A MID-INFRARED CENSUS OF STAR FORMATION ACTIVITY IN BOLOCAM GALACTIC PLANE SURVEY SOURCES

The Bolocam Galactic Plane Survey¹⁰ (BGPS; Aguirre et al. 2011) has surveyed 170 deg² of the Northern Galactic Plane in 1.1 mm continuum emission using the facility long-wavelength camera, Bolocam (Glenn et al. 2003; Haig et al. 2004), at the Caltech Submillimeter Observatory (CSO) on Mauna Kea. The survey consists of two distinct portions: a blind survey of the inner Galaxy spanning −105 < ℓ < 700 where |b| < 05 everywhere except for 10 sections in ℓ centered at ℓ = 3°, 15°, 30°, and31° where |b| < 15, and a targeted outer Galaxy portion including Cygnus-X (70° < ℓ < 905, |b| < 15), the Perseus Arm (ℓ ∼ 111°), IC1396 (ℓ ∼ 99°, b ∼ 35), the W3/4/5 region (ℓ ∼ 135°, b ∼ 05), and the Gemini OB1 molecular cloud (ℓ ∼ 190°, b ∼ 05).

Bolocam is a hexagonal array of 144 bolometers with a filter centered at 268 GHz with an effective band center of 271.1 GHz (Aguirre et al. 2011) and a bandwidth of 45 GHz. The filter excludes the CO(2–1) emission line. Each individual bolometer has a Gaussian beam with an FWHM of 31'', and the instrument has an instantaneous field of view of 75 due to the separation of the bolometers in the focal plane of the instrument. For more information regarding Bolocam, see Glenn et al. (2003) and Haig et al. (2004).

A reduction pipeline was created specifically for the BGPS survey, and is described in Aguirre et al. (2011). In order to retain the extended structure in the final maps, an iterative sky cleaning method was employed. At each iteration, a model of the sky emission is updated and subtracted from the overall data time stream to reveal a time stream containing only the astrophysical signal. The astrophysical signal is then mapped with 72 × 72 pixels and the effective beam size for the BGPS is 33''.

Observations were obtained with scans along both l and b using the raster scan mode and a scan speed of 120'' s⁻¹. Sensitivity to extended structure up to 59 angular size was retained by not utilizing chopping. The full flux density of objects larger than 59 is not recovered, but long filaments with at least one dimension smaller than 59 are still detected (Aguirre et al. 2011). The flux density was calibrated based on observations of planets. Aguirre et al. (2011) compared BGPS with 1.2 mm data acquired with MAMBO on the IRAM 30 m (Rathborne et al. 2006; Motte et al. 2003, 2007) and SIMBA on the SEST 15 m (Matthews et al. 2009) and found that the v1.0 BGPS data were systematically lower and require a mean scaling factor of 1.5 ± 0.15 to align the BGPS fluxes with the previous MAMBO and SIMBA data sets. Here we present the v1.0 data with the scaling factor of 1.5 ± 0.15 applied.

Millimeter continuum sources were extracted from the iteratively mapped images using the BGPS source extraction software, Bolocat (Rosolowsky et al. 2010). Bolocat employs a seeded watershed method (Soille 1999) which first identifies all pixels above a signal-to-noise ratio (S/N) of 2.0, identifies contiguous groups of pixels above this S/N, culls any groups which contain fewer than a beam's worth of pixels (22 72 pixels), and then expands each remaining high signal-to-noise region through a nearest-neighbor algorithm to include all adjacent pixels above an S/N of 1.0. Extending the region to include pixels down to 1σ is based on the reasoning that marginal emission next to regions of significant emission is likely real. The software then breaks each region up into smaller substructures based on the contrast between local maxima. Through the nearest-neighbor algorithm, each source is assigned a group of contiguous pixels and a source number. Bolocat then produces a label map, in which every pixel assigned to a source is assigned the source number. Source properties are then computed via emission-weighted moments. All flux-dependent properties presented in this work are based on the integrated flux density which is simply the sum of all pixels assigned to a BGPS source. This flux density avoids contamination from nearby sources that can occur with aperture photometry. For more details regarding source extraction and parameter estimation, see Rosolowsky et al. (2010).

In the generation of the Bolocam catalog (Rosolowsky et al. 2010) we evaluated both the completeness limit (false negatives as a function of S/N) and the spurious detection incidence (false positives as a function of catalog parameters). The completeness study was presented as part of the original catalog manuscript. The catalog parameters were specifically chosen to minimize false detections as well as false negatives. To evaluate the false-positive incidence, we inserted an array of 2600 false sources into the data time stream for a blank field of observation. The time stream was for the l = 111 field which had been cleaned of signal as a byproduct of the iterative mapping procedure (Aguirre et al. 2011). The injected sources had a range of brightnesses and the recovery fraction as a function of brightness established the completeness limit. The algorithm recovered 0 false detections—all sources in the final catalog were the injected sources. While this may be surprising, the catalog's relatively high effective completeness limit of 5σ is a byproduct of eliminating false detections. Taking this as 0 ± 1 over the 4 deg² area of the field leads to an upper limit of ∼40 false detections in the survey, or 0.5%. We note that the injected sources were point sources and extended source recovery tests found that the BGPS catalog software often broke up extended emission into multiple objects, but it did not lead to the false detection of sources not associated with emission. Based on this test, we believe that the BGPS catalog contains only a very small number of false sources.

The BGPS catalog is >99% complete at the 5σ level. While σ varies across the survey due to the varying number of observations and observing conditions, the survey as a whole is >98% complete at the 0.4 Jy level (see Figure 9 in Rosolowsky et al. 2010). Assuming a dust temperature of 20 K (Dunham et al. 2010), this completeness level translates into a minimum mass of 5 M_☉, 21 M_☉, 130 M_☉, 524 M_☉, and 750 M_☉ at 1 kpc, 2 kpc, 5 kpc, 10 kpc, and 12 kpc, respectively. However, since the BGPS filters out diffuse emission on scales larger than 59 (Aguirre et al. 2011), the types of sources the BGPS is sensitive to depends on distance (see Section 7.2 of Dunham et al. 2010 and Section 6 of Rosolowsky et al. 2010). At the nearest distances (up to approximately 2 kpc), the BGPS will be sensitive to cores (mass M = 0.5–5 M_☉, volume-averaged density n = 10⁴–10⁵ cm⁻³, and physical radius R = 0.01–0.1 pc; Bergin & Tafalla 2007), while at intermediate distances the BGPS will be sensitive to clumps (M = 50–500 M_☉, n = 10³–10⁴ cm⁻³, R = 0.15–1.5 pc; Bergin & Tafalla 2007), and at the furthest distances BGPS will detect entire molecular clouds (M = 10³–10⁴ M_☉, n = 50–500 cm⁻³, R = 1–7.5 pc; Bergin & Tafalla 2007).

The BGPS images and catalog have been released to the public and are hosted by the Infrared Processing and Analysis Center via the NASA/IPAC Infrared Science Archive¹¹ (IPAC).

In addition, we made use of the GLIMPSE survey, a Spitzer/IRAC Legacy survey of the Galactic mid-plane (Benjamin et al. 2003; Churchwell et al. 2009) at 3.6, 4.5, 5.8, and 8.0 μm. The GLIMPSE I survey covers 10° ⩽|ℓ| ⩽ 65° and |b| ⩽ 1°  and the GLIMPSE II survey fills in the region for |ℓ| < 10°  with |b| ⩽ 1° for |ℓ| > 5°, |b| ⩽ 15 for 2°<|ℓ| ⩽ 5°, and |b| ⩽ 2° for |ℓ| ⩽ 2°. The total area of the GLIMPSE I and II surveys is 274  deg², and the overlap region with the BGPS survey is −105 < ℓ < 65°, |b| < 05 and |b| < 10 at ℓ = 3°, 15°, 30°, and 31°. The data products include both highly reliable Catalogs, and less reliable but more complete archives.

Robitaille et al. (2008, hereafter R08) compiled a highly reliable census of 18,949 GLIMPSE point sources with excess emission at mid-infrared wavelengths, of which 11,649 were classified as candidate YSOs, and 7300 as candidate asymptotic giant branch (AGB) stars. The AGB classification was further separated into two categories consisting of "standard" AGB stars and "extreme" AGB stars. The "extreme" AGB stars have high mass-loss rates and therefore significant circumstellar dust. In this paper, we refer to the "standard" and "extreme" AGB stars as sAGB and xAGB stars, respectively, and both types together as simply AGB stars. The separation of the sources into YSOs and AGB stars was based on IRAC and MIPS color and magnitude selection criteria, and was only approximate. In reality, 50%–70% of the sources are likely to be YSOs, and 30%–50% are likely to be AGB stars.

The R08 census was designed to maximize reliability. As the sensitivity to point sources decreases in areas of bright diffuse emission—which are common at 8 μm—the census used stringent magnitude selection criteria so as not to be affected by this. As a result, the R08 census may be missing fainter YSOs that are still detected by GLIMPSE. Therefore, for the current work, we compile a list of red GLIMPSE sources that were missed in the R08 census, with the caveat that this complementary list is therefore less reliable, and is background rather than flux limited, especially at 8 μm.

We constructed this complementary sample as follows. We first increased the reliability of the GLIMPSE catalog fluxes in a similar way to R08. First, each position in the GLIMPSE survey was observed at least twice, and we therefore removed fluxes from the catalog that depend only on a single detection. We required the fractional rms of the individual detections and the fractional error in the combined flux to be less than 15 %, otherwise the flux was removed. We then rejected sources that were not detected at least at 4.5 and 8.0 μm, and finally we selected the red sources by requiring [4.5] − [8.0] > 0.75, a less stringent color selection than that used for R08 ([4.5] − [8.0] > 1.0). This results in 64,859 sources being selected, excluding the R08 sources, which we refer to as additional GLIMPSE sources.

Robitaille et al. (2008) estimated that the red source catalog is 65.7% complete. In addition, they explored the range of luminosities of YSOs detectable as a function of distance. The sensitivity of the GLIMPSE survey results in a lower flux limit, and Robitaille et al. (2008) imposed an upper flux limit in order to exclude point sources with unreliable fluxes due to saturation. They used the models of Robitaille et al. (2006) to calculate average [4.5] and [8.0] magnitudes for stage I and II YSOs as a function of luminosity, and calculated the range of distances at which a YSO would be included in their red source catalog. A 1 L_☉ YSO within 1 kpc will be included in the red source catalog, while a 10 L_☉ YSO will be included if it is between 0.2 and 2 kpc. A 10³ L_☉ YSO between 2 and 10 kpc will be included in the R08 catalog, and a 10⁴ L_☉ YSO between 4 and 11 kpc will also be included. The most luminous YSOs will only be included at the farthest distances due to the upper flux limit imposed to avoid saturation, while the lowest luminosity sources will only be found at the nearest distances due to the sensitivity limits of the GLIMPSE survey (see Figure 19 and Section 4.5 of R08).

The GLIMPSE catalogs and archives are point source catalogs, and therefore exclude any extended YSOs. In particular, massive embedded YSOs driving outflows can in some cases be seen as extended sources at 4.5 μm, as this band contains H₂ emission lines as well as CO band heads (Reach et al. 2006; Smith et al. 2006). These lines can be excited by shocks, which are expected to be present where outflows interact with the interstellar medium. Cyganowski et al. (2008) compiled a list of 304 such objects, termed Extended Green Objects¹² (EGOs), from the GLIMPSE I survey. The EGOs are likely tracing outflows from massive YSOs since they show a strong correlation with IRDCs and class II methanol masers (Cyganowski et al. 2009), both of which are associated with early stages of massive star formation (Cyganowski et al. 2008). The overlap area with the BGPS survey is 10°<ℓ < 65°, |b| < 05, and |b| < 10 at ℓ = 15°, 30°, and 31°.

The EGO catalog is certainly not a complete census of YSOs with shocked outflows. The requirement of extended 4.5 μm emission likely resulted in the preferential inclusion of YSOs at relatively small distances, as the angular extent decreases with distance. Also, as noted in Cyganowski et al. (2008), EGOs near bright sources or in areas with significant polycyclic aromatic hydrocarbon (PAH) emission and diffuse green emission extended on scales less than 10'' are likely absent from the catalog.

Thus, the EGO catalog may include more massive, higher luminosity, nearby sources which were excluded from the R08 catalog because of the saturation limits.

The RMS survey¹³ (Hoare et al. 2004; Urquhart et al. 2008a) was designed to follow-up and confirm MYSO candidates selected from the Midcourse Space Experiment (MSX) Galactic plane survey (Price et al. 2001). The Galactic plane survey included all longitudes from 0° to 360°, and latitudes within |b| < 5° and consisted of imaging at 8.28, 12.13, 14.65, and 21.3 μm with a resolution of 18'' at all wavelengths (Price et al. 2001). A total of 1992 MYSO candidates were identified using color selection criteria. Low- and intermediate-mass YSOs were excluded from the catalog. All MYSO candidates were subsequently followed up to confirm their nature (Mottram et al. 2007; Urquhart et al. 2007a, 2007b, 2008b, 2009a, 2009b) and were classified into the following categories: "Evolved star," "PN," "OH/IR star," "Young/old star?," "H ii regions," "H ii/YSO," and "YSO." In this work we include the "PN," "OH/IR star," and "Evolved star" classifications in a general "Evolved star" category. The "YSO/H ii" classification is assigned when both an H ii region and YSO are present or if a definitive classification is not possible, while the "Young/old" classification is assigned to sources which look like evolved stars but have strong CO emission along their line of sight, resulting in an uncertain classification. The BGPS overlaps the RMS survey where ℓ ⩾ 10°.

Unlike the R08 sample, the RMS selection criteria did not include an upper limit on fluxes, and as such the highest luminosity sources at all distances will be included in the catalog. YSOs with L ∼ 10³ L_☉ will be included to 3 kpc, while 10⁴ L_☉ YSOs will be included to a distance of 10 kpc, and 10⁵ L_☉ YSOs will be included across the entire Galaxy (see Figure 2 of Urquhart et al. 2008a). The luminosity range of the RMS survey overlaps with the range in the R08 red source catalog, and fills in the region of luminosity space excluded from the R08 catalog because of the saturation limitations.

The data sets were cross-matched based on spatial coincidence. All infrared sources located within a BGPS source as defined by the label maps (see Section 2.1) are considered to be associated with the BGPS source. The label maps produced as a part of the BGPS source extraction (Rosolowsky et al. 2010) represent the full extent of each 1.1 mm continuum emission source down to the 1σ level of the original image. We require that the catalog position of each mid-IR source fall within a pixel assigned to a BGPS source. The EGO sources subtend more than a single BGPS pixel; however, we find that ignoring the extended emission and simply using the catalog position corresponding to the peak of the 4.5 μm emission does not adversely affect the matching statistics for the EGO catalog. Figure 1 shows the label map and corresponding image centered near l ∼ 6° with the positions of the matched (crosses and plus signs) and unmatched (diamonds and circles) R08 and additional GLIMPSE sources, respectively. The catalog parameters for each BGPS source (major and minor axes and position angle) are displayed as the black ellipses. The BGPS sources clearly do not fill the black ellipses, highlighting the benefit of using the label maps rather than the BGPS mean source properties when cross-matching catalogs.

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In matching various catalogs of mid-IR sources to the BGPS sources, we need to take into account the possibility of chance alignment of mid-IR sources with BGPS clumps. Since we do not have distance estimates to the mid-IR sources or most BGPS sources, we cannot determine which mid-IR sources that lie along the same line of sight as a BGPS source are in fact chance alignments. Instead, we can estimate the fraction of chance alignments statistically.

In order to do this, we first consider the fraction of the BGPS area that contains millimeter emission and assume that the mid-IR sources are evenly distributed across the survey area. In this case, the fraction of area covered with millimeter emission corresponds to the fraction of mid-IR sources that are chance alignments with the millimeter continuum emission. We calculate this fraction for the region that is common to all surveys: 10° < ℓ < 65°, and |b| ⩽ 05 with extensions to |b| ⩽ 10 as described in Section 2.1. We find that 2.1% of the BGPS area contains source emission, and therefore 2.1% of the mid-IR sources will overlap millimeter continuum emission by chance.

In reality, the distribution of the mid-IR sources is not even across the survey areas, but is concentrated towards the Galactic mid-plane, and also decreases with increasing longitude (Figure 2). Furthermore, even a population of mid-IR sources unrelated to star formation could display a similar non-uniform spatial distribution. To obtain a more realistic estimate of chance alignments, we attempt to preserve the large-scale distribution of the mid-IR sources by duplicating the catalogs and randomizing each source's coordinates within a circle of radius 1° (in cases where mid-IR sources fell out of their original survey area, their positions were re-randomized). In this way, any population unrelated to star formation would preserve its large-scale distribution and would not show a difference in the number of chance alignments, while any star-forming population that was originally preferentially aligned with BGPS emission on arcsecond to arcminute scales would lose such a correlation. Figure 3 shows the distributions of Galactic longitude (left) and latitude (right) for the GLIMPSE red sources with ℓ ⩾ −10° for the original (solid lines) and randomized (dashed lines) catalogs. Overall, the trends in the distributions of the original catalog are preserved in the randomized catalog although the peak in sources toward b ∼ 0° is slightly decreased. To investigate the effect of the randomization radius used, we repeated the experiment with a radius of 01 and found that the fraction of chance alignments increases slightly. All GLIMPSE R08 source types (xAGB, sAGB, and YSO) taken together have 8.1% chance alignments with a 1° randomization. If we use only a 01 randomization, we expect 10.7% chance alignments. The choice of radius for the randomization does not severely alter the chance alignment results.

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Multiple randomized catalogs were created for each mid-IR data set in the interest of obtaining an error bar on the number of chance alignments. For the GLIMPSE catalogs, we randomized the catalogs 10 times, while for the EGO and RMS catalogs we randomized the catalogs 100 times to avoid issues due to small-number statistics. Column 5 of Table 1 presents the percentage of matched mid-IR source types that are expected to be chance alignments, and Column 9 shows the percentage of BGPS sources expected to be matched due to chance alignments with each mid-IR source type. Overall, around 7% of mid-IR sources would be expected to match the BGPS emission by chance alignments.

Columns 2–5 of Table 1 present a summary of the matching statistics for each mid-IR catalog, including both the number and fraction of mid-IR sources that are matched to BGPS emission. The EGOs are most often matched to BGPS emission, with 90% of EGO sources matched (more than 10 times that expected from random chance alignment). In comparison, the RMS sources have a lower overall matched fraction (68%). However, if we consider the different types of RMS sources separately, it becomes apparent that the types of RMS sources associated with star formation (e.g., H ii regions, H ii/YSO, and YSO) have a much higher fraction of matches with BGPS sources. Table 1 lists the matching statistics for the RMS sources by category. The young/old star, H ii region, H ii/YSO, and YSO categories have matched fractions approximately 8–10 times the fraction expected by chance alignments (80%–90%). In contrast, the fraction of RMS evolved stars matched with BGPS emission is perfectly consistent with that expected from chance alignments. Of the 133 RMS sources classified as AGB stars within the "Evolved stars" category, only 12 were matched with BGPS sources.

The GLIMPSE R08 YSOs tend to be less often associated with millimeter emission (33%, or four times that expected from chance alignments). This low fraction could be due to several reasons. First, stage II YSOs, which are present in the GLIMPSE R08 catalog, no longer have an envelope and are unlikely to possess the density and angular size required for a detection in the BGPS (Dunham et al. 2010, Section 7.2). Secondly, the separation of YSOs and AGB stars in the GLIMPSE red source catalog was only approximate, and refining the magnitude and color selection criteria could result in a higher fraction of matched YSOs. The fraction of AGB stars from the GLIMPSE R08 catalog matched to millimeter emission is slightly above the level expected for chance alignments. This could be due to the approximate YSO/AGB separation which results in contamination from genuine YSOs in the sources classified as AGB stars, or it could be indicative of some AGB sources being present in the BGPS catalog. Indeed, the dust around some AGB and post-AGB stars is detected at millimeter wavelengths (e.g., Buemi et al. 2007; Dehaes et al. 2007; Ladjal et al. 2010) and it is possible that some BGPS sources are actually evolved stars. The RMS team has performed followup observations and has identified the sources in their catalog which are AGB stars. Although the number of RMS "Evolved stars" matched with a BGPS source is consistent with the number expected due to chance alignments, we can use the matching statistics to estimate the number of GLIMPSE R08 AGB stars expected to be matched with a BGPS source. If we assume that the matching statistics for the RMS AGB stars within the "Evolved stars" category (12 of 133 were matched with a BGPS source, 9.0%) also apply to the R08 AGB stars, then we expect 296 R08 AGB stars to be matched with BGPS sources. We find that a total of 494 R08 AGB stars are matched with BGPS sources, 198 more than expected based on the matching statistics of the RMS AGB stars. If the RMS statistics are representative of the R08 AGB stars as well, then roughly 60% of the matched R08 AGB stars are likely to be AGB stars and 40% are likely to be YSOs. Further observations are required to determine the nature of the AGB sources which are matched with BGPS sources. A future paper will further explore the matching statistics in order to assess the validity of the magnitude and color cuts made to define the YSO GLIMPSE red source list presented in R08.

Finally, the additional GLIMPSE source catalog contains 21% of sources that are matched with millimeter emission (almost three times the level expected from chance alignments), indicating that it does contain a fraction of genuinely young stars.

In Columns 6–9 of Table 1, we present the detailed numbers/fractions of BGPS sources containing each type of mid-IR source. We assume that the following mid-IR source types indicate star formation within the matched BGPS source: GLIMPSE R08 YSOs, sAGB, and xAGB stars; GLIMPSE additional sources; EGOs; young RMS source types including "Young/old star," "H ii region," "H ii/YSO," and "YSO." As previously mentioned (Section 3.3), we use the R08 AGB catalogs as an indicator of star formation because of the approximate separation of the YSOs and AGB sources and the resulting contamination of the R08 AGB catalogs by YSOs (see Section 2.2). Further observations would be required to determine if R08 AGB sources matched with BGPS sources are YSOs or AGB stars, and we note that some AGB stars matched with BGPS sources will actually be AGB stars.

A total of 3712 BGPS sources were identified as containing signs of star formation via the alignment of a mid-IR source, with the caveat that some of the matched R08 AGB stars are actually AGB stars and not indicative of star formation. This equates to 44% of the entire BGPS catalog, although this is a lower limit to the true fraction since the mid-IR catalogs do not overlap completely with the BGPS catalog. Only the RMS catalog overlaps the BGPS at l > 65°, and unlike the GLIMPSE survey it will only identify the brightest mid-IR sources. If we consider only the region where all surveys overlap (10° < l < 65°), we find a total of 2457 BPGS sources containing a mid-IR source out of 5067 BGPS sources in the inner Galaxy (48%).

In order to calculate the true number and fraction of BGPS sources that show signs of active star formation, we must account for the occurrence of chance alignments. As previously discussed, the number of BGPS sources likely to have chance alignments were calculated for each mid-IR source catalog (the product of Columns 6 and 9 in Table 1). We simply subtract the number of BGPS sources identified as chance alignments from the number of BGPS sources which were matched with each individual mid-IR source type, and find that 1472 of the 8358 (17.6%) BGPS sources in the entire catalog are reliable matches. If we restrict this calculation to the 5067 BGPS sources in the area where all surveys overlap (10° ⩽ℓ ⩽ 65°), we estimate that 1035 (20.4%) BGPS sources are reliably matched with a mid-IR source. These percentages are conservative estimates of the percentage of BGPS sources that are actively forming stars and are driven so low due to the large number of BGPS sources expected to be identified via chance alignments with the additional GLIMPSE sources (1573 for the entire catalog and 976 for the overlap area only).

Since we are unable to identify which mid-IR sources are chance alignments with our current data set, we consider all matches in the subsequent discussion. Table 2 presents the number of mid-IR sources within each BGPS source. Column 1 gives the BGPS source name, Columns 2 and 3 give the R.A. and decl. of the geometric centroid, while Columns 4 and 5 give the Galactic coordinates. The angular radius of each BGPS source is given in Column 6. The number of matched sources from the EGO, RMS, GLIMPSE R08, and additional GLIMPSE catalogs are given in Columns 7–10, respectively. The full table is included in the online journal only.

We define a confidence value for each type which is the percent of matched BGPS sources which are not due to chance alignments. This is defined as the number of BGPS sources with a matching mid-IR source minus the number expected from chance alignments, divided by the number of BGPS sources with a matching mid-IR source, and is given in Column 10 of Table 1.

This confidence value allows us to estimate the probability that a match with a particular mid-IR source indicates ongoing star formation in the BGPS source. The calculated confidence values range from 26%, for BGPS sources matched with RMS evolved stars, to roughly 90%, for the BGPS sources matched to EGO and young RMS sources. The confidence is around 70% for the GLIMPSE R08 YSOs, around 50% for the additional GLIMPSE sources, and around 50% and 40% for the GLIMPSE R08 xAGB and sAGB stars, respectively.

Figure 4 shows the number of BGPS sources as a function of the flux density integrated over the entire source for the BGPS sources in each probability group. BGPS sources in group 3 with the highest probability of star formation activity have the highest mean flux, 8.0 Jy, with a standard deviation about the mean of 18.0 Jy. The mean flux decreases with probability of star formation activity, with a mean of 0.71 Jy and standard deviation of 1.4 Jy for the "starless" sources. The flux distributions are asymmetric with tails extending to large fluxes. For example, the distribution of "starless" sources has a high flux tail extending to approximately 30 Jy.

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The 1.1 mm BGPS flux densities could be contaminated by free–free emission from ionized gas if the BGPS source is coincident with an H ii region or planetary nebula, for example. The trend of increasing flux density with probability of star formation could be due to an increase in the contamination from free–free with increasing probability of star formation. To quantify the free–free contamination, we have compared the BGPS flux densities with integrated intensities from 6 cm radio continuum observations toward RMS sources (Urquhart et al. 2009a). We have identified 223 radio continuum sources from Urquhart et al., which coincide with 159 unique BGPS sources. In cases where multiple radio continuum sources coincide with a BGPS source, we have simply taken the sum of the individual 6 cm fluxes for comparison to the 1.1 mm flux. Assuming that the 6 cm emission is on the optically thin side of the free–free spectrum, we scale the 6 cm emission to 1.1 mm via $\mbox{$S_{\nu }$}(\rm {ff,1.1 mm}) =\mbox{$S_{\nu }$}(\rm {6 cm}) (\rm {1.1 mm/60 mm})^{0.1}$ since S_ν(free–free)∝ν^−0.1. If the 6 cm emission is on the optically thick side of the free–free spectrum, then S_ν(ff, 1.1 mm) underestimates the free–free flux density, as the spectrum increases as ν² on the optically thick side (Mezger & Henderson 1967; Tielens 2005).

Figure 5 shows the distribution of the ratio of the free–free flux density at 1.1 mm to the 1.1 mm BGPS flux density. The dotted line marks the mean fractional contribution from free–free of 0.039 ± 0.066, and the dashed line marks the median of 0.013. The minimum and maximum free–free contributions are 0.0002 and 0.54, respectively, and both values are for BGPS sources in the "starless" group. The RMS 6 cm observations were targeted toward potential H ii regions with the goal of further classifying the RMS sources; some RMS sources were classified as planetary nebulae, which we did not consider as a positive sign of star formation and could therefore fall into our "starless" probability group. The vast majority of the BGPS sources including 6 cm emission fall in probability group 3, with a mean free–free contribution of 0.033 ± 0.046, median of 0.012, and a maximum of 0.23. For all but four of the 159 BGPS sources with 6 cm radio observations, contamination from free–free emission does not exceed 20%, while for the remaining four BGPS sources the free–free emission contributes up to approximately half of the 1.1 mm flux density.

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Without radio observations for all BGPS sources, we are unable to correct for the free–free contamination. To assess whether the mean level of free–free contamination we see toward the 159 BGPS sources could be the cause of the increasing flux density with probability of star formation, we calculate the fraction of the group 1–3 flux that would need to be attributed to free–free emission for the mean flux density to match the mean of the "starless" group. We find 52%, 64%, and 91% for groups 1–3, respectively. This is an order of magnitude higher than the mean free–free flux density contribution we find with the RMS 6 cm observations. Therefore, it is highly unlikely that the trend of increasing flux density is due to free–free contamination. However, free–free emission could contribute significantly to the flux densities of individual sources.

The observed increase in flux density with group could also be a reflection of an increasing dust temperature. While an increase in T_D does explain some of the observed trends in flux density, it cannot explain the order of magnitude increase in mean flux density between groups 0 and 3. We discuss the effects of T_D in Section 4.2 below.

A SIMBAD search of the 22 "starless" sources in the inner Galaxy with S_ν >10 Jy revealed that only four of the brightest BGPS sources are possibly truly starless, while the remaining 18 brightest BGPS sources in the inner Galaxy had a combination of radio emission and masers as indicators of active star formation. This accentuates that while these BGPS sources are "starless" in the sense that they do not contain any mid-IR sources from GLIMPSE or RMS catalogs, they are not necessarily truly starless sources. Further comparison to other surveys will be needed in order to find a truly starless sample of BGPS sources.

Figure 6 shows the number of BGPS sources as a function of the concentration parameter in each star formation probability group. The concentration parameter is defined as the ratio of the elliptical radius containing 90% of the total source flux to the elliptical radius containing 50% of the total source flux, where the elliptical radius is given by R = (R_majR_min)^1/2. By this definition, compact sources will have a low concentration parameter while sources with large skirts of emission will have a high concentration parameter. The "starless" sources have a lower mean concentration parameter, and the mean value increases with probability of star formation activity. The majority of the most extended BGPS sources fall within probability group 3. These statistics are likely affected by chance alignments since more extended sources are more likely to be identified by chance alignments with the mid-IR sources. Since we cannot identify which BGPS-mid-IR source associations are due to chance alignments, we cannot assess the extent of the effect of chance alignments on this trend. However, we do note that the group 3 sources are unlikely to include many chance alignments since we expect a very low fraction of matched EGO and RMS sources to be the result of chance alignments.

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Another possible bias which could affect the statistics of each probability group is distance. Due to the limited sensitivity of the mid-IR catalogs, it is possible that more distant BGPS sources harbor low-mass YSOs which are not present in the mid-IR catalogs. The starless group could include a large number of distant BGPS sources which are actually forming stars.

We create a distance subsample of BGPS sources within the region where all surveys overlap that have distance estimates from a molecular line study of BGPS sources (Schlingman et al. 2011) and very long baseline interferometry (VLBI) parallax measurements (seven BGPS sources; Bartkiewicz et al. 2008; Brunthaler et al. 2009; Xu et al. 2009). Schlingman et al. (2011) used the VLBI parallax based model of Galactic rotation of Reid et al. (2009) and were able to assign the near kinematic distance to sources based on the association with a GLIMPSE IRDC (Peretto & Fuller 2009). Schlingman et al. (2011) additionally adopted distances from the well-studied sample of massive star-forming regions of Shirley et al. (2003). The "distance subsample" presented in this section consists of 280 BGPS sources which are located in the region where all the catalogs overlap. Since the dominant number of distance determinations are based on the association of a BGPS source with an IRDC, the distance subsample is significantly biased to the near kinematic distance in the inner Galaxy. Full results of the molecular line study are formally presented in Schlingman et al. (2011).

We calculate properties such as mass, volume-averaged density, and column density for the 280 BGPS sources with kinematic distances. The distance subsample samples the different probability groups well with 55, 67, 97, and 61 from groups 0–3, respectively. Figure 7 plots a histogram of the distances as a function of probability of star formation activity. The distances range from 0.21 to 7.0 kpc with no obvious trends with star formation probability (see Table 3). Since the BGPS will be sensitive to different structures over such a large range in distances, we define a subsample of sources with 2 kpc <d < 3 kpc (hereafter referred to as the 2 kpc subsample) in order to separate trends from the ambiguity introduced by a large range of distances. We have chosen this range of distances because Dunham et al. (2010) find that at distances greater than approximately 2 kpc the BGPS is sensitive to structures most closely related to clumps. Thus, we expect the 2 kpc subsample to have properties in the typical range of clumps (e.g., Table 1 of Bergin & Tafalla 2007). We find 6, 10, 18, and 8 sources with distances of 2–3 kpc for probability groups 0–3, respectively.

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Table 3. Physical Property Statistics of BGPS Sources in the Region Where All Catalogs Overlap

Property	Probability			Standard
(units)	Group	Minimum	Mean	Deviation	Median	Maximum
Sν	0	0.06	0.71	1.4	0.41	33.1
(Jy)	1	0.06	1.5	1.9	0.89	27.7
	2	0.08	2.0	2.5	1.2	25.3
	3	0.13	8.0	18.0	3.4	146.8
Concentration	0	1.3	1.6	0.11	1.6	2.1
parameter	1	1.3	1.7	0.13	1.6	2.6
	2	1.4	1.7	0.13	1.7	2.3
	3	1.5	1.8	0.20	1.8	2.7
$N_{\rm H_2}^{{\rm beam}}$	0	0.21	0.95	1.2	0.71	23.3
(1022 cm−2)	1	0.20	1.4	1.7	0.95	27.0
	2	0.22	1.6	1.6	1.1	19.3
	3	0.20	4.7	10.4	2.1	99.3
Distance Subsample
Distance	0	1.04	4.3	1.2	4.4	6.7
(kpc)	1	0.21	4.2	1.2	4.5	6.4
	2	1.9	4.1	1.2	3.8	7.0
	3	1.3	4.4	1.4	4.6	7.0
Radius	0	0.12	0.95	0.55	0.86	2.0
(pc)	1	0.07	1.1	0.63	1.0	3.4
	2	0.18	1.2	0.75	1.1	3.5
	3	0.35	1.3	0.72	1.1	3.8
Miso(TD)	0	19	1050	1720	340	1.0 × 104
(M☉)	1	2.4	1040	1130	690	5380
	2	30	1450	2110	680	1.2 × 104
	3	90	3230	5450	1160	3.6 × 104
n	0	0.73	7.1	11.0	3.3	56.1
(103 cm−3)	1	0.32	6.7	9.4	2.5	50.2
	2	0.41	5.8	10.7	2.5	85.7
	3	0.60	7.2	9.7	3.2	45.8
$N_{\rm H_2}^{{\rm avg}}$	0	3.1	12.8	9.7	9.6	56.3
(1021 cm−2)	1	3.7	12.8	9.9	9.7	47.8
	2	3.2	12.4	10.8	9.2	82.2
	3	3.4	24.2	31.3	12.6	154.0
2 kpc Subsample
Radius	0	0.19	0.49	0.29	0.51	0.90
(pc)	1	0.19	0.65	0.41	0.49	1.4
	2	0.18	0.67	0.27	0.65	1.1
	3	0.41	0.74	0.23	0.73	1.1
Miso(TD)	0	37	79	56	52	179
(M☉)	1	26	390	767	94	2520
	2	19	192	130	170	546
	3	90	792	609	710	2120
n	0	1.0	8.2	11.3	3.6	29.5
(103 cm−3)	1	0.85	5.3	5.8	3.7	16.3
	2	0.91	4.0	4.2	2.3	14.2
	3	2.0	9.1	6.9	8.1	22.3
$N_{\rm H_2}^{{\rm avg}}$	0	2.7	7.2	6.8	4.7	19.9
(1021 cm−2)	1	2.4	7.9	6.9	6.1	25.4
	2	3.1	6.4	3.5	5.0	14.5
	3	6.3	21.0	13.7	20.4	44.6

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Figure 8 plots the number of objects versus physical radius for each probability group. The gray histograms show the distance subsample, while the striped histograms mark the 2 kpc subsample. The elliptical radius was determined by the BGPS source extraction software based on the emission-weighted moments of the BGPS maps (Rosolowsky et al. 2010). Radii of unresolved sources have been set to an upper limit of half the beam size, 165. The physical radii of sources in the distance subsample range from 0.07 to 3.8 pc spanning the range of sizes expected for the entire hierarchical structure in giant molecular clouds (GMCs) including clouds, clumps, and cores (radius =1–7.5 pc, 0.15–1.5, pc and 0.01–0.1 pc, respectively; Bergin & Tafalla 2007). The radii of the 2 kpc subsample range from 0.18 to 1.4 pc, and span the range of typical clump radii (see Table 3). The physical radius increases with star formation probability group from 0.95 pc for the "starless" sources to 1.3 pc for group 3 (see Table 3).

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We calculate the isothermal dust mass, M_iso, assuming a single dust temperature, T_D, as

$$\begin{eqnarray} M_{{\rm iso}}&=&\frac{S_{\nu }D^{2}}{\kappa _{\nu }B_{\nu }(\mbox{$T_D$})}=13.1\ M_\odot \left(\frac{S_{\nu }}{1\ \rm Jy}\right)\left(\frac{D}{1\ \rm kpc}\right)^2\nonumber\\ && \times \left(\frac{e^{13.0\ \rm K / \mbox{$T_D$}}-1}{e^{13.0\ \rm K / 20.0\ \rm K}-1}\right), \end{eqnarray} \tag{ 1 }$$

where S_ν is the flux density, D is the distance, κ_ν is the dust opacity per gram of gas and dust including a gas-to-dust ratio of 100 (κ_ν = 0.0114 cm² g⁻¹ at 271.1 GHz; logarithmically interpolated from OH5 dust from Column 5 of Table 1 in Ossenkopf & Henning 1994), and B_ν is the Planck function evaluated at T_D. The right-hand side of the equation is evaluated for T_D =20 K based on NH₃ observations of BGPS sources in the Gemini OB1 molecular cloud where a mean gas kinetic temperature of 20 K was found (Dunham et al. 2010).

Although 20 K is a reasonable value of T_D to assume if no other information is available, we have both gas kinetic temperature and dust temperature measurements from other observations. M. K. Dunham et al. (2011, in preparation) have surveyed 716 BGPS sources in the inner Galaxy in NH₃(1,1), (2,2), and (3,3) and have provided a measurement of T_K toward the 408 BGPS sources detected in NH₃. They find 〈T_K〉 of 14.0 ± 3.2 K, 14.8 ± 3.9 K, 16.1 ± 4.3 K, and 22.0 ± 5.9 K based on 130, 143, 102, and 33 BGPS sources from groups 0–3, respectively. For this work, we assume the mean gas kinetic temperatures from the NH₃ study for each group. By assuming that the gas kinetic temperature is equivalent to the dust temperature, we are assuming that the density is high enough to bring the temperatures into equilibrium via collisions. This assumption holds in the dense regions where the dust effectively shields the gas from the interstellar radiation field (ISRF) and the gas is heated via collisions with the dust (e.g., Goldreich & Kwan 1974; Evans et al. 2001).

The number of BGPS sources of each M_iso are plotted for each probability group in Figure 9, where the gray histogram represents the entire distance subsample and the striped histogram denotes the 2 kpc subsample. There is a clear trend of increasing mass with increasing probability of star formation activity; the median masses in groups 0–3 are 340, 690, 680, and 1160 M_☉, respectively. Similarly, we find a median mass of 52, 94, 170, 710 M_☉ for groups 0–3 of the 2 kpc subsample, respectively. The median mass is a more accurate representation of each group than the mean mass due to the few extremely high mass (10⁴ M_☉) BGPS sources in groups 0, 2, and 3 (see Table 3).

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There are two effects that could artificially produce the observed trend in mass: contamination by free–free emission and the assumed T_D. As discussed in Section 4.1, the free–free emission is not a significant contribution to the flux densities of most BGPS sources and is unlikely to cause the trend of increasing mass.

Here we explore what effects different dust temperatures would have on the observed trend in mass. We calculate the temperature required for the median mass of each group to equal the median mass of group 1 (where we assume T_D =14.8 K). We have chosen to use the median mass of group 1 as the standard since it is very similar to the median for group 2 (690 and 680 M_☉, respectively). Dust temperatures of 9.2, 15.9, and 33.2 K would bring the median of groups 0, 2, and 3 into alignment with group 1, respectively. While these temperatures are reasonable, the values for groups 0 and 3 lie outside of the standard deviation of the mean gas kinetic temperatures derived from the NH₃ observations discussed above. The NH₃ observations are sensitive to gas kinetic temperatures well above 33 K, so the lower mean temperature observed toward group 3 sources is not the result of an observational bias.

Thus, the trend to higher masses with probability of star formation activity is likely real. Here M_iso ranges from 2.4 M_☉ to 3.6 × 10⁴ M_☉ for the distance subsample, and 19 M_☉ to 2.5 × 10³ M_☉ for the 2 kpc subsample. Again, the distance subsample spans the range of masses for cores, clumps, and clouds (0.5–5 M_☉, 50–500 M_☉, and 10³–10⁴ M_☉, respectively; Bergin & Tafalla 2007), while the 2 kpc subsample encompasses the mass range for clumps without extending into the range for clouds or cores.

From M_iso we calculate the mean particle density, n, for each source in the distance subsample via $\mbox{$n$}=3\mbox{$M_{{\rm iso}}$}/4\pi R^3$, where R is the source radius determined by the BGPS source extraction algorithm. This density calculation assumes a constant density and the effect is a volume-averaged density that is more reflective of the lower density outer regions of the BGPS source than the higher density regions. Figure 10 shows histograms of n for each probability group. All groups span almost the same range from 320 to 5.6 × 10⁴ cm⁻³. However, the BGPS sources in groups 0 and 3 have, on average, a higher density than those in groups 1 and 2 (see Table 3). The "starless" sources are not only less massive but also smaller than BGPS sources in groups 1–3 and therefore have densities similar to those of group 3. The 2 kpc subsample only extends to about 10³ cm⁻³ on the low density end of each distribution, but does extend to 10⁴ cm⁻³ on the high density end, even in the "starless" category. Clouds typically range from 50to500 cm⁻³, clumps from 10³to10⁴ cm⁻³, and cores from 10⁴to10⁵ cm⁻³ (Bergin & Tafalla 2007). Overall, the distance subsample spans the entire range of densities, but the 2 kpc subsample only spans the density ranges for clumps and cores.

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The column density of H₂ is given by $N_{\rm H_2}^{{\rm avg}}=\mbox{$M_{{\rm iso}}$}/4\pi \mu m_{\rm H} R_{{\rm obj}}^2$, where μ = 2.37 and m_H is the mass of hydrogen. Figure 11 shows the number of sources as a function of $N_{\rm H_2}^{{\rm avg}}$ for each probability group in the distance subsample (gray histogram) as well as for the 2 kpc subsample (striped histogram). There is an increase in mean $N_{\rm H_2}^{{\rm avg}}$ between groups 0–2 and group 3. Groups 0–2 have mean $N_{\rm H_2}^{{\rm avg}}$ values near 1.2 × 10²² cm⁻² while group 3 has a mean H₂ column density of 2.4 × 10²² cm⁻² (see Table 3). The dashed line denotes the threshold column density of about 123 M_☉ pc⁻² which has been observed toward nearby, low-mass star-forming regions (Lada et al. 2010; Heiderman et al. 2010). The dotted line denotes the theoretical minimum surface density, 1 g cm⁻², required to prevent fragmentation and allow a massive star to form (Krumholz & McKee 2008). Similar to the volume density, $N_{\rm H_2}^{{\rm avg}}$ is also an average quantity. There are likely higher surface density regions within the BGPS source where the YSOs are forming, but the BGPS is sensitive to the lower density outer regions of the clump (Dunham et al. 2010). This is consistent with the picture that RMS and EGO sources are high-mass YSOs even though the average surface density is not above the 1 g cm⁻² requirement to prevent fragmentation.

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Alternatively, we can calculate the H₂ column density per beam for all BGPS sources within the area where all catalogs overlap since this quantity is independent of distance. The H₂ column density per beam is given by

$$\begin{equation} N_{\rm H_2}^{{\rm beam}}=\frac{\mbox{$S_{\nu }$}(40\mbox{\mbox{$^{\prime \prime }$}})}{\Omega _{{\rm beam}}\, \mu _{\rm H_2}\, m_{\rm H}\, \kappa _{\nu }\, B_{\nu }(\mbox{$T_D$})}, \end{equation} \tag{ 2 }$$

where S_ν(40'') is the 1.1 mm flux density within an aperture with a diameter of 40'', Ω_beam is the solid angle of the beam, $\mu _{\rm H_2}=2.8$, κ_ν is the dust opacity and B_ν(T_D) is the Planck function evaluated at the dust temperature, T_D, as described above. We use S_ν(40'') as a measure of the flux within a beam since a top-hat function with a 20'' radius has the same solid angle as a Gaussian beam with an FWHM of 33''. We have applied an aperture correction of 1.46 ± 0.05 to S_ν(40'') to account for power that falls outside of the 40'' aperture due to the sidelobes of the CSO beam (Aguirre et al. 2011). We calculate this property for all BGPS sources within the region where all surveys overlap, since $N_{\rm H_2}^{{\rm beam}}$ is independent of distance. Figure 12 shows the distribution of H₂ column density per beam for the BGPS sources in the overlap region for each probability group. As above, the dotted line denotes the column density required to prevent fragmentation (Krumholz & McKee 2008) and the dashed line denotes the threshold for efficient star formation (Lada et al. 2010; Heiderman et al. 2010). The mean column density per beam increases with probability group with $\langle N_{\rm H_2}^{{\rm beam}}\rangle$ =0.95 × 10²², 1.4 × 10²², 1.6 × 10²², and 4.7 × 10²² cm⁻² for groups 0–3, respectively. The median $N_{\rm H_2}^{{\rm beam}}$ of group 0 (7.1 × 10²¹ cm⁻²) is similar to the threshold for efficient star formation (6.5 × 10²¹ cm⁻²; dashed line in Figure 12; Lada et al. 2010; Heiderman et al. 2010), such that roughly half of the "starless" BGPS sources have a peak column density high enough to efficiently form stars. It may be that these sources appear "starless" in this study because of the sensitivity limits of the mid-IR catalogs. For example, low-mass YSOs within a BGPS source at 5 kpc would not be detected by the GLIMPSE surveys. Further comparisons with other tracers of star formation are necessary to determine which sources are truly starless.

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Overall, we find that S_ν(int), R, M_iso, $N_{\rm H_2}^{{\rm beam}}$, and $N_{\rm H_2}^{{\rm avg}}$ are all higher in BGPS sources actively forming stars. Sources identified as actively forming stars are typically extended with large skirts of emission, while the "starless" sources are more compact, although this trend is likely affected by chance alignments since more extended BGPS sources are more likely to be matched with a mid-IR source by chance. BGPS sources with EGO or RMS sources (group 3) are more massive and have higher volume-averaged densities than BGPS sources with GLIMPSE sources. As expected, due to the large range of distances, these physical properties show that the BGPS sources span the entire hierarchical structure in GMCs (clouds, clumps, and cores). Based on the physical properties presented, we confirm that the 2 kpc subsample is mostly composed of clumps.