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Appendix A: Continuum and RRL data

We compare various data sets to assess calibration uncertainties and provide details of reduction for archival purposes. The data presented in this section are suitable for comparisons of Galactic to extragalactic star formation rate measurements, for example, since they are among the largest angular scale maps of radio recombination lines available with sub-parsec resolution.

Appendix A.1: Comparison between GBT and GPA data

The Galactic Plane A survey (Langston et al. 2000) covered the Galactic plane at 14.35 GHz using the Green Bank Earth Station (GBES) 13.7 m telescope, with a reported FWHM beam size of 6.6′. The published images were released with a FWHM resolution of 8′. We compared our GBT continuum observations to theirs in order to determine whether a significant DC component is missing from our data. Because the GPA used 10deg long scans in Galactic latitude, it should fully recover all diffuse Galactic Plane emission. In the released brightness temperature maps, brightness down to a scale of 1.5deg is recovered. However, because the GPA data undersampled the sky (its 5′ steps between scans were larger than the Nyquist sampling scale of the 14.35 GHz beam), point source fluxes in the GPA are underestimated by 19% and flux on small angular scales may be unreliable.

We resampled the GPA image onto the GBT grid using cubic spline interpolation, then smoothed both data sets to 9.5′. There are image artifacts (particularly vertical streaking) in the GPA data that are diminished by this large smoothing kernel.

We compared the surface brightness in the GPA and GBT data, and found that the GPA data was ~ 0.2 K brighter than the GBT in the diffuse portion of the W51 Main region; the offset

is not consistent with a purely multiplicative offset (Fig. A.1). The GBT observed the W51 Main peak to be moderately brighter, which is likely a result of the sparse sampling in the GPA. The morphological agreement between the maps is imperfect, perhaps in part because of the small area mapped in our GBT data, though there also appears to be vertical (along a line of constant longitude) stretching of the W51 Main source in the unsmoothed GPA data that is not consistent with the GBT observations.

Appendix A.1.1: Comparison between Arecibo and Urumqi data

We compare the 6 cm continuum to the Urumqi 25 m data from Sun et al. (2007) and Sun et al. (2011a). Figure A.2 shows the comparison of the Urumqi data and the Arecibo continuum data smoothed to 9.5′ resolution. The Arecibo and Urumqi data agree well as long as the main beam efficiencies of the respective telescopes (0.5 and 0.67) are accounted for.

Appendix A.1.2: Comparison of GBT and Arecibo data

In order to compare the Green Bank and Arecibo continuum data, we converted the brightness temperature maps to Janskys assuming a beam FWHM of 50′′ for both surveys and central frequencies of 4.8 and 14.5 GHz for Arecibo and Green Bank respectively. Measured beam widths for both telescopes were ~ 49 − 54″, so the relative error from assuming the same beam size should be ≲10%. In this section, the target frequencies are referred to as S_{5 GHz} and S_{15 GHz} for brevity.

The data are well-correlated, with S_{5 GHz} ~ 1.4S_{15 GHz} (S_{15 GHz} ~ 0.7S_{5 GHz}; Fig. A.3), consistent with a spectral index α_ν = −0.3 slightly steeper than usually observed for optically

Fig. A.1 Comparison between the GBT and NRAO GBES (Langston et al. 2000) data. Top left: NRAO GBES 2 cm map (top right) GBT 2 cm map of the same region smoothed to about 8.9′. The colorbar applies to both figures, showing brightness temperature units in K. The red contours in both figures show the region observed by Green Bank; flux outside of those boundaries is extrapolated with the smoothing kernel. The green contours show the region where TB(GBT) >TB(GBES). Bottom: plot of the GBT vs. the GBES surface brightness measurements. The large red dots show the region within the red contours.

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Fig. A.2 Comparison between the Arecibo and Urumqi 25 m (Sun et al. 2011b) data. Top left: Urumqi 6 cm map of the W51 region. Top right: Arecibo 6 cm map of the same region smoothed to the 9.5′ resolution of the Urumqi data set. The colorbar applies to both figures, showing brightness temperature units in K. The red contours in both figures show the region observed by Arecibo; flux outside of those boundaries is extrapolated with the smoothing kernel. Bottom: plot of the Arecibo vs. the Urumqi surface brightness measurements. The red dots show the region within the red contours.

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Fig. A.3 5 GHz and 15 GHz continuum and RRL flux densities against one another; all units are in Jy. The dashed lines show the total least squares best fit line with the slope shown in the legend. Wherever the density of points is too high to display, the points have been replaced with a contour plot showing the density of data points. The upper-right panel shows a comparison of the continuum ratio to the RRL ratio. The dashed line in the upper-right plot has slope 1, and the dotted line has slope 0.6.

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	Fig. A.4 Ratio maps of the ionized gas in W51. a) Continuum ratio S15 GHz/S5 GHz. For α = −0.1, an optically thin free-free source, the ratio is 0.9, while for α = 2, an optically thick source, the ratio is 9. b) The ratio of the H77α peak to the H112α peak. c) The line-to-continuum ratio H112α/S5 GHz. d) The line-to-continuum ratio H77α/S15 GHz.
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Fig. A.5 a) H112α electron temperature map showing in K. b) H77α electron temperature map showing in K. c) Measured electron temperature in the 6 cm vs. the 2 cm band at each spatial pixel with significant detected RRL emission. The contours show regions of increasing pixel density. The x marks the median and the + marks the mean over all valid pixels. d) Same as b), but with integrated He77α contours at levels [0.0125, 0.025, 0.05, 0.1, 0.15, 0.2] K km s-1 overlaid. The contours on the right side (ℓ< 49) most likely trace noise, since the noise in that region is higher.

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thin brehmsstrahlung and consistent with there being some contribution from synchrotron emission. The lower-brightness regions have a lower S_{15 GHz}/S_{5 GHz}, indicating that these regions are more affected by synchrotron. In Fig. A.4a, a great deal of structure in the S_{15 GHz}/S_{5 GHz} ratio is evident in the vicinity of W51 Main: the ratio is higher towards the continuum peaks, indicating that the peaks have higher free-free optical depths, or lower relative contributions from synchrotron emission, than their envelopes.

We additionally compare the radio recombination lines observed simultaneously with the continuum and H₂CO. Hydrogen RRLs are often extremely well-correlated with the continuum and are therefore good indicators of the calibration quality.

In Fig. A.4, we show the ratios between the two frequencies in RRLs and continuum and the line-to-continuum ratios at both frequencies. The line values are the integrated flux densities over the range 20 to 100 km s^-1, which includes all Hα emission but no Heα.

The ratios between the x and y axis in each plot in Fig. A.3 are fitted using a total least squares approach with uniform errors for each data point. The line-to-continuum ratio is L/C(H77α) ~ 0.15 and L/C(H112α) ~ 0.04; in both cases there is little evidence for deviation from a linear relationship.

Appendix A.1.3: Comparison of the RRL and continuum data

Radio recombination lines are generally observed to be well-correlated with the corresponding radio continuum, particularly at low frequencies. At 5 and 15 GHz, the population level departure coefficients are close to 1, b_n> 0.95 (Wilson et al. 2009; Walmsley 1990).

While radio recombination lines are purely thermal in nature, the large-scale continuum may include a contribution from synchrotron emission. The morphological similarity between the 90 cm and 4 m (meter – i.e., 74 MHz) images presented by Brogan et al. (2013) and our 6 and 2 cm data hint that synchrotron emission could be significant. However, the high degree of correlation between the 2 and 6 cm described below suggest that synchrotron contamination is minor at both wavelengths.

Figure A.3 shows a comparison between the integrated RRL surface brightness and radio continuum at both 2 and 6 cm¹⁵. The figure shows the total least squares best-fit slopes to the data assuming uniform error, which yield a measurement of the line-to-continuum ratio.

We use the line-to-continuum ratio in both bands to measure the electron temperature using Eq. (14.58) of Wilson et al. (2009), which assumes a plane-parallel, optically-thin emission region with lines formed in local thermodynamic equilibrium (the ∗ in is meant to indicate these three assumptions are made). The two lines yield consistent measurements, with mean K; these measurements are consistent with smaller-scale measurements using the VLA with H92α (Mehringer 1994). There is little structure in the maps, with a hint of higher temperatures around G49.1-0.4, coincident with the W51C supernova remnant. Other structures are most likely due to the limited S/N.

Finally, we fit a single-component Gaussian to each pixel to produce velocity maps. These are discussed in Sect. B.11.

Appendix A.2: Carbon and helium RRLs

Helium RRLs were prevalent and reasonably well-correlated with the hydrogen RRLs, but we did not examine them in detail. He77α is detected at much higher S/N than than He107-112α. There were no clear detections of C77α or C107-112α, though there is a possible C77α signal at G49.366-0.304 with v_lsr ≈ 55 km s^-1 and a possible detection toward W51 Main along the wing of the He77α line. The He77α line detections are associated with regions of high H_nα but not regions of different .

Appendix B: Geometry of individual regions

Appendix B.1: W51 main and W51 IRS 2

The W51 main and IRS 2 spectra show that both have ionized gas components at v_LSR ~ 55 km s^-1. This velocity approximately coincides with the peak of the ¹³CO emission.

The H₂CO1₁₀ − 1₁₁ spectra are deepest at ~ 68 km s^-1, while the 2₁₁ − 2₁₂ have depths approximately equal between the ~ 58 km s^-1 and ~ 68 km s^-1 components. The 55−60 km s^-1 components are too deep to be entirely behind the H ii regions. This indicates that the 55 km s^-1 ionized gas must be embedded within the molecular cloud, with molecular gas on both sides of the ionized gas along the line of sight.

Because these are well-studied regions, the low spatial resolution H₂CO spectra we present here add little new information about the gas kinematics. However, all of the velocity components observed in the W51 region are apparently kinematically connected to the W51 clusters.

	Fig. B.1 Spectrum extracted from G49.119-0.277 in a 55′′ radius aperture, showing a model in which the continuum is behind the 63 km s-1 component but in front of the 68 km s-1 component. The legend gives the fit parameters along with 1σ error bars. The parameters with no errors indicated (OPR, T, TBG) are assumed or independently measured values.
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Appendix B.2: The W51 B filament

The W51 B filament (right side of Fig. 11 at ~ 68 km s^-1), exhibits bright CO emission ( K in the Parsons et al. 2012 CO 3−2 data) but has relatively weak H₂CO absorption. The absorption models are inconsistent with the molecular gas being in front of the continuum emission, so Fig. 11 shows the continuum sources in front of the cloud at lower ℓ. Figure 8 shows an example model fit with the continuum assumed to be in front and in back, illustrating that the best-fit model parameters with continuum in the back do not reproduce the data. The relative positioning of the molecular gas behind the H ii regions suggests that the molecular gas is also behind the W51 C supernova remnant.

Appendix B.3: The edge of W51 C

W51 C is a supernova remnant that spatially overlaps with the W51 B star forming region. Brogan et al. (2013) argue that the supernova remnant must be in front of the H ii region G49.20-0.35 because the H ii-region has not absorbed all of the 4 m (74 MHz) nonthermal emission. The G49.1-0.4, G49.0-0.3, and G48.9-0.3 regions, however, show 4 m absorption signatures and may be in the foreground. There are clumps aligned along the 68 km s^-1 filamentary cloud with very high CO and H i velocities (Koo & Moon 1997b,a; Brogan et al. 2013), indicating that the SNR is interacting with the molecular gas.

The clumps at G49.1-0.3, ~ 68 km s^-1 are either lower density (n< 1.5 × 10⁴cm^-3) and in the background of the H ii region or high density (n> 1.5 × 10⁵cm^-3), low-column density and in the foreground. The 62 km s^-1 clumps have densities a few times higher, n ~ 4 × 10⁴cm^-3, and are clearly in the foreground of the continuum emission because their absorption depths are ~ 2.5 K, which cannot occur for absorption against the CMB. Figure B.1 shows a model spectrum fitted assuming the continuum lies between the two molecular velocity components. The relative strength of the ¹³CO and the H₂CO also suggests that the 68 km s^-1 component is behind the continuum.

We are seeing molecular gas both in front of and behind the supernova. This geometry can be readily confirmed by looking for molecular absorption at much lower frequencies where the SN synchrotron emission dominates over the H ii region free-free emission, i.e. the 335 and 71 MHz p - H₂CO lines.

Appendix B.4: G49.20-0.35 and G49.1-0.4

Tian & Leahy (2013) focus on the H ii regions G49.20-0.35 and G49.10-0.40 (called G49.10-0.38 in their work) to determine the relative geometry of the W51 C SNR and the W51 B H ii/star-forming region. They observe that the high-velocity H iis not detected toward either of these sources, indicating that the H ii regions must be behind the high-velocity H i features.

We detect H₂CO1₁₀ − 1₁₁ at ~ 58 and ~ 63 km s^-1 toward G49.10-0.40, with line ratios that are consistent with the H ii region being behind the molecular cloud complex. It also has an extreme RRL velocity, v_110α ≈ 72 km s^-1, the most redshifted seen in the entire W51 region (see Figs. B.3 and B.2).

G49.20-0.35 is also clearly behind the molecular cloud, as evidenced both by H₂CO absorption depth and the IRDC absorption in the foreground. It has an RRL velocity v_110α ≈ 70 km s^-1.

Because both H ii regions are extremely redshifted, they are most likely associated with the W51 B cloud complex, contrary to the interpretation by Tian & Leahy (2013) in which they are unrelated background clouds. The Galactic rotation curve doesn’t allow for velocities red of ~ 60 km s^-1, and almost none of the molecular gas exceeds ~ 70 km s^-1 even on the wings. The H ii regions are therefore probably shooting out the back side of the molecular cloud in a champagne flow, perhaps accelerating ionized gas from the ~ 68 km s^-1 component further to the red.

	Fig. B.2 Fitted H110α (red) and H77α (black) spectra extracted from 55′′ apertures centered on G49.20-0.35 (top) and G49.1-0.4 (bottom). The best-fit Gaussian parameters are shown in the legends, with the lower legend corresponding to H77α.
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Appendix B.5: The 66 km s^-1 8 μm dark cloud

Between W51 A and W51 B, there is a component of the 68 km s^-1 cloud that is filamentary and in the foreground of all of the free-free emission. This cloud component is evident as an IRDC in the Spitzer GLIMPSE images from ℓ = 49.393, b = −0.357 to ℓ = 49.207, b = −0.338; it is labeled as IRDC G49.37-0.35 in Figs. 11 and 12.

The H ii region G49.20-0.35 is clearly behind the IRDC, though there are strong morphological hints that it is interacting with and truncated by the cloud.

	Fig. B.3 a) Velocity of the peak H2CO110 − 111 signal (deepest absorption) at 1 km s-1 resolution. b) Velocity of the peak H110α emission as derived from Gaussian fits to each spectrum.
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	Fig. B.4 Maps of the fitted H2CO velocity components over the range 40 <vLSR< 66 km s-1 (left) and 66 <vLSR< 75 km s-1 (right). The regions that appear noisy have ambiguous multi-component decompositions.
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Appendix B.6: G49.27-0.34

The UCH ii region G49.27-0.34, which was considered a candidate extended green object (EGO) and subsequently rejected for lack of H₂ emission (De Buizer & Vacca 2010; Lee et al. 2013), exhibits a second velocity component at ~ 68 km s^-1, slightly but clearly redshifted of the rest of the IRDC. The dust component contains a gas mass ~ 2 × 10³M_⊙ based on the BGPS flux and using the assumptions outlined in Aguirre et al. (2011), suggesting that the high velocity could be due to infall or virialized gas within a deep potential. The virialized velocity width, given the radius and mass from the BGPS data, is σ_vir = 8.8 km s^-1, while the measured H₂CO linewidth is FWHM(H₂CO) = 7.2 km s^-1, wider than in any other part of the cloud except W51 Main.

Both radio continuum and RRLs are detected toward this source. The H77α RRL velocity is ~ 58 km s^-1, significantly blueshifted from the molecular gas. The H₂CO lines do not independently distinguish between the continuum source being in the front or back of the cloud, but the mean density from the BGPS mass and radius n ~ 2.5 × 10⁴cm^-3 is within a factor of 2 of the H₂CO-derived density, n ~ 1.4 × 10⁴cm^-3, if the continuum source is behind the gas, while the H₂CO-derived density is too low, n ~ 2 × 10³cm^-3 if the continuum source is in front.

The implied geometry therefore has the H ii region behind the molecular gas, plowing toward it at a velocity difference Δv ~ 10 km s^-1. Such a high velocity difference may indicate that the H ii region is confined by the molecular gas and on a plunging orbit into the cloud.

Appendix B.7: G49.4-0.3f, aka G49.34-0.34, aka IRAS 19209+1418

The H ii region centered at 49.34-0.34 was identified by Mehringer (1994) as part of the G49.4-0.3 complex. There are 3 distinct H₂CO line components at 51, 63.70, and 68.47 km s^-1. The 51 km s^-1 component is behind the H ii region; the ¹³CO line is detected at comparable brightness at 51 km s^-1 and 63 km s^-1, while the H₂CO1₁₀ − 1₁₁ line is ~ 10 × deeper at 63 km s^-1. The RRLs associated with this source are at v_LSR = 58 ± 1 km s^-1.

The H₂CO lines are moderately well-fit by the two-velocity-component model, but there is a relative excess of 2₁₁ − 2₁₂ absorption at 66 km s^-1 (associated with the 68 km s^-1 component). The extra absorption may indicate that there is a high-density, low-column component at this velocity.

The 8 μm GLIMPSE image shows that the 68 km s^-1 IRDC crosses in front of this source. Herschel Hi-Gal 70 μm images reveal a ring structure that is hinted at in the 8 μm image. There is no evidence for interaction between the ring feature and the IRDC. This intriguing feature will likely be difficult to study in detail because the dusty, molecular gas feature lies in front of it.

	Fig. B.5 A histogram of the abundances derived for each spatial pixel using the LVG grid fit. The abundance shown assumes a velocity gradient 1 km s-1pc-1. The overlaid fits show that 30% of the area of W51 is consistent with an abundance X(o - H2CO) = 10− 8.4 ± 0.5 and 70% with X(o - H2CO) = 10− 9.9 ± 0.6.
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Appendix B.8: G49.4-0.3

The collection of H ii regions around G49.4-0.3 vaguely resembles a cartoon mouse. As noted in Carpenter & Sanders (1998), the molecular gas in this region is separated into two distinct components, one at 51 km s^-1 and the other at 64 km s^-1. The 64 km s^-1 component is in the foreground, while the 51 km s^-1 is in the background of most of the H ii regions.

Both cloud components are in the foreground of the central H ii regions at G49.36-0.31, the eyes of the mouse. The density of the 51 km s^-1 component is an order of magnitude higher than that in the 64 km s^-1 component in this region, suggesting that the gas is being compressed by the H ii region. The clean separation between the 64 and 51 km s^-1 cloud components suggests that they are not interacting at this location.

Based on the absorption line depths, the G49.38-0.30, IRAS 19207+1422, and G49.37-0.30 H ii regions are behind the 51 km s^-1 cloud. The 8 μm absorption features are associated with the 64 km s^-1 cloud and are in front of all of the H ii regions.

The 8 μm morphology of G49.42-0.31 is bubble-like, so it is plausible that the H ii region is neither in front nor behind the 51 km s^-1 cloud but embedded within it, blowing a hole in the cloud.

Appendix B.9: 8 μm dark cloud G49.47-0.27

The cloud to the north of W51 Main/IRS2 appears as a dark feature in Spitzer GLIMPSE 8 μm maps. It is detected in H₂CO from 54 to 64 km s^-1. Throughout, it has a high 1₁₀ − 1₁₁/2₁₁ − 2₁₂ ratio, ≳7 in most voxels, indicating a low density n ≲ 10³cm^-3.

Centered at 60.6 km s^-1, the region has a line FWHM 5−7 km s^-1, indicating that it is quite turbulent, with 3D Mach number in the range 10 < ℳ < 20 for an assumed 10 <T< 20 K. At its centroid velocity, it is connected to the W51 main cloud.

There is a previously unreported bubble HII region in the north part of this cloud, which we designate G49.47-0.26, with radius ~ 70″ (1.7 pc). The H ii has RRL velocities v_lsr ≈ 50 km s^-1. Because it is not detected in Brackett γ emission (from the UWISH2 survey: Froebrich et al. 2011), it is most likely behind the cloud.

The Kang et al. (2009)Spitzer survey of YSOs in the region indicates that there are no YSOs within the boundaries of this cloud; it is very likely non-star-forming at present (see also Fig. 16).

Because the cloud is continuous with the W51 Main region in velocity and is 8 μm-dark, it is most likely at the same distance as W51 Main and associated indirectly with the massive cluster forming region.

Appendix B.10: The 40 km s^-1 clouds

There are clouds observed at 40 km s^-1 that show only weak H₂CO absorption spread across nearly the entire region. These molecular clouds are behind nearly all of the H ii regions in the W51 complex. There are additional 40 km s^-1 clouds clearly seen in H i absorption (Stil et al. 2006) that are not associated with these molecular clouds, but instead represent a foreground population of neutral atomic medium clouds.

Appendix B.11: Kinematic maps

Maps showing the overall kinematics of the region are shown in Figs. B.3 and B.4. Figure B.3 shows the velocity at peak absorption of the H₂CO1₁₀ − 1₁₁ line and the fitted radio recombination line centroid velocity. Figure B.4 shows the best simultaneous fit to the H₂CO1₁₀ − 1₁₁ and 2₁₁ − 2₁₂ absorption features over two different velocity ranges. The 1₁₀ − 1₁₁ absorption velocity in Fig. B.3a approximately shows the velocity of the front-most molecular clouds along the line of sight at each position.

Appendix B.12: Abundances

The LVG modeling also yields measurements of abundance that are degenerate with the assumed velocity gradient. The abundance within the LVG model is defined as (B.1)\newpage\noindentWe show the distribution of fitted abundances under this definition in Fig. B.5. The histogram shows the average abundance along each line of sight derived from the likelihood-weighted density divided by the likelihood-weighted column. We also show a two-gaussian fit to the abundance distribution: 30% of the area is consistent with an abundance X(o - H₂CO) = 10^{− 8.4 ± 0.5} and 70% with X(o - H₂CO) = 10^{− 9.9 ± 0.6}. We caution that these abundance measurements are highly uncertain and are contingent on both the backlighting source brightness and the assumed velocity gradient. The individual abundances going in to the histogram are generally not well-constrained. A more accurate abundance measurement could be obtained by measuring the millimeter lines of o - H₂CO at 140 and 150 GHz.

Appendix B.13: Supplementary picture

We include a large-scale WISE + BGPS composite image of the entire W51 cloud and its surroundings. The figure highlights the W51 C supernova remnant.

Fig. B.6 A large-scale color composite that highlights the W51 C supernova remnant as a white haze using 90 cm data from Brogan et al. (2013). The colors are the same as in Fig. 1: the blue, green, and red colors are WISE bands 1, 3, and 4 (3.4, 12, and 22 μm) respectively. The yellow-orange semitransparent layer is from the Bolocam 1.1 mm Galactic Plane Survey data (Aguirre et al. 2011; this paper).

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