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Thesis log and aux files
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\@writefile{lof}{\contentsline {figure}{\numberline {2.1}{\ignorespaces An overview of the W3/4/5 complex (also known as the ``Heart and Soul Nebula'') in false color. Orange shows 8 \ensuremath {\mu \textrm {m}}\xspace \ emission from the Spitzer and MSX satellites. Purple shows 21 cm continuum emission from the DRAO CGPS \citep {Taylor2003:CGPS}; the DSS R image was used to set the display opacity of the 21 cm continuum as displayed (purely for aesthetic purposes). The green shows JCMT \ensuremath {^{12}\textrm {CO}}\xspace \ 3-2 along with FCRAO \ensuremath {^{12}\textrm {CO}}\xspace \ 1-0 to fill in gaps that were not observed with the JCMT. The image spans $\sim 7\unhbox \voidb@x \hbox {$^\circ $}\xspace $ in galactic longitude. This overview image shows the hypothesized interaction between the W4 superbubble and the W3 and W5 star-forming regions \citep {oey:hierarchical:2005}.}}{15}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.2}{\ignorespaces A mosaic of the CO 3-2 data cube integrated from -20 to -60 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . The grayscale is linear from 0 to 150 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . The red and blue X's mark the locations of redshifted and blueshifted outflows. Dark red and dark blue plus symbols mark outflows at outer arm velocities. Green circles mark the location of all known B0 and earlier stars in the W5 region from SIMBAD.}}{18}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.3}{\ignorespaces Individual region masks overlaid on the FCRAO \ensuremath {^{12}\textrm {CO}}\xspace \ integrated image. The named regions, S201, AFGL4029, LWCas, W5NW, W5W, W5SE, W5S, and W5SW, were all selected based on the presence of outflows within the box. The inactive regions were selected from regions with substantial CO emission but without outflows. The `empty' regions have essentially no CO emission within them and are used to place limits on the molecular gas within the east and west `bubbles'. W5NWpc is compared directly to the Perseus molecular cloud in Section 2.4.1.1\hbox {} }}{19}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.4}{\ignorespaces Position-velocity diagrams (a), spectra (c), and contour overlays of Outflow 1 on Spitzer 4.5 \ensuremath {\mu \textrm {m}}\xspace \ (b) and 8 \ensuremath {\mu \textrm {m}}\xspace \ (d) images. This outflow is clearly resolved and bipolar. {\it (a)}: Position-velocity diagram of the blue flow displayed in arcsinh stretch from $T_A^*=$0 to 3 K. Locations of the red and blue flows are indicated by vertical dashed lines. The location of the position-velocity cut is indicated by the orange dashed line in panels (b) and (d), although the position-velocity cut is longer than those cut-out images. {\it (b)} Spitzer 4.5 \ensuremath {\mu \textrm {m}}\xspace \ image displayed in logarithmic stretch from 30 to 500 MJy \ensuremath {\textrm {sr}^{-1}}\xspace . {\it (c)}: Spectrum of the outflow integrated over the outflow aperture and the velocity range specified with shading. The velocity center (vertical dashed line) is determined by fitting a gaussian to the \ensuremath {^{13}\textrm {CO}}\xspace \ spectrum in an aperture including both outflow lobes. In the few cases in which \ensuremath {^{13}\textrm {CO}}\xspace \ 1-0 was unavailable, a gaussian was fit to the \ensuremath {^{12}\textrm {CO}}\xspace \ 3-2 spectrum. {\it (d)}: Contours of the red and blue outflows superposed on the Spitzer 8 \ensuremath {\mu \textrm {m}}\xspace \ image displayed in logarithmic stretch. The contours are generated from a total intensity image integrated over the outflow velocities indicated in panel (c). The contours in both panels (b) and (d) are displayed at levels of 0.5,1,1.5,2,3,4,5,6 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ ($\sigma \approx 0.25$ K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace ). The contour levels and stretches specified in this caption apply to all of the figures in the supplementary materials except where otherwise noted. }}{22}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.5}{\ignorespaces Position-velocity diagram, spectra, and contour overlays of Outflow 2 (see Figure 2.4\hbox {} for a complete description). While the two lobes are widely separated, there are no nearby lobes that could lead to confusion, so we regard this pair as a reliable bipolar outflow identification. }}{23}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.6}{\ignorespaces Position-velocity diagram, spectra, and contour overlays of Outflow 12. Much of the red outflow is lost in the complex velocity profile of the molecular cloud(s), but it is high enough velocity to still be distinguished. }}{24}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.7}{\ignorespaces Comparison of L1448 seen at a distance of 250 pc (left) versus 2 kpc (middle) with sensitivity 0.5 K and 0.05K per 0.5 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ channel respectively. {\it Far Left}: Position-velocity diagram (log scale) of the outflow L1448 IRS2 at its native resolution and velocity. L1448 IRS2 is the rightmost outflow in the contour plots. The PV diagram is rotated 45\unhbox \voidb@x \hbox {$^\circ $}\xspace \ from RA/Dec axes to go along the outflow axis. {\it Middle Left}: Position-velocity diagram (log scale) of the same outflow smoothed and rebinned to be eight times more distant. {\it Top Right}: The integrated map is displayed at its native resolution (linear scale). The red contours are of the same data integrated from 6.5 to 16 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ and the blue from -6 to 0 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . Contours are at 1,3, and 5 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ ($\sim 6, 18, 30 \sigma $). Axes are offsets in arcseconds. Because we are only examining the relative detectability of outflows at two distances, we are not concerned with absolute coordinates. {\it Bottom Right}: The same map as it would be observed at eight times greater distance. Axes are offsets in arcseconds assuming the greater distance. Contours are integrated over the same velocity range as above, but are displayed at levels 0.25,0.50,0.75,1.00 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ ($\sim 12, 24, 48, 60 \sigma $). The entire region is detected at high significance, but dominated by confusion. It is still evident that the red and blue lobes are distinct, but they are each unresolved. }}{27}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.8}{\ignorespaces Histogram of the measured outflow lobe separations. The grey hatched region shows \citet {curtis2010} values. The vertical dashed line represents the spatial resolution of our survey. The two distributions are similar.}}{28}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.9}{\ignorespaces Histogram of the outflow line widths. {\it Black lines}: histogram of the measured outflow widths (half-width zero-intensity, measured from the fitted central velocity of the cloud to the highest velocity with non-zero emission). {\it Blue dashed lines}: outflow half-width zero-intensity (HWZI) for the outer arm (non-W5) sample. {\it Solid red shaded}: The measured widths (HWHM) of the sub-regions as tabulated in Table 2.1\hbox {}. {\it Gray dotted}: Outflow $v_{max}$ (HWZI) values for Perseus from \citet {curtis2010}. }}{31}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.10}{\ignorespaces Histograms of outflow physical properties. The solid unfilled lines are the W5 outflows (this paper), the forward-slash hashed lines show \citet {arce2010} CPOCs , the dark gray shaded region shows \citet {arce2010} values for known outflows in Perseus, and the light gray, backslash-hashed regions show \citet {curtis2010} CO 3-2 outflow properties. The outflow masses measured in Perseus are systematically higher partly because both surveys corrected for line optical depth using \ensuremath {^{13}\textrm {CO}}\xspace . The medians of the distributions are 0.017, 0.044, 0.33, and 0.14 \ensuremath {M_{\odot }}\xspace \ for W5, Curtis, Arce Known, and Arce CPOCs respectively, which implies that an optical depth and excitation correction factor of 2.5-20 would be required to make the distributions agree (although W5, being a more massive region, might be expected to have more massive and powerful outflows). It is likely that CO 3-2 is sub-thermally excited in outflows, and CO outflows may be destroyed by UV radiation in the W5 complex while they easily survive in the lower-mass Perseus region, which are other factors that could push the W5 mass distribution lower. }}{35}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.11}{\ignorespaces Histogram of the measured outflow momentum fluxes. The black thick line shows our data, the grey shaded region shows the \citet {hatchell2007} data, and the hatched region shows \citet {curtis2010} values. Our measurements peak squarely between the two Perseus JCMT CO 3-2 data sets, although the \citet {curtis2010} results include an opacity correction that our data do not, suggesting that our results are likely consistent with \citet {curtis2010} but inconsistent with the \citet {hatchell2007} direct measurement method.}}{36}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.12}{\ignorespaces Histogram of the measured mass loss rate. The black thick line shows our data, while the grey shaded region shows the \citet {hatchell2007} data, which is simply computed by $\mathaccent "705F\relax {M} = \mathaccent "705F\relax {P} \times 10 / 5$ \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace , where the factor of 10 is a correction for opacity. Our mass loss rates are very comparable to those of \citet {hatchell2007}, but different methods were used so the comparison may not be physically meaningful. \citet {curtis2010} (hatched) used a dynamical time method similar to our own and also derived similar mass loss rates, although their mass measurements have been opacity-corrected using the \ensuremath {^{13}\textrm {CO}}\xspace \ 3-2 line. Because our mass loss rates agree reasonably with Perseus, but our outflow mass measurements are an order of magnitude low, we believe our dynamical age estimates to be too small. }}{37}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.14}{\ignorespaces Small scale map of the Sh 2-201 region plotted with CO 3-2 contours integrated from -60 to -20 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ at levels 3,7.2,17.3,41.6, and 100 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . The IRAC 8 \ensuremath {\mu \textrm {m}}\xspace \ image is displayed in inverted log scale from 800\ to 8000\ MJy \ensuremath {\textrm {sr}^{-1}}\xspace . Contours of the CO 3-2 cube integrated from -60 to -20 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ are overlaid at logarithmically spaced levels from 3 to 100 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ (3.0,7.2,17.3,41.6,100; $\sigma \approx 0.7$ K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace ). The ellipses represent the individual outflow lobe apertures mentioned in Section 2.4.1.2\hbox {}. }}{43}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.16}{\ignorespaces The northeast cometary cloud. Contours are shown at 0.5,1,2, and 5 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ integrated over the ranges -44.0 to -41.9 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ (blue) and -38.1 to -35.6 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ (red). There is a velocity gradient across the tail, suggesting that the front edge is being pushed away along the line of sight.}}{46}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.19}{\ignorespaces CO 3-2 contours overlaid on the Spitzer 8 \ensuremath {\mu \textrm {m}}\xspace \ image of the W5S cometary clouds described in Section 2.5.4\hbox {}. Contours are color-coded by velocity and shown for 0.84 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ channels at levels of 1 K (a, b) and 0.5 K (c). The velocity ranges plotted are (a) -41.5 to -33.0 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace (b) -44.7 to -36.7 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ (c) -43.6 to -35.6 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . The labels show the minimum, maxmimum, and middle velocities to guide the eye. The grey boxes indicate the regions selected for CO contours; while there is CO emission associated with the southern 8 \ensuremath {\mu \textrm {m}}\xspace \ emission, we do not display it here. The velocity gradients are discussed in Section 2.5.4\hbox {}. }}{51}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.20}{\ignorespaces Small scale map of the W5 SE region showing the star-forming clump containing outflows 39 and 40 and the non-star-forming clump at $\ell =138.0,b=0.8$. CO 3-2 contours integrated from -60 to -20 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ are displayed at levels 3,7.2,17.3,41.6, and 100 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . }}{52}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.21}{\ignorespaces Small scale map of the W5 SW region plotted with CO 3-2 contours integrated from -60 to -20 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ at levels 3,7.2,17.3,41.6, and 100 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . Outflow 13 is at the head of a cometary cloud (Figure 2.22\hbox {}) and therefore has clearly been affected by the expanding HII region, but the region including bipolar Outflow 10 shows no evidence of interaction with the HII region. }}{54}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.22}{\ignorespaces The cometary cloud in the W5 Southwest region (Outflow 13). Contours are shown at 1 K for 0.84 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ wide channels from -37.2 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ (blue) to -30.5 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ (red). The head is clearly blueshifted relative to the tail and contains a spatially unresolved redshifted outflow.}}{55}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.23}{\ignorespaces Small scale map of the W5 W region. The IRAC 8 \ensuremath {\mu \textrm {m}}\xspace \ image is displayed in inverted log scale from 800\ to 8000\ MJy \ensuremath {\textrm {sr}^{-1}}\xspace . Contours of the CO 3-2 cube integrated from -50 to -38 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ (blue) and -38 to -26 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ (red) are overlaid at levels 5,10,20,30,40,50,60 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ $\sigma \approx 0.5$ K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . The lack of outflow detections is partly explained by the two spatially overlapping clouds that are adjacent in velocity. }}{56}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.24}{\ignorespaces Integrated longitude-velocity diagram of the W5 complex from $b=0.25$ to $b=2.15$ in \ensuremath {^{12}\textrm {CO}}\xspace \ 1-0 from the FCRAO OGS. The W5NW region is seen at a distinct average velocity around $\ell =136.5$, $v_{LSR}=-34$ \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . The red and blue triangles mark the longitude-velocity locations of the detected outflows. In all cases, they mark the low-velocity start of the outflow.}}{57}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2.25}{\ignorespaces Small scale map of the W5 NW region plotted with CO 3-2 contours integrated from -60 to -20 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ at levels 3,7.2,17.3,41.6, and 100 K \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace . Despite its distance from the W5 O-stars, $D_{proj}\approx 20$ pc, this cluster is the most active site of star formation in the complex as measured by outflow activity.}}{58}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.6}{\ignorespaces Examples of input (top) and output (bottom) maps for different input power-spectrum power law $\alpha _{ps}$ values. For very steep power laws, most of the power is on the largest scales. $\alpha _{ps}=0$ is white noise. The axis scales are in pixels, where each pixel is 7.2\unhbox \voidb@x \hbox {$^{\prime \prime }$}\xspace , so each field is approximately 1\unhbox \voidb@x \hbox {$^\circ $}\xspace \ on a side. The Bolocam footprint is plotted with a circle of diameter 33\unhbox \voidb@x \hbox {$^{\prime \prime }$}\xspace representing each beam in its appropriate relative location. It is shown in the lower-right panel of the top figure as an indication of the largest possible recovered angular scales; it is about 1/8th the width of the map. The input images are normalized to have the same \textbf {peak} flux density. The pipeline recovers no emission from the simulation with $\alpha _{ps}=3$, but this value of $\alpha _{ps}$ is not representative of the real astrophysical sky - Herschel sees structure with $\alpha _{ps}\lesssim 2$, and the BGPS detected a great deal of astrophysical signal (see Section 3.6.3\hbox {} and Figure 3.9\hbox {}). }}{103}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.8}{\ignorespaces The aperture-extracted flux densities in a simulated map. The X-axis shows the flux density of the source in the input map with (blue circles) and without (red squares) the flux density in a background annulus subtracted. The Y-axis shows the flux density extracted in the same aperture from the output pipeline-processed map. The black dashed line is the 1-1 line. Section 3.8\hbox {} describes the background subtraction process; the {\rm v}2.0\xspace catalog reports background-subtracted flux density measurements. }}{107}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.9}{\ignorespaces A comparison of the power spectra of the $\ell =30\unhbox \voidb@x \hbox {$^\circ $}\xspace $ HiGal SDP fields with the BGPS power spectrum covering the same area. The area included is 1 square degree. The dashed and dotted black lines indicate power laws with $\alpha _{ps}=-2$ and $\alpha _{ps}=-1$ respectively, with arbitrary normalizations, as a guide for comparison. The vertical dashed red and green lines indicate the large angular scale 50\% recovery point of the BGPS and the BGPS beam FWHM respectively. The ratio of 500 \ensuremath {\mu \textrm {m}}\xspace to 1100 \ensuremath {\mu \textrm {m}}\xspace in this example has a spectral index $\alpha _{\nu }\sim 3.7$. Note that the 500 \ensuremath {\mu \textrm {m}}\xspace power begins falling off more steeply at $\sim 40\unhbox \voidb@x \hbox {$^{\prime \prime }$}\xspace $ because the Herschel FWHM beam size is 36\unhbox \voidb@x \hbox {$^{\prime \prime }$}\xspace , slightly larger than Bolocam's.}}{108}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.10}{\ignorespaces The `spectral index' $\alpha _{nu}$ between the BGPS and the three Herschel-SPIRE bands as a function of angular scale. This figure shows the power spectrum ratio for the $\ell =30\unhbox \voidb@x \hbox {$^\circ $}\xspace $ 1-square degree field. The vertical dashed lines are the same as in Figure 3.9\hbox {}: they show the largest angular scale the BGPS is sensitive to (red) and the beam FWHM at 33\unhbox \voidb@x \hbox {$^{\prime \prime }$}\xspace (green).}}{110}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.12}{\ignorespaces Histograms showing the sources matched between the {\rm v}1.0\xspace \ and {\rm v}2.0\xspace \ catalogs. Most of the {\rm v}2.0\xspace sources (5741 of 8004 {\rm v}2.0\xspace sources in the {\rm v}1.0\xspace -{\rm v}2.0\xspace overlap region) have matches from {\rm v}1.0\xspace , but there is a substantial population with no match. The unmatched sources tend to have lower flux densities. The shaded area shows 1-1 matches, while the solid red line shows one-way (unreciprocated) matches. }}{113}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.14}{\ignorespaces Same as Figure 3.13\hbox {}, but for the W51 complex. The area displayed is larger in order to encompass the entire source structure. The {\rm v}2.0\xspace sources are larger than the corresponding {\rm v}1.0\xspace sources because the negative bowl structures have been filled in. The red contours show regions where {\rm v}2.0\xspace sources were detected, but because of crowding no nearest-neighbor pair was identified in {\rm v}1.0\xspace : there are more {\rm v}2.0\xspace sources than {\rm v}1.0\xspace sources. In this region, the brightest {\rm v}2.0\xspace sources are larger and brighter, but there are fewer fainter sources.}}{115}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.16}{\ignorespaces Distributions of deconvolved angular sizes (left) and aspect ratios (right) of sources in the BGPS catalog. The vertical dashed line in the left figure is plotted at the FWHM of the beam. The BGPS {\rm v}2.0\xspace includes newly observed regions not in the {\rm v}1.0\xspace survey, so separate histograms excluding the new (red dashed) and excluding the old (green solid) regions are shown. In both plots, the histograms are slightly offset to reduce line overlap.}}{117}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.17}{\ignorespaces Distribution of total flux density in catalog sources as a function of longitude (\textit {left}) and latitude (\textit {right}) in the Galactic plane. The distributions contain sources extracted in the $-10 \unhbox \voidb@x \hbox {$^\circ $}\xspace < \ell < 90 \unhbox \voidb@x \hbox {$^\circ $}\xspace $ region. (\textit {right}) Vertical dashed lines indicate the extent of complete coverage in the latitude direction ($\pm 0.5 \unhbox \voidb@x \hbox {$^\circ $}\xspace $). The large excess in {\rm v}2.0\xspace compared to {\rm v}1.0\xspace at $b\sim -0.4$ is due to the W51 complex, in which the flux density recovered in {\rm v}2.0\xspace was $1.5\times $ greater than in {\rm v}1.0\xspace , largely because of reduced negative bowls around the brightest two sources (see Figure 3.14\hbox {}). }}{118}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3.18}{\ignorespaces The two-dimensional distribution of source count in both {\rm v}1.0\xspace and {\rm v}2.0\xspace . The colors in the first two panels illustrate the number of sources per half-degree-squared bin as indicated by the top colorbar. The bottom colorbar labels the ratio of the count of {\rm v}2.0\xspace to {\rm v}1.0\xspace sources. The histograms are coarse versions of Figure 3.15\hbox {} and show the projection of the 2D histograms along each axis. A preference toward negative-latitude sources is evident at $\ell <60\unhbox \voidb@x \hbox {$^\circ $}\xspace $, corresponding to our view of the Galaxy from slightly above the plane.}}{119}}
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\citation{Ginsburg2012a}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.2}{\ignorespaces The predicted optical depth ratio ({\it top}) and optical depth ({\it bottom}) vs. volume density assuming a fixed abundance $X_{\ensuremath {\textrm {o-H}_2\textrm {CO}}\xspace }=10^{-9}$ \textrm {per\nobreakspace {}km\nobreakspace {}s}\ensuremath {^{-1}}\textrm {pc}\ensuremath {^{-1}}\xspace \ shows that the dependence of the derived density on temperature is weak. At lower abundances, these curves shift to the right, providing sensitivity to moderately higher densities. Our 5-$\sigma $ detection limit is generally around $\tau \sim 0.01$. }}{173}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.3}{\ignorespaces The optical depth ratio as a function of density for turbulent density distributions with widths specified in the legend. The optical depth ratio varies more slowly with density than in the pure LVG model (the solid line is the same as the black 10 K line in Figure 5.2\hbox {}a).}}{175}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.4}{\ignorespaces The mean density from a lognormal density distribution plotted against the density derived assuming a single density per region (i.e., the directly LVG-derived density). At low densities, the wider turbulent distributions are heavily biased towards ``observing'' higher densities than the true mean density. The distributions cut off at the low end where the optical depth ratio becomes a double-valued function of density; at these low densities, no detections are expected at our survey's sensitivity. The cutoff at the high end is where the optical depth ratio becomes constant. }}{176}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.5}{\ignorespaces The filling factor corrected (FFC) density vs. the derived density with no filling factor correction. While there are some cases where the correction results in an order of magnitude or more increase in the density, most points show a small correction. The black line is the one-one line. Red squares show where the filling factor corrected point was used, while blue circles show where the uncorrected point was used. Magenta left-pointing triangles are limits where the filling factor correction was used, green downward triangles are limits where the uncorrected points were used, and orange upward triangles are lower limits where the filling-factor correction was used.}}{178}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.6}{\ignorespaces The dependence of derived parameters on the filling factor, assuming an optical depth ratio $\tau _{\ensuremath {1_{10}-1_{11}}\xspace }/\tau _{\ensuremath {2_{11}-2_{12}}\xspace } =$1 (solid), 2 (dash-dot), or 4 (dashed). The X-axis is the ``real'' optical depth, $\tau _{1-1}(real) = \tau _{1-1}(observed) / FF$. Assuming the same filling factor correction is applied to both the \ensuremath {1_{10}-1_{11}}\xspace \ and \ensuremath {2_{11}-2_{12}}\xspace \ lines, filling factor correction will only move the measurements along the X-axis of these plots. A decrease in the filling factor requires an increase in the true optical depth to maintain a constant apparent $\tau (observed)$, which in turn drives up the derived abundance and column density while leaving the volume density unchanged (except at high optical depths, $\tau \gtrsim 0.2$). }}{180}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.7}{\ignorespaces An example of the column density - density parameter space available given measured \ensuremath {1_{10}-1_{11}}\xspace \ and \ensuremath {2_{11}-2_{12}}\xspace \ optical depths. The dashed lines show abundances $\mathop {\mathgroup \symoperators log}\nolimits _{10}(X(\ensuremath {\textrm {o-H}_2\textrm {CO}}\xspace ))$ \textrm {per\nobreakspace {}km\nobreakspace {}s}\ensuremath {^{-1}}\textrm {pc}\ensuremath {^{-1}}\xspace . The contours show the regions allowed by the measurements of optical depth (\ensuremath {1_{10}-1_{11}}\xspace : black, \ensuremath {2_{11}-2_{12}}\xspace : grey, ratio: dotted); the middle curve is the measured value, while the pair of curves around it are $\pm 1\sigma $ including systematic error. The shaded region shows the allowed parameter space from which the physical parameters are derived. }}{181}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.8}{\ignorespaces Same description as Figure 5.7\hbox {} but for the strongest component in G33.13-0.09. It was only possible to measure lower limits on the volume and column density for this line; it is therefore assigned flag 8 in Table 5.5\hbox {}. }}{182}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.9}{\ignorespaces Derived density plotted against kinematic distance. No trend is obvious, demonstrating that the \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ densitometer is not biased by source distance. Black squares represent GMCs along the line of sight; red triangles represent UCH$\mskip \thickmuskip ${\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip \rmfamily II}\relax regions.}}{190}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.10}{\ignorespaces Bolocam 1.1 millimeter flux density versus the cm continuum flux density at 2 cm (left) and 6 cm (right). The BGPS 1.1 mm flux density is moderately correlated with both cm continuum measurements; the legend shows the regression parameter. The expectation for optically-thin free-free emission ( $\alpha = -0.1$, dotted) and for intermediate spectral index emission ($\alpha > 0$, dashed) are shown to illustrate that some sources have significant free-free contributions at 1.1 mm (the optically thick case is not shown for either 2 or 6 cm because it does not fit on the plot). The legend shows the predicted flux densities for a given spectral index $\alpha $, the regression parameter $r$, and its likelihood $p$. The brighter sources are likely to be less optically thick in the free-free continuum than the faint sources. }}{192}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.11}{\ignorespaces The distribution of free-free contributions to the 1.1 mm flux density assuming the UCH$\mskip \thickmuskip ${\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip \rmfamily II}\relax \xspace \ region is optically thin at 2 cm, $f_{ff} = (S_{2 cm}/1.34)/S_{1.1 mm}$. While 9 sources are either dust-dominated or optically thick at 2 cm, 6 sources have free-free contributrions of 30\% or greater. The other sources in the sample were missing 1.1 mm flux density measurements because they are outside the BGPS survey area. }}{192}}
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\citation{Sewilo2004}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.12}{\ignorespaces {\it Left:} Histograms of BGPS 1.1 mm 40\unhbox \voidb@x \hbox {$^{\prime \prime }$}\xspace \ aperture flux densities (red) and the MAGPIS 6 cm flux densities (black), and their respective best-fit power-law distributions ($\alpha (1.1 mm)=2.41\pm 0.03$, $\alpha (6 cm)=1.72\pm 0.03$). The dashed black line shows the MAGPIS best-fit power-law scaled down to the expected flux density at 1.1 mm assuming all sources are optically thin. Both distributions appear to be reasonably well-fit by power-laws above a cutoff (presumably set by completeness), although the power-law significantly over-predicts the number of sources with $S_{6 cm}>1$Jy. The histograms are binned by 0.1 dex, and while the best-fit $\alpha $ and $x_{min}$ values are independent of the binning scheme, the normalization is not. {\it Right:} The ratio of the number of MAGPIS 6 cm sources to BGPS 1.1 mm sources as a function of flux density for the best-fit power laws. Only 10 1.1 mm sources are detected above 5 Jy (in 40\unhbox \voidb@x \hbox {$^{\prime \prime }$}\xspace \ apertures), so even the brightest detected 1.1 mm sources are not purely free-free, but they probably have a substantial free-free component.}}{194}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.13}{\ignorespaces A plot of the two derived sizes discussed in Section 5.7.3.1\hbox {}. The two size estimates are at best very weakly correlated. Because of the substantial disagreement between the two methods, we choose not to explore any parameters with a strong dependence on the size. The plotted point size indicates the number of associated line-of-sight GMCs, which in principle could lead to an overestimate of the $N/n$ size because of additional mass included in the 1.1 mm continuum measurement.}}{196}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.14}{\ignorespaces Comparison of the UCH$\mskip \thickmuskip ${\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip \rmfamily II}\relax sample (blue circles are measurements, blue triangles are lower limits on volume density with poorly constrained column densities), the GMC sample (red squares), secondary lines associated with UCH$\mskip \thickmuskip ${\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip \rmfamily II}\relax \xspace \ regions (black stars) and the extragalactic sample of \citet {Mangum2008} (green squares). The errorbars on the Galactic data points are excluded for clarity. The observed galaxies have similar densities to the Galactic UCH$\mskip \thickmuskip ${\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip \rmfamily II}\relax \xspace \ sample, but significantly lower column densities, suggesting that the molecular gas in these galaxies has a filling factor $<<1$. The lack of direct density measurements of UCHII regions at high densities is due to the presence of a dominant background source; in Arp 220 a direct measurement of density was possible because \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ was seen in emission.}}{198}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.15}{\ignorespaces Plot of the derived parameters per velocity bin for the main line of G32.80+0.19; the full spectrum is shown in Figure 5.1\hbox {}. The density peak around 16 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ is slightly redshifted of the H and C RRL velocity centers, although the C RRLs are blueshifted of the H RRLs, indicating that the PDR has been accelerated towards us along the line of sight. The blueshifted emission tail is suggestive of an outflow. This source cannot therefore be easily classified under any of the scenarios in Section 5.8.3\hbox {}, but is consistent with components of scenarios 2 and 3. {\it a.} The spectra of G32.80+0.19. The GBT \ensuremath {2_{11}-2_{12}}\xspace \ spectrum (red solid) has been smoothed to a resolution of 0.38 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace \ to match the Arecibo (black dashed) spectral resolution. Labeled vertical bars indicate the measured velocity centers of H and C RRLs from this work, \citet {Roshi2005}, and \citet {Churchwell2010}. {\it b.} The measured densities in each spectral bin. The Y-scale is in log$_{10}$ units. Error bars include a 10\% systematic uncertainty in the continuum and therefore errors in adjacent channels are not independent. Limits are indicated by triangles. Bins with no information above the 1-$\sigma $ noise cutoff are left blank. The increase of density towards higher velocities led us to classify this source as a {\it red gradient} in Table 5.3\hbox {}. {\it c.} The measured column densities per spectral bin. Because these column densities are derived from a large velocity gradient code, they are in \textrm {per\nobreakspace {}km\nobreakspace {}s}\ensuremath {^{-1}}\textrm {pc}\ensuremath {^{-1}}\xspace \ units. {\it d.} The measured abundances per spectral bin. The column and abundance are somewhat degenerate, but it is possible in some cases to place tight constraints on the total \ensuremath {\textrm {o-H}_2\textrm {CO}}\xspace \ column while only placing upper limits on abundance and density. The abundance must also be interpreted \textrm {per\nobreakspace {}km\nobreakspace {}s}\ensuremath {^{-1}}\textrm {pc}\ensuremath {^{-1}}\xspace . In plots {\it b} through {\it d}, the blue square with error bars represents the measured value from Table 5.5\hbox {} using gaussian fits to the lines. }}{201}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5.17}{\ignorespaces Scenario 1: An UCH$\mskip \thickmuskip ${\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip \rmfamily II}\relax \xspace \ region forms and begins expanding spherically in a uniform density gas cloud. A cartoon of the geometry seen by the observer is shown on the left side of the figure, with arrows indicating expansion and darkness of the gray shading indicating relative density. The white region around the central star is the ionized UCH$\mskip \thickmuskip ${\relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip \rmfamily II}\relax \xspace \ region. On the right side, a cartoon of the relative velocity and width of the RRLs and \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ lines is shown. The relative heights of the \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ lines is representative of the observed density; black is \ensuremath {1_{10}-1_{11}}\xspace \ and red is \ensuremath {2_{11}-2_{12}}\xspace . The narrow emission line with a ? above it indicates a possible blueshifted carbon RRL; its height has no physical meaning. In this scenario, the hydrogen recombination and \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ lines should occur at the same velocity, and the \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ lines should show relatively low-density (high \ensuremath {1_{10}-1_{11}}\xspace /\ensuremath {2_{11}-2_{12}}\xspace \ ratio) and modest spectral line widths. A blueshifted carbon RRL may form, but is not guaranteed.}}{202}}
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\citation{Green1994}
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\citation{Troscompt2009}
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\@writefile{lof}{\contentsline {figure}{\numberline {6.2}{\ignorespaces The \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ \ensuremath {1_{10}-1_{11}}\xspace \ line widths plotted against the SO\nobreakspace {}\ensuremath {1_2-1_1}\xspace line widths where SO\nobreakspace {}\ensuremath {1_2-1_1}\xspace was detected. The Pearson correlation coefficient is $|r|<0.1$ even when excluding outliers with FWHM in either line $>3.5$ \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace , indicating that SO\nobreakspace {}\ensuremath {1_2-1_1}\xspace and \ensuremath {\textrm {H}_2\textrm {CO}}\xspace do not trace the same gas.}}{224}}
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\@writefile{lof}{\contentsline {figure}{\numberline {6.3}{\ignorespaces The \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ \ensuremath {1_{10}-1_{11}}\xspace \ (left) and \ensuremath {2_{11}-2_{12}}\xspace \ (right) line depths plotted against the SO\nobreakspace {}\ensuremath {1_2-1_1}\xspace \ line peaks where SO\nobreakspace {}\ensuremath {1_2-1_1}\xspace was detected. Taken as a whole, the SO\nobreakspace {}\ensuremath {1_2-1_1}\xspace \ lines peaks are uncorrelated with the \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ line depths, but for single-peak \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ absorption, there is moderate correlation between the SO\nobreakspace {}\ensuremath {1_2-1_1}\xspace \ peak and the \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ absorption depth.}}{224}}
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\@writefile{lof}{\contentsline {figure}{\numberline {6.4}{\ignorespaces The SO\nobreakspace {}\ensuremath {1_2-1_1}\xspace line integrals plotted against the BGPS column densities (assuming $T_{D}=20$K). The correlation indicates that SO\nobreakspace {}\ensuremath {1_2-1_1}\xspace weakly traces the total column density.}}{225}}
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\@writefile{lof}{\contentsline {figure}{\numberline {6.6}{\ignorespaces Histogram of the measured total abundance of \ensuremath {\textrm {o-H}_2\textrm {CO}}\xspace . The blue histogram shows all of the formaldehyde observations, while the red histogram shows only those consistent with the apparent gaussian distribution of abundances centered around $X_{\ensuremath {\textrm {o-H}_2\textrm {CO}}\xspace }\sim 10^{-9}$. Outliers were rejected using the \texttt {sklearn.covariance.MinCovDet} function.}}{226}}
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\@writefile{lof}{\contentsline {figure}{\numberline {6.7}{\ignorespaces The total \ensuremath {\textrm {H}_2\textrm {CO}}\xspace \ column plotted against the total 1.1 mm column density. The data are reasonably correlated, but the best fit line has decreasing abundance with increasing column density. The best fits exclude outliers from the abundance distribution.}}{227}}
\newlabel{fig:colvscol}{{6.7}{227}}
\citation{Ginsburg2011}
\@writefile{lof}{\contentsline {figure}{\numberline {6.8}{\ignorespaces (left) Regions of parameter space in which the \ensuremath {2_{11}-2_{12}}\xspace \ line will be seen in emission while the \ensuremath {1_{10}-1_{11}}\xspace line is seen only in absorption for T$=50$ K. For T$=20$ K, the regions of parameter space that allow \ensuremath {2_{11}-2_{12}}\xspace emission and \ensuremath {1_{10}-1_{11}}\xspace absorption are smaller, but follow the same general trend. (right) Regions of parameter space where the \ensuremath {1_{10}-1_{11}}\xspace line will be seen in emission and the \ensuremath {2_{11}-2_{12}}\xspace line in absorption. Since we do not detect any examples of this case, but extragalactic observations have, we show the highest temperature case for which collision rates are available, T$=50$ K. Note that the central region of this parameter space is empty: normal galactic clouds cannot have \ensuremath {1_{10}-1_{11}}\xspace emission and \ensuremath {2_{11}-2_{12}}\xspace absorption at T$=50$ K.}}{228}}
\newlabel{fig:emiabs}{{6.8}{228}}
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\citation{Aguirre2011}
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\citation{Ginsburg2011c}
\citation{Ginsburg2012a}
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\citation{Ginsburg2009}
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\citation{Clauset2007}
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\bibcite{adams1996}{{1}{1996}{{{Adams} \& {Fatuzzo}}}{{}}}
\bibcite{Aguirre2011}{{2}{2011}{{{Aguirre} {et~al.}}}{{{Aguirre}, {Ginsburg}, {Dunham}, {Drosback}, {Bally}, {Battersby}, {Bradley}, {Cyganowski}, {Dowell}, {Evans}, {Glenn}, {Harvey}, {Rosolowsky}, {Stringfellow}, {Walawender}, \& {Williams}}}}
\bibcite{Alexander2012a}{{3}{2012}{{{Alexander} \& {Kobulnicky}}}{{}}}
\bibcite{Anderson2009}{{4}{2009}{{{Anderson} {et~al.}}}{{{Anderson}, {Bania}, {Jackson}, {Clemens}, {Heyer}, {Simon}, {Shah}, \& {Rathborne}}}}
\bibcite{Andre2010a}{{5}{2010}{{{Andr{\'e}} {et~al.}}}{{{Andr{\'e}}, {Men'shchikov}, {Bontemps}, {K{\"o}nyves}, {Motte}, {Schneider}, {Didelon}, {Minier}, {Saraceno}, {Ward-Thompson}, {di Francesco}, {White}, {Molinari}, {Testi}, {Abergel}, {Griffin}, {Henning}, {Royer}, {Mer{\'{\i }}n}, {Vavrek}, {Attard}, {Arzoumanian}, {Wilson}, {Ade}, {Aussel}, {Baluteau}, {Benedettini}, {Bernard}, {Blommaert}, {Cambr{\'e}sy}, {Cox}, {di Giorgio}, {Hargrave}, {Hennemann}, {Huang}, {Kirk}, {Krause}, {Launhardt}, {Leeks}, {Le Pennec}, {Li}, {Martin}, {Maury}, {Olofsson}, {Omont}, {Peretto}, {Pezzuto}, {Prusti}, {Roussel}, {Russeil}, {Sauvage}, {Sibthorpe}, {Sicilia-Aguilar}, {Spinoglio}, {Waelkens}, {Woodcraft}, \& {Zavagno}}}}
\bibcite{Araya2002}{{6}{2002}{{{Araya} {et~al.}}}{{{Araya}, {Hofner}, {Churchwell}, \& {Kurtz}}}}
\bibcite{Araya2004}{{7}{2004}{{Araya {et~al.}}}{{Araya, Hofner, Linz, Sewilo, Watson, Churchwell, Olmi, \& Kurtz}}}
\bibcite{arce2010}{{8}{2010}{{{Arce} {et~al.}}}{{{Arce}, {Borkin}, {Goodman}, {Pineda}, \& {Halle}}}}
\bibcite{Arvidsson2010a}{{9}{2010}{{{Arvidsson} {et~al.}}}{{{Arvidsson}, {Kerton}, {Alexander}, {Kobulnicky}, \& {Uzpen}}}}
\bibcite{Arzoumanian2011a}{{10}{2011}{{{Arzoumanian} {et~al.}}}{{{Arzoumanian}, {Andr{\'e}}, {Didelon}, {K{\"o}nyves}, {Schneider}, {Men'shchikov}, {Sousbie}, {Zavagno}, {Bontemps}, {di Francesco}, {Griffin}, {Hennemann}, {Hill}, {Kirk}, {Martin}, {Minier}, {Molinari}, {Motte}, {Peretto}, {Pezzuto}, {Spinoglio}, {Ward-Thompson}, {White}, \& {Wilson}}}}
\bibcite{Bachiller1996}{{11}{1996}{{Bachiller}}{{}}}
\bibcite{Bally2010}{{12}{2010}{{{Bally} {et~al.}}}{{{Bally}, {Aguirre}, {Battersby}, {Bradley}, {Cyganowski}, {Dowell}, {Drosback}, {Dunham}, {Evans}, {Ginsburg}, {Glenn}, {Harvey}, {Mills}, {Merello}, {Rosolowsky}, {Schlingman}, {Shirley}, {Stringfellow}, {Walawender}, \& {Williams}}}}
\bibcite{bally-perseus2008}{{13}{2008}{{{Bally} {et~al.}}}{{{Bally}, {Walawender}, {Johnstone}, {Kirk}, \& {Goodman}}}}
\bibcite{Barmby2006}{{14}{2006}{{{Barmby} {et~al.}}}{{{Barmby}, {Ashby}, {Bianchi}, {Engelbracht}, {Gehrz}, {Gordon}, {Hinz}, {Huchra}, {Humphreys}, {Pahre}, {P{\'e}rez-Gonz{\'a}lez}, {Polomski}, {Rieke}, {Thilker}, {Willner}, \& {Woodward}}}}
\bibcite{Bastian2008}{{15}{2008}{{Bastian}}{{}}}
\bibcite{Battersby2011}{{16}{2011}{{{Battersby} {et~al.}}}{{{Battersby}, {Bally}, {Ginsburg}, {Bernard}, {Brunt}, {Fuller}, {Martin}, {Molinari}, {Mottram}, {Peretto}, {Testi}, \& {Thompson}}}}
\bibcite{Beaumont2009}{{17}{2010}{{{Beaumont} \& {Williams}}}{{}}}
\bibcite{Benjamin2003}{{18}{2003}{{{Benjamin} {et~al.}}}{{{Benjamin}, {Churchwell}, {Babler}, {Bania}, {Clemens}, {Cohen}, {Dickey}, {Indebetouw}, {Jackson}, {Kobulnicky}, {Lazarian}, {Marston}, {Mathis}, {Meade}, {Seager}, {Stolovy}, {Watson}, {Whitney}, {Wolff}, \& {Wolfire}}}}
\bibcite{Berriman2004a}{{19}{2004}{{{Berriman} {et~al.}}}{{{Berriman}, {Good}, {Laity}, {Bergou}, {Jacob}, {Katz}, {Deelman}, {Kesselman}, {Singh}, {Su}, \& {Williams}}}}
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by the relatively insensitive \ensuremath {2_{11}-2_{12}}\xspace \ spectrum.
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all, but otherwise a somewhat vanilla spectrum. W51e2 has a large, high-density
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[236] [237
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3 40 \textrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace cloud. The bac
kground image shows Herschel SPIRE 70 \ensuremath {\mu \textrm {m}}\xspace (
red), Spitzer MIPS 24 \ensuremath {\mu \textrm {m}}\xspace (green), and Spit
zer IRAC 8 \ensuremath {\mu \textrm {m}}\xspace (blue) in the background wit
h the \ensuremath {^{13}\textrm {CO}}\xspace integrated image from $v=36 \te
xtrm {km\nobreakspace {}s}\ensuremath {^{-1}}\xspace $ to $v=43 \textrm {k
m\nobreakspace {}s}\ensuremath {^{-1}}\xspace $ at contour levels of 1, 2, a
nd 3 K superposed in orange contours. The red and black circles show the locati
ons of \ensuremath {\textrm {H}_2\textrm {CO}}\xspace pointings, and their
labels indicate the LSR velocity of the strongest line in the spectrum. The W49
HII region is seen behind some of the faintest \ensuremath {^{13}\textrm {CO
}}\xspace emission that is readily associated with this cloud. The dark swath
in the 8 and 24 \ensuremath {\mu \textrm {m}}\xspace emission going through
the peak of the \ensuremath {^{13}\textrm {CO}}\xspace emission in the lower
half of the image is likely a low optical depth infrared dark cloud associated
with this GMC.}}{237}}
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[238
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l depth spectra of the \ensuremath {1_{10}-1_{11}}\xspace and \ensuremath {2
_{11}-2_{12}}\xspace lines towards the two W49 lines of sight, G43.16 (left) a
nd G43.17 (right). The fitted parameters, along with the statistical 1-$\sigma
$ errors, are shown in the legend. The optical depth ratio falls in a regime wh
ere temperature has very little effect and there is no degeneracy between low a
nd high densities \citep [see Figure 2 of][]{Ginsburg2011a}. For the right lin
e, it is also unaffected by lognormal turbulence, i.e. no matter what the width
of the density distribution, the measured density remains unchanged \citep [s
ee Figure 3 of][]{Ginsburg2011a}.}}{238}}
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