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%\input{preface}  \section{\formaldehyde Mapping}  We were lucky enough to be awarded \emph{double} the time we asked for on the GBT,  allowing us to observe large areas in mapping mode.   Naturally, we picked the brightest and best-known regions for mapping studies.  In the inner galaxy, we mapped out an area $\sim50\arcmin\times20\arcmin$ centered  on the W51 massive star forming complex. This region is ideally suited to study from Arecibo,  the GBT, and the VLA, since it is at declination +14 and is one of the brightest continuum  sources in the Galactic plane. It also turns out to be the nearest proto-massive cluster  at a VLBI-parallax-measured distance of 5.1 kpc (see Chapter \ref{ch:ympc} for a discussion  of massive proto-clusters). The simple reduction of this data is nearly complete, but   analysis has only begun.  In the outer galaxy, we targeted two regions: the Sh 255 complex in Gem OB1 and  the Sh 233-IR/IRAS 05358 complex I studied for my Comps II project. We made  small ($\sim 5\arcmin\times 5\arcmin$) maps of these objects in order to  evaluate the density profiles and determine what systematic biases may have  been present in our single-pointing observations. These outer galaxy sources  are both at $D<2$ kpc, so our resolution is $\lesssim 0.5 $pc and we therefore  have some marginal hope of discovering dense cores without diluting their  signal too badly.  \subsection{\formaldehyde maps of S233IR}  For the S233IR region, we were able to create a density map, but found the  surprising and counterintuitive result that the density was smallest at the  peak of the BGPS 1.1 mm emission. The ``envelope'' is at a nearly constant density  $n\sim10^{3.5}\percc$, but the core is either at a low density (which is effectively  ruled out on other considerations) or is significantly self-absorbed. It turns out   that \formaldehyde \twotwo \emph{emission} fills in the absorption.  Figure \ref{fig:s233irmulti} shows the mapping results for the S233 IR region, where  `envelope' densities are measured to be $n\sim10^{3.3}-10^{3.7} \percc$, but the `core'  density is more weakly constrained to be $10^{4.5}\percc < n < 10^{5.5}\percc$ based  on the presence of \formaldehyde \twotwo emission and the absence of \oneone emission.  The lack of a direct measurement makes density profile measurement with the current  observations impossible.   The moderate densities observed in the envelopes are nonetheless an order of  magnitude higher than typical volume-averaged GMC densities  \citep{Roman-Duval2010} as was previously noted for ordinary GMCs with  \formaldehyde detections in \citet{Ginsburg2011}.   Perhaps most interesting is the contrast between the two BGPS sources shown   in Figure \ref{fig:s233irmulti}. In \citet{Ginsburg2009}, I examined primarily  S233IR, but its neighboring region G173.58+2.45 is also a well-studied proto-cluster.  Unlike S233IR, which has a B1/B2 10 \msun star that is probably still accreting,  G173.58 contains no massive stars and has an upper mass limit $M\lesssim4 \msun$  \citep{Shepherd2002}. The \formaldehyde observations reveal that the density in this  clump is $\sim10^{3.6} \percc$, substantially less than the expected $n\sim10^5 \percc$  in the massive-star forming S233IR.  The BGPS data show this difference as well, but less strikingly. In the BGPS  data, the inferred masses of S233IR and G173 are 840 and 190 \msun,  respectively, though lower by a factor of $\sim2$ in each when considering only  their condensed $r\lesssim0.4$ pc cores. Their densities differ by a smaller  amount using the BGPS data and assuming spherical symmetry, with peak densities  $n\sim10^{4.1}$ in G173 and $n\sim10^{4.8}$ in S233IR. The density difference  reinforces the conclusion drawn from the \formaldehyde data, but also show that its  density measuring power is greater, since the spherical symmetry assumption is known  to be flawed.  % S233IR:  % peak column: 6.09*2.08e22*(np.exp(13.01/20)-1) = 1.16e23  % h2co column: "%e" % (6.09*2.08e22*(np.exp(13.01/20)-1) * 1e-9) = 1.16e14  % total flux = 220 / 23.8 = 9.24  % mass is then 9.2 * 1.8**2 * 14.3 * (np.exp(13.01/20)-1) = 400 msun (600 by other measures; close enough)  % radius ~30 arsec ~ 0.3pc  % n ~ 6.7e4, 10^4.8  % TOTAL flux/mass, in full aperture, is 471/23.8=19.7 Jy, or 840 msun  %  % G173:  % flux ~62 Jy/bm, /ppbeam = 2.6 Jy ~ 2.6 * 1.8**2 * 14 = 120 msun  % TOTAL 107 Jy/beam /ppbeam=4.5 -> 190 msun  % radius = 40 arcsec = 0.35 pc  % density = 120 * 2e33 / (4/3*np.pi*(0.35*3.08e18)**3) / ( 2.8 * 1.67e-24 ) = 1.3e4  \Figure{figures_chH2CO/S233IR_multipanel}  {The S233IR / IRAS 05358+3543 region and its neighbor G173.58+2.45.  {\it Top left:} The \formaldehyde density map covering densities  $10^2 \percc  regions of low density ($n<10^3$ \percc), while green show high-density  regions ($n\gtrsim10^3.5$ \percc). The `hole' at the peak of the contours  is likely very high density, $n>10^5$ \percc.  {\it Top center: } The \formaldehyde \oneone absorption map.  {\it Top right: } The \formaldehyde \twotwo absorption map.  Note the lack of absorption at the contour peak: this is probably \twotwo emission  filling in \twotwo absorption, indicating a high $n\gtrsim10^5$ \percc density.  {\it Bottom left: } CO 3-2 map.  {\it Bottom center: } The BGPS v2.0 1.1 mm emission map, with contours at 0.2, 1.0, and 3.0 Jy.  These contours are shown on all of the other maps for reference.  {\it Bottom right: } SO $5_6-4_5$ map. This line has a very high critical density $n\sim3.5\ee{6}$ \percc  and an upper level energy $T_U=35$ K.  Its morphology, with a hole at the peak of the dust emission, backs the claim that the density is highest  in the area around the dust peak.}  {fig:s233irmulti}{0.2}{0}  % tried subtracting "envelope" from "core" and still got absorption  \subsection{W51}  The W51 survey was completed in September 2011. The data reduction process  presented unique challenges: at C-band, the entire region surveyed contains  continuum emission, so no truly suitable `off' position was found within the  survey data. Similarly, \formaldehyde is ubiquitous across the region, so it  was necessary to `mask out' the absorption lines when building an off position.  This was done by interpolating across the line-containing region with a  polynomial fit (Figure \ref{fig:h2comask}.   \Figure{figures_chH2CO/a2705.20120915.b0s1g0.00000_offspectra.png}  {An example of the \formaldehyde line masking procedure for building an Off  spectrum. The line-containing regions for each polarization are shown in cyan  and purple, with the interpolated replacement in red and green.  }{fig:h2comask}{0.4}{0}  The W51 data are converted into ``optical depth'' data cubes by dividing the  integrated \formaldehyde absorption signature by the measured continuum level.  These $\tau$ cubes are then fit with the RADEX models used for other  \formaldehyde fitting. However, there are multiple velocity components in W51,  so I used a two-component (unconstrained) fit for each pixel, which is  frequently unstable but in the case of W51 looks to have produced reasonable  results. Note that there was \emph{no} \formaldehyde emission detected anywhere  in the W51 region.  A first interesting note is that a local cloud at $v_{lsr}\sim5 \kms$ is  detected in \formaldehyde \oneone across most of the cloud and not detected at  \twotwo, with $\tau_{\oneone}/\tau_{\twotwo} \gtrsim 3$, implying a  very low column  $N_{\formaldehyde}\sim10^{11.5}$ or $N_{\hh} \sim 10^{20.5}$.   The cloud is seen in \thirteenco as a very weak, diffuse feature, and in HI absorption  as a very sharp, deep (self)-absorption feature.  % This density measurement  % is consistent with observations from \citet{Ginsburg2011} of high density in  % GMCs. However, GMCs are generally thought of as being low-density clouds, so  % this result may be surprising.  %FIGURE: mcmc column vs density   I successfully made density maps of the W51 cloud, though because the velocity  structure is quite complicated, it was necessary to fit two components to most of the  map. Two-component fits are never particularly stable, so it was necessary to  restrict the parameters being fitted, and even then the results aren't  perfectly reliable. Despite those caveats, there are some reliable fits,  particularly towards the `core' of W51 Main / W51 IRS 2. There are two  high-density components with $n\sim10^5-10^{5.5}$ \percc at different velocities evident  in Figure \ref{fig:w51h2cofits}. The southern component, centered on W51 Main,  has $v_{LSR}\sim56-59$. The northern component, a strip going through IRS 2  and towards the west, peaks around $v_{LSR}\sim68-69$ \kms. A 10 \kms difference  between two extremely dense components, both which are necessarily in the  foreground of the HII region, is shocking (probably, anyway, unless the sound  speed is very high).  \FigureTwo{figures_chH2CO/W51_H2CO_2parfit_v1_densityvelocity.png}  {figures_chH2CO/W51_H2CO_2parfit_v2_densityvelocity.png}  {Density and velocity fits to the W51 Arecibo and GBT \formaldehyde   data cubes. The yellow regions in the top panel correspond to \oneone  detections and \twotwo nondetections, indicating upper limits $n<10^{3.8}$  (68\% confidence) or $n<10^{4.3}$ (99.7\% confidence).}  {fig:w51h2cofits}{1}  There is a large area where \oneone was detected, but \twotwo was not. Our  sensitivity allows us to place a modest upper limit on the gas density, with  $3-\sigma$ upper limits $\lesssim10^{4.3}$ \percc (but the most likely  densities are $10^2 < n < 10^4$ \percc). Figure \ref{fig:w51MCMCcompare} shows  a particular model for a spectrum that is especially unconstrained. The  \oneone/\twotwo optical depth in this object is $\sim10-20$, indicating that  the volume density must be low.  \FigureTwo{figures_chH2CO/MCMC_DensColplot_67_64.png}{figures_chH2CO/spec67_64_bestfit_MCMC.png}  {Plots demonstrating upper limit fits. The left plot shows the allowed  parameter space from MCMC sampling of the data given the RADEX model. The  right plot shows the `best-fit' model to the optical depth spectra, which is  clearly unconstrained by the relatively insensitive \twotwo\ spectrum. The  sensitivity in the \oneone line is better in large part because of brighter 6  cm background across the whole W51 region. Despite the lack of constraint on the  volume density, there is a reasonably strong constraint on the column density.}  {fig:w51MCMCcompare}{1}  The molecular gas is concentrated near, but not exactly on, the bright cm  peaks. W51 IRS2 has a massive clump of gas at 65 \kms, and W51 e2 has a  similar clump. However, e2 also seems to have a very dense ($n>10^5 \percc$)  infalling clump. The spectra, along with multicomponent fits, are shown in  Figure \ref{fig:w51hiispectra}.  \FigureTwo{figures_chH2CO/W51_bestfit_spec53_49_IRS2.png}{figures_chH2CO/W51_bestfit_spec53_49_W51e2.png}  {Plots of the optical depth spectra centered on W51 IRS2 (left) and W51 e2, an  ultracompact HII region (right). IRS2 shows high-density gas with a slight  hint of infall, but otherwise a somewhat vanilla spectrum. W51e2 has a large,  high-density red shoulder, indicating high-density gas at the most red velocity  in the system. Because this is foreground gas, that high-density gas  \emph{must} be moving towards the \uchii region.}  {fig:w51hiispectra}{1}  %\input{solobib}  %\end{document}  diff --git a/thesis.pdf b/thesis.pdf  index dd9b052..4ee9e2e 100644  Binary files a/thesis.pdf and b/thesis.pdf differ