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Appendix A: Comparing ATLASGAL and Herschel

Every observational technique to estimate N-PDFs has its own limitations. The ATLASGAL data reduction process filters out extended emission from the maps in scales larger than 2.5′ (Schuller et al. 2009). The FIR emission observed by Herschel (Pilbratt et al. 2010) is very likely to be contaminated by emission from dust unrelated to the cloud of interest (Schneider et al. 2015b). We explore now how the N-PDFs derived with Herschel and ATLASGAL differ. We do this for one example object of each evolutionary class using the H ii  region M17 (#248), the SFC IRDC G11.11-0.12 (#54) and the SLC (#54c).

The Herschel data of the SFC the SLC were taken as part of the Herschel guaranteed time key program Earliest Phases of Star formation (Henning et al. 2010; Ragan et al. 2012, EPOS). The data of M17 was obtained from the Herschel program Hi-GAL (Molinari et al. 2010). We used the three SPIRE (Griffin et al. 2010) wavelengths (250 μm, 350 μm and 500 μm), reduced using scanamorphos  v23 (Roussel 2013), and PACS 160 μm (Poglitsch et al. 2010), reduced using HIPE v12 (Ott 2010). In the flux calibration process, the Planck zero-point correction was applied only to the M17 data.

We derived the column density and temperature maps for each of the three selected regions through a pixel-to-pixel modified greybody fit to the four Herschel continuum maps, all of them smoothed to a resolution of 36″. For consistency with the ATLASGAL data analysis, we adopted the dust opacity by interpolation of the Ossenkopf & Henning (1994) dust model of grains with thin ice mantles and a mean density of n = 10⁶ cm^-3. The mean uncertainty obtained in our greybody fitting technique for the temperature maps is ~2.5 K. The relative uncertainty of the column density maps is ~40%. The column density maps are shown in Fig. A.1.

The area over which a molecular cloud shows significant emission is different in ATLASGAL and Herschel column density maps. We face this issue by comparing the N-PDFs over two different areas: the area over which ATLASGAL shows significant emission, which we will refer to as dense gas area (white contours in Fig. A.1 and panels in the mid row in the same figure). We also compare the N-PDFs derived from the entire areas shown in Fig. A.1.

We now describe how the N-PDFs derived from Herschel and ATLASGAL data look like. In the SFC and the H ii  region Herschel-derived N-PDFs show a clear log-normal and power-law combination. This combination is seen in both cases of area selection: dense gas area and whole map. The ATLASGAL-derived N-PDFs of the SFC and the H ii  region also have power-law tails at high column densities but they do not show a log-normal distribution at low column densities. In both cases, Herschel-derived N-PDFs do not probe regions with A_V ≲ 10 mag. Both, the ATLASGAL-derived and Herschel-derived N-PDFs of the SLC are unfortunately dominated by noise, making a comparison impossible. At 36″ of resolution the SLCs do not have enough pixels for an analysis.

The absence of column densities A_V ≲ 10 mag in the Herschel data-set is very likely related to the line-of-sight contamination. To compare N-PDFs of the datasets without this contamination, we subtracted the background emission from the Herschel column density maps. We estimated the magnitude of the line-of-sight contamination averaging the Herschel-derived column densities inside the white boxes shown in the top row of Fig. A.1. We found  mag in the SFC and SLC regions and  mag in the H ii  region. The background-subtracted N-PDFs are shown in the fourth and fifth rows of Fig. A.1 for the whole map and the dense gas area. The background subtraction significantly widens the Herschel-derived N-PDFs in the low column density regime. It has, however, very small effect in the high column-density regime, which is slightly flattened.

To estimate the difference between the fitted parameters in the datasets we fitted the power-law tails of the N-PDFs, following the same procedure as in Sect. 3.1.1. The fits were performed in the column density regimes A_V> 30 mag and A_V> 40 mag in the SFC and H ii  region respectively. In all cases, the power-law portion of ATLASGAL is somewhat shallower (p_HII,AG = −1.2, p_SFC,AG = −2.0) than that obtained for Herschel (p_HII,H = −1.6, p_SFC,H = −2.3). The power-law slopes obtained in this work for the SFC are shallower than those reported by Schneider et al. (2015a). The difference is probably caused by the different column density ranges used to fit the power-law in the works. When the background component of Herschel is removed, the power-law tails flatten and become much more similar to those observed by ATLASGAL (, ). Using only the ATLASGAL emission area (middle row of Fig. A.1) or the whole map (bottom row of Fig. A.1) makes no significant difference in the slope of the power-law tails obtained. We conclude that the high-column density power-law parts of the N-PDFs are in good agreement between ATLASGAL and Herschel. The agreement is even better when the background contamination component of Herschel is removed. Note that a background correction to the Herschel column densities is usually necessary, as the diffuse Galactic dust component is significant at the Galactic plane. Therefore, one should consider the background subtracted N-PDF as a better estimate of the N-PDF of the cloud.

We identify the absence of log-normal components in the ATLASGAL-derived N-PDFs as an effect associated to the spatial filtering in the data reduction process. This effect is significant in both H ii  regions and SFCs, being less important in denser regions of molecular clouds where SLC objects lie. Spatial filtering is clearly seen at column densities A_V ~ 10−20 mag in Fig. A.1, where the Herschel-derived N-PDFs shows a clear excess compared to the ATLASGAL-derived N-PDFs. Despite the significant differences shown by the N-PDFs derived at low column density regimes, the power-law tails at high column densities are in good agreement, showing the ATLASGAL-derived N-PDFs marginally flatter distributions than the Herschel-derived N-PDFs. Similar results are obtained when the ATLASGAL-derived and Herschel-derived DGMFs are compared.

Fig. A.1 Top row: Herschel-derived column density maps of M17 (H ii  region), G11 (SFC) and #53c (SLC), in units of AV. The white contours show the dense gas area (AV> 2 mag, 4.5 mag and 9 mag for the H ii  region, SFC and SLC respectively). The white dashed boxes show the regions where the background contamination of Herschel has been calculated. Second row: N-PDFs as seen by Herschel (blue) and ATLASGAL (black) in the maps shown in the top row. The vertical error bars show the Poison standard deviation. The solid lines show the best fit to the power-law tail. Third row: ATLASGAL-derived and Herschel-derived N-PDFs in the dense gas area. Fourth row: background corrected ATLASGAL-derived and Herschel-derived N-PDFs in the whole map area of the top row. The background emission was estimated as the mean column density in the dashed boxes of the first row, seen by Herschel. Bottom row: background corrected N-PDFs evaluated in the dense gas area.

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Appendix B: Effects of the isothermal assumption on the N-PDFs

Obtaining column densities via dust emission maps at sub-mm wavelengths requires the use of the dust temperature (see Eq. (3)). When only one wavelength is available, as in the case of this paper, the most simple assumption is that the dust is isothermal. However, molecular clouds are not isothermal and the isothermal assumption can therefore generate artificial features in the column density distributions of the maps derived with this method. When several wavelengths are available, as in the case of Herschel observations, the line-of-sight averaged temperature and column density distributions can be simultaneously obtained via modified blackbody fitting to the FIR/sub-mm spectral energy distribution.

To study the temperature effects on the resulting N-PDFs we used the Herschel derived temperature distributions in the previous section to reconstruct the ATLASGAL column density maps of the same three regions. The results of this experiment are shown in Fig. B.1. In the H ii  region, the isothermal

assumption underestimates the low column density regimes of the N-PDF, which remain practically unaffected at A_V> 40 mag. The isothermal N-PDF of the SFC overestimates the low column density regime and remain similar to the N-PDF of the Herschel-derived temperature distribution at A_V = 10−90 mag. The isothermal N-PDF in the SLC is shifted to lower column densities.

The isothermal assumption is therefore valid in the high column density regime (i.e. in the power-law tail) of the H ii  region and the SFC examples shown here. We note that the relative temperature uncertainties are larger in the coldest regions (T ~ 12−15 K) of molecular clouds (i.e. in the densest regions) and these uncertainties could also result in the underestimate of the N-PDF observed at A_V> 90 mag in the SFC. Unfortunately, we cannot quantify the possible differences in the shape of the isothermal and the Herschel-derived temperature distribution N-PDFs of the SLC. The isothermal N-PDF therefore offers a more accurate reproduction of the Herschel-derived temperature distribution N-PDF in the column density regime of the power-law tail than at low-column densities.

	Fig. B.1 Isothermal ATLASGAL-derived N-PDFs (black) and N-PDFs derived using ATLASGAL emission maps together with Herschel-derived temperature maps (red). From left to right, H ii  region, SFC and SLC. The vertical error bars show the Poison standard deviation. The solid lines show the power-law fit to the data in the column density range covered by the lines.
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Appendix C: MIPSGAL 24 μm maps with ATLASGAL contours and regions

Fig. C.1 Greyscale MIPSGAL 24 μm map of the Galactic plane region comprised between Galactic longitudes l = 10.5−13.5deg. Overlayed yellow contours show 3σ level (0.15 Jy/beam) isocontours of ATLASGAL survey. Red circles and ellipses show our defined H ii  regions while molecular cloud regions are shown in blue. Starless clumps are shown as green filled circles. In all cases, size of region markers matches their sizes.

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	Fig. C.2 Same as Fig. C.1 for Galactic longitudes l = 13.5−16.5deg.
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	Fig. C.3 Same as Fig. C.1 for Galactic longitudes l = 16.5−19.5deg.
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	Fig. C.4 Same as Fig. C.1 for Galactic longitudes l = 19.5−21deg.
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Appendix D: ATLASGAL maps from starless clumps

	Fig. D.1 Dust emission, in Jy/beam, of the starless clumps studied.
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Appendix E: H II regions

	Fig. E.1 Dust emission, in Jy/beam, of the H ii  regions studied.
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Appendix F: Star-forming clouds

	Fig. F.1 Dust emission, in Jy/beam, of the SFC regions studied.
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© ESO, 2015