279 research outputs found
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
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