Physical Manifestations of Chaos and Regularity Around Galaxies

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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.