件开始的轨道集合的演变。 他们将把他们的研究扩展到两个新的领域：混沌轨道在短时间尺度（数十个轨道）上的演化，以及这种演化在轨道集合的全相空间结构中的可观察特征。 他们还将探索规则和混沌轨道如何支持恒星结构，超越传统的自洽星系成分研究，包括未绑定的恒星协会。

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.