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，恒星在星系内绕恒星运行，星系相互绕星系运行。我们对这些轨道应该如何运行有了预期。行星绕恒星运行椭圆轨道。多年来，它们重复同样的路径数百万甚至数十亿次，每次革命都需要相同的时间，称为“周期”。当恒星在星系中移动时，它们本身的轨道形成“玫瑰”图案。这些轨道可能需要数亿年才能绕一圈。玫瑰轨道可以用两个周期来描述：“方位角周期”包含了恒星绕星系一周所需的时间；“径向周期”描述了恒星在其轨道上离星系中心最近和最远的点之间往返所需的时间。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转。星系中的恒星在恒星、气体和暗物质的混合分布中移动。椭圆轨道和玫瑰轨道都被称为“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“混沌的”。这些轨道没有明确周期的重复模式，因此是不可预测的。正如椭圆轨道和玫瑰花形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。如果可见和暗物质的分布很复杂，轨道就更有可能是混沌的。该研究人员还将继续在科学界代表性不足的群体中开展工作。她寻求促进体制结构，以便从多样化的劳动力中获益；减少在不同群体之间做出决策的挑战；为少数族裔在学术界担任领导角色提供支持；并随着学术机构的发展而逐步过渡。虽然行星绕恒星运行的性质可以在人类有生之年观察到，但星系的巨大规模意味着恒星的轨道需要数百万年的时间。这项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，我们在银河系周围观测到了类似轨道上的恒星流。在先前的工作中，提出者已经表明，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，这些流才能保持一致。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。在动力系统（星系只是一个例子）中，对轨道本质（规则或混沌）的理论研究对于深刻理解轨道所支持的全局结构至关重要。在最近的工作中，研究人员发现，可以在我们银河系周围的结构中观察到轨道性质的特征，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帕洛马5有关的恒星流，它又长又细，结构简单。蛇夫座的另一群恒星被截断了。研究人员将(i)更普遍地探索恒星碎片中规律性和混沌的物理表现，（ii）开发利用这些特征绘制星系周围轨道性质地图的方法。该项目结合了非线性动力学经典研究的工具和技术，以及从初始条件开始紧密聚集在相空间的轨道集合的演变的数值实验。他们将把他们的研究扩展到两个新的领域：在短时间尺度（几十个轨道）上混沌轨道的演化，以及在轨道集合的全相空间结构中这种演化的可观察特征。他们还将探索规则和混沌轨道如何支持恒星结构，而不是传统的自洽星系成分研究，包括未绑定的恒星关联。

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.