Techniques for Reconstructing a Riemannian Metric Via the Boundary Control Method

In this dissertation, we consider some new techniques related to the solution of the inverse boundary value problem for the wave equation with partial boundary data. Most results are formulated in a geometric setting, where waves propagate in the interior of a smooth manifold with smooth boundary M, and the wave speed is modelled by an unknown Riemannian metric g. For data, we focus mostly on using the Neumann-to-Dirichlet (N-to-D) map with sources and receivers restricted to a measurement set Γ ⊂ ∂M. The goal of the inverse problem, in this setting, is to use these wave boundary measurements to recover the geometry of (M, g) near the measurement set. We note that this geometric perspective accomodates, as special cases, both the scalar acoustic wave equation and elliptically anisotropic wave speeds. We consider three problems. In the first problem, we provide a technique to use the N-to-D map to construct the travel times between interior points with known semi-geodesic coordinates and boundary points belonging to Γ. Such travel times can be used to reconstruct the metric in semi-geodesic coordinates using one of several existing techniques, so this procedure can be viewed as providing a data processing step for a metric reconstruction procedure. In the second problem, we consider a redatuming procedure, where we use data on the boundary and known near-boundary geometry to synthesize wave measurements in this known near-boundary region. This allows us to construct a map which plays a similar role to the N-to-D map, but for interior sources and interior measurements. Our motivation for this procedure is that it can serve as a data propagation step for a layer stripping reconstruction method, in which one first reconstructs the metric near the boundary and then propagates data into this region to serve as data for an interior reconstruction step. In the third problem, we restrict attention to the case where M is a domain in Rn, and consider two related procedures to use the N-to-D map or Dirichlet-to-Neumann (D-to-N) map to directly reconstruct the metric. In the anisotropic case, we construct the metric in semi-geodesic coordinates via reconstruction of the wave field in the interior of the domain. In the isotropic case, we can go further and construct the wave speed in the Euclidean coordinates via reconstruction of the coordinate transformation from the boundary normal coordinates to the Euclidean coordinates. In addition to providing constructive procedures, we analyze the stability of some steps from these procedures. In particular we consider the stability of the redatuming procedure and the stability of the metric reconstruction procedure from internal data (for the third problem). Moreover, we provide computational experiments to demonstrate our three main procedures

Radio continuum observations of local star-forming galaxies using the Caltech Continuum Backend on the Green Bank Telescope

We observed radio continuum emission in 27 local (D < 70 Mpc) star-forming galaxies with the Robert C. Byrd Green Bank Telescope between 26 GHz and 40 GHz using the Caltech Continuum Backend. We obtained detections for 22 of these galaxies at all four sub-bands and four more marginal detections by taking the average flux across the entire bandwidth. This is the first detection (full or marginal) at these frequencies for 22 of these galaxies. We fit spectral energy distributions (SEDs) for all of the four-sub-band detections. For 14 of the galaxies, SEDs were best fit by a combination of thermal free-free and nonthermal synchrotron components. Eight galaxies with four-sub-band detections had steep spectra that were only fit by a single nonthermal component. Using these fits, we calculated supernova rates, total number of equivalent O stars, and star formation rates within each ~23 arcsecond beam. For unresolved galaxies, these physical properties characterize the galaxies' recent star formation on a global scale. We confirm that the radio-far-infrared correlation holds for the unresolved galaxies' total 33 GHz flux regardless of their thermal fractions, though the scatter on this correlation is larger than that at 1.4 GHz. In addition, we found that for the unresolved galaxies, there is an inverse relationship between the ratio of 33 GHz flux to total far-infrared flux and the steepness of the galaxy's spectral index between 1.4 GHz and 33 GHz. This relationship could be an indicator of the timescale of the observed episode of star formation.Comment: 36 pages, 9 figures; accepted for publication in ApJ. First and second author affiliation updated to reflect departmental name chang

A High-Resolution Study of the HI Content of Local Group Dwarf Irregular Galaxy WLM

Dwarf irregular galaxies are unique laboratories for studying the interaction between stars and the interstellar medium in low mass environments. We present the highest spatial resolution observations to date of the neutral hydrogen content of the Local Group dwarf irregular galaxy WLM. We find that WLM's neutral hydrogen distribution is typical for a galaxy of its type and size and derive an HI mass of 6.3e7 Msun for WLM. In addition, we derive an HI extent for WLM of 30 arcmin, which is much less than the 45 arcmin extent found by Huchtmeier, Seiradakis, and Materne (1981). We show that the broken ring of high column density neutral hydrogen surrounding the center of WLM is likely the result of star formation propagating out from the center of the galaxy. The young stars and Ha emission in this galaxy are mostly correlated with the high column density neutral hydrogen. The gap in the central ring is the result of star formation in that region using up, blowing out, or ionizing all of the neutral hydrogen. Like many late-type galaxies, WLM's velocity field is asymmetric with the approaching (northern) side appearing to be warped and a steeper velocity gradient for the approaching side than for the receding side in the inner region of the galaxy. We derive a dynamical mass for WLM of 2.16e9 Msun.Comment: 38 pages, 15 figures, 5 tables, accepted by AJ, high resolution version at http://www.astro.wisc.edu/~kepley/kepley_wlm.p

Global Properties of Neutral Hydrogen in Compact Groups

Compact groups of galaxies provide a unique environment to study the evolution of galaxies amid frequent gravitational encounters. These nearby groups have conditions similar to those in the earlier universe when galaxies were assembled and give us the opportunity to witness hierarchical formation in progress. To understand how the compact group environment affects galaxy evolution, we examine the gas and dust in these groups. We present new single-dish GBT neutral hydrogen (HI) observations of 30 compact groups and define a new way to quantify the group HI content as the HI-to-stellar mass ratio of the group as a whole. We compare the HI content with mid-IR indicators of star formation and optical [g-r] color to search for correlations between group gas content and star formation activity of individual group members. Quiescent galaxies tend to live in HI-poor groups, and galaxies with active star formation are more commonly found in HI-rich groups. Intriguingly, we also find "rogue" galaxies whose star formation does not correlate with group HI content. In particular, we identify three galaxies (NGC 2968 in RSCG 34, KUG 1131+202A in RSCG 42, and NGC 4613 in RSCG 64) whose mid-IR activity is discrepant with the HI. We speculate that this mismatch between mid-IR activity and HI content is a consequence of strong interactions in this environment that can strip HI from galaxies and abruptly affect star-formation. Ultimately, characterizing how and on what timescales the gas is processed in compact groups will help us understand the interstellar medium in complex, dense environments similar to the earlier Universe.Comment: Accepted to A