A CLASSIFICATION SCHEME FOR YOUNG STELLAR OBJECTS USING THE WIDE-FIELD INFRARED SURVEY EXPLORER AllWISE CATALOG: REVEALING LOW-DENSITY STAR FORMATION IN THE OUTER GALAXY

In order to understand how WISE in general, and specifically the AllWISE point-source extraction, perform in Galactic star-forming regions, we analyzed two test regions covering parts of the W3 and W5 giant molecular clouds and part of the W4 region (Westerhout 1958). Both the W3/W4 and W5 test fields encompass on-cloud, bright, nebular emission and off-cloud, lower background regions in their neighboring, ionized H ii regions. The W3/W4 field (from here on referred to as just the "W3" field) additionally incorporates a dark lane or infrared dark cloud. To clarify the following discussion, we adopt lowercase italics to refer to the four WISE bands, w1, w2, w3, and w4, and uppercase W3, W4, and W5, to refer to the massive star-forming regions.

To estimate the maximum potential completeness of WISE in Galactic star-forming regions like W3, W4, and W5, we start by constructing a "truth" catalog for each band for each field from the large WISE mosaics of W3, 4, and 5 made by K12 from raw WISE frames, since these have slightly higher resolution than the WISE atlas tiles available online. This property of the WISE image atlas tiles is due to the co-addition process that slightly smoothes these images to optimize them for point-source detection, but degrades their angular resolution by a factor of $\sqrt{2}$ (see the AllWISE Explanatory Supplement, section IV.4.l). We search our images for point sources in the test fields by eye, verifying these with reference to the Spitzer images of Koenig et al. (2008) for W5 and mosaics from the Spitzer Heritage Archive⁴ for W3. The Spitzer IRAC 3.6 and 4.5 μm and MIPS 24 μm images are a close match to WISE bands 1, 2, and 4. The IRAC 8 μm band is not an exact match to WISE band 3 at 12 μm, but is close enough in wavelength that bright point sources in these Spitzer images are similarly evident in WISE 12 μm images, allowing a determination if an apparent WISE band 3 point source is in fact a nebular emission knot when seen at the higher sensitivity and resolution of Spitzer. In the following discussion, we refer to objects in this list and their matched entries in the WISE photometric database as "real" sources, while objects in the database with no match in the truth catalog in a given band are referred to as "fake" or "spurious" sources.

Since the point-source density varies strongly with waveband, the size of the region surveyed by eye is different between bands. Table 1 lists the test field locations and source sample sizes.

The nominal 95% completeness listed for the WISE survey in the Explanatory Supplement is appropriate for high Galactic latitude fields with |b| > 30°. In magnitudes, the values are w1 = 17.1, w2 = 15.7, w3 = 11.6, and w4 = 7.7. In the Galactic Plane, as already mentioned, star-forming regions contain bright, structured emission from PAH molecules and dust grains excited and heated by radiation from nearby and embedded young stars (Li & Draine 2001) and extinction features like infrared dark clouds. The point-source density is also higher in the Galactic Plane and stars are frequently found in dense clusters. As described in Appendix A.1, we determine a measure of the magnitude at which 90% of sources that were detected by Spitzer in our test fields are found in the WISE images. Table 2 summarizes the results of this calculation. In regions of bright background, the intrinsic detection limit of WISE is lower, thus we generate a completeness estimate for regions of high- and low-sky background in each of our test regions. Because the WISE source list was determined by eye with no deblending capability, the true completeness may be slightly better than the quoted values.

The AllWISE source extraction pipeline is only able to retrieve a subset of the sources visible in Galactic Plane WISE images because of the issues described earlier. Table 1 lists the number of truth catalog sources found in the AllWISE catalog within 2'' (for w1 and w2) or 3'' (for w3 and w4) with non-null photometric error (the w?sigmpro column in the online table). We calculate the 90% magnitude completeness limit of the AllWISE source extraction in these test fields by comparing histograms of source magnitude of AllWISE objects that match the truth catalog (so as to filter off spurious detections), to the Spitzer catalogs for the same regions. The completeness estimates for AllWISE are presented in Table 3.

The "truth" catalog allows us to estimate the rates of contamination by fake sources in the AllWISE point-source catalog by band, on and off cloud in areas of high- and low-sky background, respectively. In each test field, we search for objects within 2'' (for w1 and w2) or 3'' (for w3 and w4) of our by-eye source lists. In Table 4, we present the number of objects that match the truth catalog with signal to noise ⩾5 in that band, in high- and low-sky regions, versus the number of objects with signal to noise ⩾5 in AllWISE that have no visible point source in that band in the test fields. In low-sky regions, the contamination in w1 and w2 is ≈10%, but in high-sky regions about one-third of sources above a signal-to-noise ratio (S/N) of 5 appear spurious. In the w3 and w4 bands, the vast majority of sources above S/N = 5 in the AllWISE catalog are likely spurious detections and simply represent upper limit measurements of the nebular background. At the same time, adding up the total number of real sources in Table 4, or looking at the final column in Table 1 also shows that in bands 1 and 2 only about one-third of all the sources visible in the images are detected by AllWISE at all (compare N_SRC and N_non-null in Table 1). In band 3, AllWISE picks up 50%–60% of truth catalog sources, while in band 4, AllWISE finds about three-fourths of truth catalog sources. We now look for parameters in the AllWISE data release that can help mitigate its unreliability as a YSO finding tool if used incautiously. At the same time we attempt to maintain a high retrieval rate of real sources.

We note that photometric quality flags that designate sources as upper limit detections exist in the AllWISE catalog in the $ph\_qual$ column. However, by requiring sources to have non-null photometric error as a first, basic requirement, we already implicitly allow $ph\_qual$ to be only "A", "B", or "C" in that band, or equivalently S/N > 2. In the key challenge of suppressing the huge amount of fake detections in bands 3 and 4, even requiring only $ph\_qual$ "A" sources only reduces the contamination rate to 85% and 94%, respectively. In bands 1 and 2, the contamination rate is already quite low (Table 4) and would only drop by a few percent by requiring $ph\_qual$ = "A" only.

3.1.1. Signal to noise and Chi-squared

The signal-to-noise (w?snr) and reduced chi-squared (w?rchi2) parameters given in the AllWISE photometric catalog give a strong discriminating power between real and fake point sources. The behavior of w?rchi2 versus w?snr in the two test fields in the four WISE bands is shown in Figure 1 and Figure 20 in the Appendix. Hereafter, we use $\chi _{\nu }^2$ and S/N to refer to reduced chi-squared and signal to noise, respectively.

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In general, the behavior seen in Figure 1 is consistent with the expectation that a true point source will have $\chi _{\nu }^2 \approx 1$ from the profile fitting procedure. Fake sources have $\chi _{\nu }^2 \approx 1$ at low signal to noise, but start to deviate away as the measured signal to noise increases. When examined in the WISE images, real sources with $\chi _{\nu }^2 > 2$ are crowded by nearby neighboring sources, are in regions of complex and/or bright background emission, or are extended.

We apply the following cuts in S/N versus $\chi _{\nu }^2$ space as shown in Figure 1 to suppress the fake component:

$$\begin{eqnarray} w1rchi2 & < & (w1snr - 3)/7 \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray} w2rchi2 & < & 0.1 \times w2snr - 0.3 \end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray} w3rchi2 & < & 0.125 \times w3snr - 1 \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} w4rchi2 & < & 0.2 \times w4snr - 2. \end{eqnarray} \tag{ 4 }$$

These criteria also allow some fraction of the real sources with high $\chi _{\nu }^2$ to be included. We tabulate the retrieval rate of real sources and the residual contamination rate by spurious catalog entries in Table 5. In this and the following subsections, our starting point for the retrieval rate is the final column of Table 1, so we implicitly always require that AllWISE sources in a given band have non-null photometric uncertainty w?sigmpro. For example, in band 1 in the W3 test field, Table 1 shows that we find 501 real sources with non-null w?sigmpro. Table 5 shows that ≈57% of these sources are retrieved by the band 1 S/N versus $\chi _{\nu }^2$ cut, and 3% of all the AllWISE sources that have non-null w?sigmpro and pass this cut are fake. With these parameters it is possible to suppress the contamination rate in any band down to <7%, although this success comes at a cost of cutting about two-thirds of the real sources in bands 3 and 4.

Table 5. Signal to Noise and Chi-squared

	Real Retrieval Rate		Residual Fake
Band	(%)		(% of total)
	W3	W5	W3	W5
1	56.9	74.8	3.1	3.8
2	60.0	78.3	5.5	4.8
3	23.7	32.1	4.3	6.4
4	41.1	34.3	1.4	6.5

Notes. Retrieval rates are given as the percentage of the real 'truth' catalog sources found in AllWISE with non-null photometric error, that are retrieved by the w?rchi2 versus w?snr selection criteria in Section 3.1.1. The residual fake columns are the percentage of all the sources allowed through by these criteria that are still fake/spurious.

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3.1.2. w?nm and w?m

3.1.3. nb and na

3.1.4. $cc\_flags$

3.1.5. Profile Fit versus Aperture Magnitudes

In this paper, our goal is to search for young stars with infrared excess emission which, given the techniques laid out in K12, requires that we obtain reliable photometry in at least three bands. The key parameters that appear to have the strongest discriminatory effect in suppressing fake source contamination in WISE bands w3 and w4 are S/N and $\chi _\nu ^2$. While combining many parameters to reduce fake sources as much as possible is appealing, the cost would be to sacrifice real sources we are interested in. Our approach is thus to mitigate contamination using only the criteria based on signal to noise and profile-fit reduced chi-squared. As noted in Section 3.1.1, the retrieval rate of real sources in bands 3 and 4 is poor using these criteria, so we recover low signal-to-noise sources in band 3 by allowing sources with 0.45 < w3rchi2 < 1.15 and w3snr > 5, which means our potential retrieval rate of real sources rises to about 60% in w3. Although such a decision also brings in a large quantity of fake detections, in our particular application, the observed WISE colors of young stars provide an additional discriminant for these objects. We use a 2'' search radius to find YSOs in the AllWISE catalog from the Taurus compilation of Rebull et al. (2010) and the transition disk objects (TDs) in Andrews et al. (2011) and Cieza et al. (2012). Transition disks are a subclass of young star with inner opacity holes in their disks and reduced levels of near infrared and/or mid-infrared excess emission. The color–color diagram shown in Figure 2 shows the distinct locations occupied by these known YSOs and catalog entries with fake w3 photometry in our test fields. Thus in searching for YSOs in WISE color space, we can avoid regions with a high probability of reliance on a spurious catalog entry.

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The uncertainty/signal-to-noise/chi-squared criteria we use in the following work are as follows. The color–magnitude criteria for YSOs follow in Section 4.

WISE band 1: non-null w1sigmpro and w1rchi2 < (w1snr − 3)/7.

WISE band 2: non-null w2sigmpro.

WISE band 3: w3snr ⩾ 5 and either: w3rchi2 < (w3snr − 8)/8 OR 0.45 < w3rchi2 < 1.15 (the approximate 1σ range of real-source w3rchi2 below the initial chi-squared, signal-to-noise cut).

WISE band 4: non-null w4sigmpro and w4rchi2 < (2 × w4snr − 20)/10.

We first remove objects from the catalog that are likely to be unresolved external galaxies. The requirements for their removal are similar to those of K12, but in this case based on sources found in the AllWISE catalog around the north and south Galactic Poles, which will likely consist mostly of galaxies and Galactic halo stars. We extract sources from circles of area 100 deg² centered on the poles by querying AllWISE for sources with |b| > 843558. Figure 4 shows a color–color diagram of objects detected in the north polar field (gray points). We overplot tracks showing the location of the galaxy spectral energy distribution (SED) templates of Assef et al. (2010). These templates are intended to reproduce the typical components of galaxies: old (E/"elliptical"), intermediate (Sbc/"spiral"), and young stellar populations (Im/"irregular"), as well as nuclear activity (AGNs, i.e., active galactic nuclei). Since these selection cuts rely on WISE bands 1, 2, and 3, we additionally apply the w3 photometry requirement of Section 3.2 and remove objects meeting all the following criteria as likely star-forming galaxies ("SFG" in Figure 3 and the region marked in the left panel of Figure 4):

$$\begin{eqnarray} w2-w3 & \;{>}\; & 2.3 \end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray} w1-w2 & \;{<}\; & 1.0 \end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray} w1-w2 & \;{<}\; & 0.46 \times (w2-w3) - 0.78 \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} w1 & \;{>}\; & 13.0 \end{eqnarray} \tag{ 8 }$$

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Likely broad-line AGNs are removed with a color–magnitude cut, see Figure 4 (right). We label those sources that meet the band 1, 2, and 3 requirements and either of the following sets of criteria as candidate AGNs:

$$\begin{eqnarray} w1 & \;{>}\; & 1.8 \times (w1-w3) + 4.1 \end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray} &&\hbox{and} \nonumber \\ w1 & \;{>}\; & 13.0 \qquad\qquad\qquad \end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray} &&\hbox{or } \nonumber \\ w1 & \;{>}\; & w1-w3 + 11.0. \qquad \end{eqnarray} \tag{ 11 }$$

In these and the following figures, we include arrows representing the extinction vector for A_KS = 0.4, 0.8, and 2, computed using an interpolation of Figure 1 of McClure (2009). We present our estimated extinction law in the WISE bands in Table 10. The vectors shown in the various figures are not parallel to each other due to the variations in the extinction law as a function of the total extinction as derived by McClure (2009).

Having removed the previously defined contaminants, we identify and classify YSOs first using the list of objects that meet the band 1, 2, and 3 requirements. The scheme—as in K12—is developed to follow the observed colors of Taurus region YSOs in Rebull et al. (2010) and transition disk young stars, guided by the catalogs of Andrews et al. (2011) and the compilation of Cieza et al. (2012). To better understand the distribution in WISE color–color and color–magnitude spaces of potential astrophysical contaminants to our young star candidates, we use the AGB carbon star catalog of Alksnis et al. (2001), the OH/IR AGB star catalogs of Chengalur et al. (1996), Sjouwerman et al. (1998), and Lindqvist et al. (1992), and the Classical Be stars from Mathew et al. (2008). We search the AllWISE catalog within a 2'' search radius for all these object types, requiring their catalog parameters pass our signal-to-noise and χ² cuts and plot them in Figure 5 (young stars in the left panel and other object types in the center panel). To guide the large-scale classification of AllWISE data, we also extract a large section of the outer Galaxy (105 <l < 153, |b| < 5, hereafter the outer Galaxy strip) to examine how these different object types manifest themselves in the catalog (Figure 5, right). In contrast to Figure 4, several additional clouds of sources can now be seen in the right panel of Figure 5. The extragalactic objects are still obvious and present, but are now joined by Galactic young stars and the other Galactic object types with infrared excess seen in the left and center panels of the figure. The streak of objects with roughly zero w1 − w2 color but a wide range of w2 − w3 color are a mix of source types. They may be objects with fake band 3 detections that slip through the photometric quality criteria of Section 3.2. They may also be foreground photospheres/main-sequence stars with a coincidental background galaxy that gives them an apparent red color. Finally, some fraction may be young transition disk stars, or older, evolved "debris disk" stars similar to Vega (see, for example, Dominik & Decin 2003).

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Class I YSOs (candidate protostars) are the reddest objects, and are classified as such if their colors match:

$$\begin{eqnarray} w2-w3 & \;{>}\; & 2.0 \qquad\qquad\qquad\quad \end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray} &&\hbox{and} \nonumber \\ w1-w2 & \;{>}\; & -0.42 \times (w2-w3) + 2.2 \end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray} &&\hbox{and} \nonumber \\ w1-w2 & \;{>}\; & 0.46 \times (w2-w3) - 0.9 \quad \end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray} &&\hbox{and}\nonumber \\ w2-w3 & \;{<}\; & 4.5. \quad\quad\qquad\qquad\qquad \end{eqnarray} \tag{ 15 }$$

These requirements modify the scheme of K12 to better reflect the divisions in SED slope (α = dlog (λF_λ)/dlog λ, Greene et al. 1994) on which the Class system is based and to eliminate contamination by spurious detections in WISE band 3.

Class II YSOs (candidate T Tauri stars and Herbig AeBe stars) are classified from the remaining pool of objects if their colors match the following criteria:

$$\begin{eqnarray} w1-w2 & \;{>}\; & 0.25 \quad\quad\qquad\qquad\quad \end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray} &&\!\!\hbox{and} \nonumber \\ \!\!\! w1-w2 & \;{<}\; & 0.9 \times (w2-w3) - 0.25 \end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray} &&\hbox{and} \nonumber \\ w1-w2 & \;{>}\; & -1.5 \times (w2-w3) + 2.1 \end{eqnarray} \tag{ 18 }$$

$$\begin{eqnarray} &&\!\!\hbox{and} \nonumber \\ \!\!\! w1-w2 & \;{>}\; & 0.46 \times (w2-w3) - 0.9 \end{eqnarray} \tag{ 19 }$$

$$\begin{eqnarray} &&\!\!\!\!\hbox{and}\nonumber \\ \!\!\!\!\! w2-w3 & \;{<}\; & 4.5. \qquad\qquad\quad\quad\quad \end{eqnarray} \tag{ 20 }$$

As can be seen in Figure 5, the revised Class II criteria attempt to avoid the AGB stars seen in the catalog of Alksnis et al. 2001 and the region occupied by Classical Be stars to the blue. This latter region is also where some AGB stars reside, as well as Class III/weak disk YSOs and blue transition disks (Cieza et al. 2012). The criteria also attempt to eliminate a region likely dominated by the reddest star-forming galaxies to the lower right in this color space.

4.2.1. YSOs Found with 2MASS and WISE

To compensate for the relative drop in sensitivity in WISE bands 3 and 4, both intrinsic and due to the bright background emission at these wavelengths, we use the 2MASS JHK_S point-source catalog (Skrutskie et al. 2006) that is automatically provided with the AllWISE catalog. Here we alter the scheme from K12 and use the H − K_S versus w1 − w2 color–color diagram to find and classify YSOs. In H − K_S versus w1 − w2 color–color space, there is less overlap between the reddening vector due to extinction and that due to dust excess emission (see Figure 6). In other words, it is easier to define a line that follows the standard extinction law that excludes most extragalactic contamination for the H − K_S, w1 − w2 plot than it is in the K_S − w1, w1 − w2 plot, where reddened background galaxies and main-sequence stars may easily have colors resembling disk excess sources.

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One further alteration we make to the scheme of K12 and the original Spitzer-2MASS concept of Gutermuth et al. (2009) is to not apply any dereddening to the colors of sources we classify. Lacking an independent method to remove the foreground extinction to each source, or an extinction map, we develop our selection and classification based on the raw photometry. In general, in the outer Galaxy, line-of-sight extinction due to dust in between the solar system and the main star-forming regions is low; for example, Hillwig et al. (2006) derive an extinction A_V ≈ 2 to the O stars in the H ii region cavity of W5. Within star-forming regions, however, the most embedded young stars can be hidden behind an A_V > 15 (for example, Masiunas et al. 2012, who find peak A_V = 19.8 in their extinction map of AFGL 490). Thus in general, the extinction vector in H − K_S versus w1 − w2 will have a magnitude <0.3, but could be as large or larger than 1 in the most embedded cases, meaning some of the objects classified as Class I protostars in this part of the scheme could be reddened Class II stars.

We search for YSO candidates using the following criteria amongst previously unclassified objects with non-null photometric error in 2MASS H and K_S, and which pass the WISE band 1 and 2 requirements of Section 3.2 and fail those for WISE band 3:

$$\begin{eqnarray} H-K_S & \;{>}\; & 0.0 \qquad\qquad\qquad\qquad\qquad \end{eqnarray} \tag{ 21 }$$

$$\begin{eqnarray} &&\hbox{and }\nonumber \\ H-K_S & \;{>}\; & -1.76 \times (w1-w2) + 0.9 \qquad \end{eqnarray} \tag{ 22 }$$

$$\begin{eqnarray} &&\hbox{and }\nonumber \\ H-K_S & \;{<}\; & (0.55/0.16) \times (w1-w2) - 0.85 \end{eqnarray} \tag{ 23 }$$

$$\begin{eqnarray} &&\hbox{and }\nonumber \\ w1 & \le & 13.0. \qquad\qquad\qquad\qquad \end{eqnarray} \tag{ 24 }$$

These objects are initially classified with the Class II objects. The subset of them that pass the following criteria are grouped with the candidate Class I/protostar objects:

$$\begin{equation} H-K_S \,{>} -1.76 \times (w1-w2) + 2.55. \end{equation} \tag{ 25 }$$

The ratio (0.55/0.16) in the criteria above comes from the calculation of the ratio of color excesses: (A_H − A_KS)/(A_w1 − A_w2) computed for A_KS > 1, since this gives the greatest slope in the extinction law, and thus the most cautious cut of galaxies in H − K_S, w1 − w2 space.

4.2.2. WISE 22 μm Photometry

As in K12, we use w4 photometry to identify candidate transition disk objects and to retrieve possible protostars from the AGN candidates. Figure 7 shows the location of the search box for transition disk objects. As can be seen, there is considerable overlap between literature transition disks and Class II sources, likely owing to the sensitive dependence of mid-infrared emission on small changes in the dust distribution and disk inclination. These properties make a scheme like this one an imprecise tool for finding these objects. The streak of objects with roughly zero w1 − w2 color and a range of w3 − w4 colors is similar to the one seen in Figure 5 and is likely made up of the same types of sources. As can be seen, literature transition disks are typically not as blue in w1 − w2 as this streak, so we avoid this portion of color–color space. We select candidate transition disks with the following criteria, from the sources that meet the requirements on all four bands given in Section 3.2:

$$\begin{eqnarray} w3-w4 & \;{>}\; & 1.5 \qquad\qquad \end{eqnarray} \tag{ 26 }$$

$$\begin{eqnarray} &&\!\!\!\!\hbox{and}\nonumber \\ \!\!\!\!\!\! 0.15 & \;{<}\; & w1-w2 < 0.8 \quad \end{eqnarray} \tag{ 27 }$$

$$\begin{eqnarray} &&\hbox{and}\nonumber \\ \!\! w1-w2 & \;{>}\; & 0.46 \times (w2-w3) - 0.9 \end{eqnarray} \tag{ 28 }$$

$$\begin{eqnarray} &&\hbox{and}\nonumber \\ \!\!\!\! w1 & \le & 13.0. \qquad\qquad\quad \end{eqnarray} \tag{ 29 }$$

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The last two criteria attempt to mitigate the contamination by background galaxies in the same way as with Class II objects. The bluest transition disk objects seen in the literature catalogs are too hard to separate from AGB and CBe stars without follow-up spectroscopy (as in Cieza et al. 2012) and we make no attempt to find them in this work.

AGN occupy a similar part of color space to protostars, but we can retrieve an additional set of those objects as candidate protostars if they have a w4 magnitude that makes them brighter than the majority of external galaxies. We take the sample of objects previously classified as AGN candidates and identify new protostars with the following color–magnitude cuts, additionally requiring that they meet the band 4 quality criteria given in Section 3.2 (see Figure 8):

$$\begin{eqnarray} w4 & \;{<}\; & 5.0 \qquad\qquad \end{eqnarray} \tag{ 30 }$$

$$\begin{eqnarray} &&\hbox{and}\nonumber \\ 4.5 & \;{<}\; & w2-w4 < 8.0 \end{eqnarray} \tag{ 31 }$$

$$\begin{eqnarray} &&\hbox{and}\nonumber \\ w1-w2 & \;{>}\; & 1.0 \qquad\qquad\qquad \end{eqnarray} \tag{ 32 }$$

$$\begin{eqnarray} &&\hbox{and}\nonumber \\ w3-w4 & \;{>}\; & 2.0. \qquad\qquad\qquad \end{eqnarray} \tag{ 33 }$$

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4.2.3. AGB Stars and CBe Stars

Both AGB stars and CBe stars possess a degree of infrared excess, originating in the circumstellar material around these objects. In the case of AGB stars, these objects are in general much brighter than YSOs unless they are at great distance or strongly extincted and have a slightly different distribution in color–color space, with the OH/IR category of AGB stars the most similar to YSOs (a similar finding to Robitaille et al. 2008, using Spitzer data). CBe stars in general possess a weaker infrared excess than do YSOs, but can be confused with blue transition disk objects. Our initial WISE band 1, 2, and 3 classification of YSOs filters some fraction of these object types. After passing through all the preceding steps, we make one final pass to remove these objects. We use a combination of the WISE w1 − w2, w3 − w4 color–color diagram (see Figure 7) and the w1 versus w1 − w2 color–magnitude diagram (Figure 9). An initial run of the classification scheme up to this point on the Outer Galaxy strip described in Section 4.2 is shown in the left panel of Figure 9. The prominent clustering of objects with bright w1 magnitudes is almost certainly dominated by AGB stars as can be seen in the right panel of the figure. Thus, stars previously classified as any type of YSO are rejected if they meet the following conditions:

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First, they are rejected if any of the YSO candidates from the previous sections that are bright in WISE band 1 with

$$\begin{eqnarray} w1 & \;{<}\; & (-10/3) \times (w1-w2) + 9 \end{eqnarray} \tag{ 34 }$$

$$\begin{eqnarray} &&\hbox{or}\nonumber \\ \!\! w1 & \;{<}\; & (6/7) \times (w1-w2) + 5.5 \end{eqnarray} \tag{ 35 }$$

or any of the YSO candidates from the previous sections that meet the requirements on all four bands given in Section 3.2 and have

$$\begin{eqnarray} w3-w4 & \;{<}\; & 1.9 \qquad\qquad\quad \end{eqnarray} \tag{ 36 }$$

$$\begin{eqnarray} &&\hbox{and }\nonumber \\ w1-w2 & \;{<}\; & w3-w4 - 0.45. \end{eqnarray} \tag{ 37 }$$

The right panel of Figure 9 also shows that for nearby regions like Taurus, some bright YSOs may be lost to a cut for AGB stars like this one. In cases like this, analysis of the data for the region considered would be necessary to establish a compromise cut appropriate for the data considered.

Unresolved planetary nebulae (PNe) are potentially a source of contamination to the YSO sample, and are considered in Section 4.6 when we compute the residual contamination likely from Galactic sources. However, we make no attempt to avoid their detection in this scheme. As can be seen in Figure 10, their typical colors in the WISE bands when filtered by our signal-to-noise and chi-squared cuts place them mainly outside the regions occupied by young stars and our selection regions. We draw samples of PNe from a 2'' search in AllWISE for objects in the Macquarie/AAO/Strasbourg Hα (MASH) catalog (Parker et al. 2006; Miszalski et al. 2008; Cohen et al. 2011; and Acker et al. 1992).

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A recent paper by Nikutta et al. (2014) used a model of a spherical circumstellar dust shell to predict the location of AGB stars and young stars in WISE color–color diagrams. This model leads them to conclude that young stars should be found in the streak of objects that we note in Sections 4.2 and 4.2.2, which we suspect are more likely to be stars with debris disks (see, for example Morales et al. 2012). Their model also leads them to predict that young stars could be found by searching for objects with 10 <w1 < 11, 0.4 <w1 − w2 < 1.4, and 4 <w2 − w3 < 5.7. As can be seen in Figure 10, while some Class I young stars will be found by such a search, the majority of this search space is occupied by planetary nebulae.

Although the photometric quality requirements in Section 3.2 attempt to ensure a reliable source catalog is used to search for young stars, it is possible that at the end of the process of cleaning the AllWISE catalog and classifying the sources that some of the YSO candidates are reliant on a spurious detection for their classification.

We test the combined effect of the photometric quality criteria and the YSO identification scheme on our W3 and W5 test fields by classifying the AllWISE catalog sources and flagging those where the classification was reliant on a fake detection. We find 1/11 WISE Class I's (9%), and 1/76 WISE Class II's (1.3%) had a spurious w3 detection. None of the YSO candidates relied on a spurious band 1 or 2 detection.

Having developed the classification scheme, we test it on the outer Galaxy strip described in Section 4.2. We query the AllWISE online database, applying the criteria for w1 and w2 in the built-in SQL tool, since these apply to all parts of the YSO classification scheme. From an initial 9.1 million catalog sources, we retrieve the following distribution of YSO types shown in Figure 11 and listed in Table 11.

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Several notable star-forming regions are picked out by the distributions of young stars, in particular (from left to right): AFGL 490, the W5-W4-W3 complex, Cep OB3 (Allen et al. 2012), and the NGC 7538 complex (Ungerechts et al. 2000). The less evolved Class I sources are fewer in number and appear to be spatially concentrated in smaller structures than their neighboring Class II counterparts. We return to this point in a later section.

We note that despite the scheme, contaminant astrophysical objects may contribute to the observed distribution of young stars in the Outer Galaxy Strip seen in Figure 11. To estimate the number of these contaminants, we run the following tests.

For external galaxies, we download an equivalent area of sky around the north and south Galactic poles (simply searching the AllWISE catalog with |b| > 81.25668). We randomly place these objects in the outer Galaxy strip and retrieve the extinction value of the nearest pixel of the Schlegel et al. (1998) extinction map for each object. We redden their 2MASS and WISE photometry according to the extinction law in Table 10 and run the full catalog cleaning and classification scheme. We present the average number of objects that fall into our various YSO class bins in this particular field after 20000 repeats of this process in Table 12. As expected, WISE-selected Class I YSOs are the most highly contaminated by galaxies at a rate of about 13%. All other classes are contaminated by external galaxies at a rate of 2% or less.

For Galactic contaminants, we use the Galactic populations model of Wainscoat et al. (1992) and the extension to all infrared wavelengths of Cohen (1993) over this field of view, but with no extinction, so the results are an upper limit (a code implementation of this model was kindly supplied by Miranda Dunham and Paul Harvey). We select the following categories of objects from Table 2 of Wainscoat et al. as likely contaminants for confusion with our YSOs in Class I or II by their location in WISE or 2MASS-WISE color–color spaces:

Our Class I objects may be confused with Wainscoat types: X 1E, 2, 3, 4, (the ultraluminous 12 μm sources) AGB_CI_01–05, (carbon rich, "optically invisible" AGB stars with IRAS [12] − [25] color in the range 0.1–0.5) AGB_M_17–25, (oxygen rich AGB stars with IRAS [12] − [25] color in the range 1.7–2.5), PNE BLUE, RED ("blue" and "red" planetary nebulae).

Our Class II objects may be confused with Wainscoat types: X 1E, (the ultraluminous 12 μm sources with silicate emission) AGB_CI_01–31, (C-rich, "optically invisible" AGB stars, 0.1 <[12] − [25] < 3.1) AGB_M_07–15, (O-rich AGB stars, 0.7 <[12] − [25] < 1.5) RNE BLUE, RED ("blue" and "red" reflection nebulae).

Since the Wainscoat–Cohen model code allows the user to select which of the different object categories are present in a particular portion of the Galaxy, we use it to generate L-band magnitude histograms for these specific Class I and II contaminants separately, applying our average WISE band 1 completeness curve for the W5 test field at the faint end and cutting everything brighter than L = 7 (to replicate our AGB exclusion method). This method assumes that the L-band is a good match for w1.

Objects in the X1E, AGB_M_07 and 09, and AGB_CI_01–11 categories all have colors which mean they would be rejected by our WISE w1 − w2 versus w3 − w4 category if detected in WISE band 4. We remove these from our Galactic contaminant estimation if their apparent IRAS 25 μm magnitude is less than 6 in the final computation (an approximate band 4 completeness cut).

We run the Wainscoat–Cohen model code once for the Class I-like sources and once for the Class II-like sources. We apply an additional faint cut of 13th magnitude for the Class II sources, since these are rejected by the YSO scheme, and derive a final numerical estimate of the total number of non-YSOs that may be in the field of view. We predict 68 Class I and 222 Class II sources at most may be contaminant Galactic objects. Since we do not separate this simulated population of Galactic contaminant objects into the different bins of our classification scheme, these estimates represent ∼7.5% and ∼5% of the total Class I and Class II YSO candidates found in the Outer Galaxy strip. The robust population of young stars detected by the AllWISE catalog and our classification scheme is thus about 730 Class I and 3900 Class II objects.

The question of the existence of two distinct modes of star formation, one "clustered" where stars are formed in groups, associations or true clusters as observed in general in star-forming regions, and one "isolated" has been raised in the literature for decades. For example, Roberts (1957) attempted to calculate whether all O and B stars form in clusters and associations or whether "individual stars form in the general field." A bimodality in star formation clustering has been suggested to explain, for example, the widespread detection of X-ray bright and, presumably, young stars in and around molecular clouds (Carpenter 2000). If an isolated population does exist, a natural question would be to ask if it has different properties to the clustered mode. In this paper, we use the term "isolated" or "non-clustered" to specifically refer to a distinct population that is separate from the continuum of cluster sizes that are observed in star forming regions and molecular clouds. If a clustered environment is necessary for the formation of massive stars (see Zinnecker & Yorke 2007 for a discussion of this hypothesis), then the mass function of the isolated population may differ from that of the clustered population, although the calculations of de Wit et al. (2005) show that isolated O stars can be explained by the combined effects of a universal cluster size/density distribution and stellar mass function.

One of the simplest ways to analyze the clustering properties of stars projected onto the sky is to compute the distribution of local surface densities. We compute a proxy for the surface density, μ at the position of each star using the angular distance to the sixth nearest neighbor of each object, s₆. Following Casertano & Hut (1985), the jth surface density estimator μ_j is

$$\begin{equation} \mu _j = \frac{j-1}{\pi s_j^2}, \end{equation} \tag{ 38 }$$

where s_j is the distance to the jth nearest neighbor of an object. Casertano & Hut (1985) conclude that choosing j = 6 provides the best balance between an accurate computation of density (which would require large j) and a "local" density estimate, which would call for small j. Thus

$$\begin{equation} s_6 \propto \mu _6^{-2} . \end{equation} \tag{ 39 }$$

Since we do not know exactly which of our YSO candidates are background galaxies or Galactic contaminant objects, we compute an average angular distance distribution, applying a Monte Carlo style method to subtract off these sources of contamination by repeatedly, randomly removing samples of objects with the same w1 magnitude distributions and total number as that predicted previously and re-computing the angular distance distribution. In each iteration, we derive a new calculation of the expected contamination due to galaxies. The final averaged angular distance distributions for the Class I sources and for a combined sample of the Class I and II sources are shown in Figure 12 in the left and right panels, respectively. Both distributions in Figure 12 peak at small angular distances because of the large fractions of these objects in clusters and aggregates of various sizes. Since our YSO survey is incomplete, the true peaks of the distributions are likely at smaller angular distances than those shown in the figure. The distributions both have tails that extend to large angular distances >2°, some of which could be explained by a population of very isolated/non-clustered young stars.

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We investigate the possibility of a non-clustered population by assuming that such sources would exist in a distribution with some scale height in the Galactic disk. For a simple test, we construct a comparison sample with an exponential distribution in the vertical (latitude) direction and uniform in the plane of the Galaxy. We assign each object an absolute w1 magnitude by drawing from the distribution of the c2d catalog sources of Evans et al. (2009), where we match their list to the AllWISE catalog and separate their sources into the YSO Class divisions set in Section 4. We apply the average W5 w1 completeness curve to the resultant apparent magnitude distribution of sources and additionally require objects have w1 ⩽ 13, since our extragalactic filtration technique essentially imposes this cut on our data. In Figure 12, we show the angular distance distributions of these samples where we find an approximate match to the shape of the low density end of the true YSO distribution, separately matching Class I objects (left panel) and a combined Class I and II sample (right panel). Increasing the total number thrown into the sample (with constant scale height) pushes the number of sources at the peak of the curve above the data. Decreasing the total input number produces an excess of sources at very low density/large angular distance (more than a factor of two). The WISE YSO histograms contain on average 760 Class I and 3910 Class II stars after contaminant subtraction. The best matching histograms contain on average 320 sources (left panel) and 1800 sources (right panel). If a uniform, scale height component makes up part of this observed distribution of YSOs in this way, this analysis shows that it is not more than ≈one-third of the total number of sources.

We note that WISE's incompleteness means the observed stellar densities are underestimates (or in apparent nearest neighbor angular distances, overestimates) of the true values. In the prominent star forming regions in Figure 11 are the well-studied regions: AFGL 490 ((l, b) = (142.0, +1.82), distance = 900 pc, Masiunas et al. 2012); Cep OB3 ((l, b) = (111.26, +2.98), d = 700 pc, Allen et al. 2012); W5 ((l, b) = 138, +1.5, d = 2 kpc, Koenig et al. 2008). A 3'' match of our YSO catalog to these published lists of Class I and II sources (excluding transition disks and Class III/weak-line T Tauri stars) retrieves 26% (AFGL 490), 25% (Cep OB3) and 16% (W5) of the Spitzer-classified stars. Thus the true stellar densities in these clusters are at least a factor of ≈five or greater.

To test if a scale height distributed component could still explain the low density end of the young star density distribution, we crudely imitate the effect of WISE's incompleteness by scaling all the nearest neighbor distances by 1/$\sqrt{5}$ and increasing the total number of objects in the histogram by five. This experiment assumes that we have missed a fixed fraction of the total number of young stars in the outer Galaxy, whether in or out of massive regions. We repeat the experiment of trying to match scale height distributions of stars to the new scaled histogram. In this test, we apply the Spitzer completeness calculation from Koenig et al. (2008) to the sample of sources and apply a faint cut off of IRAC band 1 <14 to represent their more lenient galaxy removal technique. Figure 13 shows the results of this trial applied to the combined Class I and II sample. In this case, a smaller fraction—roughly 2400 objects out of the increased YSO count of 23350 stars—can be fit with the uniform component, which also suffers from the problem of overpredicting the number of low density sources (nearest neighbor distance >50') by a factor of five. Since Spitzer itself is also incomplete to the low mass end of the initial mass function in this field, and we have only considered those young stars which still possess a visible infrared excess, the fraction of stars in a random, non-clustered population may be lower still.

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We compute the two-point correlation function (TPCF) of a single output of the contaminant-subtracted sample of YSOs, separated into Class I and II samples. We use the following estimator of the TPCF following Peebles & Hauser (1974):

$$\begin{equation} \xi (\theta) = \frac{N_R}{N}\frac{DD(\theta)}{RR(\theta)} - 1, \end{equation} \tag{ 40 }$$

where DD and RR are the numbers of pairs as a function of angular separation θ in the YSO catalog and in a randomly distributed catalog with three × the number of objects, respectively. We generate RR(θ) by randomly populating the latitude–longitude range of our test region. In this formulation, a random distribution of sources would have ξ(θ) = −2/3, or log (1 + ξ(θ)) = −0.477. Figure 14 shows a plot of (1 + ξ(θ)) versus θ for the Class I and II samples (with logarithmically scaled axes), overlaid with weighted least-squares fits to the roughly linear part of the data (left-hand panel). The right-hand panel shows the same data without error bars and unweighted fits to the data between 200 and 4000''.

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Both the Class I and II data fall below the random level at separations θ ≳ 18000'', or about 5°, likely due to edge effects becoming significant in the calculation of ξ(θ). The features evident in the data at the longest separations (roughly 100,000'' or 28°) are the result of the real clusters visible in Figure 11. The Class I distribution appears to follow a power law up to separations of about 4000'' or just about one degree. The Class II distribution is shallower, and appears to have a power-law shape up to separations θ ≈ 7000'' with a turnover at about 200''. As discussed by Kraus & Hillenbrand (2008), work by Larson (1995), Simon (1997), and others has shown evidence that young stars are distributed in a fractal manner with self-similar structure over a range of angular scales in star-forming regions like Taurus. Following the methodology of Kraus & Hillenbrand, in a fractal distribution the number of neighbors within angular distance θ goes as N(θ) ∝ θ^D, where D is the fractal dimension, or the degree to which the distribution fills space. In such a distribution the mean surface density of companions Σ(θ) ∝ 1 + ξ(θ) ∝ θ^{D − 2}. For the Class I sources, the weighted least squares fit technique finds a slope of −0.69 ± 0.06 and thus D = 1.31 and for the Class II's a slope of −0.70 ± 0.02 and D = 1.30. These slopes are statistically equal, but the fits are strongly skewed to match the data around 2000'' where the error bars are smallest due to the random distribution peaking around this value of object separations. The unweighted fits (slopes of −0.87 ± 0.02 for the Class I's and −0.72 ± 0.01 for the Class II's) capture the fact the Class I source correlation function falls below the Class II function at scales >300'', consistent with the more evolved Class II sources being more spread out in space and the younger Class I sources more filamentary and concentrated. This interpretation is consistent with the findings of André et al. (2010) and others who show that star-forming gas as seen in the far-infrared with the Herschel space telescope appears to be dominated by filamentary structure. The difference in the intercepts of the straight-line fits in the left-hand panel of Figure 14 is ≈0.17, or a size ratio of about 1.5.

One possible contributor to the population of sources outside the prominent, obvious clusters in Figure 11 is the dispersal of young stars from parent clusters or small groupings. The infrared excess emission that allows us to identify candidate young stars has a half life of around 2 Myr, although objects with an infrared disk signature can still be seen in star-forming regions as old as 10 Myr (Sicilia-Aguilar et al. 2006). In 5 Myr, a Class II object traveling at a typical velocity of 3 km s⁻¹ (Fűrész et al. 2006) would travel about 15 pc. At a distance of 200 pc it would have moved about 4° on the sky, at 1 kpc about 1° and about 30' at a distance of 2 kpc. The combined lifetime for the Class I and Flat SED phase of young stellar objects (Evans et al. 2009) is roughly 1 Myr. At a typical velocity of 1 km s⁻¹ (Offner et al. 2009), at a distance of 200 pc it would have moved about 17' on the sky, or ≈100'' if at a distance of 2 kpc. Thus it is possible that some of the most isolated young stars in the outer Galaxy strip are runaways from clusters, the Class II sources in particular. The isolated Class I sources are harder to explain away completely in this manner and some may be genuinely forming in very sparsely populated environments. A more sophisticated model of the distribution of young stars in the outer Galaxy strip that incorporates cluster dispersal would help us understand exactly how many stars may be forming in isolation. Follow-up observations of the isolated Class I candidates with higher spatial resolution and sensitivity and at other wavelengths would also help understand how many of these objects are cluster escapees or contaminant objects we have not previously accounted for.

The AllWISE photometric filtration scheme presented in this paper is imperfect and ideally researchers would visually inspect AllWISE images of objects of interest found in the catalog in all four bands. In the current era where big data is a powerful tool to test theories in new and creative ways, this step may become prohibitively time consuming, thus the scheme presented here at least allows a first pass to reduce the number of objects that need to be manually checked. It is very important to note that different areas of the Galactic Plane may behave differently than the star-forming test regions analyzed here, particularly the Galactic Center region, where confusion is likely to strongly affect performance. However, the behavior of the various catalog parameters like signal to noise and chi-squared in response to real and spurious sources and objects that are confused or extended is generally applicable. It is certainly important to note the relative strength and weakness of different catalog parameters and we hope to have provided starting points for researchers needing to find a pathway through the AllWISE catalog to conduct the source searches and studies they care to do.

Observations of the distributions of young stars in very large fields with a survey like WISE enable us to take steps beyond previous studies of star formation by allowing us to begin to connect the observations made in nearby galaxies with those of individual star forming regions in our own Milky Way. If a future complete theory of star formation is to be able to predict the star formation rate and spatial distribution of stars in a large subsection of a galaxy given the gas distribution and kinematics, then we need to have observations of the large-scale distribution of star formation in similar sized regions against which to test such a theory. Our observations in this paper, while limited by the properties of the WISE survey, provide a beginning to the process of extracting and analyzing a full census of star formation in a large portion of a spiral galaxy.

Our first observation of the distribution of the stars in our sample extracted field shows an obvious degree of clustering into large regions, but with a lower density population between them. We have found that when considering this large-scale distribution of young stars in the outer Galaxy, at most about one-third of stars can be fit with a simple scale height distribution. We argue that this means that it is a true statement that the majority of stars form in a clustered environment, that is to say, in prominent massive star-forming regions whose density distribution is sharply peaked toward high densities. However, we have also shown that in a simple test to correct for WISE's incompleteness with respect to hypothetical Spitzer Space Telescope observations, the size of the isolated or non-clustered or scale height component may be a much smaller fraction of the total distribution of stars and may not be required at all. The fact that the low density end of the distribution of stars observed with WISE appears to be well fit with a scale height similar to that of OB stars (∼50 pc, Reed 2000) and molecular gas (∼70 pc, Cox 2005) in the Galactic Plane may simply reflect the fact that WISE only detects a small fraction of the true population of young stars. Since the WISE survey in this paper is magnitude limited, we tend to include distant, bright objects and miss their possible neighboring cluster members. The ≈6'' resolution of WISE also becomes significant for more distant young stars. At 2 kpc, 6'' equates to a distance of 0.06 pc. At 3 kpc, this resolution is 0.09 pc, which is approaching the median separation of stars in Taurus (about 0.17 pc, from a simple computation of nearest neighbor distances for the sample of Hartmann et al. 2005). Thus the observed clustering properties of more distant stars may reflect only the smooth, large-scale distribution of the gas and may miss their true nature as part of the continuum of cluster sizes.

The largely hierarchical nature of the distribution of stars is also reflected in the power-law shape of the two-point correlation function, ξ(θ). The break in the power law at roughly 2° may also indicate a transition to isolated star formation. As can be seen in our data, two degrees is approximately the size of regions like W5, W3, W4, and Cep OB3.

As described in Section 5.3 it is possible that some fraction of the apparently isolated young stars we see are the dispersed members of young groups or clusters, in particular the Class II sources and especially if there are a large quantity of objects within 500 pc. The isolated protostars are harder to explain in this way as dispersed cluster members, however since they are younger they are more likely to be concentrated in physically small regions, like the star-forming pillars around H ii regions (e.g., Koenig et al. 2008). As we probe deeper, with higher-resolution observations and gain more information about stellar proper motions, it may be that further observations of the low density population reveal all young stars to be part of a single cluster continuum. We intend to pursue this approach with a forthcoming study combining data from the Spitzer GLIMPSE360 Galactic Plane survey with WISE to examine the distribution of these stars when observed at higher spatial resolution and sensitivity.

The work of Bressert et al. (2010) and others has already shown that within star-forming regions, there is no obvious break in the density distribution of young stars that would indicate a separate, isolated component. If higher resolution and sensitivity observations do indeed bear out the result that a truly distinct, isolated population is either small or non-existent, this would be consistent with the work of Hopkins (2013), who argues that observed density distributions of young stars are simply a continuum resulting from the imprint of the hierarchical nature of supersonic turbulence in molecular clouds (although as noted by Krumholz 2014, Klessen & Burkert 2000 also produce hierarchical structure in star-forming gas without turbulence) over all scales. In this picture, isolated (or at least, apparently isolated) star formation would represent <10% of the total in a single, unified mechanism of star formation. If a truly isolated population is supported by future observations, however, it will be interesting to scrutinize its origins and mass function.

We derive the completeness, by band, on and off cloud (i.e., in regions of high- and low-sky background) in two test regions covering W5 and W3/W4. We define high- and low-sky regions by a threshold sky value (as given in the AllWISE catalog) that as best as possible traces the observed cloud boundaries in our WISE mosaic images when catalog sources are overplotted and color-coded according to their listed local sky value. These thresholds in sky background value in digital numbers are listed in Table 13. Figure 15 shows plots of AllWISE catalog sources in the test fields color-coded in this way, showing high (red) or low (blue) sky emission regions.

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A.1.1. WISE Potential Completeness

To derive a value for the completeness in each band, we extract Spitzer photometry from Koenig et al. (2008) in W5 and an extraction of photometry from data in the Spitzer Heritage Archive for W3/W4 in IRAC bands 1, 2, and 4 and MIPS 24 μm corresponding roughly to the four WISE bands, respectively. Each source in the Spitzer lists is assigned the sky value of the nearest object in the AllWISE catalog. We match our manually generated WISE source list to the Spitzer catalogs with a 2'' search radius to determine what fraction of the Spitzer objects could be detected by WISE. Figure 16 shows the histograms of the Spitzer catalog and potential-WISE-retrieved subset, separated by field, by high- or low-sky background, and by band. We then plot the "detected" fraction (and Poissonian error on the fraction) as a function of Spitzer magnitude by field and band in Figure 17. The magnitude where the error bar crosses the 90% completeness line is our completeness limit.

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A.1.2. AllWISE Completeness

The AllWISE source extraction pipeline is only able to retrieve a subset of the sources visible in Galactic Plane WISE images. We calculate the completeness of the AllWISE source extraction by comparing histograms of source magnitude of AllWISE objects that match the truth catalog (so as to filter off spurious detections) to the Spitzer catalogs for the same regions. Figure 18 shows the histograms of the Spitzer catalog and the AllWISE "real" sources over the same area of the test regions. The mismatch in the histograms (for example the W5 w1 high-sky background plot in the upper right) is largely due to the binning in the plots and slight differences in the magnitudes between WISE and Spitzer, but may also be due to differences in how the background subtraction is handled or source variability. In the w3 plots on the third row, WISE is able to detect bright objects that are saturated in Spitzer images, the bandpasses are less similar and spectral features (e.g., the 10 μm silicate feature, which can vary with evolutionary stage, Kessler-Silacci et al. 2005) in these young objects' infrared spectra may cause other mismatches. We plot the AllWISE-detected fraction (and Poissonian error on the fraction) as a function of Spitzer magnitude by field and band in Figure 19. The magnitude where the error bar crosses the 90% completeness line is our completeness limit.

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Here we show the plots of the various catalog parameters analyzed in this paper and discussed in Section 3 and their behavior in the "real" by-eye source list and "fake" sources found in the AllWISE catalog. Black and red points show fake and real sources, respectively.

Figure 20 shows the behavior of w?snr and w?rchi2 in real and fake sources in the four WISE bands. The left and right columns of plots show different zoom levels of the full distribution in these parameters (left: zoomed out, right: zoomed in). For each band we show the distribution separately between the two test fields (as labeled in the upper corner of the plots). Real and fake sources are found in overlapping, but different regions of this parameter space that we use to separate the two in the AllWISE catalog.

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Figure 21 shows the behavior of w?nm/w?m versus w?m in "real" and "fake" sources in the four WISE bands, where w?nm is the number of profile-fit flux measurements for a source with w?snr > 3 and w?m is the number of profile-fit flux measurements for a source. The symbol size scales with the number of objects at that set of values for the two parameters as shown in the figure legend. The left column of plots shows the behavior in the W3 test field, while the right column shows the W5 test field. For the most part in bands 1, 2, and 3, both real and fake sources have similar distributions of these parameters when plotted in this way. In band 4, a different pattern appears, with a much larger fraction of the fake sources having w4nm/w4m < 0.2. The contrast between real and fake source distributions is not strong enough to be used as an effective discriminant in the catalog, however.

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Figure 22 shows the behavior of the profile fit (w?mpro) and aperture (w?mag) magnitudes values for "real" and "fake" sources in the AllWISE catalog in the two test fields. We plot w?mpro − w?mag versus w?mpro, with the left column of plots showing the behavior in the W3 test field and the right column showing the W5 test field. In bands 1 and 2, a cut of |w?mpro − w?mag| < 0.5 would effectively remove the fake sources, while at the same time allowing through the majority of the real objects (see Table 9). A reader may validly pursue a cut based on aperture and profile fit magnitude offsets in bands 1 and 2 as an alternative to S/N versus $\chi _{\nu }^2$. However, in bands 3 and 4, fake sources are so numerous and occupy such a large portion of this parameter space that no good cut to remove them and keep enough real sources can be found to compete with our w?snr and w?rchi2-based cut in these bands.

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