COSMOS PHOTOMETRIC REDSHIFTS WITH 30-BANDS FOR 2-deg²

Fluxes are measured in 30 bands from data taken on the Subaru (4200–9000 Å), CFHT (3900–21500 Å), UKIRT (12500 Å), Spitzer (3.6–8 μm), and GALEX (1500–2300 Å) telescopes. We refer to P. Capak et al. (2008, in preparation) for a complete description of the observations, data reduction, and the photometry catalog. The equivalent width and the effective wavelength of each filter are listed in Table 1. The sensitivities are given by P. Capak et al. (2008, in preparation) and in Table 1 of Salvato et al. (2008). Table 1 indicates the fraction of sources detected in each band with an error less than 0.2 mag for a selection at i⁺ < 24.5, i⁺ < 25, and i⁺ < 25.5. We summarize below the datasets used in this paper.

• 1.  
  UV: Very deep u* band data were obtained at the 3.6 m CFHT using the Megacam camera (Boulade et al. 2003). The u* band data were processed at the TERAPIX data reduction center.²² The u* band data cover the entire COSMOS field and reach a depth of u* ∼ 26.5 mag for a point source detected at 5σ. The u* band images are also used as priors in the measurement of FUV (1500 Å) and NUV (2300 Å) fluxes in order to ensure a proper deblending of sources in the GALEX images (Zamojski et al. 2007). GALEX fluxes are then extracted using the EM-algorithm (Guillaume et al. 2006). They reach a depth of FUV ∼26 mag and NUV ∼25.7 mag.
• 2.  
  Optical: The COSMOS-20 survey (Y. Taniguchi et al. 2008, in preparation) entailed 30 nights of observation at the Subaru 8.2 m telescope using the Suprime-Cam instrument. The observations are complete in 20 bands: six broadbands (B_J, V_J, g⁺, r⁺, i⁺, z⁺), 12 medium bands (IA427, IA464, IA484, IA505, IA527, IA574, IA624, IA679, IA709, IA738, IA767, IA827), and two narrowbands (NB711, NB816).
• 3.  
  NIR: The catalog includes deep J and K band data obtained using the WFCAM and WIRCAM wide-field infrared cameras on UKIRT and CFHT, respectively. The NIR data reduction is detailed by P. Capak et al. (2008, in preparation) and H. J. McCracken et al. (2008, in preparation). The data reach J ∼ 23.7 mag and K ∼ 23.7 mag for a point source detected at 5σ.
• 4.  
  Mid-IR: Deep IRAC data were taken during the Spitzer cycle 2 S-COSMOS survey (Sanders et al. 2007). A total of 166 hr were dedicated to cover the full 2-deg² with the IRAC camera in four bands: 3.6 μm, 4.5 μm, 5.6 μm, and 8.0 μm. Source detection is based on the 3.6 μm image and the fluxes were measured in the four IRAC bands using the "dual mode" configuration of SExtractor. The IRAC catalog is 50% complete at 1 μJy at 3.6 μm (m_3.6 μm ∼ 23.9 mag).

All of the imaging data were combined to generate a master photometry catalog (P. Capak et al. 2008, in preparation). Photometry was done using SExtractor in dual mode (Bertin & Arnouts 1996). Source detection was run on the deepest image (i⁺ ∼ 26.2 for a point source detected at 5σ). For the UV-NIR data, the point-spread function (PSF) varies from 05 to 15 from the K to the u* images. In order to obtain accurate colors, all the images were degraded to the same PSF of 15 following the method described by Capak et al. (2007). The final photometry catalog contains PSF-matched photometry for all the bands from the u* to the K band, measured over an aperture of 3'' diameter at the position of the i⁺ band detection. For the FUV and NUV data, we transformed the total flux provided for the GALEX-FUV and -NUV counterpart by multiplying it by a factor of 0.759. This factor is the fraction of the flux observed in optical into a 3'' aperture flux as determined for point sources from simulations by Capak et al. (2007). To compensate for this approximation, we add in quadrature 0.1 and 0.3 mag to all the measured errors in the GALEX-NUV and -FUV bands.

For the mid-IR data we did not degrade the optical data to the larger IRAC PSF. Instead, the following procedures were used. An IRAC flux was first associated with the optical sources by matching their positions in each of the four IRAC bands within a search radius of 1''. Following Surace et al. (2004), the IRAC fluxes were then measured in a circular aperture of radius 19. The aperture flux was then converted to a total flux using the aperture correction factors 0.76, 0.74, 0.62, and 0.58 at 3.6 μm, 4.5 μm, 5.6 μm, and 8.0 μm, respectively (Surace et al. 2004). Since the optical fluxes were measured over an aperture of 3'' diameter which encloses ∼75% of the flux for a point-like source, we then multiply the IRAC total fluxes by a factor of 0.75. This approximation provides good agreement between the predicted and observed colors (z⁺ − 3.6 μm and 3.6 μm − 4.5 μm colors). In order to compensate for this approximation, we add in quadrature 0.1, 0.1, 0.3, and 0.3 mag to the errors in the IRAC 3.6, 4.5, 5.6, and 8.0 μm, respectively.

Finally, all magnitudes are corrected for galactic extinction, estimated for each object individually using dust map images from Schlegel et al. (1998). We limit the photo-z analysis to an area of 2-deg² (149.41140 < α < 150.826934 and 1.49878 < δ < 2.91276) which has a uniform and deep coverage in all the bands. Poor image quality areas (e.g., field boundary, saturated stars, satellite tracks, and image defects) are masked. Photo-z are computed only in the non-masked regions with a total covered area of 1.73 deg². There are 126,071, 293,627, and 607,617 sources detected at i⁺ < 24, i⁺ < 25, and i⁺ < 26, respectively.

The spectroscopic samples were observed with the Very Large Telescope (VLT) Visible Multi-Object Spectrograph (VIMOS) spectrograph (zCOSMOS; Lilly et al. 2007) and the Keck Deep Extragalactic Imaging Multi-Object Spectograph (DEIMOS) spectrograph (J. Kartaltepe et al. 2008, in preparation). These two spectroscopic samples have very different selection criteria (see below); they therefore cover very different ranges of redshift and color space, providing a broad sample for evaluation of the photo-z.

The zCOSMOS survey (Lilly et al. 2007) has two components: zCOSMOS-bright with a sample of 20,000 galaxies selected at i* ⩽ 22.5 and zCOSMOS-faint with approximately 10,000 galaxies color-selected to lie in the redshift range 1.5 ≲  z ≲ 3. In the latter, galaxies are selected by color based either on the BzK criterion (Daddi et al. 2004) or the UGR "BM" and "BX" criterion of Steidel et al. (2004), and the magnitude cut was B_J < 24–25 (depending on the color cut). zCOSMOS-bright galaxies were observed using the red grism of VIMOS covering a wavelength range 5500 Å < λ < 9000 Å at a resolution of 600 (MR grism). For the zCOSMOS-faint sample, observations were carried out with the blue grism of VIMOS (3600 Å < λ < 6800 Å) at a resolution of 200.

The zCOSMOS-bright survey is now ∼50% complete. Here we make use of only the extremely secure spectro-z measurements with a confidence level greater than 99% (class 3 and 4). This secure zCOSMOS-bright sample contains 4148 galaxies with a median redshift of ∼0.48. The zCOSMOS-faint survey is in its early stages, and here we use a preliminary sample of 148 galaxies with a median redshift of z_m ∼ 2.2 and as faint as i⁺ ∼ 25. This zCOSMOS-faint spectroscopic sample is not fully representative of the average population at 1.5 < z < 3 due to the selection criteria (e.g., B_J < 24–25).

The Keck II spectroscopic follow-up of 24 μm selected sources (J. Kartaltepe et al. 2008, in preparation) is ongoing and we refer to this sample as MIPS-spectro-z. The DEIMOS spectra cover a wavelength range 4000 Å < λ < 9000 Å at a resolution of 600. This sample of 24 μm selected galaxies contains 317 secure spectro-z (at least two spectral features) with an average redshift of z ∼ 0.74 and apparent magnitude in the range 18 < i⁺ < 25.

For all of the spectroscopic samples used in this paper for testing and verification of the photo-z, we include only secure spectro-z. Therefore, the uncertainties in the spectro-z are neglected and the spectro-z are used as a reference to assess the quality of the photo-z.

Ilbert et al. (2006) and Mobasher et al. (2007) used a set of local galaxy SED templates (Coleman et al. 1980, hereafter CWW) which have been widely employed for photo-z (e.g., Sawicki et al. 1997; Fernández-Soto et al. 1999; Arnouts et al. 1999; Brodwin et al. 2006). Here, we employ a new set of templates generated by Polletta et al. (2007) with the code GRASIL (Silva et al. 1998). Polletta et al. selected their templates for fitting the VIMOS VLT Deep Survey (VVDS) sources (Le Fèvre et al. 2005) from the UV-optical (CFHTLS; McCracken et al. 2007) to the mid-IR (SWIRE; Lonsdale et al. 2003). Therefore, this set of templates provides a better joining of UV and mid-IR than those by CWW. The nine galaxy templates of Polletta et al. (2007) include three SEDs of elliptical galaxies and six templates of spiral galaxies (S0, Sa, Sb, Sc, Sd, Sdm).

We did find that the blue observed colors of the spectroscopic sample were not fully reproduced by the Polletta et al. (2007) templates. We therefore generated 12 additional templates using Bruzual & Charlot (2003, hereafter BC03) models with starburst (SB) ages ranging from 3 to 0.03 Gyr. We extend the BC03 templates beyond 3 μm rest-frame using the Sdm template of Polletta et al. (2007). The full library of template SEDs, nine from Polletta et al. (2007) and 12 from BC03, is shown in Figure 1. Finally, we linearly interpolated between some Polletta et al. templates to refine the sampling in color–z space.

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Figure 2 shows the observed colors and redshifts of the spectroscopic sample compared with the predicted colors for the library SEDs.

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Figure 2 clearly shows how the observed colors oscillate with the redshift, especially when the colors are measured with the medium bands (top panels). Comparing the template curves with (dashed) and without (solid) emission lines, one sees that the expected line fluxes can cause up to 0.4 mag changes in the color. This effect is particularly important when colors involving intermediate and narrowband filters are computed (see, for example, the upper right panel in Figure 2) but can be already noticed using broadband colors. The color oscillations are well explained by the contribution of emission lines like Hα, [O iii], and [O ii] to the observed flux, thus the contribution of the emission lines to the flux must be taken into account to obtain accurate photo-z; this is a major change implemented here compared with Ilbert et al. (2006) and Mobasher et al. (2007).

In order to include the emission line contribution to the SED, we need to model the emission line fluxes (O ii, O iii, Hβ, Hα, Lyα) at any redshift, template, and extinction. The rescaling of the template (A in Equation (2)) determines also the emission line fluxes (therefore, the modeling of the fluxes must be done galaxy by galaxy).

Our new procedure estimates the [O ii] emission line flux from the UV luminosity of the rescaled template, using the Kennicutt (1998) calibration laws. In the template fitting, a UV rest-frame luminosity corrected for dust extinction can be computed at every step of the redshift/template/extinction grid (the rescaling factor A is taken into account in the UV luminosity). The UV luminosity (at 2300 Å) is then related to the star formation rate (SFR) using the relation SFR(M_☉ yr⁻¹) = 1.4 × 10⁻²⁸L_ν(erg s⁻¹ Hz⁻¹) from Kennicutt (1998). This SFR can then be translated to an [O ii] emission line flux using the relation ${\rm SFR}\;(M_{\odot }\;{\rm yr}^{-1})= (1.4 \pm 0.4) \times 10^{-41} L_{[{\rm O}\,\hbox{\sc} \mathsc{ii}]}\;({\rm erg}\;{\rm s}^{-1})$ (Kennicutt 1998). This translates to

$$\begin{equation} \log (F_{[{\rm O}\,\hbox{\sc} \mathsc{ii}]}) = -0.4\times M_{\rm UV} + 10.65 - \frac{{\rm DM}(z)}{2.5}, \end{equation} \tag{ 1 }$$

where DM is the distance modulus, $F_{[{\rm O}\, \mathsc{ii}]}$ is expressed in units of 10⁻¹⁷ erg s⁻¹ cm², and M_UV is the dust-corrected UV(2300 Å) absolute magnitude.

Figure 3 shows the measured [O ii] fluxes from VVDS (F. Lamareille et al. 2008, in preparation) and the relation (solid line) expected from Kennicutt (1998). We can perform this comparison only at 0.5 < z < 1.4, when the [O ii] line is observable in the VIMOS spectra. Figure 3 shows good correlation between the measured and predicted [O ii] fluxes, with an rms dispersion of 0.2 dex. In the acknowledgment of this dispersion, we allow the intrinsic [O ii] flux to vary by a factor of 2 in the templates with respect to the nominal flux predicted by Equation (1).

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With our procedure, we can predict for each galaxy the [O ii] flux at every redshift, template, and extinction combination. For the other emission lines, we adopt intrinsic, unextincted flux ratios of [O iii/O ii] = 0.36, [Hβ/O ii] = 0.61, [Hα/O ii] = 1.77, and [Lyα/O ii] = 2 (McCall et al. 1985; Moustakas et al. 2006; Mouhcine et al. 2005; Kennicutt 1998). When we apply an additional extinction to the template, we modify these ratios with the corresponding attenuation. Then, we sum the emission line fluxes to the template continuum before integrating through the filter transmission curves.

The effect of these emission lines on the modeled color–redshift relation is shown in Figure 2 for a galaxy at M_UV = −20. The oscillations in the observed colors versus redshift are well reproduced by the models.

The χ² template-fitting method is meaningful only if the color–z relation predicted from the templates is a good representation of the observed color–z relation. Uncertainties in the zero-point offsets of photometric bands can lead to systematic shifts between the predicted color–z relation and the observed colors of the spectroscopic sample.

To evaluate the zero-point errors, we use the spectroscopic sample and set the redshift to the spectro-z value. Then, we determine the best-fit template for each spectroscopic galaxy. For random, normally distributed uncertainties in the flux measurements, $\overline{\Delta F_f}$ should be ∼ 0 (where $\overline{\Delta F_f}$ is the average difference between predicted and observed fluxes in the filter f). Instead, we initially find systematic offsets of $\overline{\Delta F_f}$ (as for earlier photo-z derivations, e.g., Brodwin et al. 2006; Ilbert et al. 2006; Mobasher et al. 2007). Such offsets are mainly due to (1) uncertainties in the absolute calibration of the photometric zero points and (2) uncertainties in the color modeling (filter transmission curves, incomplete set of templates, or an incorrect extinction curve). These systematic offsets were removed using the iterative procedure detailed in Ilbert et al. (2006). For each filter, f, we estimate the values s_f which minimize $\overline{\Delta F_f}$. After having applied the corrections, s_f, in each band f, the systematic offsets derived in a second iteration can change. The values converge after three iterations and we adopted the systematic offsets listed in Table 1.

Ilbert et al. (2006) adopted the dust-extinction law measured in the Small Magellanic Cloud (Prevot et al. 1984). However, considerable changes in the extinction curve are expected from galaxy to galaxy. Maraston et al. (2006) considered as a free parameter the different extinction curves of the "Hyperz" package (Bolzonella et al. 2000; e.g., Milky Way, Large and Small Magellanic Clouds, and Calzetti). In order to limit the risk of catastrophic failures, we adopt an intermediate approach here, using the most suitable extinction curve depending on the SED template.

For each galaxy of the zCOSMOS sample, we set the redshift to the spectro-z value. Then, we determine the best fit-template and the appropriate color excess E(B − V)^best. In this fit, we assume an extinction curve k(λ) (=A(λ)/E(B − V)). Since the extinction curves do not differ strongly at λ > 3000 Å (the blue and green curves in Figure 4), we fit the templates using only passbands with λ>3000(1 + z) Å. With this procedure, the E(B − V)^best value does not depend significantly on the adopted extinction curve.

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The extinction curves differ strongly at λ <  3000 Å. Therefore, we use the rest-frame observed SEDs at λ_rest-frame < 3000 Å to discriminate between the different extinction curves. Using m^obs to represent the observed magnitude and m^template_uncor to represent the predicted magnitude from the best-fit template (uncorrected for extinction), the extinction A(λ) is given by A(λ) = m^obs − m^template_uncor. Figure 4 shows the rest-frame (m^obs − m^template_uncor)/E(B − V)^best for each flux measurement, i.e., the extinction curve k(λ). These points are compared with the Calzetti et al. (2000) and the Prevot et al. (1984) extinction curves. We scaled the Prevot et al. (1984) curve to the same A_V value as Calzetti et al. (2000) by applying a factor of 4.05/2.72, which is the ratio between the R_V of the Calzetti and Prevot laws. The Small Magellanic Cloud extinction curve (Prevot et al. 1984) is well suited for galaxies redder than the starburst template SB3. For galaxies bluer than SB3, the Calzetti et al. (2000) extinction curve is found to be more appropriate (see Figure 4). For the IR sources which are strongly star forming, Caputi et al. (2008) show also that the Calzetti et al. (2000) extinction law is more appropriate. This result is not surprising since the Calzetti law was determined from observed starburst galaxies. A broad absorption excess at 2175 Å (UV bump) seems necessary to explain the UV flux in some starburst galaxies. The presence of this UV bump can be seen in a theoretical modeling of the Calzetti law (Fischera et al. 2003) and in the K20 sample of high-redshift galaxies at 1 < z < 2.5 (Noll et al. 2007).

To summarize, we apply an additional extinction to the templates according to a grid E(B − V) = 0, 0.05, 0.1, 0.15, 0.2, \\0.25, 0.3, 0.4, 0.5. We use the Prevot et al. (1984) extinction curve for the templates redder than SB3, and Calzetti et al. (2000) for the templates bluer than SB3. We allow an additional bump at 2175 Å for the Calzetti extinction law if it produces a smaller χ². No reddening is allowed for galaxies redder than Sb.

The photo-z is the redshift value which minimizes the merit function χ²(z, T, A):

$$\begin{equation} \chi ^2=\sum _{f=1}^{N_f} \left(\frac{ F_{\rm obs}^f-A\times F_{\rm pred}^f(z, T) \; 10^{-0.4 s_f}}{\sigma _{\rm obs}^f} \right)^2, \end{equation} \tag{ 2 }$$

where F^f_pred(T, z) is the flux predicted for a template T at redshift z. F^f_obs is the observed flux and σ^f_obs is the associated error. The index f refers to each specific filter and s_f is the zero-point offset listed in Table 1. The opacity of the intergalactic medium (Madau et al. 1996) is taken into account. The photo-z is estimated from the minimization of χ² with respect to the free parameters, z, T, and the normalization factor A. The color excess E(B − V) is included in the term T (see Section 3.4). The grid spacing in redshift is δz = 0.01 and the final redshift is derived by parabolic interpolation of the redshift probability distribution. The redshift probability distribution function (PDFz) is derived directly from the χ²(z) distribution:

$$\begin{equation} P(z) \propto {\rm exp}\left(- \frac{\chi ^2(z)-\chi ^2_{\rm min}}{2}\right). \end{equation} \tag{ 3 }$$

The minimum and maximum redshifts around the photo-z solution, corresponding to the 1σ errors, are estimated from the equation χ²(z) = χ²_min + 1. As in Ilbert et al. (2006), we increased the SExtractor flux errors by a factor of 1.5. This factor does not shift the best-fit photo-z value but broadens the χ² peak and derived redshift uncertainty.

For each object, χ² is evaluated for both the galaxy templates and stellar SED templates (Chabrier et al. 2000; Bixler et al. 1991). If χ²_gal − χ²_star > 0, where χ²_gal and χ²_star are the minimum χ² values obtained with the galaxy and stellar templates, respectively, the object is flagged as a possible star. Leauthaud et al. (2007) catalogued point-like sources in the COSMOS field using the peak surface brightness measured on the Advanced Camera for Surveys (ACS) images. The SED χ² and morphological classification methods were found to be in excellent agreement—84% of the point-like sources at i⁺ < 24 are classified as stars with the SED χ² criterion mentioned above, while only 0.2% of the extended sources on the ACS images are misclassified as stars with the same χ² criterion. As shown in Figure 5, the star sequence colors are well distinguished from the bulk of the galaxy population if the colors include a NIR band. NIR and mid-IR data are crucial to separate stars from galaxies. Therefore, we limit the χ² star classification to K < 24 or F_3.6 μm > 1 μJy. Two percent of the point-like sources with i⁺ < 24 have K > 24 and F_3.6 μm > 1 μJy. These objects, which are only 2% of the total population at i⁺ < 24, could be stars not recognized as such by our SED χ² classification.

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AGN can be identified by their point-like X-ray emission. Most (∼90%) of the 1887 sources detected in XMM-COSMOS (Brusa et al. 2007) are dominated by an AGN. Their photo-z determinations require a different treatment: a correction for variability of the photometric data and the use of SED templates specifically tuned to AGN and their host galaxies. Accurate photo-z for the XMM-COSMOS sources are derived in a companion paper (Salvato et al. 2008). Due to the flux limit in XMM-COSMOS (Brusa et al. 2007), the moderately luminous (log(Lx) = 42–43 erg s⁻¹) and luminous (log(Lx) = 43–44 erg s⁻¹) AGN are not sampled by XMM-COSMOS at z = 0.5–1.25 and z = 1.5–3, respectively. Therefore, this population is not identified as AGN in the galaxy catalog.

We first assess the quality of the photo-z by comparison with the spectro-z. If Δz = z_s − z_p, we can estimate the redshift accuracy from $\sigma _{\Delta z /(1+z_{\rm s})}$ using the normalized median absolute deviation (NMAD; Hoaglin et al. 1983) defined as 1.48 ×  median(|z_p − z_s|/(1 + z_s)). The NMAD is directly comparable to other papers which directly quote the rms/(1 + z). This dispersion estimate is robust with respect to catastrophic errors (i.e., objects with |z_p − z_s|/(1 + z_s)>0.15). The percentage of catastrophic errors is denoted by η.

Figure 6 (left panel) shows the comparison between z_p and z_s for the zCOSMOS-bright sample selected at i⁺ < 22.5. The spectro-z sample is selected only by apparent magnitude and is therefore representative of the entire i⁺ < 22.5 population. We obtain an accuracy of σ_Δz/(1+z) = 0.007 at i⁺ < 22.5 and the distribution of offsets ((z_p − z_s)/(1 + z_s)) is well fit by a Gaussian with σ = 0.007 (Figure 6, right panel). The percentage of catastrophic failures is below 1%.

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The zCOSMOS-faint sample (Figure 7, left panel) with a median apparent magnitude of i⁺_med ∼ 24 provides a quality check for the photo-z at 1.5 < z < 3 where the photo-z are expected to have a significantly higher uncertainty. The faint sample includes galaxies at i⁺ ∼ 25 and the Balmer break is shifted into the NIR where the filter set has gaps. At 1.5 < z < 3, the accuracy is found to be σ_Δz/(1+z) = 0.06 with 20% catastrophic failures. The fraction of high-redshift galaxies (z_s > 1.5) for which a low-redshift photo-z (z_p < 0.5) was assigned is 7%, but this failure rate drops to 4% if the sample is restricted to galaxies detected at IRAC(3.6 μm)>1 μJy. The zCOSMOS-faint sample actually includes 54 galaxies with low spectro-z (z_s < 0.5); 53 out of the 54 galaxies (>98%) were assigned the correct photo-z low redshift. In summary, we conclude that, for the faint galaxies, the photo-z of low-redshift objects are still assigned correctly, while the failure rate for high-redshift objects is significantly reduced if the objects have good IRAC detections. Such result is expected since the photo-z are already including the same information present in high-z color selections such as BzK (Daddi et al. 2004) or similar diagnostics using the IRAC bands (Figure 5) to isolate the good redshift range.

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The zCOSMOS-bright and zCOSMOS-faint samples do not probe 0.2 < z < 1.5 at i⁺ > 22.5. Here, we use as a comparison sample the MIPS-spectro-z (J. Kartaltepe et al. 2008, in preparation). In Figure 7 (right panel), we split the MIPS-spectro-z sample into bright (i⁺ < 22.5), faint (22.5 < i⁺ < 24), and very faint samples (24 < i⁺ < 25). For the bright subsample, the dispersion of the MIPS-selected galaxies is $\sigma _{\Delta z/(1+z_{\rm s})}=0.009$, only slightly greater than that of the optically selected sample at i⁺ < 22.5. For the faint subsample (median apparent magnitude i⁺ ∼ 23.1), $\sigma _{\Delta z /(1+z_{\rm s})}=0.011$, i.e. slightly worse than for the brighter optically selected objects. For the very faint subsample, the accuracy is degraded to $\sigma _{\Delta z /(1+z_{\rm s})}=0.053$ with a catastrophic failures rate of 20%. This degradation is due to decreasing signal-to-noise photometry for faint objects and could be amplified by the IR selection, which picks up more heavily obscured galaxies and higher redshift galaxies (e.g., Figure 4 of Le Floc'h et al. 2005).

Since evaluation of the photo-z accuracy from the comparison with spectro-z is limited to specific ranges of magnitude and redshift, we use the 1σ uncertainty in the derived photo-z probability distribution to extend the uncertainty estimates over the full magnitude/redshift space.

The reliability of the 1σ uncertainty estimate for the photo-z as derived from the PDFz (see Section 3.5) can be checked by comparing this uncertainty with that derived directly from the photo-z–spectro-z offsets for the spectroscopic sample. Figure 8 shows the cumulative distribution of these offsets normalized by the 1σ uncertainty in the probability function for the zCOSMOS-bright sample (the ratio |z_p − z_s|/(1σ error) is lower than 1 if the measured offset z_p − z_s is lower than the 1σ uncertainty). Sixty-five percent of the z_p are within the 1σ error bars, whereas the expected fraction is 68%. We therefore conclude that the 1σ uncertainties in the probability function as derived here provide a robust assessment of the accuracy in z_p.

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Figure 9 shows the 1σ negative and positive uncertainties derived from the probability function as a function of redshift and apparent magnitude. Two clear conclusions emerge: the accuracy is inevitably degraded for fainter galaxies at all redshifts and the photo-z have significantly higher uncertainty at z ≳ 1.25.

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From z > 0 out to z = 1.25, the 1σ errors do not depend significantly on the redshift, with σ_Δz ≲ 0.02 at i⁺ < 24 (note that we dropped out the division of σ by (1 + z) in this analysis). To first order, the photo-z are accurate when the wavelengths of the Balmer and/or Lyman breaks are well constrained. Therefore, the wavelength coverage of the filter set and the photometry sensitivities determine the photo-z accuracy as a function of redshift. The COSMOS photometry coverage is continuous and dense in the optical from the u* band (λ_eff ∼ 3911 Å) to the z⁺ band (λ_eff ∼ 9021 Å). The average wavelength spacing between consecutive filters is also only 230 Å. The Balmer break at redshift z = 0 out to z = 1.25 is always at λ < 9000 Å, thus the high accuracy in this redshift range.

The accuracy degrades at z > 1.25, where the 4000 Å Balmer break goes out of the z⁺ band; at z ∼ 1.8 it is a factor of 3 larger than at z ∼ 1.25 (σ_Δz ∼ 0.14 for i⁺ ∼ 24). The lack of coverage between the z' and the J band accounts for the discontinuous increase in uncertainty at z > 1.25 since the Balmer break cannot be located with precision. At z > 1.5, the estimated error from the photo-z–spectro-z comparison is σ_Δz = 0.19 (see Section 4.1; $\sigma _{\Delta z/(1+z_{\rm s})}=0.06$ at the median redshift z ∼ 2.2). This accuracy is ∼1.4 higher than that estimated from the 1σ uncertainty (σ_Δz ∼ 0.14 at i⁺ ∼ 24). Errors due to bias in photo-z will not be recovered from the PDFz, which could explain this difference. At z > 1.25, all the optical filters, which are about 80% of all the used filters, are sampling the rest-frame UV at λ < 3500 Å. Uncertainties in the adopted extinction law have considerable impact on the UV slope and could introduce small biases in the estimate of the photo-z.

At z > 2.5, the accuracy improves again (σ_Δz ≲ 0.1 for 24 < i⁺ < 25) when the 4000 Å Balmer break enters in the J band (z ∼ 2) and the UV light shortward of L_α enters the u* band (z ∼ 2.3).

The major improvements in the technique implemented here are the carefully iterative evaluation of the photometric zero-point offsets for all bands and the allowance for a range of emission line contributions to the fluxes of template SEDs.

The left panel of Figure 10 shows the comparison between z_p and z_s computed without correction of the systematic band offsets (see Section 3.3) and without including the emission lines (see Section 3.2). Some systematic biases (horizontal and vertical stripes in Figure 10) greater than δ_z ∼ 0.1 are clearly seen in the photo-z estimate. For example, galaxies with z_s ∼ 0.8 are often shifted to z_z ∼ 0.7. With the iterative calibration of the band offsets turned on (the right panel of Figure 10), these biases are limited to δ_z < 0.05. This clearly demonstrates the importance of zero-point calibration to reduce the photo-z bias (as already shown by Brodwin et al. 2006 and Ilbert et al. 2006).

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The right panel of Figure 10 shows the comparison between z_p and z_s without including the emission lines (see Section 3.2). The accuracy is $\sigma _{\Delta z/(1+z_{\rm s})} \sim 0.02$. When the emission lines are included in the templates, the accuracy is improved by a factor of 2.5 ($\sigma _{\Delta z/(1+z_{\rm s})}=0.007$; the left panel of Figure 6). Therefore, including emission lines in the SEDs is crucial, especially when the medium bands are used to measure z_p.

We now compare the accuracy of the COSMOS-30 photo-z (this work) with those obtained previously for COMBO-17 (Wolf et al. 2004) and CFHTLS-DEEP (Ilbert et al. 2006). The accuracies can be compared as a function of apparent magnitude using the 1σ measured uncertainties in the photo-z probabilities. Once again, we check also the validity of the 1σ uncertainties for other surveys following the method described in Section 4.2. For the COMBO-17 and CFHTLS photo-z, we use the spectro-z from the VIMOS-VLT Deep Survey (Le Fèvre et al. 2004, 2005). Figure 11 shows that about 53% and 67% of the values for z_s are included inside the 1σ uncertainties for COMBO-17 and CFHTLS-DEEP survey, respectively. The 1σ errors for z_p in COMBO-17 are rescaled by ∼1.2 to obtain 68% of the z_s within the 1σ error (this rescale is small and changes nothing in our conclusions).

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Figure 12 shows the redshift dependence of the 1σ uncertainties in photo-z as a function of magnitude for 0.2 < z < 1.25. The z_p for the CFHTLS-DEEP were derived from five broadbands (u*, g', r', i', z'). The accuracy of the COSMOS photo-z is improved by a factor of 3 when compared to CFHTLS-DEEP. This improvement is largely due to the 12 medium bands in this redshift range (NIR data have a real impact only at z > 1.25). We checked this by deriving photo-z without the 12 medium bands, obtaining an accuracy of $\sigma _{\Delta z/(1+z_{\rm s})}=0.03$ at i⁺ < 22.5 (similar to the COSMOS release of Mobasher et al. 2007 using eight broadbands u*, B_J, V_J, g⁺, r⁺, i⁺, z⁺, and K_S). COMBO-17 includes 12 medium bands in addition to the five broadbands and Wolf et al. (2004) achieved an accuracy of σ_Δz/(1+z) = 0.02 at i⁺ ∼ 21.5. The accuracies of COMBO-17 photo-z are intermediate between those of COSMOS-30 and CFHTLS for i⁺_AB < 22.5 but become larger than the CFHTLS accuracies at fainter magnitudes, because the COMBO-17 data are about 1.5 mag shallower than the CFHTLS data. Since only secure photo-z (one solution) have been kept in the COMBO-17 catalog, it explains the flattening of the error bars at i⁺_AB > 24.

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Figure 13 shows the galaxy redshift distribution per deg² from the COSMOS and CFHTLS surveys (for 21.5 < i⁺_auto < 24.5). Although the surveys are largely independent and the photo-z are computed with different codes, the overall agreement in the redshift distributions is excellent. The agreement is particularly good between COSMOS and CFHTLS-D2 which covers 1 deg² within the COSMOS field.

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The density of galaxies at z > 1.5 in the CFHTLS fields is of crucial interest for weak lensing analysis (Benjamin et al. 2007). The CFHTLS redshift distribution presents a bump at z ∼ 3, but this excess could be due to misidentifications between the z < 0.4 and z > 1.5 photo-z (L. van Waerbeke 2008, in preparation) when no NIR data are available (as is the case for CFHTLS). The COSMOS photo-z are computed with NIR data and such catastrophic failures are limited (see Section 4.1). Figure 13 shows that this bump seems created by a deficit of galaxies at 2.5 < z < 3, by comparing CFHTLS-D2 and COSMOS.

Fu et al. (2008) used the CFHTLS photo-z distribution to estimate the matter density parameter Ω_m and the amplitude of the matter power spectrum σ₈. The redshift distribution from Fu et al. (2008) at 21.5 < i⁺ < 24.5 and z < 2.5 is over-plotted in Figure 13 with and without (J. Coupon 2008, private communication) the weight applied for the weak lensing selection (dashed and dashed-dot lines, respectively). Given the 20% variation expected from cosmic variance (Ilbert et al. 2006), it is in excellent agreement with the COSMOS-30 redshift distribution. This agreement suggests that the derivation of σ₈(Ω_m/0.25)^0.64 = 0.785 ± 0.043 by Fu et al. (2008) is not suffering from biases due to the photo-z or significant cosmic variance.

The COSMOS-30 redshift distribution can be fit with a parametrization similar to that used by Fu et al. (2008):

$$\begin{equation} n(z) = A \frac{(z^a+z^{ab})}{(z^b+c)}, \end{equation} \tag{ 4 }$$

where A is the normalization factor and a, b, and c are free parameters. The best-fit parameters a, b, and c are given in Table 2, as well as the median redshifts. Figure 14 shows the best-fit redshift distribution per apparent magnitude bin. As expected, the median redshift increases at fainter apparent magnitude, ranging from z_m = 0.66 at 22 < i⁺ < 22.5 to z_m = 1.06 at 24.5 < i⁺ < 25.

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