THE BOLOCAM GALACTIC PLANE SURVEY. XIV. PHYSICAL PROPERTIES OF MASSIVE STARLESS AND STAR-FORMING CLUMPS

The RMS (Lumsden et al. 2002, 2013) with observations at 8, 12, 14, and 21 μm defines a sample of massive YSOs complete above L_bol > 10⁴ L_⊙ and d_⊙ < 10 kpc, approximately a B0-type main-sequence star. The RMS catalog region has complete overlap with the BGPS for ℓ > 10°, where confusion does not dominate the MSX data. Extensive follow-up observations of RMS sources yield detailed classifications: protoplanetary nebula, planetary nebula, evolved star, H ii region, YSO, OH/IR star, young/old star, H ii/YSO, carbon star, and a miscellaneous "other." We use the RMS classifications associated with YSOs (YSO, H ii/YSO, young/old star) to classify BGPS sources in the mid-IR category. We do not associate BGPS sources with star formation activity for the other categories because contamination between the RMS classifications is low. This is further evidenced by the minimal overlap in Table 4. The RMS sources provide a well-vetted sample of massive YSOs, but for spectral types later than B0, or YSOs that are at distances >10 kpc, the survey is incomplete. Recent Galactic plane surveys by Spitzer and Herschel offer sensitive data sets through the mid- and far-IR to probe the star formation activity in BGPS clumps and complement the RMS data.

The GLIMPSE survey is a Spitzer/IRAC Legacy survey of the Galactic midplane, at 3.6, 4.5, 5.8, and 8.0 μm (Benjamin et al. 2003; Churchwell et al. 2009). The GLIMPSE I and II fields provide complete overlap coverage with the BGPS for 10° < ℓ < 65°. R08 use the GLIMPSE catalog to select a total number of 18,949 intrinsically red ([4.5]–[8.0] ≥ 1) sources that also meet photometric quality criteria. MIPS 24 μm magnitudes are also calculated at the same positions for 86.9% of the sources from the MIPSGAL survey (Carey et al. 2009). Because GLIMPSE has better spatial resolution and sensitivity than the MSX survey, lower-luminosity YSOs can be detected. R08 estimate that a 100 L_⊙ Stage I YSO should be detected at distances between 0.2 and 10 kpc and a 10⁴ L_⊙ YSO between 2 and 30 kpc. Intrinsically red sources are further classified by color–magnitude and color–color selection criteria (see Equations (7)–(9) Robitaille et al. 2008) into candidate YSOs, "standard" C- and O-rich asymptotic giant branch (AGB) stars (sAGB), and "extreme" AGB stars (xAGB). The color criteria select sources with spectral index α ≥ −1.2, which, following the "Class" system of Greene et al. (1994), selects all Class I and a significant number of Class II YSOs. Contamination from planetary nebula and background galaxies is expected to be between 2% and 3%. However, because AGB and YSO sources have similar mid-IR colors, the YSO/AGB discrimination is uncertain based on 4.5, 8.0, and 24 μm photometry alone, with up to 50% contamination between the two categories. Dunham et al. (2011b) estimate a ∼40% contamination fraction of YSOs in the R08 candidate AGB sources. We shall account for this contamination in the MC sampling in Section 5. The number of R08 candidate YSO or AGB sources matched to BGPS clumps is listed in Table 4.

An additional class of sources called extended green objects (EGOs) have been identified from the Spitzer GLIMPSE data (Cyganowski et al. 2008; Chen et al. 2013). EGOs are sources of extended 4.5 μm emission from shocked H₂ driven by strong outflows from massive star formation. A total of 72 BGPS clumps match EGOs, and all except one clump (G044.008-00.026) contain RMS YSOs, R08 YSOs, or 70 μm compact sources (see Section 3.2.4).

The Version 3.0 data products from the Spitzer MIPSGAL survey cover −69° < ℓ < 68° and $| b| \lt 1^\circ$ at 24 μm (Carey et al. 2009). The MIPS 24 μm band is sensitive to the hot dust found around YSOs and H ii regions, but also to envelopes of evolved stars. Gutermuth & Heyer (2015) have created a comprehensive point-source catalog from the MIPSGAL 24 μm maps. Two catalogs are presented: a high-quality catalog and more complete archive. Combined, the catalogs total 268,430 point sources in the fields of the BGPS overlap region, with 4.9% of MIPSGAL sources associated with clumps and 80.9% of clumps associated with MIPSGAL point sources. While some subset of MIPSGAL sources do represent observational indicators of embedded protostellar activity, this low match fraction of 4.9% is consistent with the 6.8% ± 2.2% randomized match fraction calculated in Dunham et al. (2011b) for RMS evolved stars (i.e., sources with no physical association). Figure 2 illustrates this poor correspondence to BGPS clumps. Two maps at 70 and 24 μm are shown of the same field centered on a single, isolated clump. Whereas the 24 μm image shows identified point sources from both the catalog and archive, only a few point sources have direct association with the clump 1.1 mm emission. In contrast, the 70 μm image uniquely associates a single compact source with the clump. The 70 μm dust continuum emission is more sensitive to the deeply embedded star formation activity that is better positionally correlated to BGPS clumps. We conclude that line-of-sight association of 24 μm point sources from the MIPSGAL catalog are not a sufficient sole indicator of star formation activity because of the high contamination from evolved stars. Thus, while the MIPSGAL flags are not used in any calculations of physical properties, for completeness we present the flags in Table 4 (see Section 3.5). These contamination issues also strongly affect the lower-resolution WISE 22 μm observations. To further refine our set of star formation indicators, rather than pursue color- and quality-selection criteria to identify a less contaminated subsample from the MIPSGAL catalog, we associate clumps with 70 μm compact sources.

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The Hi-GAL is a far-IR survey of the Galaxy with the 70 and 170 μm PACS bands and the 250, 350, and 500 μm SPIRE bands (Molinari et al. 2010). The Hi-GAL survey completely covers the BGPS fields that we discuss. Previous survey data sets in the 100 μm regime from IRAS and Akari are not suitable for detecting faint point sources owing to their poor angular resolution (>1'). The Herschel Hi-GAL 102 resolution (Traficante et al. 2011) at 70 μm is essential to disentangling the far-IR emission reprocessed by dust around embedded YSOs and their often active environment. Most important, however, is the less severe contamination in the Hi-GAL 70 μm images from evolved stars compared to the MIPS 24 μm or WISE 22 μm images. Whereas >80% clumps have at least one associated MIPSGAL source, only 46% of clumps have an associated 70 μm compact source from visual identification with clearly correlated positions to the 1.1 mm maps.

Owing to complicated background structure, identifying compact sources algorithmically is difficult. The CuTeX algorithm (Molinari et al. 2011) was developed specifically for identifying sources in highly spatially variable backgrounds such as those found in the Hi-GAL images. Careful visual inspection is necessary because of false negatives, where CuTeX misses faint sources, and false positives, where CuTeX misidentifies sources in regions of strong emission. Cuts on CuTeX fit parameters were trained on publicly available data in the ℓ = 30° field (Bally et al. 2010) and then applied to all cutout images to compare with the results of the visual inspection classifications. The comparisons show that 77.7% of the classifications agree and 22.3% disagree; 81% of the disagreements originate from sources flagged with fainter 70 μm sources from the visual inspection but missed by CuTeX.

We visually inspect 5' × 5' cutouts of the reduced Hi-GAL 70 μm band images (Molinari et al. 2011) for comparison against the BGPS data. For consistency with the catalog-matching scheme used for the other surveys in this study, we classify clumps as containing a Hi-GAL 70 μm source if it is within the Bolocat label mask. Visual inspection was carried out on the 70 μm images alone, without simultaneous comparison to GLIMPSE or MIPSGAL images to prevent systematic bias in the classifications. We assign BGPS clumps one of five flags in the visual inspection process. Multiple flags are necessary to qualify the image background level and source characteristics. Flags 1, 2, and 4 represent clumps identified with a compact source within the label mask, while flags 0 and 3 lack a clearly identifiable source. Representative 70 μm cutouts of these flags are shown in Figure 3. Flag 1's show a high confidence compact source on the scale of the Herschel 102 point-spread function (PSF). Flag 2's are more diffuse than the PSF but identifiable as compact sources owing to strong, localized emission above the background level. These are common for extremely bright 70 μm sources with ≥80% of uniquely high-mass indicators, RMS sources, ${\mathrm{CH}}_{3}\mathrm{OH}$ masers, and UCH ii regions, assigned flag 2's. We identify 944 flag 1 and 1044 flag 2 clumps, or 42.5% of clumps. Flag 4's show a weak, PSF-like source whose classification is lower confidence. Adding the 182 flag 4's increases the total to 46.3% of clumps classified with a Hi-GAL source. The brightness and complexity of the 70 μm background can make the visual source identification difficult. Because of this, we assign 1847 flag 0's to clumps with quiescent, smooth, and low-level backgrounds and 655 flag 3's to clumps with bright and more complex backgrounds. The far-IR background of the Milky Way changes locally and as a function of Galactic longitude (generally 10²–10³ MJy sr⁻¹), and thus the flux threshold for source detection changes as well.

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The high rate of overlap between 70 μm sources and more extreme indicators, along with the large number of unique 70 μm associations, suggests that the Hi-GAL data are broadly probing a lower YSO bolometric luminosity, L_bol, than the other indicators. To assess the low-luminosity limit of the associations, we compute L_bol completeness functions for a representative sample of background levels given the sample of DPDFs in the Distance Catalog. The 70 μm background level and complexity are the limiting factors in the identification of compact sources. A detailed analysis of the background level distribution for the full Hi-GAL 70 μm data set with the identification threshold quantified through fake source injection is beyond the scope of this paper. Instead, we bracket the completeness function with a sample of 30 clumps associated with the least confident 70 μm identifications (classified as Hi-GAL flag 4), evenly split between low background levels of 500–1000 MJy sr⁻¹ and high background levels of 2000–3000 MJy sr⁻¹. Values are calculated from the cutouts described above. Aperture photometry of the 70 μm sources in these selected regions yields sources identified with flux densities ≲0.3 Jy for the low backgrounds and ≲1 Jy for the high backgrounds. Using these two detection thresholds, we compare to fluxes derived from the 20,000 axisymmetric YSO radiative transfer models computed in Robitaille et al. (2006, 2007). We use the PACS 70 μm fluxes from the largest physical aperture, 100,000 au, which corresponds to the 20'' diameter aperture at the median clump distance of 5 kpc (see Section 5.1.2). We then draw from MC simulations for each clump DPDF (described in Section 5.1) to scale the Robitaille et al. (2006) PACS 70 μm model flux and apply the detection threshold cut. Figure 4 shows the completeness function for all clumps with well-constrained distances, and the cyan line shows the same but for the subset of clumps between 28° < ℓ < 31° for which publicly available Hi-GAL data exist (Bally et al. 2010). The dotted lines show the 50% and 90% limits. We find that in the low-background environments the 70 μm visual flags are 50% complete to YSOs with L_bol > 10 L_⊙ and 90% complete to YSOs with L_bol > 50 L_⊙. For the high-background environments, we find the 50% completeness limit to YSOs at L_bol > 45 L_⊙ and 90% complete to YSOs with L_bol > 140 L_⊙. To put these luminosities in perspective, a ∼1 M_⊙ and ∼5 R_⊙ YSO accreting at ∼10⁻⁵ M_⊙ yr⁻¹ corresponds to an accretion luminosity of ∼30 L_⊙ (N.B. episodic accretion rates result in large variations in the accretion luminosity at a given epoch; see Dunham et al. 2014). While the true sample completeness limits likely lie between these two values, it should be kept in mind that these limits are below the L_bol of the other star formation indicators by several orders of magnitude.

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Among the positive Hi-GAL classifications, 1027/2170 (47.3%) have one or more additional star formation indicator and 1143/2170 (52.7%) are Hi-GAL 70 μm unique, representative of a sample of deeply embedded and early protostellar candidates. In the following analysis, this sample of clumps uniquely identified with star formation activity from 70 μm compact sources is treated separately as its own category. It should be noted that the 70 μm unique category sources may have an MIPS 24 μm counterpart but do not contain any other star formation indicator (unique is defined in terms of our set of star formation indicators).

We complement the mid- and far-IR star formation indicators with radio observations of masers. The outflows driven by young protostars shock dense regions of the ISM and collisionally pump ${{\rm{H}}}_{2}{\rm{O}}$ that creates a population inversion that drives the maser emission. The typical physical conditions for a masing region are a spatial density n ∼ 10⁷–10⁹ cm⁻³, kinetic temperature T_K ∼ 400 K, spatial extent of d ∼ 0.66 au, and an aspect ratio of ∼50:1 (Hollenbach et al. 2013). ${{\rm{H}}}_{2}{\rm{O}}$ masers are time variable on scales of months to years. The beaming effect of ${{\rm{H}}}_{2}{\rm{O}}$ masers makes them a sensitive probe at large distances, but because of the necessary narrow geometrical alignment, the nondetection of an ${{\rm{H}}}_{2}{\rm{O}}$ maser does not imply a lack of star formation activity. In addition to YSO molecular outflows, ${{\rm{H}}}_{2}{\rm{O}}$ masers are also observed in the shells around AGB stars (Imai et al. 2002). From high-resolution follow-up of the ${{\rm{H}}}_{2}{\rm{O}}$ Southern Galactic Plane Survey (HOPS; Walsh et al. 2011) and association with catalogs of star formation indicators, Walsh et al. (2014) find that 69% of water maser sites are associated with star formation, 19% with evolved stars, and 12% with unknown identification. We expect limited contamination of AGB stars coincident with our GBT pointings because the observations are targeted toward the clump peak S_{1.1 mm} and N(H₂) positions (θ_HPBW ≈ 30'') where a YSO is likely to be located, but a chance alignment by a field AGB star is unlikely. Thus, we use the detection of an ${{\rm{H}}}_{2}{\rm{O}}$ maser as an observational indicator of star formation activity.

Large observational ${{\rm{H}}}_{2}{\rm{O}}$ maser survey programs have been carried out by the Arcetri survey (Valdettaro et al. 2001), HOPS (Walsh et al. 2011), and the RMS ${{\rm{H}}}_{2}{\rm{O}}$ Maser Survey (Urquhart et al. 2011). The variability of ${{\rm{H}}}_{2}{\rm{O}}$ masers makes multiple catalogs at different epochs complementary for systems that drop below a survey's sensitivity limits (Furuya et al. 2003). The Arcetri catalog aggregates observations of all known literature ${{\rm{H}}}_{2}{\rm{O}}$ water masers prior to 2001. HOPS is a blind Galactic plane survey with overlap coverage with the BGPS extending to ${\ell }\lt 20^\circ$. The HOPS team discovered a number of new ${{\rm{H}}}_{2}{\rm{O}}$ masers not found in the Arcetri catalog, most in the southern sky, which is inaccessible to the Arcetri survey. While the survey overlap between HOPS and the BGPS GBT ${{\rm{H}}}_{2}{\rm{O}}$ maser survey is limited to 10° < ℓ < 20°, it provides valuable context to evaluate the targeted GBT observations. In this range, the GBT observations have a 3.4 times higher detection rate toward BGPS clumps. This is likely due to the tighter beam coupling of the GBT compared to Mopra and the lower baseline RMS for the targeted, single-pointing observing strategy. The GBT observations primarily detect weaker ${{\rm{H}}}_{2}{\rm{O}}$ masers with median integrated intensity of ∼5 Jy km s⁻¹ compared to HOPS with ∼5 × 10² Jy km s⁻¹.

The 6.7 GHz Class II methanol (${\mathrm{CH}}_{3}\mathrm{OH}$) maser is thought to be exclusively associated with high-mass star formation because of the environments necessary for IR pumping (Breen et al. 2013). A comparison between 6.7 GHz ${\mathrm{CH}}_{3}\mathrm{OH}$ maser emission from the MMB and ATLASGAL 870 μm dust emission finds that 99% of MMB sources are associated with ATLASGAL emission, indicating that methanol maser emission is almost ubiquitously associated with massive protostellar clumps (Urquhart et al. 2015). We associate BGPS clumps with ${\mathrm{CH}}_{3}\mathrm{OH}$ maser indicators based on available literature data. We use data from the Arecibo ${\mathrm{CH}}_{3}\mathrm{OH}$ survey (Pandian et al. 2007, 2011), MMB (Breen et al. 2012a, 2012b, 2014, 2015), and aggregated literature data in Pestalozzi et al. (2005). Within the overlap region, MMB data extend from 10° < ℓ < 60°, Arecibo data extend from 35° < ℓ < 54°, and the data in Pestalozzi et al. (2005) are all-sky targeted observations. Thus, there is a small gap in the ${\mathrm{CH}}_{3}\mathrm{OH}$ maser survey data from 60° < ℓ < 65°, but there are only 15 BGPS clumps in this range, so there should not exist a strong sampling bias. While the MMB is the most uniform and complete of the surveys, multiple overlapping data sets are useful because the intensity of ${\mathrm{CH}}_{3}\mathrm{OH}$ masers is time variable. This can be important for masers that drop below the sensitivity limits of a single survey. With multiple surveys at different epochs we create a more complete catalog of ${\mathrm{CH}}_{3}\mathrm{OH}$ masers.

We combine these catalogs of observational indicators of star formation activity into a series of flags to sort clumps into groups for joint analysis of their physical properties. The most basic distinction is between clumps that are associated with no star formation indicators, the SCCs, and "protostellar" clumps that are associated with one or more indicator. The star formation indicator groups are then ranked by the approximate luminosity of a single protostar that produces the indicator (see Figure 5). These rankings are a heuristic motivated by proposed linear clump evolutionary sequences (Chambers et al. 2009; Battersby et al. 2010, 2011), but the ordering is settled upon because it consistently yields monotonic trends for clump properties. "70 μm Unique" are clumps that only contain a Hi-GAL compact source and thus are candidates for deeply embedded (≈ Class 0/I) protostellar activity. "Mid-IR" clumps are associated with one or more R08 YSO-flagged source, RMS protostellar source, and/or EGO. We group R08, RMS, and EGOs together because they are frequently coincident with the same protostellar sources and they use similar wavelengths to identify activity. "${{\rm{H}}}_{2}{\rm{O}}$" clumps are associated with one or more ${{\rm{H}}}_{2}{\rm{O}}$ masers from the BGPS GBT survey, Arcetri, and/or HOPS. Similarly, "${\mathrm{CH}}_{3}\mathrm{OH}$" clumps are associated with one or more ${\mathrm{CH}}_{3}\mathrm{OH}$ masers from Pestalozzi et al. (2005), Arecibo, and/or MMB. "UCH ii" clumps are associated with the CORNISH UCH ii regions. In Section 5 we will use these categories to compare physical properties.

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Table 4 lists the detection statistics for sources matched to the BGPS in the overlap region and the number of clumps matched to sources. We find that in the common overlap region 2223/4683 (47.5%) are starless candidates and 2460/4683 (52.5%) show some indicator of protostellar activity. This fraction of SCCs is lower than the upper limit of 67% estimated from the ATLASGAL survey by Csengeri et al. (2014), which compares ATLASGAL clumps to WISE 22 μm and MSX 21 μm point-source catalogs. The smaller fraction of SCCs in our analysis is likely due to the inclusion of protostellar indicators with lower-luminosity sensitivity such as Herschel 70 μm sources in our analysis. The Herschel 70 μm sources account for the largest fraction of star formation indicators detected toward protostellar clumps (2168/2460 [88%] of protostellar clumps contain a 70 μm source flag). No strong variation in the Galactic longitude distribution is observed between SCCs and protostellar clumps (Figure 5). Individual star formation indicator flags for each clump are listed in Table 5.

Except for 70 μm unique, the BGPS indicator groups are not mutually exclusive. Indeed, 70/170 (41%) of UCH ii clumps are also associated with a ${\mathrm{CH}}_{3}\mathrm{OH}$ maser and 103/170 (61%) are associated with an ${{\rm{H}}}_{2}{\rm{O}}$ maser. There are no BGPS clumps uniquely associated with ${{\rm{H}}}_{2}{\rm{O}}$, ${\mathrm{CH}}_{3}\mathrm{OH}$, or UCH ii flags; those clumps are always associated with another protostellar indicator. This fact indicates that it is unlikely that a population of H₂O unique clumps (meaning that H₂O masers are the only indicator of star formation activity) exist toward clumps that have been targeted by our GBT observations (Sections 2.2 and 3.3.1). Figure 6 shows the intersection between indicators with the fraction of the total calculated for each. For example, 70 clumps are associated with both ${\mathrm{CH}}_{3}\mathrm{OH}$ masers and UCH ii regions: 0.412 (70/170) of those with UCH ii regions are also associated with ${\mathrm{CH}}_{3}\mathrm{OH}$ masers; alternatively, 0.235 (70/298) of those with ${\mathrm{CH}}_{3}\mathrm{OH}$ masers are also associated with UCH ii regions.

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Among these indicators, the ${\mathrm{CH}}_{3}\mathrm{OH}$ and UCH ii clumps are the most consistent indicators of high-mass protostellar activity. However, it is important to note that more extreme indicators of star formation activity do not necessarily represent a later stage in a linear clump evolutionary sequence. For one, not all clumps will have sufficient mass to form an OB star to drive an observable ${\mathrm{CH}}_{3}\mathrm{OH}$ maser or UCH ii region. The sequence of star formation indicators outlined in Battersby et al. (2010) is consistent with the expected sequence of observational indicators for a high-mass protostellar core, but BGPS clumps are hierarchical constructs of density, likely composed of multiple cores (Merello et al. 2015). The surveys also do not have high enough resolution to identify single protostellar sources at large distances. For example, what appears to be a Hi-GAL compact source could be a protocluster at several kiloparsecs. In this case, the only certain true evolutionary transition is from the starless clump phase to the protostellar phase.

We compare our protostellar indicator flags to the previously published starless clump catalog of Tackenberg et al. (2012), which identified 210 starless candidates with peak column density $N({{\rm{H}}}_{2})\gt {10}^{23}$ cm⁻² from ATLASGAL 870 μm images in the 10° < l < 20° range. Tackenberg et al. (2012) use a combination of mid-IR colors from Spitzer imaging plus visual analysis of 24 μm point sources to identify starless candidates. Within this longitude range, there are 52 BGPS catalog sources with peak positions that lie within the BGPS angular resolution (33'') of the Tackenberg et al. (2012) starless candidate position. We find that 30 out of those 52 clumps (58%) contain an indicator of star formation activity in our catalog. Nearly all of those associations result from identification of a 70 μm source in our catalog. This result highlights the necessity of far-IR imaging to identify deeply embedded and lower-luminosity YSOs.

We also compare to the Traficante et al. (2015a) catalog of 1684 Hi-GAL clumps associated with IRDCs in the 10° < ℓ < 55° and $| b| \leqslant 1^\circ$ range. Clumps are extracted from the IRDC catalog of Peretto & Fuller (2009). A novel algorithm (Hyper; Traficante et al. 2015b) is used for clump extraction and photometry, and counterparts at 70 μm are used for protostellar identification. When compared by positions, 963 clumps in Traficante et al. (2015a) are associated with 692 BGPS clumps (14.8% of the BGPS clumps in the overlap region), whereas the remaining 721 clumps are not associated. Among the 692 BGPS clumps with associations, 550 (80.3%) star-forming categorizations agree and 142 (19.7%) conflict. The conflicts are dominated (109 of 142 conflicts) by cases of a smaller "subcomponent" starless clump in the Traficante et al. (2015a) catalog associated with a larger "parent" BGPS clump with a protostellar indicator (N.B. the Herschel Hi-GAL resolution at 160 μm is 136, which is 2.4 times higher resolution than the BGPS at 1.1 mm). A minority of 33 (4.8%) BGPS clumps remain that we have classified as starless candidates that contain 70 μm counterparts from the Traficante et al. (2015a) catalog. In these cases we have conservatively assigned Hi-GAL flag 3's (28/33) for ambiguous high backgrounds in the visual inspection.

Contamination from AGB stars is a significant source of uncertainty when the only indicator of star formation activity within a clump is from the mid-infrared colors of a point source. In order to propagate this uncertainty due to AGB contamination, we resample flags discriminating between R08 YSO and AGB sources in the MC simulations. We use conservative estimates of the contamination fractions between the R08 YSO contaminants in the AGB classification and AGB contaminants in the YSO classification. As described in Section 3.2.2, we apply contamination fractions of 40% for AGB sources and 50% for YSO sources. All R08 sources within clumps are resampled this way. If a clump is associated with another star formation indicator besides R08, then it is still flagged as protostellar and the MC flag resampling will not affect the clump's overall designation. In the overlap region, only 280 clumps (6.0%) are uniquely associated with R08 sources, and 122 clumps (7.4%) in the distance sample. Resampling propagates our uncertainty in the R08 flags, but because of significant coincidence with other star formation indicators, it introduces only a minor effect in discriminating between SCCs and protostellar clumps. In the following analysis, AGB contamination resampling is used in all MC calculations.

For the calculation of quantities that are distance dependent (e.g., R, M), we draw the heliocentric distance from the source DPDF. Each MC simulation consists of 10⁴ random draws. Since the output distributions of the physical properties may be skewed, we use robust statistical indicators such as the median (μ_1/2) and median absolute deviation (σ_1/2)¹² as conservative characterizations of the distribution of properties for a particular subsample.

Before we compare physical properties among clumps with different star formation indicators (Sections 5.2–5.4), we compare the distribution of DPDFs for each star formation indicator subsample defined in Section 3.5. Figure 8(c) shows the mean distribution or average DPDF for each indicator. The indicator categories show similar distributions of heliocentric distance. While the number of clumps associated with each indicator varies, the range and distribution of d are similar, with medians between 4.4 and 5.1 kpc. As a result, physical properties that depend linearly or quadratically on distance will not be strongly biased by the underlying distance distribution for each indicator subsample. Sources with associated ${\mathrm{CH}}_{3}\mathrm{OH}$ masers and/or UCH ii regions show a relative deficit of distances from 2 to 4 kpc. This could be an effect from the method of resolving distances with the 8 μm absorption prior, where better spatially resolved clumps at the near distance are dominated by mid-IR emission from a high-mass YSO. These regions may not have the necessary contrast in the GLIMPSE 8 μm maps to result in a well-constrained distance estimate, whereas further, and thus larger, clumps could have sufficient surrounding 8 μm absorption. In addition, the PPV method of associating nearby clumps with known distances for a fixed radius in angle and a fixed velocity better associates regions at larger distances where the angular separation between clumps is smaller.

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When comparing distance-independent quantities between starless candidate and protostellar categories, the total number of sources is nearly equal (2223 SCCs versus 2460 protostar-containing clumps); however, when comparing distance-dependent physical properties, it should be noted that in the distance sample there are 1.675 times as many protostellar-containing clumps than SCCs (613 SCCs versus 1027 protostellar clumps). The fraction of clumps in the distance sample that contain at least one star formation indicator is shown as a function of heliocentric distance in Figure 9. The median protostellar clump fraction in the distance sample is 0.60, and there is no significant trend in this ratio out to heliocentric distances of 12 kpc. Since only 58 clumps (3.5%) in this study have maximum-likelihood distances greater than 12 kpc, this result indicates that differences in the properties of starless candidates compared to protostellar clumps are not driven by a bias in the protostellar fraction by distance.

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We can only calculate distance-dependent quantities from the subset of clumps in each category of the distance sample. We run MC simulations for both the subsamples that have a well-constrained DPDF and those without to test how this selection criterion may bias our distributions. Figure 8(a) shows the observed total flux density ${S}_{1.1}^{\mathrm{Total}}$ for each indicator, with the total sample (light gray) and distance sample (dark gray). Figure 8(b) shows the cumulative results of 10⁴ draws from the MC simulation of the 1.1 mm flux density Gaussian deviates and R08 AGB contamination resampling. The subsamples with DPDFs have greater median S_1.1 when compared to full samples. Similarly, Figure 8(d) shows the distribution of the ratio of medians for each MC simulation. All indicator categories show a factor of 1.5–2.2 higher median flux for clumps with DPDFs; however, there is not a consistent trend in the ratio between star formation indicators. The ratio of median flux densities for protostar-containing clumps is only a factor of 1.1–1.2 times larger than the corresponding ratio for SCCs. If we make the simple assumption that sources without well-constrained DPDFs follow the average DPDF distributions for the distance sample, then this result implies that physical quantities that depend linearly on flux density (i.e., mass) are biased by factors of 1.5–2.2 larger in the distance sample versus the total sample.