WISE × SuperCOSMOS PHOTOMETRIC REDSHIFT CATALOG: 20 MILLION GALAXIES OVER 3π STERADIANS

WISE (Wright et al. 2010) is a NASA space-based mission that surveyed the celestial sphere in four infrared bands: 3.4, 4.6, 12, and 23 μm (W1–W4), with an angular resolution of 61, 64, 65, and 12'', respectively. We use the AllWISE full-sky release¹⁹ (Cutri et al. 2013), which combines data from the cryogenic and post-cryogenic survey phases and provides the most comprehensive picture of the full mid-infrared sky currently available. The AllWISE Source Catalog and Image Atlas have enhanced sensitivity and accuracy compared with earlier WISE data releases, especially in its two shortest bands. This results in a larger effective depth than available from an earlier "All-Sky" release (Cutri et al. 2012), used for example, in B14. AllWISE includes more than 747 million sources (mostly stars and galaxies) detected with S/N ≥ 5 in at least one band. The 5σ sensitivities in the four respective bands are approximately²⁰ 0.054, 0.071, 0.73, and 5 mJy, and the 95% completeness averaged over large areas of unconfused sky is about²¹ W1 < 17.1, W2 < 15.7, W3 < 11.5, and W4 < 7.7 in the Vega system.²² However, the depth of coverage does vary over the sky due to the survey strategy, being much higher in the ecliptic poles and the lowest near the ecliptic plane (Jarrett et al. 2011); there are also some anomalous stripes resulting from moon avoidance maneuvers and instrumental issues.

The WISE photometric pipeline was not optimized for extended sources and the online database does not include a formal extended source catalog. The basic magnitudes (which we use here) are the w?mpro mags, based on PSF profile-fit measurements, where "?" stands for the particular channel number, from 1 to 4. This information is available for all objects, whereas existing attempts to handle extended images are somewhat heterogeneous. For instance, the w?gmags, which are measured in elliptical apertures derived from associated 2MASS XSC sources, are available only for the 483,000 largest WISE galaxies. Circular aperture magnitudes are in fact provided for practically all sources, namely the w?mag_n, where $n=1,2,\ldots ,8;$ these were obtained from the coadded Atlas images in a series of different fixed radii. But the angular sizes of the sources have not been determined; in addition, this photometry does not account for source ellipticities, is prone to contamination from nearby objects, and is not compensated for saturated or missing pixels in the images.

In any case, as we eliminate all the bright (W1 < 13.8) sources from our cross-matched catalog (see Section 4), we are thus left with galaxies that are typically smaller than the WISE resolution threshold, which are well-described by PSF magnitudes, although we note that their fluxes might be underestimated by WISE. This is supported by independent analyses showing that the eventual WISE XSC will mainly include 2MASS XSC galaxies and be limited to W1 ≲ 14 (Cluver et al. 2014; T. H. Jarrett et al. 2016, in preparation). In any case, any residual biases in photometry for resolved sources, which may influence source colors, will not be propagated to the photometric redshifts derived via the neural network framework employed here, as such systematics are automatically accounted for in the empirical training procedure.

Initially, we selected AllWISE sources with signal-to-noise ratios larger than 2 in its two shortest bands. This selection, meaning that we use detections in the two bands and not upper limits (the latter having ${\rm{S}}/{\rm{N}}\lt 2$ in WISE), is practically equivalent to selecting objects with ${\mathtt{w}}{\mathtt{1}}{\mathtt{snr}}\geqslant 5$, as those with low S/N in W1 but high in W2 are extremely rare. Having cleaned the sample of obvious artifacts (cc_flags[1,2] = 'DPHO') and saturated sources (${\mathtt{w}}?{\mathtt{sat}}\gt 0.1$), we ended up with more than 603 million AllWISE objects over the whole sky. In order to optimize all-sky uniformity, we applied a global magnitude cut of W1 < 17. This removes ∼20% of AllWISE (mostly around the ecliptic poles, where the WISE depth is greatest), leaving 488 million objects (pictured in Figure 1). From this image, it is apparent that low Galactic latitudes are entirely dominated by stars and blends thereof; as we will show below, stellar contamination remains significant even at high latitudes (see also Jarrett et al. 2011; T. H. Jarrett et al. 2016, in preparation). A minimal Galactic restriction to $| b| \gt 10^\circ$ lowers the total to 340 million sources (see Table 1 for a summary), but we will show that the final masking needs to be more severe than this.

Zoom In Zoom Out Reset image size

Table 1.  Statistics of the Parent Photometric Catalogs and the Final WISE × SuperCOSMOS Cross-match Used in This Paper

Catalog	Flux Limit(s)	Sky Cut	# of Sources
WISE	none	none	604 × 106
(preselected in W1 and W2)	none	$| b| \gt 10^\circ$	457 × 106
	W1 < 17	none	488 × 106
	W1 < 17	$| b| \gt 10^\circ$	343 × 106
SuperCOSMOS XSC	none	none	288 × 106
(preselected in B and R)	none	$| b| \gt 10^\circ$	158 × 106
	B < 21 and R < 19.5	none	208 × 106
	B < 21 and R < 19.5	$| b| \gt 10^\circ$	85.1 × 106
WISE × SuperCOSMOS XSC	none	none	109 × 106
	none	$| b| \gt 10^\circ$	78.3 × 106
	W1 < 17 and B < 21 and R < 19.5	none	77.9 × 106
	W1 < 17 and B < 21 and R < 19.5	$| b| \gt 10^\circ$	47.7 × 106
after star and quasar cleanup	13.8 < W1 < 17 and B < 21 and R < 19.5	$| b| \gt 10^\circ$ + Bulge, masked	18.8 × 106
galaxies in WISE, not in SCOS XSC	W1 < 17	$| b| \gt 10^\circ$	∼100 × 106

Download table as:  ASCIITypeset image

Note that some sources observed during the early three-band cryo survey phase are not captured by the above selection, as they have missing W1 magnitude uncertainties and are listed as upper limits in the database. This is discussed in detail in the AllWISE Explanatory Supplement²³ and applies mostly to two strips within ecliptic longitudes of 447 < λ < 548 or 2309 < λ < 2387 (visible in Figure 1). This will be rectified in our final galaxy sample that is cross-matched with SuperCOSMOS by adding data from the earlier WISE data release, All-Sky (Cutri et al. 2012). Some other issues are caused by variable coverage due to moon avoidance maneuvers, which results in several under- or oversampled stripes crossing the Ecliptic.²⁴

Galactic extinction corrections are very small in the WISE bands, over an order of magnitude smaller than in the optical, which does not mean they are totally negligible. Following Indebetouw et al. (2005) and Schlafly & Finkbeiner (2011), we use A_W1/E(B − V ) = 0.169 and A_W2/E(B − V ) = 0.130 as coefficients to be applied to the original Schlegel et al. (1998) maps; these values in part implement a general recalibration of the original E(B − V) values, which need to be lowered by 14% (Schlafly & Finkbeiner 2011).

The SuperCOSMOS Sky Survey (SCOS, Hambly et al. 2001a, 2001b, 2001c) was a program of automated scanning and digitizing sky atlas photographic plates in three bands (B, R, I ), using source material from the last decades of the 20th century obtained by the United Kingdom Schmidt Telescope (UKST) in the south and the Palomar Observatory Sky Survey-II (POSS-II) in the north. The data are stored in the SuperCOSMOS Science Archive,²⁵ with multicolor information provided for 1.9 billion sources, in the form of integrated quasi-total and point-source photometry (where available). The derived resolved-source data were accurately calibrated using SDSS photometry when possible, with the calibration extended over the full sky by matching plate overlaps and using the average color between the optical and 2MASS J bands as a constraint to prevent large-scale drifts in zero point (Francis & Peacock 2010; J. A. Peacock et al. 2016, in preparation). The typical resolution of SuperCOSMOS images is ∼2'' (Hambly et al. 2001b) and the photometric depth is R ≃ 19.5, B ≃ 21 in a pseudo-AB system, in which SCOS and SDSS coincide for objects with the color of the primary SDSS standards; detailed color equations are given in J. A. Peacock et al. (2016, in preparation). The third band available from the catalog, I, offers shallower coverage and will not be used here.

For the present work, we are interested only in resolved images. SCOS supplies a classification flag for every image in each of the three bands, as well as a combined one, meanClass. These are equal to one if a source is non-stellar, two if it is consistent with unresolved, three if unclassifiable, and four if likely to be noise; the last two classes constitute a negligible fraction of all sources (≪1%) in any given plate. The image classification is based on image morphology via a two-stage process (Hambly et al. 2001b, and references therein). The first stage uses image surface brightness, size, and shape to identify isolated, point-like images with good reliability and high completeness. The second stage takes this first-pass selection and analyses the 1D radial profile of those unresolved images as a function of plate position and source brightness. Finally, every image is assigned a profile statistic η—the probability distribution of which has zero mean and unit variance—to quantify the point-likeness. This continuously distributed statistic is used to define discrete classification codes when cut at fixed thresholds: sharper-than-point-like images with η < −3 are assigned class = 4 (noise), point-like images with −3 < η < 2.5 are assigned class = 2 (stellar), and resolved images having η > 2.5 are assigned class = 1 (non-stellar). Where data from two or more plates are available for the same image, the individual profile statistics are averaged to form a single, zero mean unit variance statistic via $\bar{\eta }={\rm{\Sigma }}\eta /\surd N$ for N plates with a discrete merged classification code, meanClass, assigned using the same ranges as above for the individual class codes. For brighter images with good detections in all bands, this increases the precision of classification, but for faint objects lacking good I-band data, this overall classification may be less reliable than the B or R plates individually. The data we use here have cuts that eliminate the faintest objects, so we use the meanClass parameter in all cases. We verified by comparison with SDSS test regions that this choice leads to better star-galaxy separation than using individual B and R classes.

Note that the classification flags also affect the photometric calibration procedure (Hambly et al. 2001b): separate calibrations were applied for stars and galaxies. This is mainly because of the limited dynamic range of SCOS when compared to, for example, some of the much slower modified PDS scanning machines or the highly optimized "flying spot" APM system (Hambly et al. 2001c and references therein). SCOS employed a linear CCD in the imaging system and a strip of emulsion was therefore illuminated to quickly scan lanes of ∼1 cm width. When scanning over denser spots in an otherwise less dense emulsion, the core density measured was limited by light from the entire illuminated strip diffracting in the imaging lens. This was not the case for extended objects because the amount of light subject to diffraction was significantly reduced. The diffraction limit of the measurement process for stars occurred at much lower densities than any emulsion saturation in the photographic emulsions themselves. Hence the calibration curve of instrumental magnitude versus externally measured magnitude bifurcated into separate star and galaxy loci was only a magnitude or so above the plate limit, despite both the point and extended images being well exposed on the log–linear part of the photographic response curve. In any case, the galaxy calibration was performed at a later date (J. A. Peacock et al. 2016, in preparation), following the wider availability of SDSS photometry.

Because of a slight difference between the passbands of the UKST and POSS-II, there is in effect a small color-dependent offset in the SCOS magnitudes between the north and the south (here meaning above and below δ₁₉₅₀ = 25). As discussed in B14, direct corrections were designed by comparison with SDSS to compensate for this effect. The following appropriate formulae (revised over B14) aim to correct the southern B and R data (δ₁₉₅₀ < 25) to be consistent with the north²⁶ :

$$\begin{eqnarray}&&{B}_{{\rm{S}}}^{{\rm{cal}}}=B+0.03{(B-R)}^{2}-0.005(B-R),\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{R}_{{\rm{S}}}^{{\rm{cal}}}=R+0.03{(B-R)}^{2}-0.06(B-R)+0.015.\end{eqnarray} \tag{ 2 }$$

However, even these corrections may not fully guarantee N−S uniformity: within our fiducial flux limits, the mean high-latitude surface density in the north is up to 4% larger than in the south; it is hard to be sure whether this is a remaining very small calibration offset or a genuine cosmic variance. On the other hand, these offsets do not induce significant additional scatter to the corrected magnitudes. For typical galaxy colors, B − R ∼ 1, by error propagation in Equations (1)–(2) we see that the random error in ${B}_{{\rm{S}}}^{{\rm{cal}}}$ is increased by less than 6% with respect to the original values, while in ${R}_{{\rm{S}}}^{{\rm{cal}}}$ there is a fortuitous cancellation and the error is not changed at all. For a general discussion of SCOS magnitude errors, see J. A. Peacock et al. (2016, in preparation).

We also revised the extinction corrections used in 2MPZ—a series of papers using SDSS (Schlafly et al. 2010; Schlafly & Finkbeiner 2011) and Pan-STARRS data (Schlafly et al. 2014) show that the original Schlegel et al. (1998) maps overestimate the E(B − V) values by roughly 14%, and that one should use the Fitzpatrick (1999) reddening coefficients rather than the Cardelli et al. (1989) ones. Based on the revised extinction coefficients for the SDSS g and r bands (Schlafly & Finkbeiner 2011), the new corrections for the B and R SCOS bands are, respectively, A_B/E(B − V ) = 3.44 and A_R/E(B − V ) = 2.23 (J. A. Peacock et al. 2016, in preparation) for the full sky.²⁷ These numbers already incorporate the rescaling of the E(B − V) values by Schlafly & Finkbeiner (2011); they should thus be applied to the original Schlegel et al. (1998) E(B − V) to obtain band-dependent extinction corrections for a given galaxy in magnitudes. In what follows, all the quoted SCOS magnitudes refer to hemisphere-calibrated and extinction-corrected values in the AB-like system.

For the purposes of the present work, our requirements for SCOS preselection were that the sources be properly detected with aperture photometry in B and R bands: gCorMagB and gCorMagR2 are not null in the database, quality flags qualB and ${\mathtt{qualR}}{\mathtt{2}}\lt 2048$ (no strong warnings nor severe defects: Hambly et al. 2001b). In addition, as described above, we used the sources with SCOS morphological classification flag ${\mathtt{meanClass}}=1$. This selection greatly enhances the purity of our final cross-matched sample by eliminating most of the stars from unconfused regions, as well as many quasars (see further discussion on these issues in Section 4). On the other hand, it only slightly reduces the completeness of the catalog, removing less than 1% of galaxies, which we estimated based on GAMA and SDSS galaxies cross-matched to our data. As with WISE, for SCOS we will also not be using low-latitude sources in the present work (almost 50% of SCOS "extended" sources are in the $| b| \lt 10^\circ$ strip—mostly blends of stars). On the other hand, we have supplemented our catalog over what is publicly available by adding sources that were originally omitted from the SCOS catalogs due to areas excluded around stepwedges, which affected mostly plate corners (564,000 objects in our case).

The above selections in SCOS resulted in the "SCOS extended source catalog" (XSC), with about 158 million sources at $| b| \gt 10^\circ$. Owing to the remaining low-latitude stellar blends, only part of these sources are actually extragalactic. Simple cross-matching of this catalog with AllWISE would give a highly contaminated sample, therefore extra effort was needed to derive the best possible purity and completeness criteria for our catalog. This is discussed in Section 4.

As far as reliability is concerned, the main limitation here and for the cross-matched catalog is the depth of the SCOS data. We decided to adopt B < 21 and R < 19.5 as the optical limits, motivated by our analysis of galaxy counts from direct comparison with very deep SDSS photometric data (Ahn et al. 2014; see also J. A. Peacock et al. 2016, in preparation). Applying these magnitude cuts to the $| b| \gt 10^\circ$ sample removes almost 50% of the SCOS XSC there, leaving 85 million sources. Had we included the Galactic Plane data, the flux-limited sample would include almost 208 million objects (see Table 1). Their distribution is shown in Figure 2; in addition to the Galactic Plane, the Magellanic Clouds are also clearly dominated by spurious overdensities from star blends. The plate pattern is noticeable at low latitudes because the degree of blending varies with plate quality. Note also that the dynamic range of the counts is much wider than in the case of WISE.

Zoom In Zoom Out Reset image size

In the following, all the cross-matches will be performed within a radius of 2'', unless otherwise specified.²⁸ In the case of the WISE × SCOS cross-match, the radius is motivated by the large beam of the former (∼6'' in the W1 band; Wright et al. 2010) and the angular resolution of the latter (∼2''). The mean matching radius for the resolved WISE × SCOS sources that pair up is 054 ± 042, and less than 14% of the cross-matched sources are separated by more than 1''. It is important to note that both surveys offer comparable, sub-arcsecond astrometric accuracy: ≲015 for WISE (Wright et al. 2010) and ≲03 for SCOS (Hambly et al. 2001a). Thus, it is highly unlikely for a source identified in the two catalogs and detected in the four bands used here to be spurious.

As already mentioned, all the WISE-based magnitudes are in the Vega system, while the SCOS ones are AB-like. We will also keep this convention for source colors derived from the two catalogs. From this point on, all magnitudes are corrected for extinction as described earlier.

After selecting the AllWISE and SCOS objects as discussed above, the resulting cross-match at $| b| \gt 10^\circ$ gave us more tha 78 million sources if no flux limits were applied, of these almost 48 million were within (extinction-corrected) magnitude cuts of W1 < 17, B < 21, and R < 19.5 (Table 1). These numbers include sources that were added to the sample from the earlier WISE release ("All-Sky") to remove the incompleteness in AllWISE data visible as undersampled strips in Figure 1 and discussed in Section 2.1, as well as the SCOS objects lost through stepwedge exclusion. Figure 3 shows the sky distribution of this flux-limited sample. One expects the angular distribution of extended (extragalactic) sources to be relatively uniform on the sphere, whereas here the foreground Milky Way clearly dominates the counts at low latitudes and the Magellanic Clouds do the same at their respective positions. Although the contamination from stellar blends is much reduced with respect to the two parent catalogs considered individually, less than half of these sources are actually extragalactic, despite being classified by SCOS as extended.

Zoom In Zoom Out Reset image size

To purify this sample, in Section 4 we present color cuts aimed at removing some problematic quasars (Section 4.1) and the remaining stars (Section 4.2). In Section 4.3 we describe the mask that needs to be applied to the data to remove regions where the stellar and other contaminations cannot be corrected. However, in Section 3 we first analyze the properties of the photometric catalogs used here by pairing them up with the GAMA spectroscopic sample. Table 1 summarizes the surveys contributing to our sample for different flux and sky cuts, including the cross-match after the removal of stars and quasars as described later in Section 4.

Our core data set of extended objects is expected to contain a number of AGN and quasars. These will occasionally be outliers in the size distribution, which are much rarer than stars, as well as blends. Low-luminosity, relatively low-redshift, morphologically extended AGN, which dominate the quasar population in our sample, are acceptable as long as their redshifts can be reliably reproduced photometrically. However, blends of a high-redshift quasar with a foreground star, which mimic extended sources and have peculiar colors, as well as quasar-galaxy projections that also can have compromised colors, will be problematic for the photo-z procedure. Such blends lying at high redshifts should preferably be removed from the catalog before the photometric redshift estimation, because their presence may contaminate the derived galaxy sample that is expected to reach up to $z\sim 0.5$. In what follows, we often use the terms "AGN" and "quasar" interchangeably.

Most of the quasars from the WISE × SCOS sample were eliminated through the morphological preselection of resolved SCOS sources, as well as through the flux limits in the optical and infrared bands: high-redshift quasars are typically fainter than low-redshift galaxies in terms of their apparent magnitudes. There are, however, some quasars bright enough to be captured in the sample, while still classified as extended: about 30% of the Sloan quasars/AGN (i.e., CLASS=QSO in SDSS) identified in our flux-limited sample have SCOS ${\mathtt{meanClass}}=1$ (30,000 sources). These are mostly at redshifts of z < 0.6, but some reach up to z > 3.5. The latter are blends of background point-like quasars with a low-redshift foreground galaxy or with a foreground Galactic star, and might be problematic for photometric redshift estimation, regardless of the method used to obtain the photo-zs. AGNs experiencing significant dust obscuration, such as type 2 AGNs, where the accretion disk and the broad-line region are completely obscured, have colors similar to galaxies. In broad-band photometry, quasars at z ≳ 2.3 can be mistaken for low-redshift galaxies because the Lyα spectral break can mimic the 4000 Å break. Additionally, at z ∼ 2.7 and ∼3.5, the optical colors of broad-line, unreddened quasars and Galactic stars are the same (Richards et al. 2006).

To remove as many of the remaining quasars in our sample as possible, we analyzed their multicolor properties, based on the SDSS spectroscopic data cross-matched with our catalog. Stern et al. (2012) proposed $W1-W2\gt 0.8$ as an efficient AGN finder in WISE, which was subsequently used in several other studies to select quasars (e.g., DiPompeo et al. 2014; Donoso et al. 2014). By looking additionally at GAMA sources (which are practically free of quasar contamination), we slightly revised this cut to preserve the completeness of the galaxy sample, and added a second criterion using the optical R band (see Figure 5). Our color cuts to remove quasars are:

$$\begin{eqnarray}&&R-W2\gt 7.6-4(W1-W2)\ \ \mathrm{or}\ \ W1-W2\gt 0.9,\end{eqnarray} \tag{ 3 }$$

where the WISE magnitudes are Vega and the SCOS one AB-like. These criteria remove 71% of SDSS quasars present in our extended source sample, while affecting less than 1% of GAMA galaxies. Nearly all the quasars with 0.5 < z < 2.1 are eliminated through this cut; those that remain are mostly at low redshifts (peaking at z ∼ 0.2), with some at 2.1 < z < 3.5. An alternative way of selecting quasars by using only WISE information through a comparison of W1 − W2 and W2 − W3 colors (Jarrett et al. 2011; Mateos et al. 2012) cannot be applied here because the detection rate of our sources in the W3 band is too low.

Zoom In Zoom Out Reset image size

The cut defined in Equation (3) removed nearly 300,000 quasar candidates from our flux-limited, $| b| \gt 10^\circ$ photometric sample of WISE × SCOS extended sources. Rescaling from the SDSS-based numbers, we thus estimate that there are about 115,000 quasars remaining in the all-sky catalog, which is about 0.6% of the total number of galaxies. Thus our photo-zs derived in Section 5 will only be minimally affected by the high-z quasars that were not filtered out.

We also paired the SDSS DR12 stars with reliable spectra (${\mathtt{zWarning}}=0$ and 0 < Δz < 0.001) against our core sample, and used the result to derive typical stellar colors for star removal. Thanks to the morphological information from SCOS (${\mathtt{meanClass}}=1$ only sources), many of the stars had already been eliminated and only 8% of those common to the Sloan spectroscopic and WISE × SCOS are present in our sample. These "stars" in the catalog of extended sources are expected to be blends, which might be the reason why the separations from their SDSS counterparts are usually larger than in the case of extragalactic sources: 031 ± 026 for SDSS galaxies, 030 ± 029 for quasars, but 040 ± 024 for stars. To avoid mismatches when deriving the color cuts for star removal, we used only the stars paired up within 1'' with our photometric catalog. Note that poorer matching accuracy for the stars might also be partly due to proper motions between the epochs of SCOS photographic material and these of the SDSS (see Madsen & Gaensler 2013 for a related discussion).

To remove stellar contamination we examined the source distribution presented in Figure 3, which clearly shows spurious overdensities (caused by stellar blends) at low Galactic latitudes and at the Magellanic Clouds. We began by rejecting by hand regions in the Galactic Plane and Bulge where the contamination was too severe to contemplate reliable correction (an enhancement in surface density by a factor ∼10). We applied a latitude cut depending on the distance from the Galactic Center (GC): it goes smoothly from $| b| \lt 17^\circ$ at ℓ = 0° to $| b| \lt 10^\circ$ at ℓ ∼ 80° or ℓ ∼ 280°. Detailed equations are provided in the Appendix. This cut removed almost 6 million sources from the flux-limited sample at $| b| \gt 10^\circ$. To this we added circular cutouts around the most prominent nearby galaxies, namely the Magellanic Clouds and M31.

We then investigated what other cuts need to be taken to purify the sample further. This is traditionally done in multicolor space, and we explored different combinations of the available bands based on the cross-match with SDSS spectroscopy. Stars are much more difficult to remove than quasars from our catalog without seriously compromising the completeness of the galaxy sample; this is due to blends of stars with other stars and with galaxies, especially at low redshift, where galaxies from our data set often have colors that are similar to stellar ones. In particular, the SCOS optical bands were found not to be useful for star identification. We were left with the option to use only WISE colors for star-galaxy separation, as had been discussed in earlier studies (Jarrett et al. 2011; Goto et al. 2012; Yan et al. 2013; Ferraro et al. 2015). An advantage of applying infrared-only cuts to our sample is less sensitivity to variations in plate zero points, or in extinction corrections and their errors.

The colors usually considered for WISE source identification are W1 − W2 and W2 − W3, and the former is particularly useful for this task (Jarrett et al. 2011). We found that using W2 − W3 does not add much information, mostly due to the low level of signal-to-noise in the W3 band, and a similar effect is observed in the automatic galaxy identification of T. Krakowski et al. (2016, in preparation). In a related effort, Ferraro et al. (2015) treated as stellar anything with W1 − W2 < 0 or (W1 < 10.5 and W2 − W3 < 1.5 and W1 − W2 < 0.4). However, once these conditions are applied to WISE, they leave a certain degree of contamination that is dependent on the distance from the GC—see Figure 1 in Ferraro et al. (2015). The same is found in our WISE × SCOS catalog, namely a fixed W1 − W2 color cut would give purity levels largely varying over the sky; this is also expected because we are using extinction-corrected magnitudes, so effective stellar colors will be correlated with the E(B − V) map.

To account for star contamination changing with Galactic coordinates, we examined the source density and the W1 − W2 color as a function of distance from the GC and found that the stellar locus shifts as the GC is approached, which we interpret as a reflection of older stellar populations being located toward the Bulge. This lead us to design a position-dependent color cut, the details of which are provided in the Appendix. In brief, at high latitudes we remove sources with W1 − W2 < 0, while this cut is gradually shifted toward W1 − W2 < 0.12 closer to the GC. This adaptive star removal, together with the sky cuts discussed earlier, eliminated more than half the sample, mostly from low Galactic latitudes, as expected (90% of removed sources are within $| b| \lt 34^\circ$). This approach slightly degrades the completeness of the final galaxy sample: almost 6% of WISE × SCOS × GAMA galaxies are removed with this cut. On the other hand, a completeness level of ∼90% in the final sample is preserved for $| b| \gtrsim 15^\circ$, which gives almost 3π sr of the extragalactic sky comprehensively sampled with the catalog. A more detailed discussion of completeness and purity of the galaxy data set is provided in Section 4.4.

In addition, we removed the bright end of our sample (W1 < 13.8) for two main reasons. First, the galaxies that have counterparts in the 2MASS XSC K_s < 13.9 already have precise photometric redshifts derived in the 2MPZ (B14). At low redshifts the typical galaxy color is K_s − W1 ≃ 0, so most of these 2MASS sources are removed by applying this bright-end cut in WISE. Second, most of the bright WISE sources that are not present in 2MASS XSC are stars, because they dominate W1 number counts there (Jarrett et al. 2011) and are concentrated toward the Galactic plane. There were more than 5 million objects with W1 < 13.8 in the cross-matched catalog before the cleanup, of which 90% lay at $| b| \lt 50^\circ$.

Figure 6 shows the all-sky distribution of our sources after the purification and manual cutouts but before final masking, which is addressed in the following Section. In Figure 7 we show source counts per square degree, as a function of the sine of Galactic latitude b, for the cross-matched sample: before and after the star and quasar cleanup, as well as for the sources removed with our cuts. A uniformly distributed (extragalactic) sample should have roughly constant counts in this scaling, which is approximately true for the final data set, as well as for the quasars removed. The bump at $| \mathrm{sin}b| \simeq 0.7$ in the removed sources is the LMC. For comparison, we also show the case of a constant W1 − W2 > 0 cut as in Ferraro et al. (2015). Stellar contamination becomes prominent from $| \mathrm{sin}b| =0.5$ ($| b| =30^\circ$), that is, for half the sky, and the surface density of the sources close to the Galactic Plane is almost twice as large as in the Caps, as visualised in the right panel of Figure 7.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The above cuts helped improve the fidelity of the catalog, reducing the numbers of non-galaxy entries resulting from stellar blends and other problems. Nevertheless, a casual inspection of the sky distribution reveals clear imperfections, especially at low Galactic latitudes; Figure 6 exhibits some spurious source overdensities and a lack of extragalactic data behind Galactic molecular clouds such as Orion, Taurus/Perseus, and Ophiuchus. We thus need to develop a mask that excludes significantly affected regions. This is a common task, but not a trivial one: the human eye is highly adept at spotting artifacts of this sort, and it takes some effort to design an objective, automated process that performs as well. As a starting point, one can identify pixels where the surface density is discrepant, using the fact that the galaxy surface density very nearly obeys a log-normal distribution (Hubble 1934) and clipping pixels in the tails of this distribution. This approach can be made more effective if we perform it at a variety of resolutions: large-scale regions where the density is systematically slightly in error can be found more sensitively by using coarse pixels where the pixel-to-pixel variance is reduced. We therefore constructed a HEALPix³⁰ (Górski et al. 2005) map of the galaxy counts, initially at N_side = 256, identified discrepant pixels, and then repeated the process degrading the resolution by successive factors of two. The final mask is the accumulation of flagged sky areas at all resolutions. However, this process requires an unsatisfactory compromise: in order to remove all apparent artifacts, the clipping threshold has to be set at a rather high probability ( p(δ) ∼ 0.001), with the unacceptable result that the extreme regions of real cosmic structures are also removed.

To deal with this problem, we take the Bayesian approach of bringing in prior information. Most of the problems are associated with the Milky Way, so we can make a good guess in advance about whether a given region should be masked. We therefore consider two indicators of potential problems: extinction and stellar density, measured via E(B − V) and the empirical total WISE density, Σ (to W1 < 17). The latter additionally brings in information on WISE coverage issues that cause spurious over- and underdensities in the source distribution. We use the first estimate of the mask derived from clipping to estimate a prior probability that a given pixel is masked as a function of these variables; this is shown in Figure 8. From this, it is clear that regions at E(B − V) > 0.25 should be completely clipped. We can now repeat the clipping analysis, but considering a full posterior probability that a given pixel is clean:

$$\begin{eqnarray}&&{p}_{c}={f}_{{\rm{prior}}}\times p(\delta ),\end{eqnarray} \tag{ 4 }$$

where f_prior is the fraction of pixels accepted at that Galactic location. It is now possible to clip with a more discerning threshold, p_c ∼ 10⁻⁵, which removes negligible amounts of real large-scale structures, while still remaining sensitive to anomalies at low latitudes. As a further precaution, we apply "guilt by association," and mask all pixels within 1 degree of a masked pixel. Finally, this process can be iterated, updating the prior when a revised mask has been generated. The final mask, shown in Figure 9, it removes 32% of the sky, leaving a satisfactorily clean galaxy sample on 28,000 deg². Applying the mask to the data gives us a final catalog of almost 18.7 million sources, as illustrated in Figure 10. The mean surface density of the sources is about 670 deg⁻², which is a more than 20-fold increase over 2MASS. We note, however, that for cosmological applications it might be more appropriate to repeat the above masking procedure on data that is first preselected in photo-z or other bins (e.g., magnitude).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Having applied all the cuts and the mask aiming at optimizing the reliability of the WISE × SCOS galaxy catalog, we now quantify its levels of completeness and purity. This was done using external data that will be treated as the "truth," ignoring any imperfections. Because our catalog was created by requiring detection in three independently surveyed wavebands, we assume that all our objects are genuine astronomical sources. We then need to measure the purity of the catalog (i.e., the fraction of our objects that are actually galaxies rather than stars) and its completeness (the fraction of all true galaxies that are included).

Purity is relatively easy to assess via cross-matching with SDSS. We selected a one-degree-wide strip centered at $\delta =30^\circ$ with magnitude limits much fainter than those of WISE × SCOS, which yielded more than 130,000 matched sources at $| b| \gt 12^\circ$. From this, we found that at high latitudes, approximately 95% of our sources are indeed galaxies. For latitudes of $| b| \gt 60^\circ$ the stellar contamination of our catalog does not exceed 6%, and remains less than 10% down to almost $| b| =40^\circ$. One could further improve the purity at the expense of completeness; for instance, using a color cut of W1 − W2 > 0.2 instead of the fiducial one used in Section 4.2, would allow for a catalog with a stellar contamination of ≲3% down to $| b| \sim 40^\circ$. Of course, this would also lead to a significant drop in completeness, because about 30% of galaxies have W1 − W2 ≤ 0.2 (typically early types).

Completeness is slightly more complicated to assess thanks to magnitude errors. Even if our catalog was perfect in all other respects, it will still miss many galaxies that are really just brighter than our magnitude limits, and include many that are in reality just slightly fainter. Therefore, the assessment of completeness involves two questions that go beyond noisy magnitudes: (1) What fraction of true galaxies are incorrectly classified by SCOS as stars? (2) What further fraction of galaxies are lost as a result of the color cuts aimed at purifying the sample? The first question can be addressed by looking at a pairing of SDSS data with both the SCOS galaxy and star catalogs (the latter classified as ${\mathtt{meanClass}}=2$). We started with the same SDSS strip centered at δ = 30° as above, synthesized SCOS magnitudes (J. A. Peacock et al. 2016, in preparation), and cut the sample to ${B}_{\mathrm{syn}}\lt 21$ and ${R}_{\mathrm{syn}}\lt 19.5$, looking at the relative numbers that paired with SCOS galaxies and stars. The conclusion is that the overall misclassification incompleteness is about 15%, with some dependence on Galactic latitude. Averaged completeness exceeds 90% for $| b| \gt 40^\circ$ and equals 88% for half the sky ($| b| \gt 30^\circ$). Unsurprisingly, the limited image quality on Schmidt plates leads to compact galaxies being classified as stars. According to Baldry et al. (2010), the corresponding figure for SDSS is about 2% (GAMA does much better because it uses near-IR colors in addition to image width).

Finally, we can use GAMA to measure the effect of the additional color cuts applied in Sections 4.1 and 4.2. The depth and completeness of GAMA are large enough that we can assume that practically each WISE × SCOS galaxy should also be present in GAMA. We thus treat the cross-match of the two catalogs before star and quasar removal as the reference. As already mentioned, the quasar cutout criterion (Equation (3)) affects less than 1% of GAMA galaxies; thus the most important for the final completeness will be the color cut used to discard stellar contamination. Using our prescription for star removal (Section 4.2), we lose about 6% of galaxies at $| b| \geqslant 30^\circ$, increasing to 10% for the lowest latitudes of b ∼ 22 observed by GAMA. We can thus safely assume that, including the 1% drop in completeness due to quasar cutout, our catalog is about 93% complete for half the sky ($| b| \gt 30^\circ$) and more than 90% complete over at least 2.4π steradians (in addition to the classification incompleteness).

This completeness analysis is ultimately limited by the fact that our catalog is a cross-match of two independent samples of different characteristics. Our data set will thus miss some sources that could not be detected by one of the parent surveys, or by both. For instance, WISE is not sensitive to low surface brightness galaxies, while SCOS is biased against the dusty ones that WISE detects very well. Quantification of these effects is beyond the scope of this paper and it would require using much deeper reference catalogs of otherwise very similar preselections than those employed here.

In B14 we presented the potential of applying GAMA as a photo-z training sample for WISE × SCOS all-sky data. Using the shallower GAMA DR2 public release (complete to $r\lt 19.0$ in two of the equatorial fields and to r < 19.4 in the third one; Liske et al. 2015) together with the WISE "All-Sky" and SCOS extended source data, we obtained an accuracy of σ_z ≃ 0.035 at a median redshift of z ∼ 0.18. Here we extend that study using a complete flux-limited r ≤ 19.8 GAMA-II sample, along with deeper AllWISE data, corrected SCOS color calibrations, and Galactic extinction coefficients revised according to Schlafly & Finkbeiner (2011).

We start with the WISE × SCOS × GAMA sample as described in Section 3. We tested photo-z performance for various cuts applied to this data set, such as flux limits being the same as in the all-sky sample discussed in Section 2.3, star and quasar color cuts (Section 4), and so on. We found that photo-z statistics are practically independent of whether the cuts are first applied both on the training and test sample, or only on the latter once ANNz had been trained on the full sample; in other words, it is enough to train the neural networks on the most general training set possible and apply the required cuts on the test set only. The only cut applied a priori to all the GAMA samples discussed in this Section was δ₁₉₅₀ < 25, to avoid residual passband mismatch between SCOS "north" and "south." More discussion of this issue will be provided in Section 5.2.

The WISE × SCOS × GAMA sample of 142,000 sources was divided randomly in proportion 1:9 into training and test sets, and a validation set was additionally separated out from the former (20% of the full training set). Summary statistics for the photo-z tests are provided in Table 3. Note that the outlier fraction is defined here relative to the scatter of each of the particular test sets, so the decrease in the scatter may lead to a slight increase in the outlier rate. The table also includes the statistics computed separately for the three GAMA equatorial patches (in the case of no flux limits in WISE × SCOS), showing that the variations in the photo-z accuracy between these fields are not significant. Comparing the general results with Table 2 of B14 shows that the current photo-z performance is very similar to the one achieved with GAMA DR2, taking into account the increased depth of the present sample. It is also worth noting that our uncertainty of σ_z ≃ 0.03 for the flux-limited case is comparable to the results of Christodoulou et al. (2012), where GAMA spectroscopy was applied to train a large SDSS r < 19.4 sample using five-band ugriz photometry. Last but not least, this accuracy is very close to the prediction for future surveys such as Euclid or LSST (Ascaso et al. 2015).

Table 3.  Statistics for the Photometric Redshift Estimation Generated for a Test Sample of WISE × SuperCOSMOS Sources in GAMA Equatorial Fields

# of	Mean $\langle z\rangle$		Median $\bar{z}$		1σ Scatterd	Scaled	Norm.	Mean Biasg	Median	% of
Sourcesa	Specb	Photc	Specb	Photc	σδz/(1+z)	MADe	SMADf	$\langle \delta z\rangle$	Errorh	Outliersi
Trained and tested on GAMA
no flux limits
127,703	0.231	0.231	0.223	0.233	0.045	0.044	0.036	−7.3e−5	14.1%	2.8%
separate fields
(G09) 37,810	0.242	0.240	0.242	0.244	0.044	0.045	0.037	−2.0e−3	14.0%	2.4%
(G12) 48,974	0.229	0.230	0.221	0.231	0.045	0.044	0.036	6.8e−4	14.5%	2.7%
(G15) 40,919	0.223	0.224	0.211	0.224	0.044	0.043	0.036	7.6e−4	14.6%	2.9%
flux limited B < 21 and R < 19.5 and W1 < 17
86,516	0.200	0.200	0.191	0.202	0.041	0.040	0.033	−3.7e−4	14.7%	2.8%

Notes. Two cases are shown: (i) no flux limits applied to the photometric sample; (ii) fiducial flux limits as in the final data set. In the former case, we also show statistics for the particular GAMA fields.

^aIn the test set. ^bInput (spectroscopic) redshift sample. ^cOutput (photometric) redshift sample. ^dNormalized 1σ scatter between the spectroscopic and photometric redshifts, σ_{δz/(1 + z)}; unclipped. ^eScaled median absolute deviation, $\mathrm{SMAD}(\delta z)=1.48\times \mathrm{med}(| \delta z-\mathrm{med}(\delta z)| )$. ^fScaled median absolute deviation of the normalized bias, $\mathrm{SMAD}(\delta z/(1+{z}_{\mathrm{sp}}))$. ^gMean bias of z_phot: $\langle \delta z\rangle =\langle {z}_{{\rm{phot}}}-{z}_{{\rm{spec}}}\rangle ;$ unclipped. ^hMedian of the relative error, $\mathrm{med}(| \delta z| /{z}_{\mathrm{sp}});$ unclipped. ⁱPercentage of outliers for which $| ({z}_{\mathrm{ph}}-{z}_{\mathrm{sp}})/(1+{z}_{\mathrm{sp}})| \gt 3\;\mathrm{SMAD}(\delta z/(1+{z}_{\mathrm{sp}}))$.

Download table as:  ASCIITypeset image

Figures 11–13 illustrate the general performance of our photometric redshifts trained and tested on GAMA for the flux-limited WISE × SCOS sample. A comparison of ${z}_{\mathrm{spec}}$ with ${z}_{\mathrm{phot}}$ (Figure 11) and ${z}_{\mathrm{phot}}$ with the difference between them (Figure 12) confirms the expected property of the photo-zs being unbiased in the true ${z}_{\mathrm{spec}}$ at a given ${z}_{\mathrm{phot}}$ (Driver et al. 2011; B14; Sadeh et al. 2015); a non-flat N(z) must lead, however, to the redshifts being photometrically overestimated at the low end and underestimated at high z.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The redshift distribution (Figure 13) shows similar features to those in Figure 13 of Driver et al. (2011), where photo-zs were derived using ANNz for an earlier version of GAMA. The ${dN}/{{dz}}_{\mathrm{phot}}$ diagram is narrower than the spec-z one and the former is unable to reproduce sharp features in the latter, such as the dip at z ∼ 0.23 and several peaks related to clusters and walls. However, the quality of our photometric redshifts is impressive given that we used only two optical bands. The latter limitation cannot currently be overcome when constructing nearly all-sky photo-z samples with the presently available data, because they are covering much more of the sky at z ∼ 0.2 than available from, for example, SDSS only (D'Abrusco et al. 2007; Oyaizu et al. 2008; Brescia et al. 2014; Beck et al. 2016).

5.1.1. Dependence on Apparent Properties

We have examined the photometric redshift performance as a function of various observed and intrinsic properties of the galaxies. As far as the former are concerned, we found no alarming patterns in the photo-z accuracy as a function of apparent magnitudes in the four bands used in the procedure, other than a general deterioration in the photometric redshift quality as the sources become fainter, which is consistent with expectations. Note, however, that because our catalog is produced by combining optical and infrared preselections, in some magnitude bins, the fainter sources are not necessarily more distant. This, together with the dependencies of photometric redshifts on varying magnitude, is illustrated for the W1 band in Figure 14. Here we inverted the axes with respect to Figure 11 to emphasize possible systematics for samples selected in photo-z and magnitude bins, as will be practical for the full-sky sample where spectroscopic redshifts are not available. Some issues are evident, such as the lack of ${z}_{\mathrm{phot}}\gt 0.3$ galaxies for W1 > 15.5.

Zoom In Zoom Out Reset image size

This analysis of photometric redshift properties can be made more detailed by binning the data further. In particular, in addition to W1 intervals, we also divided the test set into bins of the observed B − R color (in ${\rm{\Delta }}(B-R)=0.5$ mag), as well as of ${z}_{\mathrm{spec}}$ and ${z}_{\mathrm{phot}}$ (in bins of Δz = 0.1). This gives two 3D "tables," each cell of which contains photo-z statistics as in Table 3. The extracts of these two tables are provided in Table 4 for a particular bin of ${z}_{\mathrm{spec}}$ (${z}_{\mathrm{phot}}$) and of B − R. Full electronic versions of these tables can be made available on request.

Variations of the photometric redshift quality are also observed with WISE W1 and W2 signal-to-noise levels, which are already strongly correlated with the flux. In particular, there is a noticeable decrease in photo-z accuracy for sources with ${\mathtt{w}}{\mathtt{2}}{\mathtt{snr}}\lt 5$, as compared with those with ${\mathtt{w}}{\mathtt{2}}{\mathtt{snr}}\gt 5$: the former have an order of magnitude larger mean bias $\langle \delta z\rangle$ than the latter and a considerably larger scatter in δz. Interestingly, in the cross-matched WISE × SCOS × GAMA sample, the low-${\mathtt{w}}{\mathtt{2}}{\mathtt{snr}}$ sources are on average located at smaller distances than the high-${\mathtt{w}}{\mathtt{2}}{\mathtt{snr}}$ ones: the ${\mathtt{w}}{\mathtt{2}}{\mathtt{snr}}\lt 5$ galaxies have ${z}_{\mathrm{med}}\simeq 0.13$ (spectroscopic) and practically never reach beyond z = 0.4. The low-${\mathtt{w}}{\mathtt{2}}{\mathtt{snr}}$ sources, however, constitute a small fraction (less than 5%) of our galaxy catalog, and are mostly localized in several strips crossing the ecliptic, resulting from moon avoidance maneuvers.

5.1.2. Dependence on Intrinsic Properties

After performing all the tests discussed above, we trained the ANNz algorithm on the full GAMA-south sample (142,000 sources, of which 98,000 fall within the flux limit of the core WISE × SCOS catalog) and applied the resulting networks to the cleaned data set described in Section 4. Figure 15 compares the normalized redshift distributions of the WISE × SCOS × GAMA spectroscopic input (red bars) with the all-sky WISE × SCOS photometric output (black line). In Figure 16 we present the absolute ${dN}/{dz}$, in logarithmic scaling, for three "all-sky" data sets: 2MASS Redshift Survey (2MRS; Huchra et al. 2012), 2MASS Photometric Redshift catalog (2MPZ; B14), and the WISE × SCOS photo-z sample. This clearly illustrates the great improvement in information that WISE × SCOS brings at z > 0.1 as compared with 2MASS.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

As described in Section 2.2, and discussed earlier in Francis & Peacock (2010) and B14, the SCOS passbands between the north ("N," δ₁₉₅₀ > 25) and the south ("S") were slightly different; if not accounted for, this can lead to a bias between the photometric redshifts in the two "hemispheres." The first step toward making N and S consistent was to calibrate the two parts using Equations (1)–(2) from Section 2.2. In B14 a possible residual photo-z bias due to imperfect calibration was avoided by training the neural networks separately for N and S, which was possible thanks to comprehensive training sets in both parts of the sky. At the depths of the present sample, using GAMA data for photo-z derivation in each hemisphere is not practical because the majority of the data set is below δ = 25: only 9% of the GAMA sample is in the north. Such a training set of ∼10,000 sources is too small for proper calibration of the photo-zs for ∼10⁷ WISE × SCOS objects.

In the absence of a large northern spectroscopic data set of GAMA's depth, there is no direct solution to this problem. We therefore rely, in the first instance, on the color corrections by which we attempt to place SCOS photometry in both hemispheres on a uniform basis. However, there exist remaining inconsistencies in the photo-zs between N and S, which we address in the same way as in Francis & Peacock (2010): examine the probability distribution of photo-zs in the two "hemispheres" and make an adjustment to the redshift scale so that these distributions are consistent. The result of the procedure is illustrated in Figure 17, where the derived offset z_S − z_N is plotted as a function of z_N. In all cases, such a correction is a small fraction of the photo-z precision, but it does seem to be real. Therefore, for the sources at δ₁₉₅₀ > 25, we added this offset to the individual photo-zs derived with ANNz.

Zoom In Zoom Out Reset image size

An additional test of photometric redshift quality comes from extending the purity analysis of Section 4.4. Examining photo-z distributions of the sources identified as galaxies and as stars in the cross-match with the photometric SDSS data, we found that the stars contaminating the full-sky sample are assigned photo-zs peaking at z ∼ 0.05 rather than zero; because the training sample used to derive the photo-zs contains no stars, the neural networks will then assign them redshifts of galaxies that are closest in the parameter space. But interestingly, some stars are assigned very high redshifts: at ${z}_{\mathrm{phot}}\gt 0.4$, more than 40% of the WISE × SCOS photo-z sample is stellar contamination. However the absolute source numbers are very small at these redshifts: only 144,000 of the sources have such photo-zs (less than 1% of the full sample). In general, we conclude that the final sample can be purified further over what was discussed in Section 4 by removing the lowest- and highest-photo-z bins. The contamination is always smaller than 20% for a cutout of $0.085\lt {z}_{\mathrm{phot}}\lt 0.345$, which is 90% of the full sample; the purity improves further if the lowest Galactic latitudes are discarded. We would like to emphasize that for cosmological studies benefiting from "tomographic" slicing in redshift bins, the z < 0.1 range is better sampled by 2MPZ (B14), rather than the present catalog owing to the much higher completeness, purity, and photo-z accuracy of the former.

With these reservations, Figure 18 shows examples of three photo-z shells of Δz = 0.1 extracted from the full WISE × SCOS sample, centered, respectively, on z = 0.15, z = 0.25, and z = 0.35, and including, respectively, 7.3, 7.4, and 1.7 million sources. To produce these images we made one final correction for the redshift-dependent stellar contamination discussed above, which serves to mitigate large-scale non-uniformities, especially in the lowest redshift shell. We correlated the surface density in the slice with the total WISE sky density (treated as a proxy for stellar density) and removed the appropriate scaled fraction to remove the stellar gradients. This process is successful in yielding redshift slices with no apparent large-scale artifacts. These are the most comprehensive illustrations of all-sky galaxy distribution at these redshifts available so far, revealing new large-scale structures. In particular, neither 2MASS, nor especially 2MRS or PSCz, could reach to depths of z > 0.15 in a comprehensive manner. Three-dimensional sampling of the cosmic web at these scales has been so far possible only with SDSS, covering three times less sky than our catalog, and being less complete beyond r > 17.77 as far as the spectroscopic data are concerned.

Zoom In Zoom Out Reset image size

As a final "blind" test of the photometric redshifts in our catalog, and to verify whether they exhibit noticeable variations in performance over the sky, we cross-matched the sample with a number of external redshift catalogs. Such an exercise is only meaningful for auxiliary data sets that are complete to a depth at least similar to the present sample. For that reason, the cross-matched catalogs mainly cover small fields: other than GAMA, there are currently no other wide-angle spectroscopic data sets complete to its depth (otherwise we would have used them for the photo-z training). In fact part of the GAMA data is included in this test, as some of them were not used in the photo-z derivation and tests described above. These include the equatorial data from the G09 and G15 fields above δ₁₉₅₀ > 25 (cf. Section 5.1), as well as the southern G02 and G23 fields (which are less complete than the equatorial ones; Liske et al. 2015), and the much deeper G10/COSMOS field (Davies et al. 2015). Except for the very deep but small (∼2 deg²) G10 field, all of these have high matching rates with WISE × SCOS because they have the same (G09 and G15) or very similar (G02 and G23) preselections as the "fiducial" GAMA data used for the photo-z training.

We paired several other publicly available data sets³⁴ with WISE × SCOS; however, only a fraction had a significant matching rate, and we discuss here only those that had at least 500 common sources with our catalog. In all cases, we used a 2'' matching radius, which is a compromise between minimizing spurious cross-matches that could result from imprecise astrometry, and maximizing the matching rate for cases of not well defined centroids.

Details regarding the fields' central coordinates, areas, and the WISE × SCOS photo-z statistics (calculated with respect to the redshifts provided in the external data sets) are provided below and listed in Table 4. The samples included are:

• 1.  
  GAMA data in the equatorial G09 and G15 fields located at ${\delta }_{1950}\gt 2\buildrel{\circ}\over{.} 5;$ this is part of the sample comprehensively described in Section 3, removed from the photo-z training and test phase due to the SuperCOSMOS north–south band difference (cf. Section 2.2); this sample includes 17,523 galaxies with ${z}_{\mathrm{med}}=0.217$ after cuts of z > 0.002 and redshift quality ${\mathtt{NQ}}\geqslant 3$.
• 2.  
  GAMA G02 field (TilingCat v04): a spectroscopic redshift survey of a ∼56 deg² field centered at α = 345, δ = −7°, currently not publicly available (part of GAMA-II, Liske et al. 2015), with targets preselected from SDSS DR8 (Aihara et al. 2011) and CFHTLenS (Heymans et al. 2012) photometric data sets to a limiting magnitude of r < 19.8, although not fully complete to this limit over the whole field (Liske et al. 2015); this sample includes 33,677 galaxies with ${z}_{\mathrm{med}}=0.226$ after cuts of z > 0.002 and redshift quality ${\mathtt{NQ}}\geqslant 3$.
• 3.  
  GAMA G23 field (TilingCat v11): a spectroscopic redshift survey of a ∼87 deg² field centered at α = 345°, δ = −325, currently not publicly available (part of GAMA-II, Liske et al. 2015), with targets preselected from KiDS (de Jong et al. 2013) to a limiting magnitude of i < 19.2, although not fully complete to this limit over the whole field (Liske et al. 2015); this sample includes 47,489 galaxies with ${z}_{\mathrm{med}}=0.208$ after cuts of z > 0.002 and redshift quality ${\mathtt{NQ}}\geqslant 3$.
• 4.  
  AGES (AGN and Galaxy Evolution Survey; Kochanek et al. 2012): a spectroscopic redshift survey covering ∼10 deg², centered at α = 2178, δ = 343, with targets preselected to a limiting magnitude of I < 20 from several data sets at various wavelengths; this sample includes 21,805 galaxies with ${z}_{\mathrm{med}}=0.342$ after a cut of ${z}_{\mathrm{spec}}\gt 0$ (measured spectro-z).
• 5.  
  SHELS (Smithsonian Hectospec Lensing Survey; Geller et al. 2014): a spectroscopic redshift survey of a ∼5 deg² field centered at α = 140°, δ = 30°, with targets preselected from the Deep Lens Survey (Wittman et al. 2006), complete to a limiting magnitude of R ≤ 20.6 with part of the sources beyond this limit; this sample includes 15,591 galaxies with ${z}_{\mathrm{med}}=0.317$ after a cut on the redshift error e_z < 0.001 and using only unmasked sources.
• 6.  
  G10/COSMOS data set: a publicly available redshift catalog (Davies et al. 2015), part of GAMA, covering 2 deg² in the COSMOS field (α = 1501, δ = 22), obtained by re-reducing archival spectroscopic zCOSMOS-bright data (Lilly et al. 2007, 2009), together with input from other sources (PRIMUS, SDSS, VVDS); the sample includes 16,128 galaxies with ${z}_{\mathrm{med}}=0.533$ after applying the flag ${\mathtt{Z}}\_{\mathtt{USE}}=1$ (reliable high resolution spectroscopic redshift) and a cut on redshift z > 0.
• 7.  
  PRIMUS (PRIsm MUlti-object Survey; Coil et al. 2011; Cool et al. 2013): a low-resolution spectroscopic redshift survey covering a total of ∼10 deg² in nine fields to a depth of ${i}_{\mathrm{AB}}\sim 23.5$, preselected from several imaging data sets; here we used only the ${\mathtt{ZQUALITY}}=4$ sources (highest quality redshifts) that gave 87,742 objects in total with ${z}_{\mathrm{med}}=0.476;$ one should bear in mind, however, that even for these sources, the PRIMUS spectroscopic redshift precision is σ_δz/(1+z) = 0.005 (Cool et al. 2013).
• 8.  
  COSMOS photometric redshift catalog (Ilbert et al. 2009): providing very accurate photo-zs based on 30-band photometry from UV through mid-IR; this is the same field as in the case of G10/COSMOS GAMA release, but the number of sources is much larger because there is no requirement of spec-z availability; we used version 1.5 of the catalog, magnitude-limited to I < 25, which includes 304,999 objects with photo-zs measured ($0\lt {\mathtt{zp}}\_{\mathtt{best}}\lt 9.99$ in the catalog), with ${z}_{\mathrm{med}}=0.888;$ at the bright end of interest for this exercise, the COSMOS photo-zs have a scatter of σ_δz/(1+z) = 0.007 (Ilbert et al. 2009), which is comparable to the accuracy of PRIMUS low-res spectro-z.

Table 4.  Extract from Tables Showing Photometric Redshift Statistics in Bins of Redshift (Separately Spectroscopic and Photometric), Observed B − R Color and Apparent W1 Magnitude

redshift bin	B − R color bin	W1 mag bin	% of sourcesa	mean biasb	1σ scatterc
Trained and tested on GAMA
binned in spectro-z
0.2 < ${z}_{\mathrm{spec}}$ < 0.3	1.5 < B − R < 2.0	W1 < 14	113	−0.0135	0.0251
		14 < W1 < 15	2667	0.0111	0.0245
		15 < W1 < 16	4001	0.0152	0.0236
		16 < W1 < 17	92	−0.0131	0.0284
binned in photo-z
$0.2\lt {z}_{\mathrm{phot}}\lt 0.3$	1.5 < B − R < 2.0	W1 < 14	112	−0.0135	0.0287
		14 < W1 < 15	2591	−0.0002	0.0261
		15 < W1 < 16	4179	−0.0015	0.0336
		16 < W1 < 17	144	−0.0025	0.0437

Notes.

^aIn the test set. ^bMean bias of ${z}_{{\rm{phot}}}$: $\langle \delta z\rangle =\langle {z}_{{\rm{phot}}}-{z}_{{\rm{spec}}}\rangle ;$ unclipped. ^cNormalized 1σ scatter between the spectroscopic and photometric redshifts, σ_{δz/(1 + z)}; unclipped.

Download table as:  ASCIITypeset image

Table 5.  Statistics for the Photometric Redshift Estimation, Calculated for WISE × SuperCOSMOS Sources Cross-matched with External Redshift Catalogs

External	Area	Coords.	# of	Mean $\langle z\rangle$		Median $\bar{z}$		1σ sc.e	Scaled	Norm.	Biash	Median
Data set	(deg2)	(α, δ)a	Sourcesb	Specc	Photd	Specc	Photd	σδz/(1+z)	MADf	SMADg	$\langle \delta z\rangle$	Errori
lGAMA
equatorial		(135, 2.65) and
δ1950 > 2.5	16.8	(217.5, 2.65)	9,404	0.213	0.203	0.202	0.205	0.041	0.041	0.034	−9.9e−3	14.8%
G02	55.9	(34.5, −6.95)	17,812	0.211	0.205	0.207	0.207	0.039	0.038	0.031	−6.2e−3	13.4%
G23	87.2	(345, −32.5)	29,270	0.200	0.202	0.201	0.205	0.039	0.039	0.033	+1.6e−3	14.4%
AGES	10.4	(217.9, 35.9)	4,770	0.209	0.199	0.195	0.198	0.042	0.038	0.032	−9.7e−3	13.8%
SHELS	4.8	(139.9, 30)	2,272	0.222	0.208	0.216	0.209	0.043	0.043	0.035	−9.8e−3	14.6%
G10/COSMOS	2	(150.1, 2.2)	603	0.226	0.202	0.218	0.201	0.068	0.039	0.033	−2.4e−2	15.6%
PRIMUSj	∼ 10	−44 < δ < 3k	3,222	0.227	0.215	0.215	0.217	0.059	0.046	0.038	−1.2e−2	15.3%
COSMOSl	2	(150.1, 2.2)	918	0.214	0.207	0.220	0.209	0.045	0.045	0.037	−7.5e−3	15.8%

Notes. See text for details on the auxiliary data sets.

^aCentral coordinates of the field(s) in degrees. ^bIn the cross-match with the WISE × SCOS fiducial sample. ^cExternal redshifts for a sample cross-matched with WISE × SCOS. ^dWISE × SCOS photometric redshifts for a sample cross-matched with the external data set. ^eNormalized 1σ scatter between the spectroscopic and photometric redshifts, σ_{δz/(1 + z)}; unclipped. ^fScaled median absolute deviation, $\mathrm{SMAD}(\delta z)=1.48\times \mathrm{med}(| \delta z-\mathrm{med}(\delta z)| )$. ^gScaled median absolute deviation of the normalized bias, $\mathrm{SMAD}(\delta z/(1+{z}_{\mathrm{spec}}))$. ^hMean bias of z_phot: $\langle \delta z\rangle =\langle {z}_{{\rm{phot}}}-{z}_{{\rm{spec}}}\rangle ;$ unclipped. ⁱMedian of the relative error, $\mathrm{med}(| \delta z| /{z}_{\mathrm{spec}});$ unclipped. ^jLow-resolution spectroscopy, σ_{δz/(1 + z)} = 0.005. ^kNine fields over this declination range. ^lAccurate photometric redshifts, σ_{δz/(1 + z)} = 0.007.

Download table as:  ASCIITypeset image

Several other data sets were tested, but they either gave less than 500 cross-matches with WISE × SCOS each, or were too shallow for meaningful photo-z statistics. The latter case includes the SDSS spectroscopic data: while it does provide a very high matching rate with our catalog (more than 1/3 of SDSS DR12 spectroscopic galaxies are also in the WISE × SCOS fiducial sample), the specific preselections of SDSS targets leads to biased photo-z statistics. In order to circumvent this, one could try applying some weighting procedures, such as those discussed in Lima et al. (2008), which is beyond the scope of the present work.

The mean and median redshifts quoted in Table 4 differ from those in Table 2 (flux-limited case) either because of different preselections of the external fields and/or, as in the case of GAMA equatorial data at δ₁₉₅₀ > 2.5, due to the bright-end flux cut of W1 = 13.8 applied to the fiducial WISE × SCOS sample, but not to the one referred to in Table 2. This is a minor detail that does not influence the conclusions.

Overall, the statistics provided in Table 4 do not indicate any significant variations of the WISE × SCOS photo-z quality among the tested samples, and hence over the sky. In particular, in most cases the scatter in δz/(1 + z) (as measured through SMAD) is within 0.035, the mean bias of δz is <0.01 and the median error in $| \delta z| /z$ is within 15%. These numbers are very similar to those obtained in the GAMA equatorial fields in the test phase summarized in Table 2. On the other hand, the apparently worse results for the G10/COSMOS, PRIMUS, and COSMOS catalogs should be taken lightly. These data sets have either a very low matching rate with our catalog (being very deep but covering small areas), and/or have low-resolution spectroscopy, or provide only photometric redshifts, even if they have very high accuracy. In particular, the PRIMUS scatters in the spectroscopic redshifts of ∼0.005 and the COSMOS scatter in photo-z of ∼0.007 are comparable to the mean bias of WISE × SCOS photo-zs and are less than an order of magnitude smaller than the SMAD of the latter. Thus for these samples, the comparison of the "true" redshift with the WISE × SCOS photometric one brings in uncertainty in the former parameter, which leads to apparent deterioration of the photo-z statistics.