CLOUD STRUCTURE OF GALACTIC OB CLUSTER-FORMING REGIONS FROM COMBINING GROUND- AND SPACE-BASED BOLOMETRIC OBSERVATIONS

Table 1 summarizes the basic properties of the selected target sources. More details on the individual sources are given in the following subsections.

Table 1.  Source Information

Target Source	R.A.	decl.	Distance	Massa	Luminositya	Referenceb
	(J2000)	(J2000)	(kpc)	$({M}_{\odot })$	$({L}_{\odot })$
W49A	19${}^{{\rm{h}}}$10${}^{{\rm{m}}}$13000	09°06'0000	${11.4}_{-1.2}^{+1.2}$	2.30 × 105	3.67 × 107	Zhang et al. (2013)
W43-main	18${}^{{\rm{h}}}$47${}^{{\rm{m}}}$36427	−01°59'0248	${5.49}_{-0.34}^{+0.39}$	1.32 × 105	1.23 × 107	Zhang et al. (2014)
W43-south	18${}^{{\rm{h}}}$46${}^{{\rm{m}}}$02084	−02°43'0083	${5.49}_{-0.34}^{+0.39}$	6.43 × 104	6.29 × 106	Zhang et al. (2014)
G10.2-0.3	18${}^{{\rm{h}}}$09${}^{{\rm{m}}}$23000	−20°16'1700	${4.95}_{-0.43}^{+0.51}$	1.03 × 105	6.43 × 106	Corbel & Eikenberry (2004)c
G10.6-0.4	18${}^{{\rm{h}}}$10${}^{{\rm{m}}}$2926	−19°55'595	${4.95}_{-0.43}^{+0.51}$	2.33 × 104	3.20 × 106	Sanna et al. (2014)
W33	18${}^{{\rm{h}}}$14${}^{{\rm{m}}}$1365	−17°55'389	${2.40}_{-0.15}^{+0.17}$	3.63 × 104	2.43 $\times {10}^{6}$	Immer et al. (2013)
G10.3-0.1	18${}^{{\rm{h}}}$08${}^{{\rm{m}}}$58000	−20°05'1500	${3.22}_{-0.12}^{+0.12}$/${2.56}_{-0.28}^{+0.28}$	2.70 × 104/1.70$\times {10}^{4}$	1.54 × 106/9.71 × 105	Kazi Rygl, Katharina Immerd

Notes.

^aTotal masses were summed from our derived column density maps (Figures 4–10) above a common threshold of $7\times {10}^{21}$ cm⁻². Considering the threshold chosen for adding up total masses, we note that these mass values should be considered as lower limits of these sources. Total bolometric luminosity is calculated by integrating from 0.1 μm to 1 cm of the obtained SED for each pixel, and adding all the values in each field. ^bDistances were quoted from the Bar and Spiral Structure Legacy Survey (BeSSeL; e.g., Brunthaler et al. 2011) water maser trigonometric parallaxes if without further notes. ^cSince the distance of G10.2-0.3 is still uncertain, we now adopted the same distance as with G10.6-0.4. Corbel & Eikenberry (2004) point out that the two sources are likely to be located at approximately the same distance in the −30 km s⁻¹ spiral arm (sometimes called the 4 kpc arm, Menon & Ciotti 1970; Greaves & Williams 1994). ^dPreliminary results based on 6.7 GHz masers, which require further confirmation (K. Rygl, K. Immer 2016, private communication). In this work, we used the larger distance value for analysis on source G10.3-0.1.

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2.1.1. W49A Mini-Starburst

2.1.2. W43 Mini-Starburst

2.1.3. G10.2-0.3 and G10.3-0.1

2.1.4. G10.6-0.4

2.1.5. W33 Molecular Cloud Complex

High angular resolution, ground-based continuum observations at 350 μm toward W43-Main, W43-South, W49A, W33, G33.92+0.11, G10.2-0.3, G10.3-0.1, and G10.6-0.4 were carried out using the SHARC2 bolometer array, installed on the CSO Telescope. The array consists of 12 × 32 pixels.¹¹ The simultaneous field of view (FOV) provided by this array is 259 × 097, and the diffraction limited beam size is ∼88.

The data of W43-Main, W43-South, W49A, and G33.92+0.11 were acquired on 2014 March 24th (${\tau }_{\text{225 GHz}}\,\sim$ 0.06), with an on-source exposure time of 20, 20, 42, and 30 minutes respectively. W33 was observed on 2014 March 27th (${\tau }_{{\rm{225}}{\rm{GHz}}}\,\sim$ 0.05), with 50 minutes of on-source exposure time. The data of G10.3-0.1 was acquired on 2015 June 9th (${\tau }_{{\rm{225}}{\rm{GHz}}}\,\sim$ 0.04), and the data of G10.6-0.4 and G10.2-0.3 were acquired on 2014 April 5th (${\tau }_{{\rm{225}}{\rm{GHz}}}\,\sim$ 0.03); the integration time was 30 minutes for each of the three sources.

The telescope pointing and focusing were checked every 1.5–2.5 hr. Mars was observed for absolute flux calibration. We used the standard 10' × 10' on-the-fly box scanning pattern, and the scanning center for each source is listed in Table 1.

Basic data calibration was carried out using the CRUSH software package (Kovács 2008). We used the -faint option of the CRUSH software package during data reduction, which optimized the reconstruction of the faint and compact sources with the cost of the more aggressive filtering of extended emission. Nevertheless, the extended emission components will ultimately be complemented by the observations of space telescopes (more in Section 2.4.3). The final calibrated map was smoothed by a 2/3 beam FWHM (-faint option) yielding an angular resolution of 96 for optimized sensitivity and source reconstruction. The rms noise levels we measured from the approximately emission-free areas of W43-main, W43-south, W49A, G10.2-0.3, G10.3-0.1, and W33 were ∼76, 42, 67, 42, 102, and 68 mJy beam⁻¹, respectively. The observations of G33.92+0.11 were published separately by Liu et al. (2015), however, they were left out of the present paper since there are no high quality ground based 450 and 850 μm observations for this target source.

We retrieved the available nightly observations of James Clerk Maxwell Telescope (JCMT)¹² Submillimetre Common-User Bolometer Array 2 (SCUBA2) (Chapin et al. 2013; Dempsey et al. 2013; Holland et al. 2013 ) at 450 and 850 μm from the online data archive. (Program ID:S13AU02 (W43; W31), MJLSJ02 (W33; G10.2-0.3; G10.3-0.1; G10.6-0.4), M13BU27 (W49A)).

We retrieved the level 2.5/3 processed, archival Herschel¹³ images that were taken by the Herschel Infrared Galactic Plane (Hi-GAL) survey (Molinari et al. 2010) at 70/160 μm using the PACS instrument (Poglitsch et al. 2010) and at 250/350/500 μm using the SPIRE instrument (Griffin et al. 2010; obsID: W43: 1342186275, 1342186276; G10.2-0.3, G10.3-0.1, G10.6-0.4: 1342218966; W49A: 1342207052, 1342207053; W33: 1342218999, 1342219000.)

Since we are interested in the extended structures, we adopt the extended emission products, which have been absolute zero-point corrected based on the images taken by the Planck space telescope.

We retrieved the Planck/High Frequency Instrument (HFI) 353 GHz images (and also 217 GHz images when a MAMBO2 image is available for a particular source), which are in units of K_CMB. We convert the Planck images to Jy beam⁻¹ units based on the conversion factors provided by Zacchei et al. (2011) and the Planck HFI Core Team et al. (2011a, 2011b).

For the combination of 850 μm images, we also used the APEX-LABOCA ATLASGAL survey (Siringo et al. 2009) observations for our sources. The ATLASGAL survey (Schuller et al. 2009) data products are reduced in a way of optimizing the compact sources recovery with flux calibration uncertainty of ∼15%. Some information of the data used is listed in Table 2.

In our procedure, we first replace the saturated pixels in the archival Herschel images by interpolating (see Section 2.4.1). The interpolated Herschel images are then convolved with the kernels provided in Aniano et al. (2011), to suppress the defects caused by the non-Gaussian beam shapes of the Herschel space telescope. Afterwards, images were linearly combined with the ground-based observations of CSO-SHARC2 at 350 μm and the observations of JCMT-SCUBA2 at 450 μm (Sections 2.4.3, 2.4.4), yielding high-resolution millimeter and submillimeter images that have little or no loss of extended structures. We combined the JCMT-SCUBA2 850 μm images and the IRAM-30 m-MAMBO2 1200 μm images with those taken by the Planck space telescope, in the cases that the SCUBA2 and MAMBO2 images are available. Finally, we performed the pixel-by-pixel SED fitting incorporating the Herschel-PACS 70 and 160 μm images, the Herschel-SPIRE 250 μm images, and our combined images at 350, 450, 850, and 1200 μm, assuming a single blackbody component in each line of sight (if available; Section 2.4.2). A flow chart of the overall procedure is given in Figure 1.

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There are fundamental limits to the accuracy of our SED fitting, which is typically dominated by the noise level of the 450 μm and 850 μm images, and the degeneracy when optimizing the dust opacity index (β) and the dust temperature T_d. For the case in which the brightness sensitivity of the ground-based image is a lot worse than that of the space telescope image, flux scales of the bright structures can still be corrected after combining with the space telescope image. However, in such cases, the extended diffuse structures in the combined image may still be immersed in thermal noise. We are subject to this issue because we used the archival JCMT-SCUBA2 450 μm and 850 μm images, which were not all planned to achieve a matched brightness sensitivity with the Herschel Hi-GAL images. For our selected target sources, these problems are not very serious for dense structures in the molecular clouds, which are of major interest to us. We will only analyze structures above certain column density thresholds to avoid confusion by the Galactic foreground/background emission, which further alleviates the effects of the aforementioned defects.

2.4.1. Interpolating Saturated Pixels

Some Herschel images of our target sources were saturated around the bright sources (see Appendix A). Before combining these Herschel images with the ground-based observations, or before using these Herschel images in the SED fitting, we replaced the saturated pixels using interpolated values, which in some cases, required iterative processes. Before the SED fitting (see also Figure 1), the Herschel images were convolved with the kernels provided by Aniano et al. (2011) to suppress the effect of the non-Gaussian beam shape, except where otherwise noted.

For the target sources W43-main, W49A, and G10.6-0.4, one, or both of the PACS 70 μm and 160 μm images show saturated pixels. The saturated pixels in these PACS images were replaced by the interpolated values from the two-dimensional Gaussian fits to the adjacent pixels.

For the sources G10.2-0.3, G10.3-0.1, and W43-south, only the SPIRE 250 μm images were saturated. Their saturated pixels were replaced following the procedure described below. First, we derived the approximated 450 μm intensity image at the angular resolution of the SPIRE 500 μm images (369), by performing the pixel-by-pixel modified blackbody SED fitting (more in Section 2.4.2) to the PACS 70/160 μm, the SPIRE 350/500 μm, and the combined 850 μm images. Then, the approximated, $36\buildrel{\prime\prime}\over{.} 9$ resolution 450 μm images were linearly combined with the SCUBA2 450 μm images, following a procedure that will be introduced in Section 2.4.4. Afterward, we performed the pixel-by-pixel modified blackbody SED fitting to the combined, higher angular resolution 450 μm image, the PACS 70/160 μm images, and the combined 350/450/850 μm images, to derive approximated 250 μm images that have an 18'' angular resolution. In the end, we use the values in the approximated 250 μm image to replace those of the saturated pixels in the original Herschel 250 μm images.

For the cases in which both the SPIRE 350 μm and SPIRE 250 μm images are saturated (e.g., Figure 2, see also Appendix A), 450 μm intensity images were derived based on SED fits to PACS 160 μm, SPIRE 500 μm, and combined 850 μm images. Adding the combined 450 μm (Section 2.4.4) and PACS 70 μm images to the SED fitting with previous bands, we derived the fluxes for the saturated pixels in the SPIRE 350 μm and SPIRE 250 μm images. The detailed procedure is similar to that of replacing the saturated 250 μm pixels, so we do not repeat it here. However, we additionally took advantage of our available SHARC2 350 μm images to double check whether the replaced pixel values in the saturated SPIRE images are reasonable or not by comparing the intensity distributions.

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2.4.2. Deriving Dust Temperature and Column Density Based on SED Fitting

Before performing any SED fitting, we smoothed all images to a common angular resolution, which is slightly bigger than the FHWM of the largest telescope beam for each iteration. In addition, all images were re-gridded to have the same pixel size, and were converted to units of Jy pixel⁻¹. We weighted the data points by the measured noise level in the least-squares fits. We adopted a dust opacity law similar to what was introduced by Hildebrand (1983).

In this case, flux density ${S}_{\nu }$ at a certain observing frequency ν is given by

$$\begin{eqnarray}&&{S}_{\nu }={{\rm{\Omega }}}_{m}{B}_{\nu }({T}_{{\rm{d}}})(1-{e}^{-{\tau }_{\nu }}),\end{eqnarray} \tag{ 1 }$$

and

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}_{2}}=\displaystyle \frac{{\tau }_{\nu }}{{\kappa }_{\nu }\mu {m}_{{\rm{H}}}},\end{eqnarray} \tag{ 2 }$$

where

$$\begin{eqnarray}&&{B}_{\nu }({T}_{{\rm{d}}})=\displaystyle \frac{2h{\nu }^{3}}{{c}^{2}}\displaystyle \frac{1}{\exp (h\nu /{{kT}}_{{\rm{d}}})-1},\end{eqnarray} \tag{ 3 }$$

is the Planck function for a given temperature T_d,

$$\begin{eqnarray}&&{\kappa }_{\nu }={\kappa }_{230}{\left(\displaystyle \frac{\nu }{230\mathrm{GHz}}\right)}^{\beta }\end{eqnarray} \tag{ 4 }$$

is the dust opacity, β is the dust opacity index, ${{\rm{\Omega }}}_{m}$ is the considered solid angle, μ = 2.8 is the mean molecular weight, ${m}_{\mu }$ is the mass of a hydrogen atom, and ${\kappa }_{230}$ = $0.09\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ is the dust opacity per unit mass at 230 GHz. The opacity ${\kappa }_{\nu }$ is interpolated from Ossenkopf & Henning (1994). We assumed a gas-to-dust mass ratio of 100.

Our iterative fitting procedure first used the available images at all wavelength bands, to simultaneously fit β, ${T}_{{\rm{d}}}$, and ${N}_{{{\rm{H}}}_{2}}$. In this step, the PACS 70/160 μm, the SPIRE 250 μm, and the combined 350/450/850 μm images were smoothed to $22^{\prime\prime}$ resolution, which is slightly larger than the measured beam size of the SPIRE 250 μm image. We used the obtained $22^{\prime\prime}$ resolution images of β, ${T}_{{\rm{d}}}$, and ${N}_{{{\rm{H}}}_{2}}$, to initialize the second fitting iteration. However, in the second fitting iteration, we use the values of β from the last iteration and only fit to the PACS 70 μm images, the combined 350 μm and 450 μm images¹⁴ , to yield the T_d and the ${N}_{{{\rm{H}}}_{2}}$ images with our best achievable angular resolution of ∼10''. The initialization of β, ${T}_{{\rm{d}}}$, and ${N}_{{{\rm{H}}}_{2}}$ using results from the previous fitting iteration helped improve the convergence of the fitting.

The quality of the SHARC2 350 μm image of G10.6-0.4 was poor, which may be due to a temporarily poorer weather condition, or imperfect focus. Therefore, it was excluded from our analysis. The SED fits of this particular source were complemented by the combined MAMBO2 1.2 mm and Planck/HFI 217 GHz images, when deriving the final, ∼11'' resolution column density and temperature maps.

Our present scientific discussion focuses on the column density distribution ${N}_{{{\rm{H}}}_{2}}$. We noticed that the possibly biased β versus T_d relation that comes from the least-squares fits due to the noise of measurements is suggested in previous works (e.g., Shetty et al. 2009a; Juvela et al. 2013). However, the anti-correlated β versus T_d is also observed in some molecular clouds (e.g., Hill et al. 2006; Désert et al. 2008). Besides, longer wavelengths in the Rayleigh–Jeans limit may recover β more accurately (e.g., Shetty et al. 2009b) and with more wavelengths in the SED fits the variation of β is alleviated, as seen in simulations (Malinen et al. 2011). Considering the large dynamical range of column density, we are measuring toward these regions (the possible change of β) and the advantage of utilizing $\geqslant 5$ wavelengths, we fit β with T_d and column density simultaneously. In future works, we will adopt a multi-level Bayesian technique in SED fits (Kelly et al. 2012) to further improve the accuracy of fitting β.

We caution that in cases in which there are multiple temperature components in the line of sight, our fits will be approximate, with ambiguous determinations for the temperature and the dust opacity index. We expect that this only results in errors of gas column density by a fraction of the actual gas column density that we are probing. Such errors are very small compared to the ranges of gas column density that we are probing and therefore will not likely impact our statistical analyses significantly. We refer to Marsh et al. (2015) for an approach to fit multiple temperature components. We will update the dust model in future works when we come to the more detailed analysis about the temperature distribution and the variation of dust properties (e.g., Galametz et al. 2016).

2.4.3. Combining SHARC2 and SPIRE Images

2.4.4. Combining the JCMT-SCUBA2 Image with the Herschel, APEX/LABOCA, and Planck/HFI Observations

Figure 3 shows the derived gas column density maps (${N}_{{{\rm{H}}}_{2}}$) of all selected sources, which were smoothed and reprojected to the distance of W49A. Figures 4–10 show the derived high angular resolution (∼10'') dust temperature (T_d) and ${N}_{{{\rm{H}}}_{2}}$ maps, obtained according to the procedures introduced in Section 2.4. The distributions of the fitted column density, dust temperature, and spectral index of each pixel for each region are provided in Appendix B.

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As a consistency check of our method with the existing studies based on Herschel PACS and SPIRE images (e.g., Nguyen-Luong et al. 2013; Schneider et al. 2015), we present gas column density (${N}_{{{\rm{H}}}_{2}}$) and dust temperature fits (${T}_{{\rm{d}}}$) of G10.2-0.3, obtained by using Herschel 160 μm, 250 μm, and 350 μm images only (β fixed to a constant 2.0) in Figure 11. We use G10.2-0.3 as an example, since the Herschel images of this source are subject to the least amount of saturation. Figures 10 and 11 show consistent T_d and ${N}_{{{\rm{H}}}_{2}}$ distributions. However, the less smeared, higher (10'') angular resolution ${T}_{{\rm{d}}}$ map presents a better contrast, which we also believe to be representative of the more accurate fitting of both ${T}_{{\rm{d}}}$ and ${N}_{{{\rm{H}}}_{2}}$. In particular, the $10^{\prime\prime}$ resolution ${T}_{{\rm{d}}}$ map reveals an embedded heated source in the highest column density molecular clump that cannot be seen merely from the SED fits of the Herschel images (Figure 11). The high resolution ${N}_{{{\rm{H}}}_{2}}$ image also separates the localized dense clumps/cores from the fluffy or filamentary cloud structures in a more clear way that is crucial for our structure identification (Section 3.5) and diagnoses the hierarchical cloud morphology. The improved sensitivity of the low resolution ${N}_{{{\rm{H}}}_{2}}$ image detects the more diffuse cloud structures on larger angular scales. However, without velocity information, it is very difficult to distinguish the extended and low column density cloud structures from the foreground and background contamination. The ${T}_{{\rm{d}}}$ maps can help visually identify some (if not all) heated diffuse dust and gas by the OB clusters around our target sources. However, in some heated but low ${N}_{{{\rm{H}}}_{2}}$ regions, our assumption of a single dominant modified blackbody component in the SED fitting breaks down (Section 2.4.2). The hotter but lower ${N}_{{{\rm{H}}}_{2}}$ component in the line of sight can dominate the luminosity, bias the fitting to a higher averaged ${T}_{{\rm{d}}}$, and therefore can lead to a locally underestimated ${N}_{{{\rm{H}}}_{2}}$. This effect may appear as jumps of column density in the ${N}_{{{\rm{H}}}_{2}}$ maps. Due to the confusion with the foreground/background, and the aforementioned issues of the single-component modified blackbody fitting, the low ${N}_{{{\rm{H}}}_{2}}$ structures were excluded from our quantitative analysis by setting the column density thresholds (e.g., Section 3.3).

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The high resolution ${N}_{{{\rm{H}}}_{2}}$ images of our target sources show distinct morphologies, which qualitatively can be separated into molecular clouds with widely varying spatial distributions of sub-structures (e.g., W43-Main, W43-South, and G10.2-0.3), molecular clouds showing a high concentration of mass at the central region (e.g., W49A and G10.6-0.4), and clouds with morphology in-between these two cases. We resolved extended heated sources and localized ones that are embedded in local overdense regions. A more detailed description of the individual sources is provided below.

The dominant dense component of W43-main exhibits a ∼15 pc scale Z-shaped filamentary structure, with several embedded internal heating sources. In addition, we resolved a large number of dense clumps/cores that are widely spread over the FOV of our SHARC2 350 μm image. The T_d in this Z-shaped dense structure is, in general, lower than ∼25 K. The >30 K localized heated sources may be associated with newly formed high-mass stars, or star clusters. On large scales, the heated dust (and gas) appears spatially not well correlated with the dense structures and presents a filamentary or irregular structure. W43-South was also resolved with numerous, widely spread dense clumps/cores. In W43-South, only some high column density structures show high T_d. There are some heated, extended diffuse structures.

For the sources W49A, G10.6-0.4, and W33, the column density peaks reside at the center of the molecular clouds, which are connected with exterior filamentary dense gas structures. In particular, the massive molecular gas clumps located at the center of W33 are connected with parsec-scale molecular gas arms, which are similar to those resolved by the SMA and the Atacama Large Millimeter Array (ALMA) observations of the OB cluster-forming region G33.92+0.11 (Liu et al. 2012a, 2015). The highest temperature regions of these sources are spatially associated with the column density peaks.

The sources G10.2-0.3 and G10.3-0.1 may be relatively evolved, as they contain extended H ii regions in the Very Large Array centimeter band observations (e.g., Kim & Koo 2002). The source G10.3-0.1 shows a clumpy, incomplete ring-like geometry over a ∼6 pc scale region. The dominant heating sources are likely encircled by this incomplete ring. From the T_d map, we see some heated dust inside the ring, which is connected to a bi-conical heated shell on large scales. The column density distribution of G10.2-0.3 appears very irregular, and presents a large number of marginally resolved, or non-spatially resolved dense cores. For this region, the highest column density structures are seen preferentially with low T_d. Some high column density structures, including the peak column density, are embedded with localized heating sources. There is extended, diffuse heated gas/dust that shows a shell-like or irregular morphology. On the ∼5 pc scale, the marginally resolved curvature of the cool and dense molecular gas structures seem to follow the shell-like geometry of the heated gas, indicating strong effects of stellar feedback on the parent molecular cloud structures.

We attempt to quantify our visual impression of the target sources using statistical methods, which are introduced in Sections 3.2–3.5. The links of the derived quantities to the underlying physics, unfortunately, are not yet certain, and deserve future comparisons with numerical hydrodynamics simulations.

The overall masses of the observed molecular clouds range from a fraction to a few times 10⁵ M_⊙, and are summarized in Table 1. The degree of matter concentration in the molecular clouds can be quantified by the enclosed gas and dust mass as a function of radius, M(r) (see e.g., Walker et al. 2016). Generally, OB cluster-forming clouds are more massive at a given radius than low-mass star-forming regions. The power-law form of the mass versus radius relation can be a consequence of the power-law density profile, since a radial density profile of $n(r)\propto {r}^{-p}$ gives a mass versus radius relation of $M(r)\propto {r}^{3-p}$. Kauffmann et al. (2010) found that the cluster-bearing clouds roughly follow $M(r)\propto {r}^{1.27}$, indicating that the slope of the mass versus radius relation, though largely uncertain, should be lower than 1.5. The radial density profile for 51 massive star-forming regions based on dust continuum maps is found to be of $n(r)\propto {r}^{1.8\pm 0.4}$ at $r\sim 0.2$ pc scales (Mueller et al. 2002), which corresponds to $M(r)\propto {r}^{1.2\pm 0.4}$.

Figure 12 shows the enclosed gas and dust mass profiles of our seven resolved target sources. In addition, we show the first (radial) derivative of the enclosed mass profiles in the bottom row of Figure 12. When calculating the enclosed mass profiles, we define the centers of W49A, G10.6-0.4, and W33, approximately at the centers of their centralized massive molecular gas clumps.

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For W43-main, W43-south, G10.3-0.1, and G10.2-0.3, the centers were defined at the most massive molecular clumps located nearest to the center of the 350 μm observational FOVs. The definitions of the centers of W43-main, W43-south, G10.3-0.1, and G10.2-0.3 are ambiguous to some extent due to their irregular cloud morphology. Nevertheless, for these four sources, the enclosed mass profiles are not sensitive to the definitions of the centers, for the same reason.

In Figure 12, the left column shows the results for the sources that have the most significant matter concentration, while the right column shows the results for those with relatively extended or randomized spatial distribution of dense structures (see Section 3.1 for more descriptions). This presentation strategy is mainly for the sake of avoiding crowded data points, but not for discriminating sources subjectively and artificially.

The $\partial (\mathrm{log}\,M(r))/\partial (\mathrm{log}\,r)$ of all presented sources resides in the range of 0.0–2.5 over all spatial scales. As expected, the sources showing a significant centralized concentration of mass (i.e., the sources presented in the left panel of Figure 12; see discussion Section 3.1) systematically show lower values of $\partial (\mathrm{log}\,M(r))/\partial (\mathrm{log}\,r)$. Qualitatively, the low value of $\partial (\mathrm{log}\,M(r))/\partial (\mathrm{log}\,r)$ occurs when a marginally spatially resolved or unresolved massive molecular gas clump located at the center of the molecular cloud contributes to a very significant fraction of the enclosed mass. Outside of the centralized molecular gas clumps, the surrounding molecular gas structures are relatively diffuse and therefore the enclosed mass does not increase rapidly with radius. On the $\lesssim 3$ pc scale, the mini-starburst region W49A is the only case in which the centralized massive molecular gas clump is spatially resolved. A peak of $\partial (\mathrm{log}\,M(r))/\partial (\mathrm{log}\,r)$ is expected on the approximate spatial scales of the massive molecular gas clump. This massive molecular gas clump appears to be dominating the mass in the central region of W49A, such that the $\partial (\mathrm{log}\,M(r))/\partial (\mathrm{log}\,r)$ drops quickly to below 1.0 on ∼3 pc scales. The massive molecular gas clump in the inner ∼3 pc of W49A is embedded with a spatially well resolved, ∼2 pc ring-like distribution of UC H ii regions that are orbiting about the center of the ring (Peng et al. 2010; Galván-Madrid et al. 2013). This massive molecular gas clump also appears at the junction of the north and south filaments in the inner few parsecs (Galván-Madrid et al. 2013), which are also spatially resolved in our column density image. The azimuthal asymmetry due to the presence of these dense gas filaments can lead to a poorly defined "center" when evaluating M(r) that further leads to jumps in M(r) and the apparent hump in $\partial (\mathrm{log}\,M(r))/\partial (\mathrm{log}\,r)$.

For all sources, the decrease in $\partial (\mathrm{log}\,M(r))/\partial (\mathrm{log}\,r)$ on the large spatial scales is due to the finite cloud size. Our observational FOVs of W43-Main, W43-South, and W33, are comparable to the angular scale of these molecular clouds. We double-checked the size of these molecular clouds from the Herschel SPIRE images. When the integrated mass of the extended cloud structures are dominate over the masses of the centralized massive gas clumps/cores (e.g., on ∼1–10 pc scales), the observed sources show a weak increasing trend of $\partial (\mathrm{log}\,M(r))/\partial (\mathrm{log}\,r)$.

Intriguingly, for most of the observed OB cluster-forming regions, the measured $\partial (\mathrm{log}\,M(r))/\partial (\mathrm{log}\,r)$ on parsec scales is smaller than that of a virialized molecular cloud, and appears close to that of a gravitationally bound H ii gas cloud that has a ∼10 km s⁻¹ sound speed. We refer to Bressert et al. (2012), where r_vir is defined as the virial radius based on a crossing time of 1 Myr, corresponding to the age found from recent high-resolution studies of several young massive clusters (YMCs). The enclosed mass profile of the aforementioned bound H ii cloud (${r}_{{\rm{\Omega }}}$) is calculated assuming an overdensity of gravitationally bound gas, with a sound speed of $\sim 10\,\mathrm{km}\,{{\rm{s}}}^{-1}$, and equal gravitational potential and kinetic energies. The critical initial gas mass to form a YMC, assuming a star formation efficiency (SFE) of 30%, is then ${m}_{\mathrm{crit}}\sim 3\times {10}^{4}\,{M}_{\odot }$.

The N-PDF of molecular clouds is a widely applied statistical measurement.

We follow the frequently used formalism of N-PDFs from previous numerical works, where the natural logarithm of the ratio of column density and mean column density is $\eta =\mathrm{ln}({N}_{{{\rm{H}}}_{2}}/\langle {N}_{{{\rm{H}}}_{2}}\rangle )$, and the normalization of the probability function is given by ${\int }_{-\infty }^{+\infty }p(\eta )d\eta ={\int }_{0}^{+\infty }p({N}_{{{\rm{H}}}_{2}})d({N}_{{{\rm{H}}}_{2}})=1$; for more details, see Schneider et al. (2015a). Figure 13 shows the N-PDF above the selected column density thresholds that were determined by the 1σ noise level in the ${N}_{{{\rm{H}}}_{2}}$ images. We found that the N-PDFs of these sources can be approximated by power laws. However, the high column density ends of the N-PDF may deviate from the overall power laws. For example, the sources G10.6-0.4 and W49A show excesses at the high column density ends. On the other hand, the sources G10.2-0.3 and W43-south show a deficit at high column densities. There are other minor variations in the observed N-PDFs, which are beyond the focus of the present paper. Part of these minor variations in the intermediate range of column density may be related to the limited FOV (more below). We note that although the excess of the very high ${N}_{{{\rm{H}}}_{2}}$ pixels in G10.6-0.4 looks marginal from Figure 13, it is difficult to ignore such excess given that they comprise the most robustly detected component in the image domain (Figure 8). Based on the previous observations of Liu et al. (2010b, 2012b), we expect this excess to become more obvious with improved angular resolution. Therefore, this excess of high ${N}_{{{\rm{H}}}_{2}}$ pixels needs to be included in any quantification of the N-PDF.

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Interestingly, the similarities in the N-PDF features seem to be linked to the similarities of their overall cloud morphology. The sources that show significant excess of high column density pixels appear to be those that are also showing significant spatial concentration of high column density structures at the center. On the other hand, for the sources that are showing widely spread or irregular dense structures, there is a deficit of high column density pixels. These two types of sources can be separated by their enclosed mass profiles and the slopes of the profiles, see Section 3.2.

We used the power-law package (Alstott et al. 2014) to fit the observed column density distributions with power laws and an additional high column density power-law tail (Figure 13) using Maximum Likelihood Estimation. In this way, it is not required to pre-bin the observed column density distributions, which has been proven to provide better accuracy compared to linear regression on histograms of the observed column density (Clauset et al. 2009).

Table 2.  Observational Parameters of Multi-band Data

λ (μm)	Beam FWHM	Pixel Size	Flux Unit
Camera	(arcsec)	(arcsec)
70/PACS	$5.8\times 12.1$	3.2	Jy pixel−1
160/PACS	$11.4\times 13.4$	3.2	Jy pixel−1
250/SPIRE	18.1	6.0	MJy sr−1
350/SPIRE	25.2	9.72	MJy sr−1
500/SPIRE	36.9	14.0	MJy sr−1
450/SCUBA2	8.0	3.0	mJy arcsec−2
850/SCUBA2	14.0	3.0	mJy arcsec−2
350/SHARC2	8.0	1.5	Jy beam−1
870/LABOCA	19.2	6.0	Jy beam−1
1200/MAMBO-2	11.0	3.50	mJy beam−1
217 GHz/PLANCK	292.2	60.0	Kcmb
353 GHz/PLANCK	279.0	60.0	Kcmb

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We estimated the background and foreground contamination as of an offset value determined from the outskirts of a larger column density map derived from Herschel data and subtracted this value from our column density data (Schneider et al. 2015b; Ossenkopf-Okada et al. 2016). Since the lower column density part can be influenced dramatically by the noise level, boundary bias, variation along the line of sight, or enclosed contours (Lombardi et al. 2015), we only considered the values larger than the threshold measured for each source, as listed in Table 3.

Table 3.  Fitting Results of Column Density Probability Distribution Functions (N-PDFs)

Target Source	Measured Threshold	Mean Column Density	Power-law Slopes with Starting η
	log10(N(H ${}_{2}))$	log10(N(H ${}_{2}))$	s0	s1	${\eta }_{1}$	s2	${\eta }_{2}$
W49A	21.87	22.08	−3.10(0.01)	−2.96(0.01)	−0.42	−2.36(0.03)	1.31
G10.6-0.4	21.73	22.00	−2.54(0.01)	−2.55(0.04)	0.51	−1.57(0.24)	2.80
W43-south	21.88	22.06	−2.96(0.01)	−3.91(0.03)	0.66	−3.76(0.07)	1.26
W43-main	22.18	22.47	−2.86(0.01)	−2.88(0.01)	0.32	−2.89(0.02)	0.52
W33	22.10	22.41	−3.18(0.01)	−2.87(0.01)	0.02	−2.89(0.01)	0.34
G10.3-0.1	21.95	22.15	−2.98(0.01)	−3.01(0.01)	−0.15	−2.91(0.01)	0.29
G10.2-0.3	22.09	22.35	−2.69(0.01)	−2.84(0.01)	−0.52	−4.68(0.05)	0.93

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We note that parts of the diffuse cloud structures of some sources may not be covered by the relatively small FOV of our CSO-SHARC2 350 μm images.

We have examined this from the JCMT-SCUBA2 and Herschel images that have wider FOVs. We found that those structures outside of our CSO-SHARC2 fields, above the column density threshold of our N-PDF analysis, mostly have small masses and sizes. Therefore, we do not expect this effect to dramatically bias our quantification of the N-PDFs. It is also not trivial to distinguish these features from foreground/background clouds.

For the quantitative description of our approximated results, we obtained an overall power-law fit (i.e., $p(\eta )\propto {\eta }^{s}$) to all the data larger than the threshold values, and a power-law fit that finds the optimal minimum column density between the empirical distribution and power-law model distributions. Due to deviations from a single power law, we also fit a second power-law component at high column densities for G10.6-0.4, G10.2-0.3, W43-South, and W49A. The power-law slopes for the three fits are denoted as s₀, s₁, and s₂, and are summarized in Table 3. We caution that the power-law index for G10.6-0.4 at the high density end was only tentatively determined, and needs to be improved with better (e.g., higher angular resolution, better sensitivity, and more frequency bands) observational data to improve the statistical reliability. A more detailed discussion of the N-PDFs is deferred to Section 4.2.

The 2PT function¹⁶ is a powerful tool to systematically diagnose the characteristic spatial scales in the molecular cloud morphology, and helps to understand the spatial distribution and clustering properties of high ${N}_{{{\rm{H}}}_{2}}$ structures. We followed the procedure outlined in Szapudi et al. (2005) to perform fast estimates of the 2PT function via Fast Fourier Transforms by zero-padding the original maps. The normalization of the geometry is calculated by filling 0's to the masked pixels and 1's to the valid ones. This form of the 2PT function is the same as the unbiased measure described in Kleiner & Dickman (1984), though we used the column density of each pixel without subtracting the mean column density. In this way, we are more sensitive to the correlation of the density field, rather than density fluctuations. We adopted a flat weighting, where all pixel pairs were assigned with an identical weight. This otherwise unbiased estimator may be biased when the scales of the lags (i.e., the spatial separation of two pixels in a pair) are comparable with the observational FOV (Kleiner & Dickman 1984).

Figure 14 shows the obtained 2PT correlation functions with the directional information averaged out.

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The averaged 2PT correlation functions of W49A, G10.6-0.4, W33, W43-Main, and G10.2-0.3, have a common feature: a rapidly decreasing (RD) correlation strength at short lags, and a sudden transition to a shallower decrease at larger lags.

The RD component corresponds to localized clumps/cores, while the shallower decreasing (SD) component comes from the broader molecular cloud. We note that all the derived 2PT correlation functions show a steep decrease in correlation strength at large lags because of the limited FOV. To avoid this bias in our analysis, we exclude the range of lags that have pixel pairs less than ∼90% of the number of total pixels.

For sources like W43-south and G10.2-0.3, where the structures of column density are composed of widely scattered overdensities, the correlation strengths at shorter lags do not decrease as significantly as the correlation strengths of the more centrally condensed sources, like W49A, W33, and G10.6-0.4.

They also do not show an obvious RD component at short lags.

There are some bumps seen in the 2PT functions for several sources at larger lags, which may present the characteristic scales of some localized overdensities. We do not quantify these features in this paper. The average azimuthal profiles of our obtained 2PT functions are intended to capture the major similarities and differences between the target sources.

We hypothesize that the steeply decreasing component and the shallower one represent structures that were created or supported with different physical mechanisms, and thereby have different characteristic spatial scales and spatial distributions. More discussion about the physical implications is deferred to Section 4.1.

For the sake of quantifying and archiving the observed 2PT functions for comparison with other observations, theories, and numerical simulations, we perform segmented linear fits of these 2PT functions in log (i.e., power-law fitting) and linear space. We note that fits in both the log and the linear space involve large simplifications of the real data. Empirically, the fits in the linear space better capture the transition point from the RD to the SD component, without being sensitive to small variations of the data or the fit parameters. However, fitting in log space presently has a more straightforward link to physical interpretations (more in Section 4.1). The nature of the 2PT functions, including the azimuthal asymmetry, demand more careful future observational and theoretical studies.

We used two-component and three-component segmented linear models to quantify the derived 2PT correlation functions in log–log space, adopting a Levenberg–Marquardt nonlinear least-squares minimization implemented in lmfit (Newville et al. 2014). The free parameters are the slopes (power-law indices in linear space) of two/three segments and the break points of lags. We tentatively used these two models since we noticed that, for several sources like W33, G10.3-0.1, and G10.6-0.4, there are apparent plateaus of correlation strength at lags between ∼2–8 pc that may bias the slopes at small lags to smaller values. We further compared AIC and BIC statistics, which provide a measure of the quality of fits between different models. Since that three-component models provide a better fit for all the sources, we have included the results of the three-component model fits listed in Table 4. The functional form of the three-component model is

$$\begin{eqnarray*}&&\mathrm{log}({S}_{{tr}}(r))\\ =\left\{\begin{array}{ll}{\alpha }_{1}\mathrm{log}(r) & r\lt {x}_{{\mathrm{break}}_{1}},\\ {\alpha }_{2}\mathrm{log}(r)+({\alpha }_{1}-{\alpha }_{2})\mathrm{log}({x}_{{\mathrm{break}}_{1}}) & {x}_{{\mathrm{break}}_{1}}\lt r\lt {x}_{{\mathrm{break}}_{2}},\\ {\alpha }_{3}\mathrm{log}(r)+({\alpha }_{1}-{\alpha }_{2})\mathrm{log}({x}_{{\mathrm{break}}_{1}}) & \\ +({\alpha }_{2}-{\alpha }_{3})\mathrm{log}({x}_{{\mathrm{break}}_{2}}) & r\gt {x}_{{\mathrm{break}}_{2}},\end{array}\right.,\end{eqnarray*}$$

where S_tr(r) represents the correlation strength at a separation of r. The first break point is the transition from the RD component to the SD component. The power-law indices ${\alpha }_{1}$, ${\alpha }_{2}$, and ${\alpha }_{3}$ indicate the decreasing rate of correlation strengths at different separation scales. We excluded the fit parameters of the second break point and third segmented component in the analysis since they are subject to the decreasing statistical instability at larger separations.

Table 4.  Fitting Results of Two-point Correlation Functions: Three Segments

Target Source	${\alpha }_{1}$	${\alpha }_{2}$	${\alpha }_{3}$	${x}_{{\mathrm{break}}_{1}}$	${x}_{{\mathrm{break}}_{2}}$	${y}_{{\mathrm{break}}_{1}}$	${y}_{{\mathrm{break}}_{2}}$
				(pc)	(pc)
W49A	−0.41(0.0016)	−0.09(0.013)	−1.85(0.032)	7.41(2.00(0.026))	16.48(2.84(0.018))	0.30	0.28
G10.6-0.4	−0.45(0.010)	−0.12(0.037)	−1.52(0.029)	2.03(0.71(0.10))	6.05(1.80(0.019))	0.35	0.31
W43-south	−0.06(0.001)	−0.51(0.01)	−1.19(0.015)	6.30(1.84(0.01))	14.03(2.64(0.01))	0.81	0.54
W43-main	−0.30(0.009)	−0.22(0.01)	−2.71(0.07)	1.77(0.57(0.35))	15.74(2.76(0.01))	0.53	0.32
W33	−0.20(0.01)	−0.06(0.09)	−0.93(0.02)	2.80(1.03(0.18))	4.41(1.49(0.02))	0.51	0.48
G10.3-0.1	−0.18(0.01)	−0.011(0.019)	−0.83(0.03)	0.81(0.21(0.16))	3.53(1.26(0.02))	0.68	0.67
G10.2-0.3	−0.017(0.003)	−0.32(0.0033)	−1.18(0.016)	3.61(1.28(0.059))	7.45(2.01(0.018))	0.93	0.74

Note. For ${x}_{{\mathrm{break}}_{1}}$ and ${x}_{{\mathrm{break}}_{2}}$, we listed the fitted values with the format of corresponding separation value (fitted value(error)), since we conducted the fits in log–log space.

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The slopes of the power-law at small scales range from −0.2 to −0.4, while the values of slopes for larger scales are more scattered, with a range of −0.8 to −2.7. One example of our fitted three-component model and two-component model of 2PT is shown in Figure 15.

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For the segmented linear model, we fit the functional form of

$$\begin{eqnarray*}{S}_{\mathrm{tr}}(r)=\left\{\begin{array}{ll}{k}_{1}r+1 & r\lt {x}_{\mathrm{break}},\\ {k}_{2}r+({k}_{1}-{k}_{2}){x}_{\mathrm{break}}+1 & r\gt {x}_{\mathrm{break}}.\end{array}\right.\end{eqnarray*}$$

The three fit parameters are the two slopes k₁ and k₂ of the two components and the break point x_break, together with the break correlation strength, listed in Table 5.

Many structure identification techniques have been developed to describe the hierarchical nature of the molecular cloud morphology. In this paper, we focus on analyzing the structures identified using the tree algorithm implemented in the dendrograms realization (Rosolowsky et al. 2008). Dendrograms are multi-level structures defined by a set of iso-surfaces, where the bottom structure represents the low-density gas that fills the vast volume of a cloud. The defined boundary in our case is the threshold we measured with the column density map. Emerging from the trunk are different levels of branches that are distinguishable from their parent structures (either a trunk or lower-level branch) as they are denser above a defined increment. The leaves are the peak levels of a dendrogram, which are essentially the densest small regions containing local maxima. This method is able to track the multi-scale density structures without relying on any assumption of the emission profile or morphology; thus, it provides an unbiased view of the underlying hierarchy in the clouds. Since our derived column density maps are able to recover extended emission, the impact of spatial filtering, as pointed out by Kauffmann et al. (2010), is expected to be alleviated when we are quantifying the properties of the dendrogram output.

Other commonly adopted structure identification techniques include the clumpfind (Williams et al. 1994) and the gaussclumps (Stutzki & Guesten 1990) algorithms. For our high angular resolution ${N}_{{{\rm{H}}}_{2}}$ images that present rich and hierarchical structures, analyzing using the clumpfind algorithm leads to artificial fragmentation (Pineda et al. 2009). On the other hand, many localized structures we resolved deviate from the assumed two-dimensional Gaussian geometry, and lead to poor results with the gaussclumps algorithm. A comparison of the structures identified by these algorithms, and the defects in the analysis, will be elaborated on in the thesis of the first author and is omitted from the present manuscript.

When deriving the dendrograms of each region, we trimmed $\sim 20^{\prime\prime}$ near the edges of all the column density maps to suppress the non-uniform noise mainly propagated from the SHARC2 observations. We set the lowest contour level as $7\times {10}^{21}$ cm⁻², a minimum increment of 5σ for a branch to be identified from its parent structure, and a minimum size of 7 pixels (comparable to the beam size) for a leaf to be considered an independent entity. A sample dendrogram output can be seen in Figure 16. For leaves that stem from a parent structure, we further calculated a "corrected" mass value obtained by subtracting the merge level, which is defined as the mean column density of the parent structure (see more details from Ragan et al. 2013). Note that the choice of setting the "increment" value will mainly impact the amount of identified leaves and is also the major factor that influences the original and the corrected mass. We caution that this merge level subtraction method can bias the masses of the relatively insignificant leaves, and may over-subtract in some cases depending on the localized column density. In particular, for the leaves that are only about 5σ more significant than their parent structure, the subtraction process may remove the majority of their mass. We have to compromise between identifying the most reliable leaves and taking advantage of our high angular resolution maps when doing a dendrogram analysis.

The effective radius is defined as ${r}_{\mathrm{eff}}={(A/\pi )}^{1/2}$ where A is the area of a certain structure. We calculated the bolometric luminosity (L_bol) and bolometric temperature (T_bol) for each leaf. L_bol is calculated by integrating our obtained SEDs,

$$\begin{eqnarray}&&{L}_{\mathrm{bol}}=4\pi {d}^{2}{\int }_{0}^{\infty }{S}_{\nu }d\nu ,\end{eqnarray} \tag{ 5 }$$

where d is the distance to our target source, and the bolometric temperature follows Myers & Ladd (1993):

$$\begin{eqnarray}&&{T}_{\mathrm{bol}}=1.25\times {10}^{-11}\,\displaystyle \frac{\int \,\nu {S}_{\nu }d\nu }{\int \,{S}_{\nu }d\nu }\,{\rm{K}}.\end{eqnarray} \tag{ 6 }$$

The integration was from 0.1 μm to 1 cm.

Our dendrogram analysis recovered 420 clumps/cores in these seven regions. The measured T_bol is less than 40 K for all the leaves. Most of the clumps/cores we measured have masses between ${10}^{2}\mbox{--}8\times {10}^{3}\ {M}_{\odot }$ with temperatures of 20–30 K. The properties of all leaves for our target sources are summarized in Tables 6–12. For each leaf, we list the center (position of the local maximum), effective radius, the uncorrected and corrected mass values, the mean column density, the merge level (if present), and the mean dust opacity index, together with the bolometric luminosity and bolometric temperature.

Table 6.  W43-Main Dendrogram Leaves Parameters

Leaf	R.A.	decl.	reff	Mass	Corrected Mass	Luminosity	$\langle {N}_{{{\rm{H}}}_{2}}\rangle$	Merge Level	$\langle {T}_{{\rm{d}}}\rangle$	$\beta$	Tbol	$\langle {N}_{{{\rm{H}}}_{2}}\rangle \geqslant 50\sigma$ a
	(J2000)	(J2000)	$(\mathrm{pc})$	$({M}_{\odot })$	$({M}_{\odot })$	$({L}_{\odot })$	$({\mathrm{cm}}^{-2})$	$({\mathrm{cm}}^{-2})$	$({\rm{K}})$		$({\rm{K}})$
1	18:47:52.9	−2:03:13	0.11	12.7	1.6	4.5×102	1.6×1022	1.4×1022	24.3	1.6	15.3	—
2	18:47:46.6	−2:02:53	0.48	270.0	15.7	1.3×104	1.6×1022	1.5×1022	25.0	1.7	15.3	—
3	18:47:54.3	−2:03:06	0.13	19.6	4.0	6×102	1.8×1022	1.4×1022	23.9	1.6	15.3
4	18:47:52.4	−2:02:42	0.49	236.0	11.7	9.7×103	1.4×1022	1.3×1022	25.4	1.6	15.5	—
5	18:47:39.6	−2:02:29	0.46	270.1	28.5	1.8×104	1.8×1022	1.6×1022	27.2	1.6	16.1
6	18:47:19.5	−2:02:42	0.33	165.6	10.3	4.3×103	2.1×1022	2×1022	23.6	1.6	15.4
7	18:47:42.7	−2:02:44	0.20	41.5	2.7	3.1×103	1.5×1022	1.4×1022	27.0	1.7	16.0	—
8	18:47:55.4	−2:02:39	0.12	15.1	0.9	5.5×102	1.4×1022	1.3×1022	25.2	1.6	15.5	—
9	18:47:30.8	−2:02:20	0.46	434.3	68.0	1.7×104	2.9×1022	2.4×1022	23.8	1.7	15.1
10	18:47:23.2	−2:02:23	0.29	161.3	10.7	4.2×103	2.7×1022	2.5×1022	23.4	1.6	15.4
11	18:47:19.9	−2:02:06	0.51	444.0	74.1	1.1×104	2.4×1022	2×1022	22.6	1.7	15.4
12	18:47:54.5	−2:01:25	0.83	668.5	30.8	3.1×104	1.4×1022	1.3×1022	25.8	1.6	15.6	—
13	18:47:35.8	−2:02:09	0.43	1116.4	403.8	5.8×104	8.5×1022	5.4×1022	26.7	1.6	16.1
14	18:47:45.6	−2:02:16	0.13	26.5	3.0	1.1×103	2.2×1022	2×1022	24.8	1.6	15.3
15	18:47:47.1	−2:02:03	0.29	116.9	15.1	5.4×103	1.9×1022	1.7×1022	24.9	1.7	15.3
16	18:47:44.6	−2:02:04	0.16	40.4	4.7	1.8×103	2.3×1022	2×1022	25.4	1.6	15.4
17	18:47:57.1	−2:01:55	0.20	37.8	1.8	1.7×103	1.3×1022	1.3×1022	26.8	1.5	15.9	—
18	18:47:24.5	−2:01:50	0.36	358.8	48.3	7.6×103	3.9×1022	3.4×1022	23.3	1.6	15.5
19	18:47:17.8	−2:01:51	0.10	13.3	0.7	3.7×102	2.1×1022	2×1022	23.2	1.7	15.3
20	18:47:33.4	−2:01:36	0.18	120.4	10.1	6.4×103	5.5×1022	5.1×1022	25.1	1.8	15.1
21	18:47:28.1	−2:01:24	0.44	923.0	154.8	2.6×104	6.6×1022	5.5×1022	24.2	1.6	15.3
22	18:47:23.9	−2:01:24	0.18	82.0	7.7	2.1×103	3.8×1022	3.4×1022	23.2	1.6	15.3
23	18:47:36.5	−2:00:57	0.66	5906.8	2542.7	1.7×105	1.9×1023	1.1×1023	23.5	1.8	15.4
24	18:47:18.7	−2:01:08	0.26	88.2	2.4	3.2×103	1.8×1022	1.8×1022	24.3	1.7	15.3
25	18:47:43.7	−2:01:10	0.12	34.1	4.5	1.4×103	3.2×1022	2.8×1022	25.7	1.6	15.5
26	18:47:45.7	−2:01:09	0.10	19.3	0.6	8.5×102	2.6×1022	2.5×1022	24.6	1.7	15.2
27	18:47:33.9	−2:01:02	0.10	78.2	4.8	2.2×103	1.2×1023	1.1×1023	23.7	1.7	15.2
28	18:47:26.0	−2:01:00	0.16	103.1	18.9	3.2×103	5.5×1022	4.5×1022	24.3	1.6	15.3
29	18:47:29.9	−2:00:45	0.32	504.5	71.4	1.8×104	7.1×1022	6.1×1022	24.3	1.7	15.2
30	18:47:45.4	−2:00:39	0.28	251.8	36.5	6.5×103	4.4×1022	3.8×1022	23.2	1.7	15.3
31	18:47:27.3	−2:00:36	0.35	683.8	146.7	2.1×104	7.7×1022	6.1×1022	24.5	1.6	15.3
32	18:47:18.4	−2:00:39	0.12	16.8	0.9	9.2×102	1.7×1022	1.6×1022	26.9	1.6	15.9	—
33	18:47:41.5	−2:00:28	0.35	1516.7	507.0	8.3×104	1.8×1023	1.2×1023	26.0	1.7	15.3
34	18:47:34.1	−2:00:33	0.12	66.6	5.5	3.8×103	6.2×1022	5.7×1022	26.0	1.7	15.3
35	18:47:39.5	−2:00:29	0.18	346.8	69.1	8.5×103	1.5×1023	1.2×1023	23.0	1.8	15.4
36	18:47:18.9	−2:00:09	0.23	61.8	1.6	3.8×103	1.7×1022	1.6×1022	27.2	1.6	16.1	—
37	18:47:50.0	−1:59:51	0.41	204.5	8.1	9.9×103	1.7×1022	1.6×1022	25.7	1.6	15.5	—
38	18:47:45.5	−2:00:10	0.13	55.4	4.4	1.6×103	4.8×1022	4.5×1022	23.6	1.7	15.2
39	18:47:32.9	−1:59:46	0.45	394.3	79.9	3.1×104	2.7×1022	2.2×1022	27.4	1.7	16.1
40	18:47:20.1	−1:59:31	0.69	651.9	59.8	3.9×104	1.9×1022	1.8×1022	26.4	1.6	15.7
41	18:47:25.5	−1:59:30	0.63	520.5	55.6	5.7×104	1.9×1022	1.7×1022	27.8	1.8	16.5
42	18:47:42.4	−1:59:35	0.46	1380.5	449.6	3.9×104	9.4×1022	6.4×1022	23.4	1.7	15.3
43	18:47:38.6	−1:59:33	0.29	272.2	28.6	2.8×104	4.6×1022	4.1×1022	27.4	1.8	15.8
44	18:47:31.8	−1:59:31	0.19	60.5	4.1	4.7×103	2.3×1022	2.2×1022	27.3	1.7	16.0
45	18:47:28.7	−1:59:20	0.37	175.1	16.1	1.7×104	1.8×1022	1.7×1022	29.4	1.6	17.3
46	18:47:22.3	−1:59:03	0.46	278.1	10.8	1.7×104	1.8×1022	1.8×1022	26.6	1.6	15.8
47	18:47:56.9	−1:58:58	0.31	106.2	8.7	5.4×103	1.6×1022	1.4×1022	26.7	1.6	15.9	—
48	18:47:45.8	−1:59:04	0.22	101.0	16.0	4.7×103	3×1022	2.5×1022	24.0	1.8	15.0
49	18:47:40.0	−1:58:40	0.60	2599.1	968.9	1.7×105	1×1023	6.4×1022	26.6	1.7	15.3
50	18:47:38.6	−1:59:08	0.21	168.3	10.0	1.6×104	5.2×1022	4.9×1022	28.1	1.7	16.1
51	18:47:34.0	−1:58:56	0.19	62.2	2.5	4.7×103	2.4×1022	2.3×1022	27.1	1.7	15.9
52	18:47:32.3	−1:58:56	0.19	72.2	9.6	4×103	2.8×1022	2.4×1022	25.6	1.7	15.4
53	18:47:46.7	−1:58:55	0.14	40.3	4.5	1.8×103	2.8×1022	2.5×1022	24.0	1.8	15.1
54	18:47:54.7	−1:58:41	0.46	315.3	74.6	1.4×104	2.2×1022	1.6×1022	25.7	1.6	15.6
55	18:47:26.7	−1:58:34	0.54	471.8	118.0	5.4×104	2.3×1022	1.7×1022	28.7	1.7	16.9
56	18:47:31.5	−1:58:34	0.42	362.1	57.2	2.1×104	2.9×1022	2.4×1022	25.3	1.7	15.3
57	18:47:47.6	−1:58:28	0.19	51.6	2.3	3.4×103	2×1022	1.9×1022	26.0	1.7	15.6
58	18:47:51.8	−1:58:20	0.35	257.8	81.9	1.1×104	3×1022	2.1×1022	25.9	1.6	15.6
59	18:47:36.9	−1:58:19	0.30	431.9	83.3	3.7×104	6.6×1022	5.4×1022	28.0	1.7	16.0
60	18:47:22.0	−1:58:04	0.47	299.0	29.4	2.6×104	2×1022	1.8×1022	27.7	1.7	16.3
61	18:47:19.5	−1:58:00	0.28	117.2	17.9	7.2×103	2.1×1022	1.8×1022	25.8	1.7	15.5
62	18:47:38.9	−1:58:01	0.09	25.6	0.8	7.4×103	4.2×1022	4.1×1022	32.8	1.8	19.6
63	18:47:48.4	−1:57:46	0.26	253.2	99.4	6.9×103	5.2×1022	3.2×1022	24.4	1.6	15.4
64	18:47:38.4	−1:57:44	0.35	577.4	226.1	1.6×105	6.7×1022	4.1×1022	34.0	1.8	20.3
65	18:47:31.1	−1:57:40	0.29	160.3	38.7	1.4×104	2.7×1022	2×1022	27.4	1.7	16.1
66	18:47:57.1	−1:57:28	0.49	445.4	96.1	1.5×104	2.7×1022	2.1×1022	25.1	1.6	15.5
67	18:47:27.0	−1:57:41	0.20	102.1	19.6	1.1×104	3.7×1022	3×1022	30.1	1.6	17.5
68	18:47:43.2	−1:57:43	0.18	55.3	3.6	9.6×103	2.3×1022	2.2×1022	30.1	1.8	17.9
69	18:47:33.1	−1:57:23	0.42	386.8	90.1	3.3×104	3.2×1022	2.4×1022	30.0	1.5	17.5
70	18:47:45.2	−1:57:31	0.28	91.6	3.7	1.4×104	1.6×1022	1.6×1022	30.3	1.7	18.1	—
71	18:47:23.7	−1:57:38	0.17	42.9	2.1	2.7×103	2×1022	1.9×1022	28.3	1.5	16.5
72	18:47:49.8	−1:57:24	0.23	185.2	15.4	4×103	5.2×1022	4.8×1022	23.0	1.6	15.4
73	18:47:40.0	−1:57:22	0.27	213.3	56.0	6.4×104	4.1×1022	3.1×1022	35.7	1.7	23.1
74	18:47:27.0	−1:57:18	0.20	95.5	16.2	1.2×104	3.6×1022	3×1022	30.8	1.6	18.1
75	18:47:50.7	−1:57:21	0.10	37.6	1.9	8.3×102	5×1022	4.8×1022	23.3	1.6	15.4
76	18:47:19.9	−1:56:42	0.39	181.0	13.3	1.4×104	1.7×1022	1.5×1022	27.5	1.6	16.2	—
77	18:47:46.0	−1:56:42	0.58	518.4	84.1	3.3×104	2.2×1022	1.8×1022	28.2	1.5	16.5
78	18:47:56.2	−1:57:00	0.18	52.7	5.5	2.4×103	2.3×1022	2.1×1022	25.6	1.6	15.5
79	18:47:39.3	−1:56:48	0.44	439.0	173.8	1.2×105	3.3×1022	2×1022	35.7	1.6	23.3
80	18:47:34.4	−1:56:51	0.15	43.8	1.6	8.8×103	2.7×1022	2.6×1022	33.5	1.6	20.7
81	18:47:29.1	−1:56:53	0.17	70.0	10.8	2.8×103	3.6×1022	3×1022	26.6	1.5	15.9
82	18:47:27.7	−1:56:51	0.18	86.4	8.5	9.9×103	3.8×1022	3.4×1022	31.1	1.6	18.2
83	18:47:24.4	−1:56:50	0.16	38.2	2.6	7.4×103	2.2×1022	2×1022	32.6	1.7	20.0
84	18:47:35.5	−1:56:33	0.29	203.2	46.7	4.8×104	3.4×1022	2.6×1022	35.7	1.6	23.2
85	18:47:27.7	−1:56:35	0.15	66.1	9.0	6.3×103	3.9×1022	3.4×1022	30.6	1.5	17.8
86	18:47:24.9	−1:56:32	0.28	122.3	7.4	2.5×104	2.2×1022	2×1022	34.3	1.6	21.7
87	18:47:31.1	−1:56:32	0.15	31.5	1.2	1.9×103	2.1×1022	2×1022	27.2	1.6	16.0
88	18:47:38.4	−1:56:10	0.30	158.0	30.6	2.8×104	2.5×1022	2×1022	33.1	1.6	20.3
89	18:47:42.8	−1:56:09	0.36	467.7	175.9	3.6×104	5.1×1022	3.2×1022	26.9	1.7	15.7
90	18:47:27.7	−1:56:00	0.40	311.9	44.3	3.6×104	2.8×1022	2.4×1022	31.5	1.5	18.7
91	18:47:57.9	−1:56:11	0.11	42.4	18.0	7.1×102	5.2×1022	3×1022	23.8	1.4	15.7
92	18:47:54.5	−1:55:48	0.41	274.2	36.8	1.2×104	2.3×1022	2×1022	25.0	1.7	15.3
93	18:47:58.5	−1:56:04	0.09	29.1	12.2	5.2×102	5.1×1022	3×1022	23.9	1.4	15.6
94	18:47:23.9	−1:55:52	0.33	155.8	9.3	3.4×104	2×1022	1.9×1022	33.4	1.7	21.1
95	18:47:51.2	−1:55:51	0.33	126.2	13.2	1.1×104	1.7×1022	1.5×1022	29.5	1.5	17.3	—
96	18:47:41.0	−1:55:56	0.23	147.0	18.5	2.1×104	4.1×1022	3.6×1022	29.7	1.7	17.2
97	18:47:35.2	−1:55:52	0.19	47.2	4.7	8.4×103	1.8×1022	1.6×1022	35.0	1.5	22.3
98	18:47:29.3	−1:55:51	0.12	27.2	1.8	3.4×103	2.5×1022	2.4×1022	30.7	1.6	18.2
99	18:47:42.0	−1:55:36	0.18	86.9	3.4	1.4×104	3.7×1022	3.6×1022	29.6	1.8	17.2
100	18:47:59.2	−1:55:40	0.13	25.1	2.5	1.1×103	2.1×1022	1.9×1022	26.9	1.5	15.9
101	18:47:52.5	−1:55:03	0.49	502.6	175.8	2.6×104	3×1022	1.9×1022	27.1	1.6	16.0
102	18:47:40.6	−1:55:14	0.31	305.2	51.4	4.9×104	4.4×1022	3.6×1022	29.7	1.8	17.2
103	18:47:49.5	−1:55:22	0.09	17.7	4.1	1.2×103	2.9×1022	2.2×1022	28.4	1.5	16.5
104	18:47:55.0	−1:55:09	0.22	79.0	8.2	3.8×103	2.2×1022	2×1022	26.4	1.6	15.7
105	18:47:37.4	−1:55:18	0.13	53.0	3.2	1.9×104	4.2×1022	4×1022	36.9	1.7	24.6
106	18:47:35.9	−1:55:05	0.43	758.1	274.8	1.5×105	5.7×1022	3.6×1022	33.0	1.7	19.9
107	18:47:48.9	−1:55:15	0.12	32.5	8.5	2.5×103	3×1022	2.2×1022	29.2	1.5	17.0
108	18:47:38.5	−1:55:11	0.21	130.1	10.6	3.5×104	4.3×1022	4×1022	33.4	1.8	20.3
109	18:47:22.6	−1:54:54	0.44	186.5	11.3	2.1×104	1.4×1022	1.3×1022	30.7	1.5	18.2	—
110	18:47:42.6	−1:55:10	0.12	55.6	4.6	5×103	5.2×1022	4.8×1022	28.3	1.7	16.3
111	18:47:57.2	−1:54:41	0.56	498.2	99.9	3.5×104	2.2×1022	1.8×1022	27.5	1.6	16.2
112	18:47:29.0	−1:54:35	0.52	258.2	11.5	3.8×104	1.3×1022	1.3×1022	32.3	1.6	19.8	—
113	18:47:50.7	−1:54:49	0.20	53.7	2.3	4.4×103	2×1022	1.9×1022	28.7	1.6	16.8
114	18:47:39.8	−1:54:40	0.13	57.8	7.6	6.9×103	5.1×1022	4.4×1022	28.8	1.7	16.5
115	18:47:45.1	−1:54:40	0.11	211.3	120.1	5.7×103	2.4×1023	1×1023	24.4	1.7	15.3
116	18:47:35.5	−1:54:34	0.16	75.1	3.2	9.3×103	4×1022	3.9×1022	28.9	1.7	16.7
117	18:47:37.8	−1:54:25	0.43	626.4	126.2	6.3×104	4.8×1022	3.9×1022	27.4	1.8	15.8
118	18:47:46.9	−1:54:26	0.41	5647.4	4436.4	1.4×105	4.8×1023	1×1023	25.5	1.6	15.6
119	18:47:24.5	−1:54:18	0.60	354.8	49.9	3.2×104	1.4×1022	1.2×1022	32.2	1.4	19.1	—
120	18:47:54.6	−1:54:25	0.29	124.7	16.4	8×103	2.1×1022	1.8×1022	26.9	1.6	15.9
121	18:47:40.8	−1:54:19	0.35	641.7	258.9	3.9×104	7.4×1022	4.4×1022	26.0	1.8	15.3
122	18:47:50.2	−1:54:21	0.19	152.9	57.5	5.3×103	6.1×1022	3.8×1022	24.6	1.6	15.3
123	18:47:34.7	−1:54:13	0.20	117.9	17.4	1.2×104	4×1022	3.4×1022	28.9	1.7	16.7
124	18:47:44.1	−1:54:13	0.09	19.1	3.3	1.9×103	3.1×1022	2.6×1022	27.6	1.7	16.1

Note.

^aA blank means the mean column density of a leaf meets the $50\sigma$ threshold while a "—" means it not.

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Table 7.  W43-South Dendrogram Leaves Parameters

Leaf	R.A.	decl.	reff	Mass	Corrected Mass	Luminosity	$\langle {N}_{{{\rm{H}}}_{2}}\rangle$	Merge Level	$\langle {T}_{{\rm{d}}}\rangle$	$\beta$	Tbol	$\langle {N}_{{{\rm{H}}}_{2}}\rangle \geqslant 50\sigma$
	(J2000)	(J2000)	$(\mathrm{pc})$	$({M}_{\odot })$	$({M}_{\odot })$	$({L}_{\odot })$	$({\mathrm{cm}}^{-2})$	$({\mathrm{cm}}^{-2})$	$({\rm{K}})$		$({\rm{K}})$
1	18:45:52.2	−2:47:12	0.21	26.7	1.5	1×103	8.8×1021	8.3×1021	21.8	2.0	15.0	—
2	18:45:56.1	−2:47:08	0.22	44.9	8.3	1.7×103	1.3×1022	1.1×1022	20.9	2.1	15.0
3	18:45:57.4	−2:47:04	0.22	46.2	8.9	1.8×103	1.3×1022	1.1×1022	21.1	2.1	15.0
4	18:46:02.1	−2:46:58	0.36	95.2	11.0	6.5×103	1.1×1022	9.3×1021	23.2	2.0	14.8
5	18:46:10.7	−2:46:24	0.57	193.9	15.2	1.3×104	8.4×1021	7.8×1021	22.9	2.0	14.8	—
6	18:46:13.7	−2:46:36	0.40	96.4	10.6	5.5×103	8.6×1021	7.7×1021	22.5	2.0	14.8	—
7	18:46:19.0	−2:46:12	0.86	417.8	22.3	2.5×104	8.1×1021	7.7×1021	22.8	2.0	14.8	—
8	18:46:00.2	−2:46:37	0.22	35.7	3.1	2.5×103	1.1×1022	9.9×1021	24.1	1.9	15.0
9	18:45:55.3	−2:45:59	0.76	610.5	162.0	2.5×104	1.5×1022	1.1×1022	21.8	2.0	14.9
10	18:45:58.7	−2:46:17	0.32	96.1	17.2	5.5×103	1.4×1022	1.1×1022	23.3	1.9	14.9
11	18:46:01.8	−2:46:01	0.40	278.4	95.5	3.2×104	2.5×1022	1.6×1022	27.5	1.8	16.3
12	18:46:23.8	−2:46:02	0.24	35.0	3.0	1.8×103	8.3×1021	7.6×1021	22.3	2.0	14.8	—
13	18:46:15.4	−2:45:48	0.31	52.9	2.4	3.5×103	7.8×1021	7.4×1021	22.9	2.0	14.8	—
14	18:45:48.4	−2:45:43	0.42	117.9	8.0	5×103	9.6×1021	8.9×1021	21.6	2.0	14.9	—
15	18:45:59.9	−2:45:52	0.17	29.1	4.4	2.4×103	1.5×1022	1.2×1022	25.2	1.9	15.3
16	18:46:23.6	−2:45:49	0.10	5.3	0.4	2.7×102	8.2×1021	7.6×1021	22.2	2.0	14.8	—
17	18:46:19.8	−2:45:27	0.22	28.0	1.7	1.8×103	8.2×1021	7.7×1021	23.0	2.0	14.8	—
18	18:46:23.5	−2:45:23	0.24	31.7	2.1	1.7×103	7.7×1021	7.2×1021	22.4	2.0	14.8	—
19	18:46:08.4	−2:45:22	0.25	39.5	2.2	4×103	8.9×1021	8.4×1021	24.8	2.0	15.1	—
20	18:46:01.5	−2:45:29	0.14	35.0	8.6	4.2×103	2.7×1022	2.1×1022	26.9	1.9	15.7
21	18:46:21.2	−2:45:18	0.23	30.0	1.2	1.9×103	7.8×1021	7.5×1021	22.7	2.0	14.8	—
22	18:45:45.7	−2:45:14	0.39	113.9	16.7	4.4×103	1×1022	8.9×1021	21.1	2.1	15.0
23	18:46:00.3	−2:45:07	0.35	274.6	99.3	4.5×104	3.2×1022	2.1×1022	27.5	1.9	16.1
24	18:45:50.0	−2:45:06	0.23	45.5	3.9	2×103	1.2×1022	1.1×1022	21.1	2.1	14.9
25	18:45:48.0	−2:44:41	0.54	316.8	93.4	1.1×104	1.6×1022	1.1×1022	20.7	2.1	15.2
26	18:46:06.1	−2:44:32	0.46	187.9	18.3	1.5×104	1.2×1022	1.1×1022	23.2	2.1	14.7
27	18:45:45.0	−2:44:43	0.19	21.8	1.3	1.1×103	8.9×1021	8.3×1021	21.4	2.1	14.8	—
28	18:45:50.9	−2:44:30	0.39	127.2	21.1	6.6×103	1.2×1022	9.7×1021	21.1	2.2	14.7
29	18:46:15.5	−2:44:14	0.54	202.5	15.0	1.4×104	9.8×1021	9.1×1021	21.8	2.2	14.6
30	18:46:22.6	−2:44:06	0.44	112.7	7.0	6.7×103	8.3×1021	7.8×1021	22.4	2.0	14.7	—
31	18:45:52.7	−2:43:49	0.54	227.2	39.6	1.9×104	1.1×1022	9×1021	23.2	2.1	14.7
32	18:45:57.3	−2:44:02	0.25	72.4	8.2	4.4×103	1.6×1022	1.5×1022	22.0	2.1	14.6
33	18:45:45.3	−2:43:19	0.73	511.6	102.4	1.8×104	1.4×1022	1.1×1022	20.9	2.1	15.1
34	18:46:12.8	−2:43:52	0.21	34.7	1.8	3.2×103	1.1×1022	1×1022	23.4	2.1	14.7
35	18:46:07.8	−2:43:39	0.43	270.4	57.0	2.4×104	2.1×1022	1.6×1022	24.4	2.0	14.9
36	18:46:22.8	−2:43:35	0.25	37.4	1.7	2.5×103	8.2×1021	7.8×1021	22.1	2.1	14.6	—
37	18:46:10.8	−2:43:21	0.26	72.9	3.8	7.3×103	1.5×1022	1.4×1022	25.0	2.0	15.1
38	18:46:00.0	−2:43:17	0.42	205.7	38.9	1.6×104	1.7×1022	1.4×1022	23.7	2.0	14.8
39	18:46:23.5	−2:43:13	0.16	14.8	0.6	1.5×103	8.7×1021	8.3×1021	23.3	2.1	14.7	—
40	18:46:03.0	−2:43:15	0.10	13.7	0.7	1.1×103	2×1022	1.9×1022	25.3	1.9	15.2
41	18:45:57.1	−2:43:10	0.15	24.2	2.1	2×103	1.5×1022	1.4×1022	22.7	2.2	14.5
42	18:46:22.7	−2:42:52	0.42	109.4	5.7	8×103	9×1021	8.5×1021	22.0	2.2	14.6	—
43	18:46:13.7	−2:43:00	0.27	73.0	5.2	4.2×103	1.4×1022	1.3×1022	22.1	2.1	14.7
44	18:46:19.4	−2:42:53	0.30	58.7	2.7	4×103	9.3×1021	8.9×1021	22.2	2.1	14.6	—
45	18:45:55.9	−2:42:46	0.40	180.6	28.4	3.2×104	1.6×1022	1.4×1022	26.4	2.1	15.7
46	18:46:07.2	−2:42:51	0.18	60.0	4.7	7.5×103	2.6×1022	2.4×1022	26.7	1.9	15.6
47	18:46:05.0	−2:42:28	0.49	980.6	442.6	4.7×104	5.8×1022	3.2×1022	24.4	1.8	15.0
48	18:45:58.8	−2:42:21	0.31	71.8	4.2	1.3×104	1×1022	9.8×1021	26.1	2.1	15.6
49	18:45:52.2	−2:42:26	0.59	447.0	131.8	5×104	1.8×1022	1.3×1022	24.6	2.1	15.1
50	18:46:10.1	−2:42:37	0.24	78.6	6.7	9.4×103	2×1022	1.8×1022	27.5	1.8	16.2
51	18:45:44.9	−2:42:28	0.30	77.9	10.1	3.1×103	1.3×1022	1.1×1022	21.3	2.0	15.0
52	18:46:07.7	−2:42:24	0.22	162.6	26.6	1.4×104	4.6×1022	3.8×1022	25.9	1.9	15.2
53	18:46:12.0	−2:42:00	0.44	641.1	221.2	5.7×104	4.8×1022	3.1×1022	25.4	1.9	15.1
54	18:46:14.1	−2:42:10	0.23	125.8	8.5	3.9×103	3.4×1022	3.1×1022	21.0	2.0	15.2
55	18:46:08.7	−2:42:08	0.22	162.3	27.8	1.2×104	4.6×1022	3.8×1022	25.3	1.9	15.0
56	18:46:22.1	−2:41:56	0.32	63.1	2.3	5.1×103	8.6×1021	8.3×1021	22.1	2.2	14.5	—
57	18:46:06.1	−2:42:00	0.15	44.3	2.3	3.6×103	3×1022	2.8×1022	26.0	1.8	15.4
58	18:46:03.4	−2:41:55	0.18	39.1	2.7	4.7×103	1.7×1022	1.5×1022	26.9	1.9	15.9
59	18:45:52.6	−2:41:51	0.24	52.3	7.9	3.7×103	1.3×1022	1.1×1022	22.7	2.1	14.6
60	18:46:06.6	−2:41:29	0.44	464.5	104.4	3.4×104	3.4×1022	2.6×1022	25.5	1.8	15.2
61	18:46:01.1	−2:41:43	0.23	53.9	9.2	1.1×104	1.5×1022	1.2×1022	28.4	2.0	16.9
62	18:46:05.0	−2:41:46	0.14	37.2	2.3	2.9×103	2.7×1022	2.5×1022	25.5	1.8	15.2
63	18:45:45.9	−2:41:34	0.23	31.9	2.3	1.5×103	8.7×1021	8.1×1021	21.5	2.1	14.8	—
64	18:46:13.4	−2:41:34	0.14	28.3	1.0	2.1×103	2.2×1022	2.1×1022	23.6	2.0	14.7
65	18:46:22.7	−2:41:24	0.23	30.3	1.2	2.9×103	8.2×1021	7.9×1021	22.9	2.2	14.6	—
66	18:46:09.0	−2:41:29	0.19	88.5	12.7	1.6×104	3.5×1022	3×1022	30.6	1.8	18.0
67	18:46:12.0	−2:41:28	0.10	20.3	2.0	2.3×103	3.2×1022	2.8×1022	25.8	2.0	15.1
68	18:46:10.0	−2:41:15	0.14	45.3	1.7	8.2×103	3.2×1022	3.1×1022	29.0	1.9	16.8
69	18:46:00.2	−2:41:14	0.12	34.4	10.5	2.4×103	3.6×1022	2.5×1022	23.6	2.0	14.6
70	18:46:21.2	−2:41:04	0.20	27.4	1.1	2.3×103	9.3×1021	9×1021	22.8	2.1	14.6	—
71	18:46:12.7	−2:40:56	0.26	131.1	19.5	8.7×103	2.8×1022	2.4×1022	23.6	2.0	14.7
72	18:45:59.4	−2:41:08	0.17	83.7	30.5	3.9×103	3.9×1022	2.5×1022	22.2	2.0	14.8
73	18:46:09.9	−2:40:57	0.18	80.0	6.3	8.1×103	3.4×1022	3.1×1022	25.3	2.0	14.9
74	18:46:08.0	−2:40:52	0.25	98.6	11.1	8.2×103	2.3×1022	2×1022	25.3	1.9	15.2
75	18:46:22.3	−2:40:42	0.23	38.3	2.6	3.6×103	1×1022	9.4×1021	23.2	2.1	14.6
76	18:45:47.8	−2:40:41	0.25	34.7	1.4	1.8×103	7.8×1021	7.5×1021	21.7	2.1	14.8	—
77	18:45:45.6	−2:40:30	0.45	111.7	5.5	5.1×103	7.9×1021	7.5×1021	21.6	2.0	14.9	—
78	18:46:15.5	−2:40:33	0.38	210.6	39.2	2×104	2.1×1022	1.7×1022	23.5	2.1	14.6
79	18:45:59.6	−2:40:34	0.38	250.0	49.2	1.2×104	2.4×1022	1.9×1022	21.4	2.1	14.8
80	18:46:10.2	−2:40:33	0.18	69.5	11.5	3.9×103	3.1×1022	2.6×1022	22.4	2.1	14.6
81	18:46:03.0	−2:40:30	0.17	45.1	4.6	3.6×103	2.2×1022	2×1022	24.3	2.0	14.9
82	18:46:22.3	−2:40:15	0.35	93.5	12.6	8.3×103	1.1×1022	9.4×1021	22.7	2.2	14.5
83	18:46:07.1	−2:40:19	0.15	26.8	1.9	2.3×103	1.7×1022	1.6×1022	24.6	2.0	15.0
84	18:46:03.2	−2:40:09	0.24	91.1	14.4	1×104	2.3×1022	2×1022	26.9	1.9	15.8
85	18:46:01.1	−2:40:12	0.25	110.6	25.4	1×104	2.5×1022	1.9×1022	24.6	2.0	14.9
86	18:45:48.5	−2:40:09	0.27	37.9	2.2	1.9×103	7.5×1021	7.1×1021	21.5	2.1	14.8	—
87	18:46:06.4	−2:40:06	0.21	58.7	7.1	6.3×103	1.8×1022	1.6×1022	25.9	1.9	15.4
88	18:46:12.9	−2:40:07	0.17	70.4	17.2	1.9×103	3.5×1022	2.7×1022	20.9	2.0	15.4
89	18:46:18.7	−2:40:03	0.19	33.0	2.0	2.3×103	1.2×1022	1.2×1022	22.6	2.1	14.6
90	18:45:45.4	−2:39:55	0.16	14.0	1.0	6.1×102	8×1021	7.4×1021	21.2	2.1	14.9	—
91	18:46:09.9	−2:39:48	0.26	93.2	5.2	4.8×103	2×1022	1.9×1022	23.2	1.9	14.9
92	18:46:16.0	−2:39:41	0.21	58.6	3.5	2.8×103	1.9×1022	1.8×1022	21.8	2.1	14.8
93	18:46:05.9	−2:39:44	0.15	31.9	3.5	4.2×103	1.9×1022	1.7×1022	26.8	1.9	15.8
94	18:46:03.9	−2:39:25	0.54	1319.2	819.4	5.9×105	6.4×1022	2.4×1022	33.6	1.9	19.4
95	18:46:13.2	−2:39:29	0.10	43.1	13.8	6.7×102	6.7×1022	4.6×1022	20.6	1.8	16.2
96	18:45:55.3	−2:39:13	0.35	129.6	15.6	7×103	1.5×1022	1.3×1022	20.4	2.3	14.7
97	18:45:46.6	−2:38:54	0.57	217.9	35.4	8.7×103	9.5×1021	7.9×1021	20.3	2.2	15.1	—
98	18:46:07.9	−2:39:03	0.56	421.1	59.8	3.8×104	1.9×1022	1.6×1022	24.2	2.0	14.8
99	18:46:13.0	−2:39:09	0.28	443.3	196.1	8.7×103	8.2×1022	4.6×1022	21.3	1.8	15.9
100	18:46:20.9	−2:39:07	0.22	39.3	1.8	2.9×103	1.1×1022	1.1×1022	22.3	2.1	14.6
101	18:46:01.2	−2:39:14	0.10	21.7	3.5	2.2×103	2.9×1022	2.4×1022	25.7	1.9	15.2
102	18:45:54.1	−2:38:56	0.16	25.7	2.6	1×103	1.4×1022	1.3×1022	19.6	2.3	15.2
103	18:46:19.6	−2:38:49	0.30	72.2	3.1	4.3×103	1.1×1022	1.1×1022	22.0	2.1	14.7
104	18:46:03.7	−2:38:48	0.34	319.3	99.8	4.1×104	3.9×1022	2.7×1022	27.3	1.9	15.7
105	18:45:59.4	−2:38:32	0.27	50.7	2.3	3.2×103	1×1022	9.6×1021	22.6	2.1	14.7
106	18:45:54.1	−2:38:28	0.28	78.3	16.8	2.9×103	1.5×1022	1.1×1022	19.7	2.3	15.3
107	18:46:04.3	−2:38:24	0.27	198.3	54.8	1.1×104	3.7×1022	2.7×1022	22.5	2.1	14.6
108	18:46:17.3	−2:38:17	0.40	192.4	40.4	8.7×103	1.7×1022	1.4×1022	21.9	2.0	14.8
109	18:45:49.1	−2:38:26	0.24	33.3	2.0	1.6×103	8.4×1021	7.9×1021	20.7	2.2	14.9	—
110	18:46:21.4	−2:37:55	0.29	67.1	5.2	4.5×103	1.1×1022	1×1022	23.0	2.0	14.7
111	18:46:06.3	−2:38:07	0.09	13.0	0.8	7.4×102	2.4×1022	2.3×1022	21.5	2.2	14.6
112	18:46:16.3	−2:37:53	0.21	49.8	7.8	2.3×103	1.6×1022	1.4×1022	22.0	2.0	14.8

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Table 8.  W33 Dendrogram Leaves Parameters

Leaf	R.A.	decl.	reff	Mass	Corrected Mass	Luminosity	$\langle {N}_{{{\rm{H}}}_{2}}\rangle$	Merge Level	$\langle {T}_{{\rm{d}}}\rangle$	$\beta$	Tbol	$\langle {N}_{{{\rm{H}}}_{2}}\rangle \geqslant 50\sigma$
	(J2000)	(J2000)	$(\mathrm{pc})$	$({M}_{\odot })$	$({M}_{\odot })$	$({L}_{\odot })$	$({\mathrm{cm}}^{-2})$	$({\mathrm{cm}}^{-2})$	$({\rm{K}})$		$({\rm{K}})$
1	18:14:22.7	−18:04:34	0.13	13.0	0.9	3.7×102	1.1×1022	1×1022	21.2	1.9	15.3	—
2	18:14:17.4	−18:04:08	0.30	93.7	16.3	2.9×103	1.5×1022	1.2×1022	22.5	1.8	15.2	—
3	18:14:20.5	−18:04:02	0.10	7.3	0.7	2.5×102	1.1×1022	9.6×1021	22.7	1.8	15.1	—
4	18:14:23.0	−18:03:14	0.26	59.5	6.5	1.9×103	1.2×1022	1.1×1022	22.0	1.9	15.1	—
5	18:14:18.3	−18:03:08	0.16	23.3	1.7	9.9×102	1.3×1022	1.2×1022	24.1	1.7	15.2	—
6	18:14:09.9	−18:03:07	0.18	30.3	1.3	1.8×103	1.4×1022	1.3×1022	25.9	1.7	15.6	—
7	18:14:25.9	−18:02:38	0.13	15.2	0.9	4.3×102	1.2×1022	1.1×1022	21.4	1.9	15.3	—
8	18:14:16.9	−18:02:22	0.24	53.7	4.0	2.8×103	1.3×1022	1.2×1022	25.5	1.7	15.5	—
9	18:14:04.0	−18:02:31	0.12	20.6	1.5	9.4×102	1.9×1022	1.7×1022	24.4	1.7	15.2
10	18:14:13.4	−18:02:31	0.13	15.5	1.1	9.3×102	1.3×1022	1.2×1022	26.2	1.7	15.7	—
11	18:13:49.0	−18:02:15	0.09	13.9	2.8	2.4×102	2.6×1022	2.1×1022	18.8	2.1	16.9
12	18:14:04.4	−18:02:00	0.11	16.6	0.7	7.1×102	1.8×1022	1.7×1022	24.3	1.7	15.2	—
13	18:13:53.6	−18:02:10	0.04	9.3	1.4	1.8×102	6.8×1022	5.8×1022	23.5	1.5	15.6
14	18:14:09.0	−18:01:56	0.12	17.8	1.4	7.2×102	1.8×1022	1.7×1022	24.1	1.7	15.2	—
15	18:13:53.5	−18:01:47	0.21	323.5	141.7	1.1×104	1×1023	5.8×1022	23.0	1.8	16.4
16	18:13:48.9	−18:01:47	0.15	46.8	4.6	9.6×102	2.8×1022	2.5×1022	19.3	2.1	16.3
17	18:14:01.6	−18:01:26	0.19	51.6	6.9	2.2×103	2.1×1022	1.8×1022	24.2	1.7	15.2
18	18:13:56.4	−18:01:40	0.07	13.2	3.4	1.4×103	4.2×1022	3.1×1022	28.6	1.7	16.5
19	18:14:06.7	−18:01:24	0.15	40.3	6.7	1.6×103	2.5×1022	2.1×1022	24.5	1.7	15.3
20	18:13:58.5	−18:01:09	0.19	45.1	3.5	2.6×103	1.8×1022	1.7×1022	25.1	1.8	15.3	—
21	18:13:51.2	−18:01:32	0.05	6.5	0.2	1.5×102	4×1022	3.8×1022	20.1	2.1	15.9
22	18:13:55.1	−18:01:19	0.15	111.0	44.8	5.3×103	7.4×1022	4.4×1022	25.1	1.7	15.2
23	18:14:03.5	−18:01:00	0.13	24.8	1.5	1.1×103	2.1×1022	2×1022	24.4	1.7	15.2
24	18:14:06.9	−18:00:40	0.23	176.9	90.9	9.4×103	4.7×1022	2.3×1022	28.8	1.5	16.9
25	18:14:21.5	−18:00:47	0.08	6.6	0.3	2.1×102	1.6×1022	1.6×1022	21.9	1.9	15.1	—
26	18:14:14.6	−18:00:37	0.16	31.5	2.2	1.3×103	1.7×1022	1.6×1022	23.3	1.8	15.0	—
27	18:14:04.9	−18:00:36	0.07	8.6	0.9	6.4×102	2.5×1022	2.3×1022	27.8	1.6	16.3
28	18:13:49.9	−18:00:21	0.17	59.2	10.8	2.1×103	3×1022	2.5×1022	23.6	1.7	15.1
29	18:14:27.9	−18:00:27	0.08	9.4	0.9	2.2×102	1.9×1022	1.7×1022	19.6	2.1	15.9
30	18:14:27.7	−16:00:00	0.11	16.8	1.5	4.1×102	1.9×1022	1.7×1022	19.4	2.1	15.9	—
31	18:14:13.4	−17:59:50	0.15	34.2	4.3	1.2×103	2.1×1022	1.9×1022	21.7	1.9	15.1
32	18:13:49.2	−17:59:36	0.10	19.8	2.2	9×102	2.8×1022	2.5×1022	24.6	1.7	15.2
33	18:14:11.2	−17:59:17	0.24	84.6	10.7	2.9×103	2.1×1022	1.9×1022	21.7	1.9	15.1
34	18:14:14.8	−17:59:13	0.14	26.8	1.4	9.3×102	1.9×1022	1.8×1022	22.0	1.9	15.1
35	18:14:07.7	−17:59:13	0.12	19.8	1.1	9.3×102	1.8×1022	1.7×1022	24.4	1.7	15.2	—
36	18:14:18.7	−17:59:10	0.16	33.1	2.5	1.3×103	1.8×1022	1.7×1022	22.0	1.9	15.0	—
37	18:13:52.9	−17:58:47	0.19	39.5	2.0	3.7×103	1.5×1022	1.4×1022	29.3	1.6	17.2	—
38	18:14:27.7	−17:58:37	0.34	160.8	9.2	4.9×103	2×1022	1.9×1022	21.1	2.0	15.3
39	18:14:33.8	−17:58:10	0.20	52.9	2.7	1.3×103	2×1022	1.9×1022	20.1	2.0	15.7
40	18:14:25.2	−17:57:59	0.17	41.0	2.0	2.4×103	1.9×1022	1.8×1022	25.3	1.7	15.5
41	18:14:10.4	−17:58:13	0.07	8.2	0.6	2.7×102	2.7×1022	2.4×1022	21.6	2.0	15.1
42	18:14:17.2	−17:57:37	0.20	51.1	3.3	6×103	1.7×1022	1.6×1022	27.8	1.8	16.4	—
43	18:14:12.0	−17:57:34	0.15	84.7	16.9	3.1×103	5×1022	4×1022	22.7	1.9	15.0
44	18:14:10.4	−17:57:36	0.08	20.9	2.3	8.4×102	4.5×1022	4×1022	23.1	1.9	14.9
45	18:14:00.6	−17:57:20	0.24	62.5	4.3	4.5×103	1.5×1022	1.4×1022	30.4	1.4	17.7	—
46	18:14:05.8	−17:57:23	0.10	29.8	7.6	1.5×103	4.2×1022	3.1×1022	25.5	1.7	15.4
47	18:14:29.0	−17:57:18	0.17	44.6	2.9	2.2×103	2.2×1022	2×1022	25.2	1.7	15.4
48	18:14:26.5	−17:57:19	0.11	19.2	1.7	1.2×103	2.2×1022	2×1022	28.3	1.5	16.5
49	18:14:13.2	−17:57:17	0.05	8.4	0.6	4.8×102	4×1022	3.7×1022	25.1	1.8	15.1
50	18:14:06.4	−17:56:44	0.11	46.5	7.3	1.9×103	5.9×1022	5×1022	24.7	1.7	15.2
51	18:14:13.5	−17:56:53	0.04	5.6	0.7	5.4×102	4.3×1022	3.8×1022	26.7	1.8	15.5
52	18:14:36.3	−17:56:28	0.28	145.0	32.4	2.6×103	2.6×1022	2×1022	19.3	2.1	16.5
53	18:13:57.5	−17:56:18	0.22	43.5	1.3	2.6×103	1.3×1022	1.3×1022	29.5	1.4	17.3	—
54	18:14:10.8	−17:56:37	0.13	121.9	32.4	7.4×103	1×1023	7.4×1022	25.2	1.8	14.8
55	18:14:44.5	−17:56:28	0.10	13.5	1.8	2.5×102	1.9×1022	1.7×1022	19.1	2.1	16.5
56	18:14:14.2	−17:56:18	0.08	21.6	1.8	5×103	4.8×1022	4.4×1022	31.7	1.8	18.7
57	18:14:43.2	−17:56:14	0.10	12.6	1.6	2.8×102	1.9×1022	1.7×1022	20.1	2.0	15.8
58	18:14:38.4	−17:56:03	0.10	15.1	1.4	3×102	2.2×1022	2×1022	19.5	2.1	16.2
59	18:14:27.1	−17:55:50	0.15	36.2	3.7	1.5×103	2.3×1022	2.1×1022	28.2	1.4	16.4
60	18:14:24.7	−17:55:55	0.09	11.8	0.9	5×102	2.1×1022	2×1022	29.8	1.3	17.1
61	18:14:09.5	−17:55:55	0.05	28.4	0.7	1.3×103	1.7×1023	1.7×1023	26.3	1.6	15.2
62	18:14:13.3	−17:55:40	0.15	566.2	292.5	1.4×105	3.4×1023	1.7×1023	38.2	1.7	19.8
63	18:14:10.2	−17:55:43	0.04	20.0	0.4	1.2×103	1.7×1023	1.7×1023	27.3	1.7	15.3
64	18:14:36.5	−17:55:00	0.38	441.0	198.5	1.7×104	4.2×1022	2.3×1022	22.7	1.8	15.8
65	18:14:11.0	−17:55:33	0.05	27.9	6.0	3.1×103	1.8×1023	1.4×1023	29.7	1.8	15.7
66	18:14:25.7	−17:55:20	0.12	23.8	1.3	9.6×102	2.3×1022	2.2×1022	26.1	1.5	15.7
67	18:14:15.6	−17:55:18	0.07	29.5	3.0	8.6×103	9.8×1022	8.8×1022	31.4	2.0	16.2
68	18:14:13.1	−17:55:07	0.18	625.6	255.3	6.8×104	2.8×1023	1.7×1023	30.2	1.7	15.7
69	18:14:00.6	−17:54:52	0.34	120.6	9.8	6.8×103	1.5×1022	1.4×1022	28.5	1.5	16.7	—
70	18:14:16.7	−17:54:58	0.06	21.2	2.7	1.4×103	7.2×1022	6.3×1022	25.3	1.8	14.9
71	18:14:30.4	−17:54:13	0.37	307.3	55.4	1.2×104	3.2×1022	2.6×1022	24.3	1.7	15.3
72	18:14:41.7	−17:54:23	0.21	160.1	48.9	4.1×103	5.1×1022	3.5×1022	22.0	1.8	16.7
73	18:14:18.8	−17:54:32	0.03	4.8	0.6	1.4×102	8.7×1022	7.6×1022	22.5	1.8	15.2
74	18:14:25.0	−17:53:58	0.31	354.1	153.9	1.3×104	5.1×1022	2.9×1022	24.9	1.6	15.6
75	18:14:18.2	−17:54:26	0.07	28.5	5.0	6.6×102	9.3×1022	7.6×1022	22.6	1.7	15.4
76	18:14:15.1	−17:54:19	0.07	11.4	0.7	6.2×102	2.9×1022	2.7×1022	23.8	1.9	14.9
77	18:14:19.5	−17:54:12	0.05	11.3	1.1	2.9×102	6.9×1022	6.3×1022	22.1	1.8	15.3
78	18:14:40.9	−17:53:52	0.07	17.2	3.1	4.3×102	5.1×1022	4.2×1022	23.5	1.6	15.5
79	18:14:42.5	−17:53:33	0.18	113.7	22.2	1.7×103	5.3×1022	4.2×1022	19.9	1.9	16.7
80	18:14:21.9	−17:53:19	0.20	95.8	11.9	3×103	3.3×1022	2.9×1022	21.5	2.0	15.2
81	18:14:10.0	−17:53:17	0.16	34.8	2.9	1.7×103	1.8×1022	1.7×1022	26.2	1.6	15.7	—
82	18:14:02.1	−17:53:17	0.13	16.5	1.2	6.8×102	1.3×1022	1.2×1022	24.1	1.7	15.2	—
83	18:14:35.0	−17:53:07	0.19	93.6	19.1	2.2×103	3.6×1022	2.9×1022	21.8	1.8	15.5
84	18:14:32.2	−17:53:00	0.13	41.5	4.4	1×103	3.6×1022	3.2×1022	21.3	1.9	15.5
85	18:14:02.8	−17:52:36	0.22	48.6	8.4	2.3×103	1.4×1022	1.2×1022	23.9	1.8	15.1	—
86	18:14:32.8	−17:52:40	0.07	13.6	0.4	3.2×102	3.5×1022	3.4×1022	20.8	1.9	15.6
87	18:14:06.0	−17:52:13	0.34	115.4	13.3	5×103	1.4×1022	1.2×1022	23.3	1.8	15.0	—
88	18:14:43.5	−17:52:35	0.07	16.6	0.7	4.7×102	4.3×1022	4.1×1022	23.1	1.7	15.2
89	18:14:09.8	−17:52:07	0.20	38.1	2.8	1.4×103	1.4×1022	1.3×1022	22.5	1.9	15.0	—
90	18:14:43.8	−17:52:20	0.07	17.4	1.3	6.2×102	4.5×1022	4.1×1022	24.5	1.6	15.3
91	18:14:39.5	−17:52:22	0.03	6.2	2.4	1.6×102	1.3×1023	8.1×1022	24.7	1.5	15.4
92	18:14:38.5	−17:51:57	0.16	312.6	167.1	1.9×104	1.7×1023	8.1×1022	27.8	1.5	16.2
93	18:14:28.0	−17:52:07	0.13	46.0	4.6	1.4×103	4.1×1022	3.7×1022	22.3	1.8	15.2
94	18:14:30.7	−17:52:07	0.12	44.8	3.9	7.3×102	4.3×1022	4×1022	20.6	1.8	16.1
95	18:14:46.8	−17:52:10	0.06	8.7	0.5	4.4×102	3×1022	2.8×1022	26.3	1.6	15.6
96	18:14:34.4	−17:51:53	0.20	201.5	60.6	3.7×103	6.9×1022	4.8×1022	21.3	1.8	16.0
97	18:14:46.1	−17:51:56	0.08	13.9	0.9	5.1×102	3×1022	2.8×1022	24.8	1.6	15.3
98	18:14:23.0	−17:51:47	0.17	37.4	2.5	1.5×103	1.9×1022	1.8×1022	23.5	1.8	15.1
99	18:14:36.9	−17:50:38	0.10	20.2	1.4	5.1×102	2.8×1022	2.6×1022	21.4	1.9	15.4
100	18:14:38.2	−17:49:48	0.17	53.3	2.6	8.1×102	2.7×1022	2.5×1022	18.2	2.2	17.6
101	18:14:18.7	−17:49:21	0.17	29.0	1.0	6.9×102	1.4×1022	1.3×1022	20.3	2.0	15.6	—
102	18:14:35.1	−17:48:28	0.13	22.1	1.0	3.7×102	2×1022	1.9×1022	18.1	2.2	17.4

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