A Photometric Redshift Catalog Based on SCUSS, SDSS, and WISE Surveys

The multiband photometric data come from three independent surveys: SCUSS, SDSS, and WISE. The adopted filters are SCUSS u, SDSS ugriz, and WISE W1 and W2. The wavelength coverage ranges from near-ultraviolet to near-infrared (3500 Å–4.6 μm). We describe each survey as below.

SCUSS: SCUSS is a deep u-band imaging survey in the south Galactic cap using the 2.3 m Bok telescope. The telescope is equipped with four 4k × 4k CCDs, which are optimized for the ultraviolet response. The adopted filter is similar to the SDSS u band but slightly bluer and narrower. The survey observations were completed at the end of 2013, covering an area of about 5000 deg². The data release was published in 2015 December. The data products contain calibrated single-epoch images, stacked images, and photometric catalogs. The area covered by the catalogs is about 4000 deg². Figure 1 shows the sky coverage of the SCUSS data. About 75% of the area is covered by SDSS (Zou et al. 2016). The median magnitude limit (5σ point sources) is about 23.2 mag. The catalogs contain coadded magnitude measurements on single-epoch images. These measurements are automatic, aperture, PSF, and model magnitudes for both SCUSS unique objects and SDSS sources. The model photometry is consistent with SDSS, which utilizes SDSS r-band model shape parameters to measure brightnesses on SCUSS images (Zou et al. 2015).

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SDSS: SDSS (York et al. 2000) is an influential survey in the world that can implement both imaging and spectroscopic observations by using a dedicated 2.5 m wide-field telescope at Apache Point Observatory. The final imaging survey covers about 14,000 deg². Most area in the south Galactic cap has been covered after SDSS DR7. SDSS uses a wide-field camera that is made up of 30 CCDs. The imaging observations were taken simultaneously with five broad bands. The magnitude limit with 95% completeness are 22.0, 22.2, 22.2, 21.3, and 20.5 mag for u, g, r, i, and z, respectively. The photometric catalogs contain a number of magnitude measurements, such as Model, cModel, Petrosian, and PSF. The "modelMag" in the SDSS catalog can give unbiased colors of galaxies. It is calculated by applying the r-band galaxy model to other filters.

WISE: WISE is an infrared-wavelength astronomical space telescope launched in 2009. It has performed an all-sky imaging surveys in 3.4, 4.6, 12, and 22 μm, known as W1, W2, W3, and W4, respectively. After 10 months of observations, the telescope depleted the coolant. A new mission called NEOWISE was conducted to search for near-Earth objects with W1 and W2 bands. The imaging resolution is quite low (about 6''). Thus, official all-sky WISE catalogs cannot match the SCUSS/SDSS data, as a large number of sources are lost. The unWISE uses a "forced photometry" technique to measure model magnitudes of SDSS objects in new coadds of WISE images (Lang 2014; Lang et al. 2016). The unWISE catalogs provide flux measurements of all SDSS sources in each WISE band.

In order to estimate photometric redshifts in this paper, the model magnitudes are adopted for all three surveys, since the forced photometry method measures a consistent set of sources between SDSS and SCUSS/WISE and it provides unbiased colors of galaxies. The angular resolutions for WISE W1, W2, W3, and W4 are 61, 64, 65, and 120, respectively. The 5σ point-source sensitivities are better than 0.08, 0.11, 1, and 6 mJy for these four bands (Wright et al. 2010). In addition, the unWISE W1 and W2 photometry makes use of new full-depth coadds of the WISE and NOEWISE-reaction images (Lang 2014) and less than 3% of objects in the W3 and W4 bands have photometric S/Ns larger than 5 in unWISE catalogs. Thus, we only use W1 and W2 bands considering low imaging resolution and much shallower photometry in W3 and W4. The SDSS photometric data in this paper are from Data Releases 10 (DR10; Ahn et al. 2014). To avoid confusion, we mark SCUSS u band as u*. Table 1 lists the information of all filters in SCUSS, SDSS, and WISE. The magnitude limits are estimated as 5σ depths of model magnitudes. All magnitudes in this paper are in the AB magnitude system. They are corrected with the Galactic extinction using the reddening map of Schlegel et al. (1998). From Table 1, we can see that the SCUSS u band is about 1.1 mag deeper than the SDSS u band. The last column in this table gives the percentage of galaxies classified by SDSS with S/Ns larger than 5 for each filter. The SCUSS u-band objects with S/N > 5 are twice more than those of SDSS. In addition to u band, the SDSS z and WISE W2 are relatively shallower.

The spectroscopic data are used as a training set and for assessing the quality of photometric redshifts in our paper. We collect spectroscopic redshifts from several surveys, including SDSS, 6DF, DEEP2, VIPERS, VVDS, and WiggleZ. Table 2 lists the references for these surveys. The SDSS DR13 is the largest contributor including early main galaxies, luminous red galaxies from the Baryon Oscillation Spectroscopic Survey (BOSS) of SDSS III and Extended Baryon Oscillation Spectroscopic Survey (eBOSS) of SDSS IV, and emission-line galaxies from eBOSS. We only select galaxies with secure spectral redshift measurements by using quality flags in the catalogs. These flags and their adopted values are also presented in Table 2. The photometric and spectroscopic data are cross-matched with a matching radius of 2''. The matched numbers of galaxies are shown in the last column of Table 2.

Figure 2 shows the distributions of galaxies with spectroscopic redshifts in both color–color diagram and redshift histogram. Combining spectra from different surveys can improve the completeness of our spectroscopic training set. However, these spectroscopic data are not representative of the full photometric data, so we apply a series of magnitude error and color cuts in Section 3.2 for spectroscopic data to constrain their applicative scope.

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The local linear regression algorithm has been used for photometric redshift estimation in SDSS DR12 (Beck et al. 2016). The basic idea is to use a linear model to describe the relation between redshift and observed colors in the local color space for each target galaxy whose redshift is to be determined. Since the model magnitudes we used are based on the SDSS r-band shape parameters, the r band is regarded as a fiducial. Assuming a target galaxy with magnitudes of (u*, g, r, i, z, W1, W2), we use a vector ${\boldsymbol{s}}$ = (u* − r, g − r, r, r − i, r − z, r − W1, r − W2) to express the photometric SED of the galaxy. The local linear model is formulated as:

$$\begin{eqnarray}&&c+{\boldsymbol{a}}\ {\boldsymbol{\cdot }}\ {\boldsymbol{s}}={z}_{\mathrm{phot}}\approx {z}_{\mathrm{spec}},\end{eqnarray} \tag{ 1 }$$

where c is a constant intercept, ${\boldsymbol{a}}$ are the linear coefficients, z_phot is the photometric redshift to be estimated, and z_spec is the spectroscopic redshift. The basic assumption is that galaxies with similar observed SEDs share the same relation. To estimate the photometric redshift for the target galaxy, we need first to find its nearest neighbors with known spectroscopic redshifts in the color space and then derive the regression coefficients in Equation (1) for these neighbors. The redshift of the target galaxy can be finally determined by filling its SED in this equation.

For this local linear regression algorithm, a training set of galaxies with spectroscopic redshifts are required. In addition, the number of nearest neighbors (k) is also a critical parameter. A value that is too large will destroy the locality of the linear model and, meanwhile, will cost a great deal of computing time. Conversely, a value of k that is too small hardly constrains the linear model. After a test of different values, we set k = 50. For larger k, it improves the redshift estimation performance very little but increases the computing time substantially. The nearest galaxies are selected according to the Euclidean distance to the target galaxy in high dimensional color space. After finding the k nearest neighbors, the model is fitted by minimizing χ² , which is expressed as:

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i=1}^{k}\displaystyle \frac{{({z}_{\mathrm{spec},i}-{\boldsymbol{a}}{\boldsymbol{\cdot }}{\boldsymbol{s}}-c)}^{2}}{{\omega }_{i}},\end{eqnarray} \tag{ 2 }$$

where ω_i is the weight. The k nearest galaxies are treated equally in this paper, so we set ω_i = 1.

The redshifts of the k galaxies are supposed to be approximate, since they have similar colors. However, sometimes there are outliers whose redshifts obviously deviate from other neighbors. It might be caused by large photometric errors or color-redshift degeneracy. We use the redshift residual of the linear regression model to remove outliers. The residual δ_z is the same as that used in Beck et al. (2016), which is expressed as:

$$\begin{eqnarray}&&{\delta }_{z}=\sqrt{\displaystyle \frac{{\displaystyle \sum }_{i=1}^{k}{({z}_{\mathrm{spec},i}-{\boldsymbol{a}}{\boldsymbol{\cdot }}{{\boldsymbol{s}}}_{{\boldsymbol{i}}}-c)}^{2}}{k}}.\end{eqnarray} \tag{ 3 }$$

Galaxies with $| {z}_{\mathrm{spec},i}-{\boldsymbol{a}}\,{\boldsymbol{\cdot }}\,{{\boldsymbol{s}}}_{{\boldsymbol{i}}}-c| \gt 3{\delta }_{z}$ are removed and the linear model are fitted iteratively. The photometric redshift is calculated using the final model. Following Beck et al. (2016), we use δ_z as the error estimation of the photometric redshift. The probability density distribution of (z_phot − z_spec)/δ_z is similar to a standard normal distribution despite a slight overall bias and more extended wings (see Figure 3). It indicates that δ_z gives a fair assessment of the photometric redshift error.

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As described above, a robust training set with known spectroscopic redshifts is required to obtain a reliable local linear regression model. The galaxies with large photometric errors can have influence on the determination of nearest neighbors. We need to introduce photometric error cuts. Besides, color cuts are also needed to exclude galaxies with erroneous color measurements and unusual colors. These error and color cuts are decided empirically and are listed as below:

$$\begin{eqnarray}{\rm{\Delta }}r & \lt & 0.15,\\ {\rm{\Delta }}(g-r) & \lt & 0.42,\\ {\rm{\Delta }}(r-i) & \lt & 0.20,\\ {\rm{\Delta }}(r-z) & \lt & 0.42,\\ {\rm{\Delta }}(r-W1) & \lt & 0.27,\\ {\rm{\Delta }}(r-W2) & \lt & 0.44,\\ 0.68\lt ({u}^{* }-r) & \lt & 6.48,\\ 0.25\lt (g-r) & \lt & 2.27,\\ 0.15\lt (r-i) & \lt & 1.37,\\ 0.27\lt (r-z) & \lt & 1.95,\\ -0.46\lt (r-W1) & \lt & 3.29,\\ -1.05\lt (r-W2) & \lt & 3.83.\end{eqnarray} \tag{ 4 }$$

The cut for r-band magnitude error (Δr) is set to 0.15, which is also adopted in Beck et al. (2016) to remove galaxies with photometric errors that are too large. About 95% of galaxies with spectroscopic redshifts have Δr < 0.15. The error cuts for other colors follow the same fraction. There is no constraint on (u − r) due to large photometric errors of redshifted galaxies at u band. As shown in Equation (4), the error cuts for (g − r) are relatively larger. Our galaxies have median spectroscopic redshift of about 0.4. As the redshift goes up to 0.5, the Balmer break shifts to 6000 Å. Correspondingly, the g-band photometric error increases. The (r − z) and (r − W2) error cuts are also large due to large photometric errors of z and W2 bands. Although these bands have larger photometric errors than other bands, we can still give secure photometric redshifts. The color cuts are set where the highest and lowest 0.5% of galaxies are located. Through both error and color cuts, about 38% of galaxies are removed. The final training set has 396,352 galaxies. Figure 4 shows both r-band magnitude and redshift distributions of galaxies with spectroscopic redshifts before and after those cuts are applied. The r-band magnitude can extend up to about 22.0 mag. After the cuts are applied, the redshift distribution becomes more homogeneous. The redshift extends up to about 0.8.

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The filtered training data through both error and color cuts are equally divided into two subsets. One is used as the training set for deriving the local linear regression model and the other is used as the testing set for accuracy estimation of the photometric redshift. The normalized redshift error presented in Beck et al. (2016) is defined as ${\rm{\Delta }}{z}_{\mathrm{norm}}=\tfrac{{z}_{\mathrm{phot}}-{z}_{\mathrm{spec}}}{1+{z}_{\mathrm{spec}}}$. With the testing set, we achieve an average bias of $\overline{{\rm{\Delta }}{z}_{\mathrm{norm}}}\,=2.28\times {10}^{-4}$ and a standard deviation of σ(Δz_norm) = 0.019. These values are calculated with an outlier rate of P_o = 4.2%, where galaxies are removed iteratively using a 3σ clipping algorithm. The left of Figure 5 shows a comparison between spectroscopic and photometric redshifts of galaxies in the testing set. About 92.7% of galaxies are located in $| {\rm{\Delta }}{z}_{\mathrm{norm}}| \lt 0.05$. The middle and right panels of Figure 5 present Δz_norm as a function of the photometric and spectroscopic redshifts. The 1σ error of Δz_norm as a function of z_spec or z_phot is also overplotted. We can see that the photometric redshift can reach up to 0.6, which is limited by our training set. The bias of Δz_norm is less than 0.01 and σ(Δz_norm) is less than 0.03 at z_spec < 0.6. For galaxies with redshifts z_spec > 0.6, the photometric redshifts tend to be underestimated mainly due to a lack of high-z galaxies in the training set. We provide a comparison of redshift distributions of the nearest neighbors for galaxies at z_spec = 0.3 and z_spec = 0.7 in Figure 6. In contrast to z_spec = 0.3 galaxies, the galaxies at z_spec = 0.7 have their nearest neighbors locating at lower redshifts, so that more neighbors with lower redshifts are involved in the redshift estimations and thus the photometric redshift is underestimated.

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Figure 7 shows Δz_norm as a function of r-band magnitude based on spectroscopic data within color cuts but without error cuts. From this figure, we can see that the photometric redshift error increases with magnitude (or photometric error). Photometric errors strongly limit the accuracy of photometric redshifts. Large photometric errors may lead observed colors of galaxies deviating from true ones and thus affect the finding of nearest neighbors. The redshift bias is less than 0.01 for galaxies with r < 21.5 and can be up to 0.03 at r = 22. The 1σ error is less than 0.04 for galaxies with r < 21 and can be up to about 0.08 at r = 22. In addition to the photometric error, the color-redshift degeneracy can also affect the photometric redshift accuracy. The nearest neighbors with similar colors might have distinct redshifts. In this case, the estimated redshift is likely to be catastrophic.

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The CFHTLS provides publicly available photometric redshifts in four wide fields (Ilbert et al. 2006; Coupon et al. 2009). These four fields cover about 155 deg² with SDSS-like filters. The mean r-band magnitude limit for 80% completeness of point-like sources is about 25.0 mag. The catalogs of Coupon et al. (2009) provide photometric redshifts for galaxies with i < 24. We choose one of the four wide fields (hereafter CFHTLS-W1) to compare with our photometric redshifts. The CFHTLS-W1 is located at (α = 345, δ = − 7°). Most of the area is covered by SCUSS. The CFHTLS-W1 photometric redshifts are calibrated by spectroscopic redshifts, giving a standard deviation of σ(Δz_norm) ∼ 0.037. We also check that there are no biases in CFHTLS-W1 photometric redshifts using our spectroscopic training set, which is shown in Figure 8(a). The CFHTLS provides a deep photometric redshift catalog, while SDSS provides a wide one. We obtain the photometric redshifts for galaxies in the CFWHLS-W1 field from SDSS DR12 (Beck et al. 2016).

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Based on the CFHTLS catalog, the comparison of our and SDSS photometric redshifts are shown in Figures 8(b) and (c). We only selected the galaxies with photoErrorClass = 1 in the SDSS photometric redshift catalog, which are regarded to have best redshift estimations as claimed in Beck et al. (2016). There are about 63,000 galaxies in total. From these plots, we can see that the photometric redshifts from three catalogs are in good agreement for galaxies with z < 0.2. However, the SDSS photometric redshift has serious bias at redshift z > 0.2. The redshift is overestimated at 0.2 < z < 0.4 and underestimated at z > 0.4. The bias can reach up to 0.05. Our photometric redshifts give much smaller bias relative to CFHTLS at z < 0.5.

Usually more photometric bands with appropriate depths give better photometric redshift estimations. Compared with SDSS photometric redshifts, we add deep SCUSS u and two WISE infrared bands. To investigate the effect of SCUSS and WISE data on the photometric redshift estimation, three sets of filters are tested by our redshift estimating method using the same training set. One set is ugriz only from SDSS and the other two are u*griz and u*grizW1W2 from SCUSS, SDSS, and WISE. The top panels of Figure 9 show σ(Δz_norm) and biases (median Δz_norm) as functions of the spectroscopic redshift for these different filter sets. In these plots, we can see that the bias for the three filter sets performs similarly and the redshift is underestimated at z > 0.6. The photometric redshift accuracy of σ(Δz_norm) is slightly improved by replacing the SDSS u band with SCUSS u* at z > 0.2. Although the improvement is less obvious, SCUSS can provide twice more galaxies within the same S/N limit as illustrated in Table 1. After adding infrared W1 and W2 bands, the photometric redshift accuracy is significantly improved, especially for galaxies of z < 0.6. We also show σ(Δz_norm) and bias as functions of the photometric redshift for the three different filter sets in the bottom panels of Figure 9. The bias is less than 0.2% of the overall redshift range. The σ(Δz_norm) at higher z_phot is somewhat larger than that at the same z_spec due to redshift underestimation of high-z galaxies.

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