The intergalactic and circumgalactic medium surrounding star-forming galaxies at redshifts 2 < z < 3

We present measurements of the spatial distribution, kinematics, and physical properties of gas in the circumgalactic medium (CGM) of 2.0<z<2.8 UV color-selected galaxies as well as within the 2<z<3 intergalactic medium (IGM). These measurements are derived from Voigt profile decomposition of the full Lyα and Lyβ forest in 15 high-resolution, high signal-to-noise ratio QSO spectra resulting in a catalog of ∼6000 HI absorbers.

Chapter 2 of this thesis focuses on HI surrounding high-z star-forming galaxies drawn from the Keck Baryonic Structure Survey (KBSS). The KBSS is a unique spectroscopic survey of the distant universe designed to explore the details of the connection between galaxies and intergalactic baryons within the same survey volumes. The KBSS combines high-quality background QSO spectroscopy with large densely-sampled galaxy redshift surveys to probe the CGM at scales of ∼50 kpc to a few Mpc. Based on these data, Chapter 2 presents the first quantitative measurements of the distribution, column density, kinematics, and absorber line widths of neutral hydrogen surrounding high-z star-forming galaxies.

Chapter 3 focuses on the thermal properties of the diffuse IGM. This analysis relies on measurements of the ∼6000 absorber line widths to constrain the thermal and turbulent velocities of absorbing "clouds." A positive correlation between the column density of HI and the minimum line width is recovered and implies a temperature-density relation within the low-density IGM for which higher-density regions are hotter, as is predicted by simple theoretical arguments.

Chapter 4 presents new measurements of the opacity of the IGM and CGM to hydrogen-ionizing photons. The chapter begins with a revised measurement of the HI column density distribution based on this new absorption line catalog that, due to the inclusion of high-order Lyman lines, provides the first statistically robust measurement of the frequency of absorbers with HI column densities 14 ≲ log(N_HI/cm^-2) ≲ 17.2. Also presented are the first measurements of the column density distribution of HI within the CGM (50 <d < 300 pkpc) of high-z galaxies. These distributions are used to calculate the total opacity of the IGM and IGM+CGM and to revise previous measurements of the mean free path of hydrogen-ionizing photons within the IGM. This chapter also considers the effect of the surrounding CGM on the transmission of ionizing photons out of the sites of active star-formation and into the IGM.

This thesis concludes with a brief discussion of work in progress focused on understanding the distribution of metals within the CGM of KBSS galaxies. Appendix B discusses my contributions to the MOSFIRE instrumentation project.

Two and Three Finger Caging of Polygons and Polyhedra

Multi-finger caging offers a rigorous and robust approach to robot grasping. This thesis provides several novel algorithms for caging polygons and polyhedra in two and three dimensions. Caging refers to a robotic grasp that does not necessarily immobilize an object, but prevents it from escaping to infinity. The first algorithm considers caging a polygon in two dimensions using two point fingers. The second algorithm extends the first to three dimensions. The third algorithm considers caging a convex polygon in two dimensions using three point fingers, and considers robustness of this cage to variations in the relative positions of the fingers.

This thesis describes an algorithm for finding all two-finger cage formations of planar polygonal objects based on a contact-space formulation. It shows that two-finger cages have several useful properties in contact space. First, the critical points of the cage representation in the hand’s configuration space appear as critical points of the inter-finger distance function in contact space. Second, these critical points can be graphically characterized directly on the object’s boundary. Third, contact space admits a natural rectangular decomposition such that all critical points lie on the rectangle boundaries, and the sublevel sets of contact space and free space are topologically equivalent. These properties lead to a caging graph that can be readily constructed in contact space. Starting from a desired immobilizing grasp of a polygonal object, the caging graph is searched for the minimal, intermediate, and maximal caging regions surrounding the immobilizing grasp. An example constructed from real-world data illustrates and validates the method.

A second algorithm is developed for finding caging formations of a 3D polyhedron for two point fingers using a lower dimensional contact-space formulation. Results from the two-dimensional algorithm are extended to three dimension. Critical points of the inter-finger distance function are shown to be identical to the critical points of the cage. A decomposition of contact space into 4D regions having useful properties is demonstrated. A geometric analysis of the critical points of the inter-finger distance function results in a catalog of grasps in which the cages change topology, leading to a simple test to classify critical points. With these properties established, the search algorithm from the two-dimensional case may be applied to the three-dimensional problem. An implemented example demonstrates the method.

This thesis also presents a study of cages of convex polygonal objects using three point fingers. It considers a three-parameter model of the relative position of the fingers, which gives complete generality for three point fingers in the plane. It analyzes robustness of caging grasps to variations in the relative position of the fingers without breaking the cage. Using a simple decomposition of free space around the polygon, we present an algorithm which gives all caging placements of the fingers and a characterization of the robustness of these cages.