THE BOLOCAM GALACTIC PLANE SURVEY. VIII. A MID-INFRARED KINEMATIC DISTANCE DISCRIMINATION METHOD

Creation of synthetic 8 μm images explicitly assumes that the dust seen in emission in the BGPS is the same dust that extincts mid-infrared light. When converted into a mid-infrared optical depth, BGPS observations represent dark clouds which may be placed at different heliocentric distances within a model of diffuse Galactic 8 μm emission. A series of synthetic images generated in this manner were compared with mid-infrared observations to compute the DPDF_emaf.

We assumed a simple radiative transfer model to describe the observed mid-infrared intensity absorbed by a cold molecular cloud clump immersed in a sea of diffuse emission (assuming that the absorbing cloud has no emission). The intensity observed within an EMAF (I_emaf) is

$$\begin{equation} I_\mathrm{emaf} = I_\mathrm{back}\ e^{-\tau _{8}} + I_\mathrm{fore}, \end{equation} \tag{ 6 }$$

where I_back and I_fore are the background (from the cloud to large heliocentric distance) and foreground (between the observer and the cloud) intensities, respectively, and τ₈ is the mid-infrared optical depth of the cloud. The total intensity along a line of sight in the absence of absorption is I_MIR = I_back + I_fore. Defining the fraction of the total intensity that lies in front of the cloud as f_fore = I_fore/I_MIR allows Equation (6) to be written as

$$\begin{equation} I_\mathrm{emaf} = [(1 - f_\mathrm{fore})\ e^{-\tau _{8}} + f_\mathrm{fore}]\ I_{\mathrm{MIR}}. \end{equation} \tag{ 7 }$$

This parameterization frames the observed EMAF intensity in terms of decrements below the unextincted intensity in the vicinity, and provides the basis for creating synthetic 8 μm images. It follows quickly from Equation (7) that clouds optically thick in the mid-infrared (τ₈ ∼ 1) will still have a 10% difference between I_emaf and I_MIR (i.e., easily detectable) for f_fore as large as 0.85. Calculation of τ₈ and f_fore are described below, and the estimation of I_MIR from GLIMPSE data is discussed in Section 4.2.

The mid-infrared optical depth of an EMAF cannot be measured directly from the GLIMPSE mosaics without significant assumptions, but it may be estimated from millimeter data. Thermal dust emission is optically thin at millimeter wavelengths, so the observed BGPS flux density (S_1.1) may be written as

$$\begin{equation} S_{{1.1}} = B_{{1.1}}(T_d)\ \tau _{{1.1}}\ \Omega _{\mathrm{BGPS}}, \end{equation} \tag{ 8 }$$

where B_1.1(T_d) is the Planck function evaluated at λ = 1.1 mm and dust temperature T_d, and Ω_BGPS = 2.9 × 10⁻⁸ sr is the solid angle of the BGPS beam. The millimeter optical depth (τ_1.1) was computed assuming the dust opacity (κ_1.1) for grains with thin ice mantles, coagulating at 10⁶ cm⁻³ for 10⁵ yr (Ossenkopf & Henning 1994, Table 1, Column 5; called OH5 dust). Interpolation of OH5 dust opacities to the central frequency of the BGPS bandpass yields κ_1.1 = 1.14 cm² g⁻¹ of dust (A11). A molecular cloud clump with τ_1.1 = 10⁻³, which corresponds to S_1.1 ≈ 0.9 Jy, has a beam-averaged molecular hydrogen column density ≈2 × 10²² cm⁻².

The 8 μm optical depth is related to τ_1.1 by the ratio of the dust opacities in the two bandpasses, R_κ = κ₈/κ_1.1. We calculated the mid-infrared dust opacity by assuming a dust emission spectrum including PAH molecules (Draine & Li 2007), finding the average attenuated intensity across IRAC Band 4, and extracting a band-averaged opacity κ₈ = 825 cm² g⁻¹ of dust (see Appendix A). At the 33'' resolution of the BGPS, the beam-averaged 8 μm optical depth is therefore

$$\begin{eqnarray} \tau _{8} &=& \frac{R_\kappa }{B_{{1.1}}(T_d) \ \Omega _{{\mathrm{BGPS}}}}\ S_{{1.1}} = \Upsilon (T_d) \ S_{{1.1}} \nonumber \\ &=& 0.778\ \left(\frac{e^{13.0\ \mathrm{K}/ T_d}-1}{e^{13.0\ \mathrm{K}/20.0\ \mathrm{K}}-1} \right) \left(\frac{S_{{1.1}}}{\mathrm{1\ Jy}} \right). \end{eqnarray} \tag{ 9 }$$

The function ϒ(T_d) has units of inverse flux density, and is normalized to 20 K in Equation (9). Because τ₈ is a function of R_κ (i.e., both millimeter-wave emission and mid-infrared absorption depend only on the dust), the gas-to-dust ratio is not relevant to the distance estimation method. Owing to the nearly three orders of magnitude difference in dust opacity between the millimeter and mid-infrared, a value of τ₈ = 0.1 corresponds to a column of only N(H₂) ≈ 3 × 10²¹ cm⁻², assuming A_[8μ]/A_V ≈ 0.05 (Indebetouw et al. 2005; Román-Zúñiga et al. 2007). Therefore, molecular cloud clumps with column densities ≳ 10²² cm⁻² will be mostly opaque at λ = 8 μm.

Using Equation (9) to obtain an 8 μm optical depth requires a dust temperature (T_d). Since we are ignorant of T_d within each molecular cloud clump used in this study, we assumed that all sources are at the same temperature. Battersby et al. (2011) showed that mid-infrared-dark molecular cloud clumps generally span the temperature range 15 K ≲ T_d ≲ 25 K. Therefore, T_d = 20 K is a reasonable representation for BGPS sources as a group. Variation of the assumed T_d affects the KDA resolutions for some sources, and is discussed briefly in Section 6.1.1. With molecular cloud clump dust temperatures derived from Herschel Hi-GAL data, more precise DPDFs for individual objects may be derived using the present methodology.

Absorption features seen at λ = 8 μm are assumed to be the result of dense clouds immersed in a smooth emission distribution, punctuated by regions undergoing active star formation. While small-scale structures are difficult to model, the broader diffuse emission is a more tractable problem. Creation of synthetic 8 μm images via Equation (7) requires a three-dimensional model for the Galactic 8 μm emission distribution.

The recent numerical Galactic stellar and dust emission model of Robitaille et al. (2012, hereafter R12), computed using the Monte-Carlo three-dimensional radiative transfer code Hyperion¹² (Robitaille 2011), offers a self-consistent estimate of diffuse Galactic emission that is well-matched to observed quantities. We used the final model presented in R12, whose parameters were chosen to fit the Galactic latitude and longitude intensity distributions from seven bandpasses in the mid- to far-infrared. This model features two major and two minor spiral arms with Gaussian radial profiles, a lack of dust in the inner few kiloparsecs of the Galactic disk (dust hole; correlated with the dearth of molecular gas in this region), and a modified PAH abundance relative to the favored model from Draine & Li (2007). An analysis of the contributions from various stellar populations and dust grain sizes to the total intensity in each bandpass indicates that some 96% of the emission detected in IRAC Band 4 images comes from PAH molecules (R12).

A three-dimensional (ℓ, b, d_☉) data cube of 8 μm emission was generated from the radiative transfer code using model grid and image parameters slightly modified from those used by Robitaille et al. Table 2 lists the comparison of Hyperion input parameters between R12 and the present study. Primary differences include an increase in azimuthal resolution of the cylindrical grid, a restriction of the vertical extent of the grid to |z| ⩽ 1 kpc (to match the region of the Galactic plane probed by the latitude range |b| ⩽ 1°), and limiting the wavelength range used in computing output images. The model was computed within a box 30 kpc on a side, containing the entire modeled stellar disk (R12); a face-on view of the model Milky Way as seen from the north Galactic pole is shown in Figure 1. Lines of sight out to 20 kpc (the distance used for DPDF generation) lie entirely within the simulation box for |ℓ| ⩽ 48°. Beyond this longitude, however, the edge of the box retreats to only d_☉ ≈ 16.5 kpc by |ℓ| = 65°.

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A series of (ℓ, b) images of the Galactic plane containing only emission between the observer and some distance d_i were computed with a useful Hyperion feature, using a resolution of 3' in latitude, and 15' in longitude for computational reasons. Images were computed for each of 22 wavelength bins logarithmically spaced from 6 to 10 μm (closely matching the wavelength bins used by R12 for this part of the spectrum), and were then convolved with the IRAC Band 4 transmission curve to yield a single simulated Spitzer image (see Robitaille et al. 2007 for complete details). The three-dimensional image was constructed by stepping d_i outward in 100 pc intervals and depicts the cumulative 8 μm emission out to each d_i. The resulting cube comprises 200 steps, with the final image slice including all model emission to the edge of the box, equivalent to the collapsed profiles presented in R12.

Hyperion cannot treat sources individually, but rather uses "diffuse" sources of emission in each grid cell. These diffuse sources are generated from the probability of emission from various populations of stars and similar objects (e.g., planetary nebulae, H ii regions), assigned a spectrum corresponding to the appropriate spectral class, and given a total luminosity based on the number of "real" sources the cell represents. While most of the emitting populations have a smooth spatial distribution, relatively rare sources with concentrated emission at λ = 8 μm (such as H ii regions) are sprinkled throughout the box according to the underlying stellar distribution model. Very nearby objects (d_☉ ⩽ 0.5 kpc) appear quite bright, and cause "hot-pixel" effects in the computed images of the Galactic plane. These objects blend into the background for images computed from large Galactocentric position (e.g., Figure 1), or are averaged out in collapsed longitude or latitude distributions (R12). To ameliorate the effect of these objects in the computed (ℓ, b) images, we ran seven realizations of the model, each with a different random-number seed, then median-combined the realizations of each d_i slice. Since the underlying distribution of sources is fixed, nearby bright sources often appear in the same pixel in the output images; the number of realizations was chosen to be large enough such that median combining the realizations removes most of these outliers. To eliminate any remaining outliers and reduce noise, the combined (ℓ, b) images were median smoothed with a 3 pixel × 3 pixel box.

The foreground fraction was computed from the intensity cubes by dividing each (ℓ, b) image slice by the final slice. The final fits data cubes of 8 μm intensity and f_fore for both the northern and southern Galactic plane (|ℓ| ⩽ 65°) are publicly available with the BGPS archive. To illustrate the Galactic features present in the modeled cube, f_fore(ℓ, d_☉) for the northern plane along b = 0° is shown in Figure 2, with contours and gray scale representing its value from 0 to 1. Since PAH molecules contribute the bulk of the model emission, the dust hole towards low longitude is visible as a flattening of f_fore(d_☉). The Molecular Ring/Scutum tangent at ℓ ≈ 30° appears where f_fore grows quickly as a function of distance. The limited distance range caused by the model box size is represented by the 1.0 contour for ℓ ≳ 48°. The tangent distance as a function of longitude (black dashed line) spans the range 0.45 ≲ f_fore ≲ 0.6, implying that clouds that are optically thick in the mid-infrared should be visible beyond d_tan.

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Synthetic images (I_emaf) for a given BGPS object is computed using Equation (7). The optical depth was modeled as a two-dimensional image, constructed by applying Equation (9) to the BGPS map data. The estimate of the total mid-infrared emission (I_MIR) is also a two-dimensional image, and its creation is discussed below. Because of the coarse resolution of the f_fore model, we simply extracted the one-dimensional f_fore(d_☉) at the (ℓ, b) of the BGPS object. The combination of these elements yields a cube of synthetic data to be compared with the processed GLIMPSE images.

We derived posterior DPDFs for the subset of BGPS sources that have a measured v_LSR from molecular spectroscopy, and are selected by the presence of an EMAF. Spatially, this set is defined by the GLIMPSE-BGPS overlap, limiting the upper end of the Galactic plane at ℓ = 6525 and a latitude spread of |b| ⩽ 10. Kinematic considerations restrict the regions of the ℓ − v diagram (Figure 5) that may be considered at lower Galactic longitude down to the ℓ = 75 limit of the spectroscopic surveys.

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The colored image in Figure 5 is the latitude-integrated ¹²CO(1–0) intensity from Dame et al. (2001), and is shown as an indicator of molecular gas location and kinematic conditions. The presence of a long Galactic bar (R_bar ∼ 4 kpc; Benjamin et al. 2005) implies significant non-circular motion at ℓ ≲ 30°. Regions at these longitudes in the ℓ–v diagram associated with the Molecular Ring feature (cf. Dame et al. 2001; Rodriguez-Fernandez & Combes 2008), however, are likely at R_gal ≳ 4 kpc. To include the Ring but exclude bar-related gas, we disallowed the two hashed regions in Figure 5. The upper region is bounded by v_LSR = (3.33 km s⁻¹)× ℓ(°) + 15 km s⁻¹, and includes the higher-velocity gas inside the Ring. The lower region excludes the 3 kpc expanding arm, and is bounded by v_LSR = (2.22 km s⁻¹)× ℓ(°) − 16.7 km s⁻¹. Both regions are defined only for ℓ ⩽ 21°. The upper hashed region does not extend past this point because the Molecular Ring feature extends to the tangent velocity at larger longitudes; the lower region is limited because the 3 kpc arm has its tangency here (Dame & Thaddeus 2008). There is likely overlap between Ring objects with nearly circular motions and objects in bar-related streaming orbits at 21° ⩽ ℓ ⩽ 30°, so kinematic distance estimates in this range, including those derived here, should be used with caution.

Black circles mark the locations of the BGPS molecular cloud clumps for which a DPDF_emaf was computed, and the histogram summarizes their longitude distribution. Stars mark the masers used for distance comparison (see Section 5.3.1).

Automated classification of dust-continuum-identified molecular cloud clumps as EMAFs was achieved using the mid-infrared contrast computed from the smoothed GLIMPSE images at the location of the BGPS source. The peak contrast was defined as

$$\begin{equation} C = 1 - \frac{I_\mathrm{min}}{\langle I_{\mathrm{MIR}} \rangle }, \end{equation} \tag{ 11 }$$

where the intensity values were measured from the processed postage-stamp images described in Section 4.2 for each Bolocat object. Due to the varied sizes and shapes of EMAFs, standardized intensities were measured in a 40'' aperture around the location of peak BGPS flux density (pink circles in Figure 3). The value of I_min is the minimum intensity within the aperture measured from the smoothed star-subtracted GLIMPSE image (Figure 3(c)), and 〈I_MIR〉 is the mean of the I_MIR postage-stamp image within 2' of the peak of millimeter flux density (cyan circle in Figure 3(d)). A preliminary contrast threshold of C ⩾ 0.01 was implemented in the automated source selection to minimize the number of spurious matches caused by unrelated variation in the GLIMPSE 8 μm mosaics. This threshold also rejects BGPS sources that are mid-infrared bright, as those objects have negative contrast.

All molecular cloud clumps meeting the above selection criteria were examined by eye to ensure their suitability for deriving a DPDF_emaf. Bolocat objects were not assigned a DPDF_emaf for the following types of deficiencies: (1) there was evidence of poor star subtraction contaminating I_min, (2) there was very bright mid-infrared emission (I_8μm ≳ 200 MJy sr⁻¹) within 2' of the location of peak BGPS flux density that could bleed into the 40'' aperture or significantly affect the IRAC scattering correction, (3) the postage-stamp estimate of I_MIR was contaminated by excessive bright emission or dark extinction, or (4) the morphology of dark regions in the GLIMPSE image clearly did not correspond to that of the millimeter emission. By-eye exclusion removed approximately 40% of sources meeting the initial automated selection criteria.

Properties of rejected sources were analyzed to reveal that nearly all very-low contrast sources were spurious matches (deficiency type 4, see above). Additionally, BGPS objects located in fields of locally very bright mid-infrared emission were almost all excluded from the final source list (types 2 and 3). As a result, the contrast cutoff was increased to C ⩾ 0.05, and two additional automated selection criteria were introduced. First, the restriction 〈I_MIR〉 ⩽ 100 MJy sr⁻¹ was placed to remove sources whose background estimate indicates significant disagreement with the 8 μm emission model, as large discrepancies may lead to improper distance estimates (type 3). Second, to automatically reject sources near very bright emission, the re-pixelated unsmoothed postage-stamp images were checked for pixels with I_8μm ⩾ 200 MJy sr⁻¹ within 2' of the image center; sources with more than 10 such (72) pixels were removed from consideration (type 2). These additions to the automated selection criteria led to fewer sources (only 28%) requiring by-eye removal, primarily due to poor star-subtraction (type 1) or complex emission structures that caused morphological mismatch (type 4).

The final source list contains 770 BGPS objects, and is presented in Table 3. EMAF-selected BGPS molecular cloud clumps are not drawn uniformly from the BGPS catalog. Comparisons of Galactic latitude and 40'' flux density distributions between this sample and the full Bolocat (within the spatial limits defined above) are shown in Figure 6. The latitude distribution of this sample follows that of the BGPS as a whole, including peaking below b = 0°. The offset is related to the Sun's vertical displacement above the Galactic midplane (Schuller et al. 2009; Rosolowsky et al. 2010). The only significant deviation is near b = 0°, where locally bright 8 μm emission along the midplane, excited by H ii regions and OB stars, obscures more distant molecular cloud clumps. The BGPS 40'' flux density histograms (Figure 6(b)) show that this sample contains, on average, brighter sources (median = 0.252 Jy) than the full Bolocat (median = 0.135 Jy). There are two likely origins of this bias. First, sources must have a v_LSR measurement from a dense-gas tracer; the HCO⁺ detection fraction, in particular, is a strong function of BGPS flux density (<20% for S_1.1 < 0.1 Jy; Y. L. Shirley et al. 2013, in preparation). Second, the selection criteria excluded sources with very low contrast or whose morphology does not correspond to dark regions in the GLIMPSE maps. Faint BGPS sources have low optical depth (S_1.1 = 0.1 Jy corresponds to τ₈ ≈ 0.07), and would be difficult to distinguish against the variable Galactic 8 μm background.

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Table 3. Observed and Derived Properties of EMAF-selected BGPS Molecular Cloud Clumps

BGPS V1.0 Catalog Propertiesa					Velocity Data		Mid-infrared	KDAc	PMLd	dMLe	$\bar{d}$f
Catalog	ℓ	b	S40b		vLSR	Reference
Number	(°)	(°)	(Jy)		(km s−1)		Contrast	Resol.		(kpc)	(kpc)
4638	30.990	0.329	0.186(0.048)		79.1	2	0.21(0.03)	N	0.88	$4.60^{+0.44}_{-0.40}$	...
4639	30.990	0.385	0.108(0.054)		78.7	2	0.08(0.03)	F	0.91	$9.88^{+0.38}_{-0.42}$	...
4650	31.016	−0.001	0.280(0.057)		74.5	1	0.25(0.04)	N	0.88	$4.46^{+0.42}_{-0.42}$	...
4653	31.026	−0.113	0.289(0.067)		76.8	1	0.40(0.03)	N	0.83	$4.50^{+0.52}_{-0.48}$	...
4655	31.032	0.783	0.267(0.110)		51.0	1	0.38(0.05)	N	0.99	$3.24^{+0.36}_{-0.36}$	...
4715	31.226	0.023	0.381(0.077)		74.5	1	0.40(0.02)	N	0.86	$4.40^{+0.48}_{-0.48}$	...
4749	31.342	−0.149	0.111(0.048)		42.0	1,3	0.15(0.03)	N	0.91	$2.84^{+0.44}_{-0.44}$	...
4769	31.432	0.167	0.117(0.039)		101.7	3	0.06(0.05)	U	0.51	...	...
4770	31.436	−0.103	0.122(0.039)		89.4	1,3	0.18(0.02)	U	0.70	...	...
4780	31.462	0.351	0.090(0.046)		97.3	3	0.09(0.01)	N	0.82	$5.56^{+0.72}_{-0.56}$	...
4781	31.466	0.185	0.255(0.054)		103.6	3	0.19(0.08)	U	0.70	...	...
4794	31.516	0.449	0.184(0.048)		83.7	3	0.11(0.04)	N	0.91	$4.94^{+0.42}_{-0.40}$	...
4811	31.580	0.227	0.186(0.048)		115.7	1,3	0.14(0.06)	T	0.57	$7.00^{+0.78}_{-0.62}$	7.13(0.66)
4814	31.584	0.205	0.218(0.052)		114.9	3	0.15(0.04)	T	0.61	$6.88^{+0.82}_{-0.56}$	7.07(0.66)
4826	31.608	0.171	0.120(0.042)		105.4	3	0.10(0.03)	U	0.60	...	...

Notes. Errors are given in parentheses. ^aRosolowsky et al. (2010). ^bFlux density and uncertainty within a 40'' aperture, corrected by the factor of 1.5 ± 0.15 from Aguirre et al. (2011). ^cN: near; F: far; T: tangent point; U: unconstrained distance. ^dIntegrated posterior DPDF on the side of d_tan containing d_ML. Larger values indicate higher certainty in the KDA resolution. ^eMaximum-likelihood distance; the distance where the posterior DPDF is largest. Not listed for unconstrained sources. ^fWeighted-average distance; the first moment of the posterior DPDF. Only listed for sources at the tangent point. References. (1) HCO⁺(Y. L. Shirley et al. 2013, in preparation); (2) CS (Y. Shirley 2012, private communication); (3) NH₃ (Dunham et al. 2011).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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The distribution of measured mid-infrared source contrast is shown in Figure 6(c), and has a median of 0.19. For images without the IRAC scattering correction, this value corresponds to an uncorrected median contrast of 0.15 (see Appendix B), considerably lower than the minimum contrast (C ≈ 0.20) used by Peretto & Fuller (2009) in their catalog of Spitzer IRDCs (which did not correct for IRAC scattering in the same manner). The majority of our sample consists of "low-contrast" sources that are missing from published catalogs of Galactic IRDCs.

We derived posterior DPDFs for the EMAF-selected BGPS sources by multiplying the kinematic distance DPDF by the two priors, and normalizing to unit total probability. By design, the prior DPDFs are broader than the peaks in DPDF_kin, so the resulting maximum-likelihood distances generally do not differ from the simple kinematic distances by more than ∼0.1 kpc. To gauge the strength of the KDA resolution, two statistics were defined: the maximum-likelihood probability (P_ML) as the integrated posterior DPDF on the d_ML side of the tangent point, and the full width of the 68.3% maximum-likelihood error bar (FW₆₈). The ranges of these statistics are 0.5 ⩽ P_ML ⩽1.0 and 0.2 kpc ≲ FW₆₈ ≲ 15 kpc, and a comparison between them for each object is shown in Figure 7. The nature of a double-peaked DPDF_kin leads to the sharp change in the distribution of FW₆₈ near P_ML = 0.78 (vertical dashed line). When the ratio of the peak probabilities of the kinematic distance peaks in the posterior DPDF becomes ≲ 3, the error bars must include both to enclose sufficient probability. For objects with P_ML ⩾ 0.78, the maximum-likelihood error bars enclose a single kinematic distance peak. We consider this set to have well-constrained distance estimates, and note that FW₆₈ ⩽ 2.3 kpc (horizontal dashed line). Objects with full-width error bars less than this value and are below the P_ML cutoff (lower left corner of Figure 7) are generally within ∼1 kpc of the tangent distance. Because of the limited distance range available to these sources, their distance estimates should also be considered well-constrained. Combining these sets, we adopted FW₆₈ ⩽ 2.3 kpc as the criteria for well-constrained distance estimates.

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Objects within a kiloparsec of d_tan have posterior DPDFs that are oftentimes asymmetric, and d_ML is not the best single-value representation of the distance. For these objects, we assigned them to the tangent distance group, and used $\bar{d}$ (and associated uncertainty) in the analysis that follows. A total of 618 sources in this sample have well-constrained distance estimates (80%). The KDA resolutions for these objects are recorded as "N" (near), "F" (far), or "T" (tangent distance) in Column 8 of Table 3; d_ML is listed in Column 10. The remaining objects are recorded as "U" (unconstrained) and have no distance estimate listed. For the tangent group, the weighted-average distance ($\bar{d}$) is listed in Column 11, and is the preferred distance representation for these objects (d_ML is shown for comparison only). DPDFs for all sources are available in the BGPS archive.

For the remaining discussion, we consider only the 618 mid-infrared-dark BGPS sources whose distances are well-constrained (as defined above). Of this set, 70 were placed beyond the tangent point, with another 25 near d_tan, indicating the significant possibility of detecting molecular cloud clumps at the far kinematic distance using mid-infrared absorption. The comparisons of latitude distribution, BGPS 40'' flux densities, and mid-infrared contrast between the near and far subsets are shown in Figure 8. For the purposes of this discussion, objects at the tangent distance are grouped with those at the far kinematic distance. The latitude distributions (panel (a)) are very similar, with the near group being slightly wider, owing to the latitude-limiting effect of DPDF$_{\mathrm{H}_2}$.

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The histograms of BGPS 40'' flux densities (Figure 8(b)) show that the far subset has a flatter distribution with a higher median than the near set. Since the source list for this study is mid-infrared-contrast limited, we do not expect to see low flux-density BGPS sources at the far distance; the low column density would not produce enough attenuation to be seen behind the significant foreground emission. The expected contrast as a function of heliocentric distance (represented by f_fore) may be computed by combining Equations (7), (9), and (11) into

$$\begin{equation} C = (1 - f_\mathrm{fore})(1 - e^{-\Upsilon S_{{1.1}}}), \end{equation} \tag{ 12 }$$

where I_emaf and I_MIR from Equation (7) are equivalent to I_min and 〈I_MIR〉 from Equation (11), respectively. A source with larger flux density may be at a farther d_☉ and still meet the contrast selection criterion.

Indeed, sources at the far kinematic distance have a lower median mid-infrared contrast (C = 0.11) than those at the near kinematic distance (C = 0.22), as shown in Figure 8(c). Of the 313 objects with C ⩾ 0.2, only 12 (4%) are placed at the far kinematic distance, reinforcing the notion that dark mid-infrared absorption features must lie relatively nearby. For comparison, of the 63 sources with C < 0.1, 40 (63%) were placed at the far kinematic distance, indicating that the majority of EMAFs with very low contrast are at or beyond the tangent point.

An interesting empirical predictor of KDA resolution is shown in Figure 9. The ratio of resolved heliocentric distance over d_tan is plotted against the ratio of BGPS 40'' flux density over the mid-infrared contrast. For BGPS data, there appears to be a boundary at S_1.1/C ≈ 2.5 that divides KDA resolutions. The exact value of this cutoff is dependent upon the (sub-)millimeter survey used, and there exists scatter across the boundary. It nevertheless suggests an additional means for KDA resolution when DPDF_emaf fails to return a well-constrained estimate.

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With well-constrained distance estimates, it is possible to construct a face-on view of the Milky Way. Sources with well-constrained KDA resolutions are plotted atop a reconstruction of the Milky Way from Spitzer data in Figure 10 (R. Hurt: NASA/JPL-Caltech/SSC) using either d_ML or $\bar{d}$ as described in Section 5.2.1. For clarity, the error bars, which account for small deviations from circular motion, are not shown. Some spiral structure is evident in the map of BGPS sources, notably portions of the Sagittarius Arm at ℓ ≳ 35°, the Scutum–Centaurus Arm/Molecular Ring at ℓ ≲ 30°, and the local arm/Orion spur within about a kiloparsec of the Sun (Churchwell et al. 2009). The kinematic restrictions on our sample led to the absence of objects within a ≈4.0 kpc radius of the Galactic center (dashed circle in the figure). Face-on views of the Galaxy derived from kinematic distances will not show narrow spiral features (like those in the background image) because of the local virial motions of individual molecular cloud clumps within larger complexes. Galactocentric positions are therefore "smeared-out" by approximately ±0.4 kpc about the true kinematic distance for the complex as a whole. Each dot in the figure, however, should be thought of in terms of its DPDF, where the kinematic distance peaks have a FWHM of 1–2 kpc.

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KDA resolutions also allow the derivation of the vertical distribution of sources about the Galactic midplane. Vertical position is particularly affected by the KDA for higher-latitude sources (|b| ≳ 04). Calculation of vertical height (z) requires a proper accounting of the Sun's ≈25 pc vertical offset above the Galactic plane (Humphreys & Larsen 1995; Jurić et al. 2008). The small scale height of Galactic molecular gas can lead to incorrect inferences about the vertical distribution of dense gas in the disk if z positions are calculated directly from Galactic coordinates without a correction for the solar offset. The matrix needed to transform (ℓ, b, d) into (R_gal, ϕ, z) is derived in Appendix C.

The vertical distribution for the set of well-constrained BGPS sources is shown in Figure 11. A Gaussian fit to the distribution yields a HWHM of 25 pc, and a positive centroid offset of 7 pc. This scale height is approximately half that found by Bronfman et al. (1988) for ¹²CO. This narrow result may, however, be a result of the limited Galactic latitude coverage of the BGPS. Analysis of the recent compact source catalog from the λ = 870 μm ATLASGAL survey (Contreras et al. 2013), which extends to |b| = 1°, shows that ≈20% of their objects lie outside the BGPS latitude limits. To gauge the effect of limited latitude coverage, the derived z are plotted against heliocentric distance in Figure 12, with |b| = 05 shown for ℓ = 30° (the limits rotate to slightly more positive z for larger ℓ). For the region d_☉  ⩽  6 kpc (which contains more than 80% of this sample), the BGPS does not fully probe the FWHM of the ¹²CO distribution (dot-dashed lines). Other indicators of a larger scale height for star-formation regions include ¹³CO clouds from the GRS (Roman-Duval et al. 2009), which have a FWHM  ≈  80 pc, and Galactic H ii regions (FWHM ≈100 pc; Anderson et al. 2012).

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Maser parallax measurements towards regions of high-mass star formation provide absolute distance validation comparisons. The Bar and Spiral Structure Legacy Survey (BeSSeL; Brunthaler et al. 2011) is conducting ongoing very long baseline interferometry (VLBI) parallax measurements of CH₃OH and H₂O maser emission in star-forming regions across the Galactic plane. Such measurements provide very accurate distances out to d_☉ ∼ 10 kpc, but the present overlap between published results and the BGPS is small (see Table 4 for the comparison set of maser sources used).

Table 4. Maser Sources for Distance Comparison

Source	ℓ	b	vLSR	Distance	NBGPSa	Reference
Name	(°)	(°)	(km s−1)	(kpc)
G23.0−0.4	23.01	−0.41	81.5	$4.6^{+0.4}_{-0.3}$	6	1
G23.4−0.2	23.44	−0.18	97.6	$5.9^{+1.4}_{-0.9 }$	2	1
G23.6−0.1	23.66	−0.13	82.6	$3.2^{+0.5}_{-0.4}$	2	2
W51 IRS2	49.49	−0.37	56.4	$5.1^{+2.9}_{-1.4}$	1	3
W51 Mainb	49.49	−0.39	58.0	$5.4^{+0.3}_{-0.3}$	1	4

Notes. ^aNumber of EMAF-selected BGPS sources within 15' and 10 km s⁻¹ of the maser location. See Figure 13 for comparison. ^bH₂O maser; all others are CH₃OH masers. References. (1) Brunthaler et al. 2009; (2) Bartkiewicz et al. 2008; (3) Xu et al. 2009; (4) Sato et al. 2010.

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The comparison set was defined as objects from our sample whose angular separations and velocity differences were ⩽15' and ⩽10 km s⁻¹, respectively, from those of a published maser. These masers tend to be in regions of high-mass star formation, and such regions are on the order of 025 in size. The velocity limit is related to the spread of virial velocities within such regions. A collection of 12 BGPS objects were associated with one of five masers; the distribution is noted in Table 4. To visualize the distance comparison, distances from Table 3 for each BGPS object are plotted against the measurements from the BeSSeL literature as magenta triangles in Figure 13. The gray dashed lines in the left panel represent ±1 kpc error margins, used for qualitative purposes. An object falling outside this region is said to have a "mismatching" distance estimate. For clarity in the figure, only mismatching objects have error bars shown; horizontal bars are from Table 3, and vertical bars are from the reference. The right panel is a zoom-in on the Δd = ± 1 kpc region of the left panel (i.e., within the dashed lines).

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For the maser comparison set, only three sources fall outside the ±1 kpc region. Two BGPS objects (overlapping triangles in Figure 13) are associated with the maser source G23.66−0.13, which has a parallax distance that disagrees with the derived (near) kinematic distance. Bartkiewicz et al. (2008) find that this object has a proper motion consistent with the parallax distance and the assumption of a flat rotation curve, but has a ≈35 km s⁻¹ peculiar motion toward the Galactic center. This radial streaming motion makes its kinematic distance appear larger, and provides a cautionary example of the effects of non-circular motion on kinematic distance methods. The other mismatching source has a DPDF distance estimate skewed away from the simple kinematic distance due to the sharply peaked DPDF_emaf caused by its bright millimeter flux density (S_1.1 = 3.9 Jy). The W51 region lies near the tangent point, so correct DPDF distance placement for these objects merely implies that the region's circular velocity is consistent with the rotation curve. The remaining EMAF-selected BGPS objects in this set have KDA resolutions that agree with the trigonometric parallax distance.

For a larger distance comparison set, we used the KDA resolutions from the BU-FCRAO GRS (Jackson et al. 2006). By matching ¹³CO(1–0) emission morphology and spectra with H i absorption features, Roman-Duval et al. (2009) estimated the distances to some 750 molecular clouds in the inner Galaxy. Those authors used a combination of H i self-absorption (HISA)¹³ and 21 cm continuum absorption features to positively resolve the KDA. These techniques exploit the spectroscopic dimension of H i surveys, where cold atomic hydrogen within dense molecular gas absorbs line emission from warm gas at the same v_LSR on the far side of the Galaxy or continuum radiation from H ii regions. Distance resolutions from this method are subject to uncertainties from non-circular and radial streaming motions, but are directly comparable with the KDA resolutions of the DPDF method.

EMAF-selected BGPS objects were associated with cataloged ¹³CO clouds based on spatial and kinematic proximity. The association volume was defined as a circle of radius 10' (approximately the median size of a GRS cloud; Roman-Duval et al. 2009), and a velocity spread equal to the ¹³CO velocity dispersion, centered on the (ℓ, b,v_LSR) coordinates from the GRS catalog. A total of 213 EMAFs lie within the association volume of one or more GRS clouds. To ensure the accuracy of the associated GRS KDA resolution, BGPS flux density maps were compared to both ¹³CO intensity maps integrated over the velocity of the appropriate dense-gas tracer from Table 1, and H i 21 cm "on"–"off" integrated intensity (HISA) maps. For a handful of sources (∼7%), a strong HISA signature was present within the BGPS source contour even though the associated GRS cloud was placed at the far kinematic distance. None of these objects was listed as having a 21 cm continuum source, so the absorption signature is the result of cold gas at the near distance. These discrepant objects may be the result of line-of-sight confusion, a slight velocity offset between the parent cloud and the BGPS object, or incorrect association with a ¹³CO cloud. Whatever the cause, the KDA resolution for the associated GRS cloud was amended to "near" to reflect the HISA signature.

Roman-Duval et al. used the Clemens (1985) curve to derive heliocentric distances, and differences in rotation curve definition can cause distance-comparison discrepancies unrelated to the KDA (see Figure 5). To eliminate potential systematic effects, the KDA resolution and v_LSR of each associated GRS cloud were mapped to a new heliocentric distance using the Reid et al. (2009) rotation curve. In the comparison between the GRS-derived distance and those from the DPDFs (black dots in Figure 13), nearly 92% of our distance resolutions match those of the GRS. This success rate is robust for the entire EMAF set, as enforcing a minimum mid-infrared contrast of C ⩾ 0.15 only increases the matching rate to 94%.

The 17 BGPS objects with mismatching distance resolutions are shown with horizontal error bars from the DPDFs. Those in the upper left of Figure 13 have a large apparent mid-infrared absorbing column, but Roman-Duval et al. (2009) did not find evidence of self-absorbing H i. Conversely, those in the bottom right have HISA signatures but were placed beyond the tangent point by the posterior DPDF. Examination by eye of this latter group showed that the two sources farthest from the one-to-one line have slight underestimates of I_MIR around the EMAF; the values in the postage-stamp image reflect dimmer nearby regions. The DPDF_emaf in these cases selects the far kinematic distance peak despite the presence of HISA for these objects.

There are four objects whose GRS distance estimate is 5.5 kpc ⩾ d_☉ ⩾ 8 kpc and disagree with the DPDF-derived distance. These all lie within ∼1.5 kpc of the tangent point. Since the kinematic distance DPDFs do not have two fully distinct peaks in this region, the particular shape of DPDF_emaf can have a significant impact on the derived single-distance estimators. The mismatches are due to the source being near d_tan, and not an incorrect KDA resolution. The remaining 11 mismatching sources in the upper left of Figure 13 (GRS-far, DPDF_emaf-near) are moderately dark EMAFs (0.1 ⩽ C ⩽ 0.3) that show no signs of HISA at the velocity of the molecular cloud clump. About half of these lie at |b| ⩾ 04, and may not have enough H i backlighting at the far kinematic distance for a HISA signature to be visible; although Gibson et al. (2005) found self-absorption features out to more than |b| = 2° in the Canadian (H i) Galactic Plane Survey. For sources in this quadrant of the figure, it is unclear which kinematic distance is correct. The future application of additional prior DPDFs may solve the small number of conflicting KDA resolutions, but the present method achieves very good correspondence with other distance estimates for molecular cloud clumps.

Using a technique for measuring three-dimensional near-infrared Galactic extinction (NIREX; Marshall et al. 2006), Marshall et al. (2009) estimated the distances to over 1200 IRDCs identified by the Midcourse Space Experiment (MSX) in the inner Galactic plane (Simon et al. 2006, hereafter S06). This approach compares the stellar colors of a section of sky with a Galactic stellar distribution model, and searches for sharp changes in color excess as a function of distance. Extinction measurements, like maser parallaxes, offer a kinematic-independent means of distance determination.

MSX dark clouds have a typical size of about an arcminute, so BGPS sources lying within 60'' of the centroid of a NIREX cloud were included in this comparison set. While there are about 275 objects from Marshall et al. (2009) within the spatial bounds of this study, only 38 EMAF-selected BGPS sources could be associated with a NIREX cloud. Peretto & Fuller (2009, hereafter PF09) noted that only a quarter of MSX IRDCs appear in their catalog of Spitzer dark clouds for a variety of reasons. This selection effect, in combination with our requirement that an object be detected in one or more molecular line transitions, makes the number of matching clouds reasonable.

Objects from the NIREX comparison set are shown as cyan diamonds in Figure 13. Most of the points lie within 2 kpc of equality. Only one object has a wildly divergent distance estimate, G31.026−0.113 (BGPS 4653; d_NIREX ≈ 9.5 kpc), which has C = 0.4 and should have been detected with a strong near-infrared absorption signature at the near kinematic distance of d_☉ = 4.5 kpc. The collection of cyan diamonds with a systemic positive offset of 1.5 kpc warrants attention. There is a cluster of objects placed 2–4 kpc from the Sun. Most of these are at ℓ ≲ 15°, and uncertainties in both the rotation curve and stellar model in that region may be contributing to the offset. Mismatching NIREX distances beyond d_☉= 4 kpc have divergent distance estimates of order the difference between the Clemens (1985) and Reid et al. (2009) rotation curves for objects at that velocity.

The combination of millimeter-wave thermal dust emission observations with mid-infrared extinction is a powerful method for resolving the KDA for molecular cloud clumps. By starting from a catalog of (sub-)millimeter sources, this method is not limited to mid-infrared-identified IRDCs (catalogs of which often have large minimum contrast). We are therefore able to include low-column nearby sources as well as more distant objects. The 92% success rate compared to distances resolutions by the GRS team indicates that EMAFs can provide a powerful means for distance discrimination. Additionally, BGPS objects placed at the far kinematic distance that agree with the GRS distance indicate that EMAFs are visible beyond the tangent point with sufficient backlighting. In comparison with the HISA KDA-resolution technique employed by Roman-Duval et al. (2009), only 4% of BGPS objects were placed at the near kinematic distance yet had no evidence of a HISA signature. Application of additional prior DPDFs may help to resolve these discrepancies.

The mid-infrared contrast distributions (Figure 8(c)) of objects on either side of d_tan clearly show that objects placed at or beyond the tangent point have lower collective contrast, and would likely not be included in catalogs of IRDCs. These distributions are consistent with the notion that dark IRDCs (C ≳ 0.2) are nearby. Since the matching rate between DPDF-derived distances and those of the GRS is nearly independent of mid-infrared contrast, the present method extends robust KDA resolution to EMAFs with lower contrast, roughly doubling the number of molecular cloud clumps for which well-constrained distances may be derived.

In addition to improving upon the axiom "if IRDC then near" for KDA resolution, this method automatically accounts for the profile of the 8 μm intensity as a function of Galactic longitude (Figure 2). The morphological matching process does not consider d_tan, and therefore offers a prior probability that is independent of the kinematic signature of a given object. The f_fore limit of visibility for a molecular cloud clump is simply a function of optical depth (Equation (12)); for instance, an object with S_1.1 = 0.3 Jy will have C ⩾ 0.05 for f_fore  ⩽  0.76, but one with S_1.1 = 0.1 Jy will not meet this contrast threshold if f_fore exceeds 0.33.

Heightened star-formation activity, which produces excess 8 μm emission in its immediate vicinity, does constitute a complicating factor in application of simple radiative transfer (Equation (6)). These regions strain the assumption of smooth, axisymmetric Galactic emission. As an example, we analyzed the distance resolutions of objects in the W43 region. W43 is defined here by 315 ⩾ ℓ ⩾ 295, −05 ⩾ b ⩾03, and 80 km s⁻¹⩾ v_LSR ⩾ 110 km s⁻¹ (as in Nguyen Luong et al. 2011), and is marked by a white box in Figure 5. Of the 43 EMAF-selected BGPS sources with well-constrained distance estimates in this region, 9 are placed at or beyond the tangent distance by the DPDF method. This is a slightly higher rate than the general sample, but is not significant. The W43 objects are plotted as cyan squares in Figure 9, and obey the empirical S_1.1/C = 2.5 limit for near versus far distance discrimination (Section 5.2.2). Only eight objects could be associated with a GRS-identified ¹³CO cloud (Section 5.3.2), and all but one have matching KDA resolutions; the outlier is one of the BGPS objects near the tangent point, where $\bar{d}$ is used, causing the >1 kpc distance discrepancy. Although the observed Galactic plane consists of clumpy emission atop a more smooth Galactic emission pattern, the simple model used here still returns consistent KDA resolutions, even in more active regions.

While the KDA resolutions for EMAF-selected BGPS objects compare favorably with previously published distance estimates, they are still based upon the assumption of circular orbits about the Galactic center. As highlighted by the case of CH₃OH maser G23.66−0.13, radial streaming motions can have a significant impact upon the derived kinematic distances. Anderson et al. (2012) presents a detailed analysis of uncertainties involved with the use of kinematic distances in the presence of non-circular motions. Future improvements in kinematic distance measurements will require a full three-dimensional vector model of Galactic motions.

Throughout this analysis we used T_d = 20 K for converting BGPS flux densities into 8 μm optical depths. The effect of different assumed dust temperatures on KDA resolutions is not a priori predictable. Generating a new set of DPDF_emaf based on different temperatures, however, is straightforward. The results of KDA resolutions from the posterior DPDFs and GRS distance comparison statistics are shown in Table 5 for the range of T_d found by Battersby et al. (2011). A warmer dust temperature pushes more objects to the near kinematic distance to compensate for a smaller derived τ₈. Interestingly, the GRS success rate is unchanged for T_d = 25 K, but there are likely many unconsidered systematic effects at play.

The use of EMAFs as prior DPDFs for kinematic distance discrimination is directly applicable to all current and future (sub-)millimeter surveys of the Galactic plane. The advantage of starting with a sample of continuum-identified molecular cloud clumps is that mid-infrared extinction may be used to resolve the KDA for many objects that may not be dark enough to be included in IRDC catalogs (e.g., S06, PF09).

The DPDF formalism encodes all information about distance determinations for molecular cloud clumps, including likely distance and uncertainty. For some purposes, however, it is useful to have a single distance; Section 3.2 describes two possible options. In the use of the DPDFs produced here, it became apparent that different distance estimates were best applied to different situations. Examples of these situations are shown in Figure 14 to illustrate the difficulties encountered in extracting a single distance from a DPDF. For each panel, the black triangle and magenta diamond mark d_ML and $\bar{d}$, respectively.

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The most common situation has well-separated kinematic distance peaks (i.e., the molecular cloud clump is far from d_tan) and the probability ratio of the two peaks is also large (i.e., P_ML ⩾0.78). The example BGPS 4484 (G030.629−00.029) is depicted in Figure 14(a). These objects fall under the "well-constrained" condition described in Section 5.2.1, whereby the maximum-likelihood error bars encompass only one kinematic distance peak. For this set of objects, d_ML is a reasonable collapse of the DPDF into a single value (with uncertainty). The second set of objects are those with kinematic distances within a kiloparsec of the tangent point. The kinematic distance DPDF for these objects have a shallow saddle feature at d_tan, as seen in Figure 14(b) for BGPS 4357 (G030.321+00.292). Since the main peak of the posterior DPDF is not symmetric, d_ML is not a robust reflection of the distance estimate. Therefore, we recommend using $\bar{d}$ for these sources (listed in Table 3 for this class of object) to more accurately reflect the available distance information. Thus, as long as the full-width of the error bars is less than 2.3 kpc (Section 5.2.1), these sources are considered to have well-constrained distance estimates. The final set of sources are those not meeting either of the above criteria, such as BGPS 3352 (G024.533−00.182; Figure 14(c)). The kinematic distance options are well-separated, but the DPDF_emaf does not place a strong discriminatory constraint. If it is desirable to use the distances for these sources, we recommend Monte Carlo sampling distances from the full DPDF in order to include all distance information about the source (see Section 3.3).

Regardless of the method used, however, care should be taken to properly propagate the uncertainty in the distance placement. If only sources in the first category are used, it is important to remember that matching success rate with GRS-derived distances was ≈92%. This may be interpreted either as two sources in 25 were placed at the wrong distance or that there is a 92% confidence in each of the distance placements.

A quick glance at the GLIMPSE mosaics suggests that the Galactic distribution of 8 μm light cannot be described simply by a smooth, diffuse model. Distances derived using the assumption of smooth emission, however, compare favorably to those derived from 21 cm H i absorption (GRS; Roman-Duval et al. 2009) and near-infrared extinction mapping (NIREX; Marshall et al. 2009). These results suggest that Galactic 8 μm emission may be primarily composed of a diffuse component punctuated by regions of active star formation. The R12 model of mid- and far-infrared emission is a greatly simplified reflection of the Galaxy, neglecting to account for individual small-scale features. Yet its match, spatially and spectrally, to existing Galactic plane observations indicates its power. The model, therefore, provides a solid basis for our distance estimation technique based on using a broad distance prior to distinguish between kinematic distance peaks.

While the R12 model was constructed to broadly match the multi-band observations of the Milky Way, it is useful to also compare it with external galaxies. Spitzer observations of SINGS galaxies (Kennicutt et al. 2003) yield a surface density of in-band emission. Figure 16 depicts the IRAC Band 4 surface brightness, normalized to R_gal = 8.5 kpc, for a collection of 17 SINGS galaxies, with galaxies represented by their Hubble stage (T).¹⁴ To enable comparison, the R12 model was viewed externally (see Figure 1) and emission was annularly integrated, following the SINGS analysis; plotted as a thick black line. The slope of the Milky Way model at R_gal ≳ 4 kpc is comparable to the ensemble, but the drop in emission due to the dust hole carved out by R12 near the Galactic center does not seem to match extragalactic observations. The model was designed to match observations from within the disk from the Sun's location, however, so discrepancies in the integrated 8 μm emission profile in the inner R_gal ⩽ 3 kpc are likely not relevant.

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Recent large (sub-)millimeter Galactic plane surveys are making it possible to trace the spiral structure of the disk. Comparing the well-constrained KDA resolutions of BGPS sources with an artist's conception of the Galaxy based on Spitzer data (Figure 10), glimmers of organization begin to appear. While the regions that trigger the collapse of molecular cloud clumps are likely very localized along spiral density waves, features in the face-on map of the Galaxy derived from kinematic distances are quite smeared out. Even small (≈5 km s⁻¹) peculiar motions can lead to ≈0.4 kpc variations in heliocentric position, making it difficult to precisely trace the locations of spiral features.

Two major features suggest themselves from the data in Figure 10: one near and one far. First, the nearby collection of sources at ℓ ≲ 30° seem to form part of a round feature that extends into the fourth quadrant. This feature has been identified as both the Molecular Ring (cf. Dame et al. 2001) and the Scutum–Centaurus Arm (cf. Dobbs & Burkert 2012). It is not possible to distinguish between these postulates in the northern plane; careful distance determinations for southern sources is required. Mapping the exact location of where this feature meets the long Galactic bar also depends on choice of rotation curve (the Clemens 1985 curve places this collection of sources at the tangent distance, whereas the Reid et al. 2009 curve does not), and may also be influenced by non-circular motions. Parallax measurements to masers in this region will help establish a benchmark for the long Galactic bar, including position angle with respect to the Sun–Galactic center line.

The other feature to note in Figure 10 is the Sagittarius Arm beyond the tangent circle (smaller dotted circle). These molecular cloud clumps are visible at the far kinematic distance because of backlighting provided by the Perseus Arm. By the same token, BGPS sources in the Perseus Arm are not visible as EMAFs due to both the large amount of 8 μm light in the foreground and the lack of any significant backlighting source. We note a collection of sources around ℓ ∼ 30° which appear at the far kinematic distance. In the underlying image, there is a void between the Sagittarius Arm and the long Galactic bar. The two possibilities, therefore, are the existence of an arm structure at that location or that those sources were improperly assigned the far kinematic distance. The analysis of the W43 region, however, suggests that active regions do not significantly misplace molecular cloud clumps at the far kinematic distance, so distinguishing between the possibilities is unclear.