CANDELS/GOODS-S, CDFS, AND ECDFS: PHOTOMETRIC REDSHIFTS FOR NORMAL AND X-RAY-DETECTED GALAXIES

Altogether the ECDFS has been covered by 50 bands from ultraviolet (UV) to mid-infrared (MIR) as listed in Table 1. Table 2 summarizes the catalogs used in each area.

• 1.  
  Area 1. In this region, we primarily used the CANDELS-TFIT multi-wavelength catalog of Guo et al. (2013, hereafter G13), which covers the CANDELS GOODS-S area with 18 broadband filters mostly from space observatories. The photometry was based on template-fitting (TFIT; Laidler et al. 2007), using the high-resolution WFC3/H-band image to detect sources and define apertures, which were then used for photometry in lower-resolution images. TFIT was also applied to the MIR data from the Spitzer Extended Deep Survey (SEDS; Ashby et al. 2013). This deblending yields more accurate photo-z and also increases the probability of making correct X-ray to IR associations (see Section 3). In addition, the Area 1 data include 18 IBs at optical wavelengths provided by the MUSYC team¹⁷ (Cardamone et al. 2010). CANDELS collaborators (J. L. Donley et al. 2014, in preparation) have produced an IB-TFIT catalog with the same parameters used by G13. Despite being up to two magnitudes shallower than the rest of the optical data, the IB data are useful for identifying emission lines, which can modify the choice of template best fitting the data and thus the photo-z (see Section 6.3). To these 36 bands we also added the near-UV (NUV) and far-UV (FUV) data from GALEX Data Releases 6 and 7. The association between GALEX data and the WFC3/H-band catalog was done via positional matching within a radius of 1''. About 5% of all sources and ∼25% of X-ray-detected sources have UV counterparts. The combined data, which we refer to as "TFIT_{CANDELS + IB}," have 34,930 sources with up to 38 bands for computing photo-z.
• 2.  
  Areas 2+3. These areas differ in depth of X-ray coverage (Section 2.2) but have the same data sets otherwise. For the CDFS and ECDFS surrounding Area 1, we merged the following photometric catalogs via coordinate cross match, allowing a maximum separation of 1'': (1) GALEX catalog (as above), (2) the original MUSYC catalog (Cardamone et al. 2010), and (3) the J- and K_s-band data from the Taiwan ECDFS Near-Infrared Survey¹⁸ (TENIS; Hsieh et al. 2012). Although TENIS is no deeper than existing NIR data, the TENIS data are more homogeneous over the entire field and have slightly different transmission curves, increasing the wavelength coverage. The MIR data for Areas 2 and 3 came from the Spitzer IRAC/MUSYC Public Legacy in ECDFS (SIMPLE; Damen et al. 2011). These data are shallower than the SEDS data available in Area 1. Table 1 lists the data sets used, and we refer to this data set as "MUSYC+TENIS." There are 70,049 sources in this photometry.

The X-ray catalogs to cross-match were obtained from the Chandra survey of 4 Ms CDFS observations covering Areas 1+2 and from the 250 ks ECDFS observations covering Area 3. Two independent groups (Xue et al. 2011; Rangel et al. 2013) have provided source catalogs for 4 Ms CDFS using different methods for data reduction and source detection. Similarly for Area 3, both Lehmer et al. (2005) and Virani et al. (2006) have released X-ray source catalogs for the 250 ks ECDFS survey. We have cross-matched X-ray sources from both catalogs in each area.

• 1.  
  For Areas 1+2 we used the following.

  • (a)  
    The 4 Ms CDFS source catalog of (Xue et al. 2011, hereafter X11) with 740 point-like X-ray sources. The sensitivity limits of the X-ray data are 3.2 × 10⁻¹⁷, 9.1 × 10⁻¹⁸, and 5.5 × 10⁻¹⁷ erg cm⁻² s⁻¹ for the full (0.5–8 keV), soft (0.5–2 keV), and hard (2–8 keV) bands, respectively.
  • (b)  
    The 4 Ms CDFS source catalog of Rangel et al. (2013) (hereafter R13)¹⁹ produced using the analysis methodology of Laird et al. (2009). The catalog contains 569 point-like X-ray sources and has sensitivity limits of 4.2 × 10⁻¹⁷, 1.2 × 10⁻¹⁷, and 8.8 × 10⁻¹⁷ erg cm⁻² s⁻¹ in the full, soft, and hard bands, respectively.
• 2.  
  For Area 3 we used the following.

  • (c)  
    The 250 ks ECDFS X-ray catalog from Lehmer et al. (2005, hereafter L05) with 762 sources in the entire ECDFS of which 457 are in Area 3 (i.e., outside the 4 Ms CDFS area). Catalog sensitivity limits are 1.1 × 10⁻¹⁶ erg cm⁻² s⁻¹ in the soft (0.5–2 keV) band and 6.7 × 10⁻¹⁶ in the hard (2–8 keV) band.
  • (d)  
    The 250 ks ECDFS X-ray catalog from Virani et al. (2006, hereafter V06) with 651 sources in the entire ECDFS of which 404 are in Area 3. Sensitivity limits are 1.7 × 10⁻¹⁶ and 3.9 × 10⁻¹⁶ erg cm⁻² s⁻¹ in the soft and hard bands, respectively.

The availability of spec-z for a subgroup of sources is essential for computing reliable photo-z via SED fitting (Dahlen et al. 2013). A subset of spec-z can first be used for training under the assumption that they are representative of the entire population. A different subset can then be used for testing photo-z quality. For this work, we cross-matched the photometric catalogs to a compilation of spec-z (N. Hathi, private communication), allowing a maximum separation of 1''. There are 2314 (∼7%) Area 1 sources that have reliable spec-z and 3880 (∼6%) such sources in Areas 2 and 3 (2016 in Area 2, 1864 in Area 3).

As discussed by Dahlen et al. (2013), optimal results are obtained when the templates used for the photo-z computation are calibrated on the photometry available for the spectroscopic training samples. For this reason, the training samples should fully span the entire magnitude–redshift parameter space. Figure 2 shows that the 1000 sources randomly selected as our training samples are indeed spread over all redshift and magnitude ranges in the respective areas. Because the photometry available in Area 1 differs from that in Areas 2+3, two sets of training samples and computations of the zero-point offsets²⁰ were used.

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For the X-ray sources, we forgo using the training sample for computing zero-point offsets and instead use it to sample the AGN population and help build the AGN–galaxy hybrid templates needed for proper SED fitting and photo-z measurement (Salvato et al. 2009). For this purpose, we randomly chose ∼25% of the 4 Ms CDFS detections with available spec-z over the entire range of redshift and magnitude that have CANDELS data and used them as the training set to build hybrid templates. The remaining ∼75% were used for unbiased testing of the results. Details are given in the Appendix.

• 1.  
  Areas 1+2.The major difference between the R13 and X11 catalogs is that R13 adopted a higher threshold for source detection. Despite that, there are some sources in the R13 catalog but not in X11. There are also astrometric differences, which can affect the association with an optical/NIR/MIR counterpart. Thus the redshift assigned to the X-ray source and also to the supposed counterparts can be different because different template libraries and priors were used for X-ray galaxies than for normal ones. In order to match X-ray catalogs, we shifted the X11 positions by −0175 in right ascension and 0284 in declination ²¹ to register them to the optical frame (Giavalisco et al. 2004). The R13 catalog is already on the MUSYC optical frame and was not shifted.After astrometric shifting, we matched the X11 and R13 catalog coordinates, allowing a maximum distance of 10''. There are 545 sources in common with a maximum offset <6'' as shown in Figure 3. For these 545 sources, neither catalog has any additional X-ray source within 10''. As expected, all of the large offsets are for sources at large off-axis angles. For off-axis angles <6', the median coordinate offset is 013, and except for one source, the maximum offset at any off-axis angle is <35. We treat each of the 545 matched sources as a single X-ray detection. 54% of these sources have a distance from each other larger than the positional error claimed for either of the catalogs. In addition, there are 195 sources detected by X11 but not R13 and 24 sources detected by R13 but not X11 for a total of 764 X-ray sources in Areas 1+2. As R13 mentioned, the unique sources to either of the two catalogs are mostly low-significance detections and therefore of lower reliability. In the following discussions, "X-" sources indicate those from X11 and "R-" those from R13.
• 2.  
  Area 3.We adopted the Cardamone et al. (2008) astrometric calibration to align the V06 positions to the MUSYC and L05 catalogs, which were already in agreement. After the shift, the two catalogs have 366 source matches with offsets <6''. These have a median separation of 016 (Figure 4). We consider these 366 sources to be the same X-ray detections. Twelve percent of these sources have a separation that is larger than the positional error associated with either of the catalogs. In addition, there are 91 sources in the L05 catalog but not in V06 and 38 sources in the V06 catalog but not in L05 for a total of 495 X-ray sources in Area 3. A compilation of the four X-ray catalogs with their original positions and fluxes is available under [Surveys] > [CDFS] through the portal http://www.mpe.mpg.de/XraySurveys.

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We used a new association method based on Bayesian statistics which allows pairing of sources from more than two catalogs at once while also making use of priors. M. Salvato et al. (2014, in preparation) will provide full details on this association method, but in brief, the code finds matches based on the equations developed by Budavári & Szalay (2008). Then additional probability terms based on the magnitude and color distributions are applied (see Naylor et al. 2013 for a similar approach). The code was developed in view of the launch of eROSITA (Merloni et al. 2012), where an expected one million sources will be scattered over the entire sky and will have a nonnegligible positional error and/or nonhomogenous multi-wavelength coverage, conditions not optimal for association methods like maximum likelihood (e.g., Brusa et al. 2007; Luo et al. 2010; Civano et al. 2012). The new method provides the same quality of results as the maximum likelihood method in a much shorter time because matches are done simultaneously across all bands. Thus, for example, sources that are extremely faint or undetected in optical bands but brighter in the IRAC 3.6 μm band can be identified as counterparts in a single iteration.

For the 4 Ms CDFS sources (X11 and R13) located in Area 1, we used the CANDELS/H-selected catalog, TENIS/$J\&K_s$-selected catalog, MUSYC/BVR-selected catalog, and the deblended SEDS/IRAC 3.6 μm catalog. For the 4 Ms-CDFS sources located in Area 2, we matched the X-ray sources to the TENIS/$J\&K_s$-selected catalog, MUSYC/BVR-selected catalog, and SIMPLE/IRAC 3.6 μm catalog. The same set of these three catalogs was also used in Area 3 to find the associations for the 250 ks ECDFS sources (L05 and V06). Table 2 summarizes the catalogs matched in each area.

For each X-ray source (740 from X11, 569 from R13, 440 from L05, and 374 from V06), we considered all catalog objects lying within 4'' of the X-ray position and computed the posterior probability p that the given object is the correct counterpart. Figure 5 shows the distribution of the posteriors for all the possible associations in the three areas. In Area 1 where the data are deeper and better resolved, more than 98% of the X-ray sources have at least one association with p > 0.7, and we consider this p value the threshold for defining an association in all three areas. Area 3 has a distribution of p that reaches lower values, but because of the shallowness and lower resolution of the data, we do not consider the association with p < 0.7 to be reliable. Our catalogs (see Section 7) include the p value to allow users to define a stricter threshold, depending on the scientific use intended.

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Figure 6 shows examples of ambiguous identifications. In all three cases shown, a single X-ray source has two possible H-band associations with p > 0.99. Even the simultaneous use of deblended IRAC photometry from SEDS does not help in associating a unique counterpart. The example in the middle shows that despite the high resolution of the CANDELS images, the upper source is still blended, and probably, a third component is present. If a further deblending were applied, the H flux would be split among multiple components, thus reducing the probability of the upper source being the right association. In practice, we attempted no further deblending and simply flagged these kinds of objects as sources with multiple counterparts. For these cases, in addition to the photo-z computed using normal galaxy templates, we also provide the values obtained by assuming that they are AGNs. The photo-z results reveal that ∼20% of these close pairs have similar redshifts and may be associated with galaxy mergers or galaxy groups. However, the majority of apparent pairs are projections of unrelated objects.

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Figure 7 shows the decision tree for X-ray source associations and computing photo-z, and Table 3 gives numbers for each case in each area. There are four cases.

• 1.  
  Case 1. An X-ray source in both catalogs with one optical/NIR/MIR association. Case 1 means the same unique association was chosen even though the X-ray catalog positions may differ between X11 and R13 or between L05 and V06. There are 714 of these sources in Areas 1 + 2 + 3.
• 2.  
  Case 2. An X-ray source in both catalogs with differing optical/NIR/MIR associations. Case 2 can arise from two causes: (1) position differences in the X-ray catalogs may point to different counterparts or (2) there may be more than one potential counterpart near the X-ray position(s), and we cannot tell which is the right one. Some of the latter may be blended sources with more than one galaxy contributing to the X-ray flux. In total, there are 181 case 2 sources in Areas 1 + 2 + 3. These sources are identified in the final catalogs and counterpart photo-zs are calculated using both AGN and normal galaxy SED templates (see Section 7).
• 3.  
  Case 3. X-ray sources found in one catalog but not the other, having a unique counterpart. There are 235 of these sources in Areas 1 + 2 + 3.
• 4.  
  Case 4. X-ray sources found in only one catalog and having multiple possible counterparts. There are 77 such sources in Areas 1 + 2 + 3. As for Case 2, the catalogs identify all the possible counterparts and provide both AGN and normal galaxy photo-z results for each.

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Table 3. Results of X-ray to Optical/NIR/MIR Associations in ECDFS

	Nx	Case1	Case2	Case3	Case4	$N_{{\rm ctp}}^{{\rm single}}$	$N_{{\rm ctp}}^{{\rm multi}}$	Nctp	$N_{{\rm ctp}}^{{\rm multi}}/N_{{\rm ctp}}$	Nctp/Nx
Area 1	509	272	67	130	29	402	96	498	19%	98%
Area 2	255	170	29	35	12	205	41	246	17%	96%
Area 3	495	272	85	70	36	342	121	463	26%	94%
TOTAL	1259	714	181	235	77	949	258	1207	21%	96%

Notes. N_x: number of X-ray sources. $N_{{\rm ctp}}^{{\rm single}}$: number of sources that have only one possible counterpart. $N_{{\rm ctp}}^{{\rm multi}}$: number of sources that have more than one possible counterpart. N_ctp: total number of sources for which at least a counterpart was found.

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In summary, 1207 out of 1259 (∼96%) of the X-ray sources are associated with multi-wavelength counterparts and 258 of them (∼21%) have possible multiple counterparts. There are 26 sources for which the counterpart is detected only in the IRAC bands and no photo-z computation is possible for these. All the other sources have at least six photometric points and a photo-z is provided. The photo-z catalog (see Section 7) entry for each source indicates the number of photometric points used for the photo-z computation. The remaining 52 sources (∼4%) either have no identifications in any of the optical/NIR/MIR catalogs (∼1%) or have possible counterparts identified with p < 0.7 (∼3%). For these sources, the photo-z are not available as well.

X11 used likelihood ratio matching to assign counterparts to 716 out of 740 X-ray sources in Areas 1+2. Our code and the newly available ancillary data give secure counterparts (with p > 0.9) for seven additional sources shown in Figure 8. Most of the new counterparts are offset from the X-ray position by one to two times the X-ray position uncertainty. The most likely reason for finding new identifications is having better imaging data available, but there remains a chance that some of the X-ray sources are not real.

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Figure 9 shows an example of a revised X-ray association. In this case, low-resolution catalogs give a single counterpart for the source (R-57 = X-234) for either X-ray position. However, the high-resolution WFC3/H-band image reveals at least four sources close together, and the slightly different coordinates provided by X11 and R13 point to different but equally likely counterparts. This difference is mainly due to the catalogs chosen for cross-matching rather than the matching method. The Bayesian method should in principle give the same result as the maximum likelihood method, but the ability to match several catalogs simultaneously greatly improves the efficiency of the matching.

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The overall outlier fraction of ∼3.8% in this region is comparable to the most recent work by the CANDELS team (Dahlen et al. 2013). However, the deblended IB photometry from MUSYC improves the accuracy to σ_NMAD = 0.012 (from σ_NMAD = 0.026 by Dahlen et al. 2013) and bias_z = −0.001 (from bias_z = −0.005). Figure 10 illustrates the results. Outlier fractions and scatter are larger for the fainter galaxies (Table 4), but bias is only a weak function of source magnitude. Bias is, however, larger for z > 1.5 galaxies than for those at lower redshifts. Scatter and outlier fraction are also larger at z > 1.5, but this mostly reflects the typically fainter magnitudes of the more distant sources.

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The decreased outlier fraction in the present survey requires both the deeper CANDELS-TFIT data and the deblended IB photometry. Table 5 gives data quality measures for 1541 sources in common using various data sets. Using only MUSYC+TENIS, but not the deep TFIT_{CANDELS + IB} data, produces the same data quality as Cardamone et al. (2010) which is expected. However, using the TFIT_{CANDELS + IB} photometry decreases the outlier fraction from ∼4% to ∼2%, and the decrease is most substantial (more than a factor of two) for the faint and distant sources (see Table 5). Figure 11 illustrates the comparison and, in particular, the decrease in outliers at z_s > 2. The difference comes from the use of deep space-based data (i.e., CANDELS) and the TFIT technique for deblending the lower-resolution bands. However, the IB data are also important. Dahlen et al. (2013) used the CANDELS-TFIT data; while their results (included in Table 5) are better than with the ground-based data alone, they are not as good as with the combined data sets (i.e., TFIT_{CANDELS + IB}). Adding the IB data improves results—mainly in accuracy but also in outlier fraction—even for the fainter subset of the sample.

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Table 5. Comparison of Photo-z Results for Normal Galaxies in Area 1

		TFITCANDELS + IB			MUSYC+TENIS			Cardamone+2010			Dahlen+2013
	N	$\mathrm{{\rm B}ias}_{z}$	σNMAD	η(%)	$\mathrm{{\rm B}ias}_{z}$	σNMAD	η(%)	$\mathrm{{\rm B}ias}_{z}$	σNMAD	η(%)	$\mathrm{{\rm B}ias}_{z}$	σNMAD	η(%)
Total	1541	0.000	0.011	2.14	0.003	0.012	3.96	0.000	0.011	3.96	−0.005	0.026	2.47
R < 23	506	0.003	0.009	0.79	0.002	0.008	0.79	0.002	0.008	0.99	−0.002	0.026	0.99
R > 23	1035	−0.002	0.013	2.80	0.003	0.016	5.51	−0.001	0.016	5.41	−0.006	0.026	3.19
H < 23	1064	0.001	0.010	1.60	0.003	0.010	2.07	0.000	0.010	2.07	−0.006	0.027	1.97
H > 23	477	−0.002	0.014	3.35	0.002	0.021	8.18	0.000	0.022	8.18	−0.001	0.024	3.56
z < 1.5	1308	0.002	0.010	2.14	0.004	0.011	3.13	0.002	0.010	2.98	−0.005	0.026	2.45
z > 1.5	233	−0.014	0.019	2.15	−0.002	0.030	8.58	−0.008	0.045	9.44	−0.002	0.023	2.58

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Outside the CANDELS area, photo-z quality using MUSYC+TENIS photometry is similar to that of Cardamone et al. (2010). Figure 12 illustrates the results. The brighter and lower-redshift subsets have photo-z quality almost as good as in Area 1 (see Table 4), but fainter galaxies have a higher outlier fraction. This is just as expected from the tests in Section 4.1.

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The entire ECDFS (Areas 1 + 2 + 3) contains ∼104, 000 normal galaxies that have photo-z up to z ∼ 7. Figure 13 shows the advantage of using WFC3 NIR to detect more sources in total and especially at z ≳ 2. An interesting paradox is that we actually have a slightly lower fraction of sources at z > 1.5 than Cardamone et al. (2010). This is probably because their higher outlier fraction, lacking deep NIR data, leads to more outliers with apparent z > 1.5.

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Luo et al. (2010) computed photo-z for sources in the 2 Ms CDFS by using the spectra of known sources as templates for SED fitting. Using the entire spectroscopic sample for template training gave an apparent accuracy ∼0.01 with almost no outliers. However, unbiased testing suggested a true accuracy of 0.059 and ∼9% outliers. This demonstrates how important the training sample is. For the same field, Cardamone et al. (2010) created hybrid templates by combining normal galaxy templates with the SED of a type 1 AGN. The method gave accurate results (σ_NMAD ∼ 0.01) but a large outlier fraction (∼12%). Salvato et al. (2009, 2011, hereafter S09, S11) pursued a different approach for X-ray sources in the COSMOS field (Scoville et al. 2007) detected by XMM (Cappelluti et al. 2009) and by Chandra (Elvis et al. 2009). This involved (1) correcting the photometry for variability when applicable, (2) separating the optical counterparts to the X-ray sources into two subgroups—point-like and/or variable sources in one and extended, constant sources in the other, (3) applying absolute magnitude priors to these two subgroups, assuming that the former are AGN-dominated while the latter are galaxy-dominated, and (4) creating AGN–galaxy hybrids, using different libraries for the two subgroups. This same procedure substantially reduced the fraction of outliers and gave higher accuracy than standard photo-z techniques when applied to X-ray sources in COSMOS. The procedure has also yielded reliable results for the Lockman Hole (Fotopoulou et al. 2012) and AEGIS fields (Nandra et al. 2014, submitted). S11 also verified the need for depth-dependent template libraries by showing that hybrids defined for XMM-COSMOS are not optimal for the deeper Chandra-COSMOS. Even though the X-ray-faint Chandra sources are AGNs (i.e., L_x > 10⁴²), normal galaxy templates gave better results for them than AGN-dominated templates.

For this work, we constructed new hybrid templates following the procedure of S09 and S11 (Section 5.1). First we point out that the difference in the X-ray flux distributions between the two X-ray surveys used in this work (i.e., 4 Ms CDFS and 250 ks ECDFS) is even more extreme than what we have found in S11 (i.e., XMM-COSMOS and Chandra-COSMOS).

Figure 14 shows the soft X-ray flux distributions of the 4 Ms and 250 ks sources, together with the distributions from the Chandra-COSMOS (Elvis et al. 2009) and XMM-COSMOS (Cappelluti et al. 2009). The left panel shows the distribution in numbers for each survey. Because of the sky coverage and the depth of the observations, most of the 4 Ms CDFS sources are located in the faint part of the flux distribution, which is opposite to the locus occupied by the shallower observations (e.g., XMM-/Chandra-COSMOS and 250 ks ECDFS). After normalizing by the total surveyed area²⁶ (see the right panel), it reveals that the X-ray bright sources that are similar to the XMM-COSMOS sources are very rare in the 4 Ms survey. This implies that the library of hybrids used in XMM-COSMOS is probably not representative of the 4 Ms population. Based on these considerations, we need to build a new library for the fainter 4 Ms CDFS population. The Appendix gives details, but in short, AGN SEDs were combined in various proportions with semi-empirical galaxy SEDs (the same as already successfully used by Gabasch et al. 2004, Drory et al. 2005, and Feulner et al. 2005) from the FORS Deep Field (Bender et al. 2001) to make hybrid templates. The AGN SEDs were the modified QSO1 and QSO2 originally from Polletta et al. (2007). Separate libraries were used for (a) point-like sources in Areas 1 + 2, (b) point-like sources in Area 3, and (c) extended sources in all areas. Because the flux distribution of point-like sources in Area 3 is similar to that of the XMM-COSMOS field, library (b) for point-like sources in that area was the same as used by Salvato et al. (2009).

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As a first step, we split the sources into extended and point-like subgroups depending on the observed source FWHM in the WFC3/H-band images for Area 1 and the MUSYC/BVR images for Areas 2 and 3. The extended sources were assumed to be host-dominated, and being seen as extended means they are likely to be at low redshift. For these sources, we applied an absolute magnitude prior −24 < M_B < −8 and used templates with at most a small AGN fraction. Point-like sources are usually AGN-dominated and can be at any redshift. We therefore applied a prior −30 < M_B < −20 to these and used hybrid AGN–galaxy templates. The library of stellar templates was the same as used by Ilbert et al. (2009) and Salvato et al. (2009).

For the XMM-COSMOS field, Salvato et al. (2009) had multi-wavelength, multi-epoch observations spanning several years. About one-fourth of sources seen in those were variable. The lack of multi-epoch data for the CDFS/ECDFS means that we cannot detect the variable objects and correct their photometry. However, these objects are a minor contributor to the X-ray population in the much smaller CDFS area (1/15 of XMM-COSMOS area). Therefore, only a minor fraction of the Area 1 and 2 sources are likely to be variable. The major effect of being unable to correct for variability will be an increased outlier fraction rather than a decreased photo-z accuracy (Salvato et al. 2009). Area 3, covering a 250 ks depth, is an intermediate case, and part of the photo-z inaccuracy there could be due to a lack of variability correction. The spectroscopic testing in the respective areas (Table 6) quantifies the outlier fractions and the inaccuracies resulting from all causes.

In Area 1, where TFIT_{CANDELS + IB} photometry and high-resolution space-based images are available, the photo-zs for X-ray sources (Table 6) are as accurate as those for normal galaxies (Table 4). Remarkably, the outlier fraction is actually lower for the X-ray sources than for normal galaxies. Excellent photo-z quality is maintained even for z > 1.5. Figure 15 shows that the results are largely attributable to the WFC3 data with their high angular resolution. Instead of using ground-based data (i.e., MUSYC+TENIS), the use of TFIT_{CANDELS + IB} catalog allows us to reduce the outlier fraction by a factor of five. The improvement is especially great for the R > 23 and z > 1.5 sources. The outlier fraction decreases from 6.3% to 2.1% for faint sources and from 12.8% to 2.6% for high-redshift sources. Comparison with Area 2 also confirms the importance of the WFC3 data. Without these data, photo-z accuracy deteriorates only slightly (Table 6), but the outlier fraction triples. Most of the outlier increase comes from the R > 23 and z > 1.5 subsets. (There are only two sources with H > 23 and numerical results for that bin are meaningless.)

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Area 3 has a larger fraction of outliers than either of the other two Areas, though accuracy for the nonoutliers is slightly worse than in Areas 1 and 2 (Table 6). Three effects probably contribute to the larger fraction of outliers. One is shallower photometry at the border of the field (Figure 1), leading to larger errors. Second, the X-ray coverage is shallower in the larger Area 3, thus the fraction of varying Type 1 AGNs is presumably higher. The lack of variability correction will therefore have a larger effect. This is likely exacerbated by the third effect, having to use ground-based images rather than higher-resolution images for classifying sources as point-like or extended. In Area 1, about 30% of sources are classified as point-like using WFC3 but extended on a ground-based image due to the low resolution of the images and being sensitive to the presence of nearby sources. Using the template library for the extended sources rather than for point-like classification would have doubled the outlier fraction.

Furthermore, in order to identify possible outliers among the sources without spec-z, we look at the distribution of observed-frame X-ray luminosity as a function of redshift. In Figure 17, three sources with apparent extreme redshift are probably outliers. They are located on the edge of the optical images and have unreliable or nonexistent MUSYC photometry, leaving only six photometric data points (from the TENIS catalog). Photo-zs with so few data points cannot be trusted.

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Using spec-z to estimate photo-z accuracy (as in Tables 4 and 6) is not representative of sources fainter than the spectroscopic limit. Quadri & Williams (2010) introduced a method for estimating photo-z accuracy based on the tendency of galaxies to cluster in space. Because of clustering, galaxies seen close to each other on the sky have a significant probability of being physically associated and having the same redshift. Therefore, the distribution of photo-z differences²⁷ (Δz_p) of close pairs will show an excess at small redshift differences over the distribution for random pairs. This is seen in Figure 18.²⁸ The excess for close pairs with a magnitude J < 28 fits a Gaussian with standard deviation σ = 0.012 in Area 1 and 0.010 in Areas 2 + 3. Because the width includes the scatter from both paired galaxies, the photo-z uncertainty for an individual object should be $\sigma / \sqrt{2}$. These values are given in Table 7.²⁹ The pair test reveals that the faint sources without spec-z have photo-z accuracies similar to that of sources bright enough to have spectroscopic data.

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Previous work has shown the importance of IB photometry for photo-z, particularly because IB data can show the presence or absence of emission lines in galaxy SEDs. For example, Ilbert et al. (2009) showed that including IBs improved photo-z accuracy from 0.03 to 0.007 for normal galaxies with i⁺ < 22.5 in the COSMOS field. Cardamone et al. (2010) found the same in the ECDFS. For AGNs, Salvato et al. (2009) showed that for both extended and point-like X-ray sources in COSMOS, accuracies and outlier fractions were substantially better when IBs were included.

In the current data, the IB photometry is much shallower than the NIR data from CANDELS (Table 1). To examine whether the shallow IB data are helpful or not in this case, we recomputed the Area 1 photo-z with exactly the same CANDELS-TFIT data set (Guo et al. 2013) used by Dahlen et al. (2013), i.e., without IBs. Results are given in Table 5, and Figure 19 compares results with IBs and without.

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Without the IBs, the outlier fraction is 5%, accuracy is 0.037, and bias_z = −0.010. These are similar to the results of Dahlen et al. (2013) "method 11H," which used the same code as this work. The negative value of bias_z indicates underestimation of photo-z on average. That results in lower galaxy luminosities and incorrect rest colors. As discussed by Rosario et al. (2013), these may lead to incorrect measurements of galaxy ages and stellar populations. The IB data improve the accuracy and mean offset substantially, creating a narrower and more symmetric peak of photo-z values around the spec-z (Figure 19).

Intermediate bands should be most important for objects that have strong emission lines in their spectra. Strong emission lines can arise either from vigorous star formation or an AGN. To quantify the effect, we applied (inverse) BzK selection (Daddi et al. 2004) to define a sample of star-forming objects among those with reliable spec-z. In order to extend the selection at high redshift, we applied the revised BzK criterion as defined by Guo et al. (2013).³⁰ Figure 20 shows the resulting distributions of photo-z minus spec-z. At all redshifts, the distribution including IB is more peaked and symmetric around zero when IBs are included.

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Ilbert et al. (2009) demonstrated the importance of taking emission lines into account for photo-z. Including lines in the templates improved photo-z accuracy by a factor of 2.5 for bright (i⁺ < 22.5) galaxies in the COSMOS field. The same effect is seen in the deeper TFIT_{CANDELS + IB} data as shown in Figure 21. Although outlier numbers remain similar (∼4%) whether emission lines are included in the templates or not, the distributions of (z_p − z_s) change. At z < 1.5, including emission lines gives much narrower peaks and lower bias. At z > 1.5, the improvement is less than at lower redshifts. Possible reasons are: (1) the contribution of the emission lines is diluted when observed in the NIR bands, which have broader bandwidths than optical bands, (2) the recipes for adding emission lines to the templates may be wrong for high-redshift galaxies, and/or (3) the IB data may be too shallow to affect the high-redshift (and therefore faint) sources. However, even at z > 1.5, the photo-z accuracy still shows a factor of 1.5 improvement (σ_NMAD decreasing from 0.032 to 0.021) when emission lines are included in the templates.

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Because of the different X-ray populations in the 4 Ms CDFS and 250 ks ECDFS surveys, we adopted different libraries for point-like sources in Areas 1 + 2 and Area 3. For the sake of template comparison, we tried using the Area 3 library (i.e., S09) to calculate photo-z for point-like sources in Areas 1 + 2. The fraction of outliers increased from 5.3% to 15%, and the accuracy became two times worse than achieved with the preferred library. Even for R < 23 sources, σ_NMAD went from 0.011 with the proper templates to 0.016 with the old ones. For R > 23 galaxies, the deterioration was from 0.027 to 0.059. In Area 3, on the other hand, using the new templates instead of the S09 ones made photo-z slightly worse: for R < 23, σ_NMAD was 0.009 for the new and 0.008 for the S09 libraries. For R > 23, accuracies were 0.025 and 0.017, respectively. Moreover, bias_z = −0.014 using the S09 library but increased to bias_z = −0.031 with the new library. The better performance of the S09 library in Area 3 can be understood because the population of point-like X-ray sources in the 250 k ECDFS is similar to the XMM-COSMOS population, and the S09 library is more suitable for counterparts of such bright X-ray sources.

UV emission from accretion disks around supermassive black holes makes type 1 AGNs distinguishable from normal galaxies. Therefore, including UV data in the photometry is crucial for SED fitting to obtain accurate photo-z and to decrease outliers for AGNs. To demonstrate this, we compared photo-z for AGNs obtained with and without photometry in the UV bands. About 25% of all the X-ray detected sources in Areas 1 + 2 + 3 have UV data available from GALEX. Among these, 221 sources have spectroscopy available and were used as our test sample. As expected, for the optically extended sources, where the host dominates the emission, there is very little difference in accuracy and fraction of outliers whether UV data are included or not. For 170 extended sources with spectroscopy, including UV data decreases σ_NMAD from 0.013 to 0.012 and η from 5.9% to 5.3%. In contrast, for the 51 point-like (i.e., AGN-dominated) sources, adding the UV data halves the number of outliers (from 23.5% to 11.8%) though with only modest improvement in accuracy (from 0.013 to 0.011). Among the five remaining outliers (see Figure 22), two are faint (mag > 23) in the UV, and three are close to other sources with the UV flux blended in the 10'' GALEX aperture. Deblending the GALEX photometry with TFIT as in the other bands could perhaps improve these cases.

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Table 8 gives cross-IDs and positions for all sources within each area as identified in Table 2. The table also indicates whether a source is a possible counterpart to an X-ray detection.

Table 9 gives the X-ray source list in Areas 1 + 2 + 3 with the position and flux information from the available catalogs. Columns are as follows.

• (1)  
  [HSN2014]: sequential number adopted in this work.
• (2)  
  ID_R13: ID from R13 catalog.
• (3)  
  ID_X11: ID from X11 catalog.
• (4)  
  ID_L05: ID from L05 catalog.
• (5)  
  ID_V06: ID from V06 catalog.
• (6)  
  R.A._x: right ascension of the X-ray source.
• (7)  
  Decl._x: declination of the X-ray sources.
• (8)  
  Flux_s: soft band X-ray flux (erg cm⁻² s⁻¹).
• (9)  
  Flux_h: hard band X-ray flux.
• (10)  
  Flux_f: full band X-ray flux.
• (11)  
  log L_s: soft band X-ray luminosity (erg s⁻¹).
• (12)  
  log L_h: hard band X-ray luminosity.
• (13)  
  log L_f: full band X-ray luminosity.

Note: From Column 6 to 10, we chose the original X-ray data from, in order of priority, R13, X11, L05, and V06.

Table 10 gives photometry for all the possible counterparts to the X-ray sources. For the CANDELS area, this includes the TFIT photometry in the IBs as described in Section 2.1. Columns are as follows.

• (1)  
  [HSN2014]: sequential number adopted in this work.
• (2)–(5)  
  XID: ID from the four X-ray catalogs with the same order as Table 9.
• (6)  
  Xflag: as described in Table 8.
• (7)  
  p: as described in Table 8.
• (8)  
  R.A._opt: right ascension of the optical/NIR/MIR source.
• (9)  
  Decl._opt: declination of the optical/NIR/MIR source.
• (10)–(109):  
  AB magnitude and the associated uncertainty in each of the possible bands (Table 1).

Table 11 gives photo-z results for all sources detected in the CANDELS/GOODS-S, CDFS and ECDFS area. X-ray detections are flagged in the catalog. Columns are as follows.

• (1)  
  [HSN2014]: sequential number adopted in this work.
• (2)  
  R.A._opt: right ascension of the optical/NIR/MIR source.
• (3)  
  Decl._opt: declination of the optical/NIR/MIR source.
• (4)  
  z_s: spectroscopic redshift (N. Hathi, private communication).
• (5)  
  Q_zs: quality of the spectroscopic redshift. (0 = High, 1 = Good, 2 = Intermediate, 3 = Poor).
• (6)  
  z_p: the photo-z value as defined by the minimum of χ².
• (7)  
  1σ^low: upper 1σ value of the photo-z.
• (8)  
  1σ^up: lower 1σ value of the photo-z.
• (9)  
  3σ^low: upper 2.3σ value of the photo-z.
• (10)  
  3σ^up: lower 2.3σ value of the photo-z.
• (11)  
  P(z_p): normalized area under the curve P(z), computed between z_p ± 0.1(1 + z_p).
• (12)  
  z_p2: the second solution in the photo-z, when the P(z_p2) is above 5.
• (13)  
  P(z_p2): normalized area under the curve P(z), computed between z_p2 ± 0.1(1 + z_p2).
• (14)  
  N_p: number of photometric points used in the fit.
• (15)  
  Mod: template number used for SED fitting. 1–48 are the templates from Lib-EXT; 101–130 are the templates from Lib-PT; 201–230 are the templates from S09; 301–331 are the templates from Ilbert et al. (2009), in the same order as the mentioned authors used.
• (16)  
  Xflag: as described in Table 8.
• (17)  
  p: posterior value which indicates the reliability of the X-ray to optical/NIR/MIR. association (as defined in Section 3.2).