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\section{Low Density \section{Non-star-forming, low column-density  clouds in absorption} In \citet{Ginsburg2011a}, we noted that the \formaldehyde densitometer revealed  volume densities much higher than expected given the cloud-average densities  from \thirteenco observations. The densities were higher even than typical 
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here we attempt to demonstrate that the clumps in GMCs are of very high density  in individual clouds.  In order to detect low-density low-column-density  clouds, we must use bright background illumination sources at 2 and 6 cm, i.e. HII regions. There are a few dozen of  these within the inner Galactic plane, including the sources observed in  \citet{Ginsburg2011a} and the majority of the bright sources in the BGPS  \citep{Ginsburg2012}.  As an example case-study, we examine G43.17+0.01, also known as W49. In the  large survey, we observed two lines of sight towards W49, the second at  G43.16-0.03. Both are very bright continuum sources, and two GMCs are easily  detected in \formaldehyde absorption and \thirteenco emission. Figure  \ref{fig:w49fullspec} shows the spectrum dominated by W49 itself, but with  clear absorption components. The continuum level subtracted from the spectra  are 73 K at 6 cm and 11 K at 2 cm for the south component, and 194 K at 6 cm  and 28 K at 2 cm for the north component.  \FigureTwo{figures_chH2CO/G43.17+0.01_H2CO_overplot_gbt9x.png}  {figures_chH2CO/G43.16-0.03_H2CO_overplot_gbt9x.png}  {Spectra of the \formaldehyde \oneone (black), \twotwo (red), and \thirteenco  1-0 (green) lines towards G43.17+0.01 (left) and G43.16-0.03 (right).  The \formaldehyde spectra are shown continuum-subtracted, and the \thirteenco  spectrum is offset by 1 K for clarity. The GBT \twotwo spectra are multiplied  by a factor of 9 so the smaller lines can be seen.  }{fig:w49fullspec}{1}  We focus on the ``foreground'' lines at $\sim40\kms$ and $\sim65\kms$, since  they are not associated with the extremely massive W49 region. It is difficult  to assess the level of star formation within these clouds, since they lie  directly along the line of sight to W49, but additional \formaldehyde spectra  of the surrounding sources that are bright at 8-1100 \um show that they are all  at the velocity of W49.   The 40 \kms cloud is observed in its outskirts, not at the peak of the  \thirteenco emission. The cloud structure is vast, spanning $\sim0.6\degrees$,   or $\sim60$ pc at $D=2.8$ kpc \citep{Roman-Duval2009}. It is detected in \oneone  absorption at all 6 locations observed in \formaldehyde, but \twotwo is only  detected in front of the W49 HII region because of the higher signal-to-noise at  that location.  The highest \thirteenco contours are observed as a modest IRDC, but no dust  emission peaks are observed at 500 \um or 1.1 mm. This is an indication that  any star formation, if present, is weak - no clusters are presently forming  from this cloud. It resembles, in that respect, the California molecular  cloud.  \Figure{figures_chH2CO/W49_RGB_aplpy.png}  {The G43 40 \kms cloud. The background image shows Herschel SPIRE 70 \um (red),  Spitzer MIPS 24 \um (green), and Spitzer IRAC 8 \um (blue) in the background with  the \thirteenco integrated image from $v=36 \kms$ to $v=43 \kms$ at contour levels of  1, 2, and 3 K superposed in orange contours. The red and black circles  show the locations of \formaldehyde 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 \thirteenco emission that is readily associated  with this cloud. The dark swath in the 8 and 24 \um emission going through the  peak of the \thirteenco emission in the lower half of the image is likely a low  optical depth infrared dark cloud associated with this GMC.}  {fig:40kmscloud}{0.5}{0}  The \formaldehyde densitometer measurements are shown in Figure \ref{fig:h2codensg43}.  The figures show optical depth spectra, given by the equation  $$\tau = -\log\left(\frac{S_\nu + 2.73}{\bar{S_\nu} + 2.73}\right)$$  where $S_\nu$ is the spectrum (with continuum included) and $\bar{S_\nu}$ is  the measured continuum.  \FigureTwo{figures_chH2CO/G43.16-0.03_40kms_h2codensfit.png}  {figures_chH2CO/G43.17+0.01_40kms_h2codensfit.png}  {Optical depth spectra of the \oneone and \twotwo lines towards the two W49 lines  of sight. The fitted parameters, along with the statistical 1-$\sigma$ errors,  are shown in the legend.}  {fig:h2codensg43}{1}  The density measurements are very precise, with $n\approx2.11\times10^4 \pm  0.17\ee{4}$ \percc and $n\approx 1.98\times10^4 \pm 0.32\ee{4}$ \percc for  G43.17+0.01 and G43.16-0.03 respectively. At this level of precision, the   density measurements are dominated by systematics - especially gas temperature  and collision rate uncertainties - which limit the accuracy to $\sim50\%$  \citep{Zeiger2010}. Nonetheless, the density is much higher than the  \thirteenco-measured cloud-average density $n\approx 400$ \percc  \citep[for cloud GRSMC\_G043.04-00.11;][]{Roman-Duval2010a}, with  $n_{\formaldehyde}/n_{\thirteenco} \approx 50$.   Since the W49 line of sight is clearly on the outskirts of the cloud, not  through its core, such a high density is unlikely to be an indication that  this line of sight corresponds to a centrally condensed density peak. Using  Figure 4 of \citet{Ginsburg2011a}, we can `turbulence-correct' the density  measurements, but even in the most extreme case with a turbulent density  distribution lognormal width $\sigma_s = 1.5$, the correction is only a factor  of 2.5, reducing the discrepancy to a factor of $\sim20$.  % We should then ask, if there is gas at high density, how much is at this density?  % To address this question, we'll assume that the densities in all of the \formaldehyde  % lines of sight in the cloud are the same, and compare the \thirteenco and  % \formaldehyde derived column densities. The \oneone line robustly reflects the  % total \formaldehyde column, even though it does not constrain the density  % without a corresponding \twotwo detection.  Comparing the integrated \formaldehyde lines to the integrated \thirteenco  lines, we have $N_(\ortho) = 2.03\ee{12} $ and $1.56\ee{12}$ \persc for G43.16  and G43.17 respectively.  The \thirteenco integrated spectra have brightness $T_{MB} = 2.6$ K and $1.3$ K  for G43.16 and G43.17 respectively. Using the cloud-averaged excitation  temperature for this cloud, $\tau_{13}=2.3$ and $0.6$ respectively, so  \citet{Roman-Duval2010a} equation 3 yields column densities $N_{13} = 6.2\ee{15}  $ and $1.6\ee{15}$ \percc respectively. Assuming an abundance relative to \hh  $X_{13} = 1.77\ee{-6}$, the resulting \hh column densities are 3.5\ee{21} and  9.0 \ee{20} \percc respectively.   The abundances of \ortho relative to \thirteenco are 3.2\ee{-4} and 9.8\ee{-4}  respectively, or relative to \hh, 5.8\ee{-10} and 1.7\ee{-9}, which are entirely consistent  with other measurements of $X_{\formaldehyde}$.  These are relatively modest column densities,  with $A_V=17$ and 4.5.  These measurements for a specific cloud validate the statistical argument made  in \citet{Ginsburg2011a}. However, upon closer inspection of the cloud  morphology, the real explanation may be simple: the filling factor of gas  within the GMC is small on large scales, not local scales. The implied volume  filling factor from this analysis and the \citet{Ginsburg2011a} analysis is  $\sim10^{-2}$; the assumption of spherical symmetry is therefore extremely  poor.   This low filling factor has major implications for the gas: if it is in  gravitational collapse, the free-fall times are shorter by an order of  magnitude than usually assumed. The long lifetimes of GMCs therefore implies  that the cloud cannot be undergoing gravitational collapse, but instead  maintains a turbulent equilibrium.  diff --git a/thesis.bib b/thesis.bib  index 3e43dfd..26175a6 100644  --- a/thesis.bib  +++ b/thesis.bib 
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  @article{Rathborne2009a,  Author = {{Rathborne}, J.~M. and {Lada}, C.~J. and {Muench}, A.~A. and {Alves}, J.~F. and {Kainulainen}, J. and {Lombardi}, M.},  Journal = {\apj},  Month = jul,  Pages = {742-753},  Title = {{Dense Cores in The Pipe Nebula: An Improved Core Mass Function}},  Volume = 699,  Year = 2009}  @article{Roman-Duval2010a,  Author = {{Roman-Duval}, J. and {Jackson}, J.~M. and {Heyer}, M. and {Rathborne}, J. and {Simon}, R.},  Journal = {\apj},  Month = nov,  Pages = {492-507},  Title = {{Physical Properties and Galactic Distribution of Molecular Clouds Identified in the Galactic Ring Survey}},  Volume = 723,  Year = 2010}  @article{Roman-Duval2011a,  Author = {{Roman-Duval}, J. and {Federrath}, C. and {Brunt}, C. and {Heyer}, M. and {Jackson}, J. and {Klessen}, R.~S.},  Journal = {\apj},  Month = oct,  Pages = {120},  Title = {{The Turbulence Spectrum of Molecular Clouds in the Galactic Ring Survey: A Density-dependent Principal Component Analysis Calibration}},  Volume = 740,  Year = 2011}  @article{Roman-Duval2009a,  Author = {{Roman-Duval}, J. and {Jackson}, J.~M. and {Heyer}, M. and {Johnson}, A. and {Rathborne}, J. and {Shah}, R. and {Simon}, R.},  Journal = {\apj},  Month = jul,  Pages = {1153-1170},  Title = {{Kinematic Distances to Molecular Clouds Identified in the Galactic Ring Survey}},  Volume = 699,  Year = 2009}  @article{Hennebelle2011a,  Author = {{Hennebelle}, P. and {Chabrier}, G.},  Journal = {\apjl},  diff --git a/thesis.pdf b/thesis.pdf  index 4ee9e2e..8ff4ab1 100644  Binary files a/thesis.pdf and b/thesis.pdf differ