The ALHAMBRA survey: Bayesian photometric redshifts with 23 bands for 3 deg2

MNRAS 441, 2891–2922 (2014) doi:10.1093/mnras/stu387 The ALHAMBRA Survey: Bayesian photometric redshifts with 23 bands for 3 deg2 A. Molino,1‹N. Ben´ ıtez,1M. Moles,2A. Fern´ andez-Soto,3,4D. Crist´ obal-Hornillos,2 B. Ascaso,1Y. Jim´ enez-Teja,1W. Schoenell,1P. Arnalte-Mur,5M. Povi´ c,1D. Coe,6 C. L´ opez-Sanjuan,2L. A. D´ ıaz-Garc´ ıa,2J. Varela,2M. Stefanon,7J. Cenarro,2 I. Matute,1J. Masegosa,1I. M´ arquez,1J. Perea,1A. Del Olmo,1C. Husillos,1 E. Alfaro,1T. Aparicio-Villegas,1,8M. Cervi˜ no,1,9M. Huertas-Company,10,11 J. A. L. Aguerri,9T. Broadhurst,12 J. Cabrera-Ca˜ no,13 J. Cepa,9,14 R. M. Gonz´ alez,1 L. Infante,15 V. J. Mart´ ınez,4,16,17 F. Prada1and J. M. Quintana1 Affiliations are listed at the end of the paper Accepted 2014 February 25. Received 2014 February 25; in original form 2013 June 24 ABSTRACT The Advance Large Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA) survey has observed eight different regions of the sky, including sections of the Cosmic Evolution Survey (COSMOS), DEEP2, European Large-Area Infrared Space Observatory Survey (ELAIS), Great Observatories Origins Deep Survey North (GOODS-N), Sloan Digital Sky Survey (SDSS) and Groth fields using a new photometric system with 20 optical, contiguous ∼300-Å filters plus the JHKs bands. The filter system is designed to optimize the effective photometric redshift depth of the survey, while having enough wavelength resolution for the identification of faint emission lines. The observations, carried out with the Calar Alto 3.5-m telescope using the wide-field optical camera Large Area Imager for Calar Alto (LAICA) and the near-infrared (NIR) instrument Omega-2000, represent a total of ∼700 h of on-target science images. Here we present multicolour point-spread function (PSF) corrected photometry and photometric redshifts for ∼438 000 galaxies, detected in synthetic F814Wimages. The catalogues are complete down to a magnitude I∼24.5 AB and cover an effective area of 2.79 deg2. Photometric zero-points were calibrated using stellar transformation equations and refined internally, using a new technique based on the highly robust photometric redshifts measured for emission-line galaxies. We calculate Bayesian photometric redshifts with the Bayesian Photometric Redshift (BPZ)2.0 code, obtaining a precision of δz/(1+zs)=1 per cent for I<22.5 and δz/(1+zs)=1.4 per cent for 22.5 <I<24.5. The global n(z) distribution shows a mean redshift z=0.56 for I<22.5 AB and z=0.86 for I<24.5 AB. Given its depth and small cosmic variance, ALHAMBRA is a unique data set for galaxy evolution studies. Key words: methods: data analysis – techniques: photometric – catalogues – surveys – galaxies: distances and redshifts–galaxies: evolution–galaxies: photometry. 1 INTRODUCTION Photometric redshifts (Baum 1962; Lanzetta, Fern´ andez-Soto & Yahil 1996;Ben ´ ıtez 2000) have become a powerful tool for cosmology and galaxy evolution studies. Several medium-band photometric surveys have been carried out in the last years: the University E-mail: [email protected] of British Columbia–National Aeronautics and Space Administration (UBC–NASA) survey (Hickson & Mulrooney 1998), Calar Alto Deep Imaging Survey (CADIS: Wolf, Meisenheimer & Roser 2001b), Classifying Object by Medium-Band Observatins in 17 Filters (COMBO-17: Wolf et al. 2001a) and most recently, the Cosmic Evolution Survey (COSMOS-21: Taniguchi et al. 2005;Ilbertetal. 2009), National Optical Astronomy Observatory Extremely Wide- Field Infrared Imager (NEWFIRM: van Dokkum et al. 2009)and Survey for High-zAbsorption Red and Dead Sources (SHARDS: C 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2892 A. Molino et al. Figure 1. The figure shows the different fields observed by the ALHAMBRA survey, along with their correspondence with other existing surveys. The mean Galactic coordinates are specified in Table 1. P´ erez-Gonz´ alez et al. 2013). The Advance Large Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA) survey (Moles et al. 2008) has been optimized to detect and measure precise and reliable photometric redshifts for a large population of galaxies over eight different fields. Broad-band photometric surveys can be significantly shallower, in terms of photometric redshift depth, than well-designed, medium-band imaging (see Wolf et al. 2001a;Ben ´ ıtez et al. 2009b, for a systematic study). ALHAMBRA uses a specially designed filter system (see also Aparicio-Villegas et al. 2010) that covers the whole optical range (3500–9700 Å) with 20 contiguous, equal-width, non-overlapping, medium-band filters along with the standard JHKs near-infrared bands. The initial goal of the project was to cover a total area of 4 deg2on the sky divided into eight non-contiguous regions (Fig. 1). The photometric system has been specifically designed to optimizephotometricredshift depthandaccuracy(Ben´ ıtezetal. 2009b), while having enough sensitivity for the detection and identification of faint emission lines (Bongiovanni et al. 2010;Matuteetal. 2012;Matuteetal.2013). The observations presented here were carried out with the Calar Alto 3.5-m telescope using both the wide-field Large Area Imager for Calar Alto (LAICA) camera in the optical range and the Omega-2000 camera in the near-infrared (NIR) from 2005–2012. In order to define a constant and homogeneous window for all ALHAMBRA fields, we generated synthetic F814Wdetectionimages (corresponding toHubble Space Telescope (HST)/Advanced Camera for Surveys (ACS)F814W). These images are photometrically complete down to a magnitude mF814W≤24.5, have a much better signal-to-noise ratio (S/N) than individual filters and allow direct comparisons with other space-based surveys such as COSMOS. Hereafter, mF814Wmagnitudes correspond to the magnitudes derived for the synthetic F814Wimages. In this article, we summarize the ALHAMBRA survey observations and data reduction in Section 2. In Section 3, we describe in detail the photometric catalogues used to derive photometric redshifts. This includes aperture-matched point-spread function (PSF) corrected photometry, the generation of synthetic F814Wdetection images and their corresponding star masking treatment, a statistical star/galaxy classification and an empirical estimation of the photometric uncertainties. We discuss several photometric checks in Section 3.8. In Section 4 we analyse the methodology used to derive the photometric redshifts, the different methods used to compute photometric zero-point calibrations and the photometric redshift accuracy quantification as a function of F814Wmagnitude, redshift and Odds. Finally, we present a description of the ALHAMBRA photometric redshift catalogues in Section 5. All optical and NIR magnitudes in this article are in the AB system. Cosmological parameters of H0=70 km s−1Mpc−1,M=0.3 and =0.7 are assumed throughout. 2 OBSERVATIONS AND DATA REDUCTION 2.1 Observations The ALHAMBRA survey has imaged a total area of 4.0 deg2in eight separated regions of the sky during a seven-year period (2005– 2012). Observations were carried out with the 3.5-m telescope at the Calar Alto Observatory (CAHA, Spain), making use of the two wide-field imagers in the optical (LAICA) and NIR (Omega-2000). The ALHAMBRA fields have been observed whenever the conditions were good (seeing <1.6 arcsec, airmass <1.8), for a total on-target exposure time of ∼700 h for the whole survey, corresponding to ∼32 h for each field. The integration time was split into ∼27.8 h for medium-band filters and ∼4.2 h for broad-band NIR filters, as explained in Cristobal-Hornillos et al. (in preparation). Although ALHAMBRA-01 has already been observed, its analysis has not been included in this article owing to issues with its primary photometric calibration at the time. For a detailed description of the NIR observations, we refer the reader to Crist´ obal-Hornillos et al. (2009). The description of the optical observations will be available in Cristobal-Hornillos et al. (in preparation). 2.2 Data reduction In order to homogenize the data sets from both imagers, NIR images from the OMEGA-2000 detector were converted from their original pixel size, 0.45 arcsec pixel−1, to 0.221 arcsec pixel−1to match the pixel size of the LAICA images. As explained in Crist´ obal- Hornillos et al. (2009), individual images from each run have been dark-current-corrected, flat-fielded and sky-subtracted. Bad pixels, cosmicrays, linear patterns andghost images havealso been masked out. Processed images have been finally combined using the SWARP (Bertin et al. 2002) software and the applied geometrical transformations have been incorporated in World Coordinate System (WCS) headers. The total 2.8 deg2considered in this work is divided into seven non-contiguous regions of the sky (as summarized in Table 1), each of which is split into two non-overlapping strips composed of four individual CCDs, as schematically illustrated in Appendix A. Each one of the 48 CCDs represents the minimum area (15.5 ×15.5 arcmin2) covered by all 23 individual filters. To quantify the survey effective area (Section 3.5.3), FLAG images have been created where pixels not satisfying established photometry quality criteria have been flagged. Meanwhile, both RMS-map and WEIGHT-maps have been generated, accounting for the level of photometric uncertainties present across individual images. 2.3 Filter set Once the instrumental set-up and exposure time are fixed, the filter set has a powerful effect on the photometric redshift (photo-z) performance (see Wolf et al. 2001a;Ben ´ ıtez et al. 2009b). Table 2 summarizes a small list of different photometric filter systems and their photometric redshift accuracy. The ALHAMBRA survey designed its own photometric system (Ben´ ıtez et al. 2009b) optimizing both photometric depth and accuracy. As seen in Fig. 2, the system covers the 3500–9700 Å optical window with 20 constant-width (∼300 Å), non-overlapping filters. We also use the J,Hand Ks NIR bands. Including both optical and NIR observations helps to break colour–redshift degeneracies, reducing the fraction of catastrophic outliers and increasing the ALHAMBRA photometric redshift depth. In Fig. 3, we show a galaxy observed through the whole MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from ALHAMBRA Survey: Bayesian photometric redshifts 2893 Table 1. The ALHAMBRA survey selected fields. Field Overlapping RA Dec. Area/Effective Number of Science Detected (a)Density (a,b) name survey (J2000) (J2000) [deg2] catalogues images sources [#/deg2] ALHAMBRA-1 – 00 29 46.0 +05 25 30 0.50/– – 192 – – ALHAMBRA-2 DEEP2 01 30 16.0 +04 15 40 0.50 / 0.45 8 192 67.791 77.144 ALHAMBRA-3 SDSS 09 16 20.0 +46 02 20 0.50 / 0.47 8 192 68.015 75.000 ALHAMBRA-4 COSMOS 10 00 00.0 +02 05 11 0.25 / 0.23 4 96 38.464 93.261 ALHAMBRA-5 HDF-N 12 35 00.0 +61 57 00 0.25 / 0.24 4 96 42.618 82.300 ALHAMBRA-6 GROTH 14 16 38.0 +52 24 50 0.50 / 0.47 8 192 66.906 77.740 ALHAMBRA-7 ELAIS-N1 16 12 10.0 +54 30 15 0.50 / 0.47 8 192 79.453 82.185 ALHAMBRA-8 SDSS 23 45 50.0 +15 35 05 0.50 / 0.46 8 192 75.109 82.452 3.00 / 2.79 48 1344 438.356 81.440 aWithout duplications. bmF814W<24. Table 2. Photometric redshift surveys. Since, for narrow/medium-band photometric surveys (*), the photometric redshift accuracy is strongly dependent on the S/N, we compared the performance from both surveys applying a similar cut in magnitude (R<23 AB for COMBO-17 and I<23 AB for ALHAMBRA). For the brightest sources, both surveys reach a performance similar to that of COSMOS or the Multiscale Systems Center (MUSYC) δz/(1 +z)<0.01. Survey Reference Bandsδz/(1 +z) HDF Sawicki, Lin & Yee (1997) 4 0.080 SDSS/DR6 Csabai et al. (2003) 5 0.035 SWIRE Rowan-Robinson et al. (2008) 5 0.035 HUDF Coe et al. (2006) 6 0.040 HDF Fern´ andez-Soto, Lanzetta & Yahil (1999) 7 0.060 CFHTLS Ilbert et al. (2006) 9 0.030 GOODS Dahlen et al. (2010) 12 0.040 CLASH Molino (in prep.) 16 0.025 COMBO-17*Wolf et al. (2008) 17 0.020 ALHAMBRA*Molino (this work) 23 0.010 COSMOS Ilbert et al. (2009) 30 0.007 MUSYC Cardamone et al. (2010) 32 0.007 JPAS Ben´ ıtez et al. (2009a,2014, in prep.) 59 0.003 ALHAMBRA filter system. The main properties of each individual filter are summarized in Table 3. 2.4 Primary photometric zero-point calibration A set of transformation equations between the ALHAMBRA and the SDSS (York et al. 2000) was derived based on a collection of primary standard stars from the HST/Space Telescope Imaging Spectrograph (STIS) Next Generation Spectral Library (NGSL: Gregg et al. 2004), as explained in Aparicio-Villegas et al. (2010). We applied these equations to all stars with good photometry in both ALHAMBRA and the SDSS/DR7 data and derived photometric zero-points from the mean differences between instrumental and synthetic magnitudes, yielding an internal error no larger than a few hundredths of a magnitude for stars in each CCD and filter combination. For an in-depth discussion of the calibration of the ALHAMBRA optical photometric system, we refer the reader to Crist´ obal-Hornillos et al. (in preparation). The ALHAMBRA survey has used the Two-Micron All-Sky Survey (2MASS) catalogue (Cutri et al. 2003) to calibrate its NIR images. As explained in Crist´ obal-Hornillos et al. (2009), several dozens of stars common to both data sets with high S/N were selected in each field, yielding photometric zero-point offsets with uncertainties of ∼0.03 mag. We will discuss the procedure to refine Figure 2. The ALHAMBRA survey filter set. On the left-hand side, solid blue lines represent the optical filter system composed of 20 contiguous, equal-width, non-overlapping, medium-band (∼300 Å) filters. The solid black line corresponds to the synthetic F814Wfilter used to define a constant observational window across fields. On the right-hand side, solid red lines represent the standard JHKs near-infrared broad bands. All transmission curves are normalized to the maximum value. MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2894 A. Molino et al. Figure 3. The ALHAMBRA survey. The figures show how a galaxy looks when observed through the ALHAMBRA filter system. The optical range is covered horizontally from top to bottom and left to right; the last row corresponds to the J,Hand Ks NIR filters, along with the synthetic F814Wdetection image. The background colour image was generated using the TRILOGY software (http://www-int.stsci.edu/ dcoe/trilogy/Intro.html). the photometric zero-point calibrations via SED-fitting techniques in Section 4.2.1. 3 PHOTOMETRY 3.1 Multi-wavelength photometry As was thoroughly described in Coe et al. (2006), measuring multicolour photometry in images with different PSFs is not a trivial task. To perform good quality multicolour photometry, it is necessary to sample the same physical region of the galaxy taking into account the smearing produced by different PSFs, as seen in Fig. 4. We show the distribution of optical, NIR and synthetic F814WPSFs in the ALHAMBRA survey in Fig. 5, for values between 0.7 and 1.6 arcsec. One of the methods to correct for PSF effects is to smooth the whole data set to the worst seeing condition, making all images look as they had been taken under the same seeing conditions (Loh & Spillar 1986;Labb´ eetal.2003; Capak et al. 2007). This methodology produces consistent apertures across the filters, but strongly degrades the best observations to the level of the worst. Here we have used COLORPRO (Coe et al. 2006), which corrects accurately for PSF effects without degrading image quality; Laidler et al. (2006), de Santis et al. (2007), Kuijken (2008) and Wolf et al. (2008)have also developed similar approaches. To improve the photometric depth and homogeneity, we relied on deep synthetic F814Wimages (Section 3.5), which are the best option for photometric aperture definitions (given the enhanced S/N) and galaxy morphology estimations. 3.2 PSF-matched aperture-corrected photometry COLORPRO derives accurate PSF-corrected photometry without degrading high-quality images. Initially the software defines every MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from ALHAMBRA Survey: Bayesian photometric redshifts 2895 Table 3. Summary of the multiwavelength filter set for ALHAMBRA. The full width at half-maximum (FWHM), exposure time and limiting magnitude (measured using a 3-arcsec diameter aperture) correspond to the average value among the 48 CCDs. Camera Filter λeff FWHM texp m(3) lim  [Å] [Å] [s] (5σ) Optical LAICA F365W 365 279 3918 23.7 LAICA F396W 396 330 2896 23.8 LAICA F427W 427 342 2774 23.8 LAICA F458W 458 332 3079 23.8 LAICA F489W 489 356 2904 24.2 LAICA F520W 520 326 2664 24.1 LAICA F551W 551 297 2687 23.7 LAICA F582W 582 324 2936 23.8 LAICA F613W 613 320 2940 23.9 LAICA F644W 644 357 4043 23.8 LAICA F675W 675 314 4575 23.5 LAICA F706W 706 332 5668 23.7 LAICA F737W 737 304 7095 23.5 LAICA F768W 768 354 8824 23.5 LAICA F799W 799 312 8992 23.2 LAICA F830W 830 296 11436 23.2 LAICA F861W 861 369 10505 22.9 LAICA F892W 892 303 9044 22.5 LAICA F923W 923 308 6338 22.1 LAICA F954W 954 319 5620 21.5 NIR OMEGA J1216 2163 5169 22.6 OMEGA H1655 2191 5055 21.9 OMEGA Ks 2146 2412 5050 21.4 Detection SYNTH F814W845 2366 73522 24.5 photometric aperture based on the selected detection image. Then it goes filter by filter and estimates how much flux a galaxy has missed within that aperture as a consequence of the difference between the PSF of the image in that filter and the detection PSF. This correction is applied to each filter, yielding PSF-corrected magnitudes with as little PSF degradation as possible. SEXTRACTOR (Bertin & Arnouts 1996) ISOphotal apertures produce the most robust colours for faint objects (Ben´ ıtez et al. 2004), while SEXTRACTOR AUTO apertures provide better estimations of galaxy total magnitudes. To encompass the usefulness of both measurements,COLORPRO definesaphotometrictransformation that provides both SEXTRACTOR ISOphotal colours and total magnitudes. Total magnitudes are defined as Mi=MISO i+MAUTO det −MISO det,i ,(1) where the first term corresponds to the standard SEXTRACTOR ISOphotal magnitude for sources detected in the ith band, while the second term incorporates the PSF correction (by applying the photometric differences when degrading the detection image (Mdet) to the ith-PSF condition (Mdet, i)). Hence, the second term extends SEXTRACTOR ISOphotal magnitudes into total magnitudes. Meanwhile, ISOphotal colours are derived as Mj=MISO j+MAUTO det −MISO det,j ,(2) Mi−Mj=MISO i−MISO j+MISO det,j −MISO det,i ,(3) Figure 4. Seeing variability across photometric bands. For a single star, solid black lines represent the scatter in the normalized stellar growth curve as a consequence of the varying PSF across filters (inset top panel). This effect has to be corrected in order to estimate accurate colours. Figure 5. Distributionofseeing conditions for theALHAMBRAfields.The figure shows the distribution of PSFs (measured as the FWHM in arcsec) for optical images (blue), NIR (red) and synthetic F814Wdetection images (green). The PSFs range from 0.7–1.6 arcsec, with the optical images having FWHM∼1.1 arcsec, NIR images FWHM∼0.9 arcsec and synthetic F814Wdetection images FWHM∼1.0 arcsec. where resulting Mi−Mjcolours are just the combination of their SEXTRACTOR ISOphotal magnitudes plus a second term including their relative PSF corrections. As expected, in those cases with equalPSFthesecondtermmightbecancelled out, providingcolours directly from the SEXTRACTOR ISOphotal magnitudes. For a more detailed explanation, we refer the reader to Coe et al. (2006). 3.3 PSF models As required by COLORPRO, it was necessary to generate PSF models for each individual image. We used the package DAOPHOT from MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2896 A. Molino et al. Figure 6. Star selection. Several hundred non-saturated and well-isolated stars were interactively selected across the images, to derive the PSF models. A careful selection is essential to ensure the accuracy of the PSF-corrected magnitudes. IRAF (Stetson 1987), which uses a hybrid method to compute PSF models. It first fits the central region of the stars by using an analytical function (Gaussian, Lorentzian, Moffat or Penny) and then the outermost parts (regions connected with the background) are empirically fitted point by point; typical residuals between stars and models are around ∼3 per cent. We initially ran SEXTRACTOR on each image using a very high threshold(∼100×σBackground)todetectonlybrightsources. We kept detections with SEXTRACTOR CLASS STAR >0.9. When plotting the magnitude versus the full width at half-maximum (FWHM) for those selected objects, we find that they are located in the region of the brightest and most compact sources (Section 3.6.1). To avoid both saturated stars and misclassified galaxies, we culled objects outside the range 16 <m<22.5, yielding a final sample of several hundred stars per image. Afterwards, we visually rejected stars with contaminating neighbours and generated mosaic-like images (Fig. 6). These images decreased the computational time required by DAOPHOT to model the PSF and generated much higher quality results. Finally, the PSF models were normalized to the same flux. Among the different analytical models considered by DAOPHOT, the most recurrent one was the Penny2 profile. This model consists of a Gaussian-like function but with Lorentzian wings. Although typical residuals for PSF models from CCD1, CCD2 and CCD4 are around 3 per cent, CCD3 shows a different behaviour, with systematically larger residuals of 5–10 per cent. This different behaviour was probably due to the differences in the efficiency of this detector (CCD3), which was not science grade and was significantly worse than CCD1, CCD2 and CCD4 (Cristobal-Hornillos et al., in preparation). 3.3.1 PSF model verification We systematically verified each PSF model. First, we compared its FWHM with the registered seeing (from the image header) and with the mean FWHM value for the stars used to derive the model. The observed scatter among PSFs does not exceed 3–5 per cent, ensuring that stars and models are well in agreement. Figure 7. Radial PSF variability across images. The figure shows the radial dependence of the PSF (expressed in arcsec and referred to the primary mirror telescope) for the compilation of stars used to derive the PSF models. The mean value of the distribution (dashed red line) has a scatter smaller than 5 per cent, enabling the usage of a single PSF model per image. The PSF stability among different CCDs was also checked. As introduced in Section 2.2, given the spatial configuration of the LAICA optical system, the four CCDs simultaneously imaged similar parts of the sky under the same atmospheric conditions and with the same passbands. This fact made it possible to perform statistical comparisons among detectors. Once again we observed good agreements among CCD1, CCD2 and CCD4, but a larger deviation for CCD3 close to 5–10 per cent. Finally, we studied the radial PSF variability across images to ascertain the usage of a single PSF model per image. We defined a new reference system linking every detection (from each CCD) to the centre of the telescope’s focal plane. In Fig. 7, we show the dependence of the FWHM as a function of the radial distance for ∼20 000 stars, finding a variation smaller than 5 per cent. 3.4 Simulations We carried out several simulations to test the accuracy of COLORPRO. To do so, we degraded a much better resolution image to the typical ALHAMBRA conditions (in terms of PSF and background noise) and ran COLORPRO on it, expecting to retrieve null colours (equal magnitudes) for galaxies observed under different PSFs. We created a mosaic image by rearranging four HST/ACS F814W images from the COSMOS survey (Scoville et al. 2007) that overlap the ALHAMBRA fields. We rescaled the mosaic to the ALHAMBRA pixel size (from the ACS 0.065 arcsec pixel−1to the LAICA 0.221 arcsec pixel−1), convolved with ∼200 PSFs randomly drawn from our models and reapplied background noise using typical values for the ALHAMBRA images (empirically measured as explained in Section 3.7). An example of the simulated images is shown in Fig. 8, which compares the HST/ACS image of a galaxy (left panel) with the ALHAMBRA image (middle panel) and the simulated image (right panel). 3.4.1 Reliability We ran COLORPRO on the new set of ∼200 mosaics, using the same configuration used for the ALHAMBRA catalogues. We excluded MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from ALHAMBRA Survey: Bayesian photometric redshifts 2897 Figure 8. Example of the simulated data set reproducing the typical observational conditions of the ALHAMBRA images (Section 3.4). From left to right, we show a galaxy in the ACS/HST image, ALHAMBRA synthetic F814Wdetection image and rescaled +PSF degraded +background reapplied ACS/HST image. all detections with photometric problems reported by SEXTRACTOR (SEXTRACTOR_Flag>1) to eliminate several ghosts and other artefacts (trails) within the original images. We found that the simulated colours showed a dispersion of σ∼0.03, which marks a photometric precision floor, for sources brighter than magnitude mF814W=23.0 and, as expected from the uncertainties arising from the photometric noise, an increasing error for fainter magnitudes. For most of the magnitude range there are negligible biases, as seen in the top panel of Fig. 9. This shows that COLORPRO is capable of performing accurate PSF corrections for ALHAMBRA-like data. 3.4.2 Completeness We studied the expected photometric completeness for the ALHAMBRA fields in terms of PSF and background level. For this purpose, we used the previous simulations to derive the statistical probability of detecting a sample of faint galaxies when observed under typical ALHAMBRA conditions. In the bottom panel of Fig. 9we show the expected fraction of missed galaxies per magnitude range and square degree. The result indicates that ALHAMBRA is photometrically complete down to a magnitude of mF814W∼24. At fainter magnitudes, the number of detections decreases rapidly, with ∼40 per cent of the galaxies lost at mF814W∼25. 3.5 Synthetic F814Wdetection images In photometric surveys it is a common practice to stack the best quality images in order to generate detection images that are deeper than the images obtained in any individual filter. To define a homogeneous detection image for all ALHAMBRA fields, we generated synthetic F814Wimages as the properly weighted combination of several individual bands. To calculate the weights we generated, using the empirically calibrated template library of Ben´ ıtez (2014), a realistic galaxy mock catalogue up to the typical ALHAMBRA depth and solved using least-squares, the system of equations between the corresponding synthetic colours (equation 4). The system of equations between filters for Nggalaxies is defined as follows: mF814W,i = Nf  j=1 ai,j ×mi,j .(4) An example of the so-derived synthetic F814Wimages is shown in Fig. 10. The least-squares solution, with an rms error smaller Figure 9. PSF-corrected photometry verifications. We designed a set of simulations (Section 3.4) to estimate both the reliability of COLORPRO in deriving PSF-corrected photometry and the expected completeness in our images. The top panel shows how COLORPRO successfully retrieved null colours (same magnitudes) across simulated images, with a dispersion below 3 per cent for magnitudes brighter than mF814W=23.0 and an increasing error, as expected from the added photometric noise, at fainter magnitudes. The bottom panel shows the expected completeness as a function of F814W magnitude. MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2898 A. Molino et al. Figure 10. Example of the synthetic F814Wimages derived for the ALHAMBRA fields. The left panel shows how the original HST/ACS F814Wimage looks after being scaled to the ALHAMBRA pixel size, convolved with the ALHAMBRA PSF and with photometric noise reapplied. The right panel shows the synthetic ALHAMBRA F814Wdetection image. than 1 per cent, is F814W= 0.105×F706W +0.178 ×F737W +0.179 ×F768W +0.142×F799W +0.115 ×F830W +0.119 ×F861W +0.073×F892W +0.049 ×F923W +0.040 ×F954W.(5) Given that the typical error in the individual bands is 2–3 per cent, total zero-point error in the F814Wimage is quite small, providing high homogeneity. To verify the calibration of the synthetic F814Wimages, we performed a photometric comparison with the COSMOS field. To reproduce the same photometric measurements as in Ilbert et al. (2009), we ran SEXTRACTOR using fixed circular apertures of 3 arcsec. We retrieved ∼10 800 common sources with ALHAMBRA in the 19 <mF814W<25.5 range. The photometric comparison is shown in Fig. 11. No photometric zero-point offsets or trends are apparent up to magnitudes mF814W=23.5. For the faintest sample, the retrieved photometric colour (COSMOS/F814Wmagnitude −ALHAMBRA/F814Wmagnitude) becomes progressively negative, indicating that COSMOS magnitudes are brighter than ALHAMBRA’s. The trend observed seems to be caused by a combination of an aperture and filter shape effect. On the one hand, as explained in Section 3.3, the ALHAMBRA PSF models seemed to prefer a Penny2 profile, which consists of a Gaussian-like function but with Lorentzian wings; in addition, the PSF is almost an order of magnitude larger than the PSF. This much more extended PSF spreads flux outside the aperture diameter, an effect that is much more important for the faintest sources. This is also observed in the simulation in Section 3.4. In Fig. 9(top panel), the same trend is observed at faint magnitudes. On the other hand, the ALHAMBRA/F814Wimages were created combining the last optical individual filters as shown in equation (5). Unfortunately, the last F892W,F923Wand F954W optical filters have relatively low S/N. Therefore our ‘F184’ filter becomes progressively bluer with magnitude, thus having a much wider PSF, which intensifies the above-described effect. Inaneffort toextendthe accuracyofthe ALHAMBRA photometric measurements, we derived a magnitude-dependent correction to make ALHAMBRA magnitudes reproduce the COSMOS estimations for fixed apertures of 3 arcsec. These corrected magnitudes are included in the final catalogues, as explained in Appendix C. We also ran SEXTRACTOR on both ACS/F814Wand synthetic ALHAMBRA/F814Wimages using the same SEXTRACTOR configuration. This analysis provided a characterization of the differences in the detections between both images. For detection magnitudes 19 <mF814W<23.5, only a few dozen sources per CCD were missing from the synthetic ALHAMBRA/F814Wimages. Detections fainter than magnitudes mF814W=23.5 showed an increasing distribution of undetected sources peaking at a magnitude mF814W∼25.5, well beyond the ALHAMBRA photometric completeness limit. 3.5.1 Masks Inorder to improve the source detection efficiency, wemaskedevery saturated star, stellar spike, ghost and damaged area. Initially we ran SEXTRACTOR on each synthetic F814Wdetection image with a special configuration to detect just very bright and extended sources. We visually checked the extracted sources to exclude any possible nearby galaxy. Then we convolved the resulting SEXTRACTOR segmentation maps with a Gaussian function to broaden the previously defined apertures and so remove residual contributions from stellar haloes. We repeated the same procedure on the inverse image to deal with negative extended regions generated by saturated stars. We combined both positive and negative segmentation maps, defining the total region to be masked out. Finally, we replaced all flagged pixels with background noise to minimize the variation of the image root-mean-square error (RMS). An example of the masking procedure for a saturated star is shown in Fig. 12. 3.5.2 SEXTRACTOR configuration Assuming an expected variability in terms of PSF (and therefore in photometric depth) among the F814Wdetection images, we explored the optimal SEXTRACTOR configuration that maximizes the number of real detections. For non-crowded fields, the most relevant parameters are the minimum number of contiguous pixels DETECT MINAREA and the threshold the signal has to exceed to be considered a real detection DETECT THRESHOLD. MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from ALHAMBRA Survey: Bayesian photometric redshifts 2899 Figure 11. Photometric comparison between the F814W/COSMOS and synthetic ALHAMBRA/F814Wimages. In order to reproduce the same photometric measurements as Ilbert et al (2009), we ran SEXTRACTOR on the synthetic ALHAMBRA/F814Wimages using fixed circular apertures of 3 arcsec. Selecting a common sample of ∼10 800 detections between ALHAMBRA and COSMOS, we found neither photometric zero-point offsets nor significant bias for detections with magnitudes 19 <mF814W<23. For sources fainter than mF814W=23.0, an increasing dependence on the magnitude is observed as a consequence of the rapidly decreasing S/N for the ALHAMBRA detections. To match the ALHAMBRA and COSMOS F814Wmagnitudes for fixed 3-arcsec apertures, we derived a magnitude-dependent correction that is included in the final catalogues, as explained in Section 5. Figure 12. Star masking. In order to improve both the photometric depth and the photometric measurements, F814Wdetection images were masked out, purging saturated stars, spikes, ghosts, negative areas and other artefacts. This figure shows an example of how a saturated star from the original image (left panel) disappears after replacing all its pixels with background signal (right panel). In the Gaussian limit, the sky noise should in principle have a symmetric structure and a similar amount of spurious objects are expected to be found on both sides of the image. Using this assumption, we looked for the SEXTRACTOR detection threshold that produced no more than 3 per cent contamination by spurious detections. We fixed DETECT MINAREA at twice the image FWHM and ran SEXTRACTOR on both the image and its inverted negative side. The results are shown in Fig. 13. In the Appendix D, we show an example of the typical configuration used to perform source detection. 3.5.3 Flag images Inorder to be ableto quantify the survey effectivearea, we generated FLAG images for each individual CCD where all problematic pixels were set to 0. As the effective exposure time rapidly decreases when approaching the image edges, we defined homogeneous areas where all sources have adequate exposure in all the 23 bands. We normalized individual weight maps to the maximum exposure time and then flagged the regions with a relative exposure time below 60 per cent (mostly near the image edges). MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2906 A. Molino et al. Figure 23. Astrometric matching with spectroscopic samples. In order to reduce the fraction of potential mismatched galaxies, we initially performed second-order astrometric corrections between the ALHAMBRA fields and other surveys, to establish a maximum distance of ∼3 pixel (<0.7 arcsec) to match our detections. This maximum separation was set manually for each survey, being the distance at which the radial matching distribution reached its first minimum. As seen in the main panel, ∼60 per cent of the selected spectroscopic sample is well accommodated within a one-pixel distance. The inset panel illustrates the astrometric dispersion between ALHAMBRA and the overlapping surveys in terms of δRA (RAALH −RAsurv)andδDec (DecALH −Decsurv) in units of pixels. being affected by catastrophic errors. The NMAD is defined as follows: σNMAD =1.48 ×median |δz −median(δz)| 1+zs(11) and δz =zb−zs,(12) where zbcorresponds to the Bayesian photometric redshift and zsto the spectroscopic redshift. Along with the scatter, it is also important to quantify both the presence of any systematic bias μ and the fraction of catastrophic errors. In this work, we use two different definitions for the outlier rate: η1=|δz| 1+zs >0.2,(13) η2=|δz| 1+zs >5×σNMAD.(14) As explained in Section 2, ALHAMBRA was designed to partially overlap with fields observed by other surveys with extensive spectroscopic coverage. We compiled a sample of ∼7200 galaxies with spectroscopic redshifts from the publicly available data by selecting high-quality (secure) objects with a good astrometric match to our data. The first condition is essential to estimate our outlier rate accurately, even if it slightly biases our sample towards the brightest magnitudes, since, as Fern´ andez-Soto et al. (2001) established, lowquality spectroscopy can be much more unreliable than photo-z.To implement the second condition, we derived accurate astrometric corrections between samples (to avoid any offset) and then established a maximum matching distance of ∼3 pixel (<0.7 arcsec), as showninFig.23. This maximum separation was manually set for each survey, being the distance at which the distribution of matching distances reached its first minimum. As seen in Fig. 24, the com- Figure 24. Spectroscopic redshift compilation. Given the overlap between the ALHAMBRA fields and other existing spectroscopic surveys, we compiled a sample of ∼7200 galaxies with secure spectroscopic redshifts to quantify the accuracy for our photometric redshifts. Each survey contribution is colour-coded (for visualization), as indicated in the legend. As seen in the figure, the compiled redshift sample mostly covers the ALHAMBRA parameter space, showing a redshift range 0 <z s<1.5 (with a mean redshift zs∼0.77) and a magnitude range (based on ALHAMBRA photometry) 18 <mF814W<25 (with a mean magnitude mF814W∼22.3). Table 4. Spectroscopic redshift samples. # Survey Reference mF814Wz 1269 DEEP-2 Koo et al. (1995) 22.64 0.92 1291 COSMOS Lilly et al. (2009) 21.36 0.54 1000 GOODS-N Cooper et al. (2011) 22.75 0.83 2977 GROTH Davis et al. (2007) 22.21 0.70 7237 22.24 0.75 piled redshift sample shows a mean redshift zs∼0.77 and a mean magnitude (based on ALHAMBRA photometry) mF814W∼22.3. In Table 4, the contribution from each survey is specified, indicating the number of selected galaxies, mean magnitude and redshift. Asseenin Fig.25,whencomparedwith thespectroscopicsample, our photometric redshift estimations show a dispersion σz=0.0106 for mF814W<22.5 with a fraction of catastrophic outliers η1∼2.7 per cent. For fainter magnitudes mF814W<24.5, the accuracy observed is σz=0.0134 and the fraction of catastrophic outliers η1∼4.0 per cent. The fraction of catastrophic outliers dramatically decreases when selecting a more restricted sample (excluding X- ray emitters, active galactic nuclei (AGNs) or detections observed in only a few bands). In addition, the photo-zerror and the fraction of catastrophic outliers decrease rapidly as the Odds interval increases. We show the expected accuracy for the photometric redshifts as a function of redshift, F814Wmagnitude and Odds range in Fig. 26. A more detailed analysis can be found in Tables 5,6and 7, respectively. In order to verify that δz/(1 +zs) is representative for the spectroscopic sample, the cumulative distribution of sources is represented in Fig. 27. We observed that ∼64 and ∼90 per cent of the photometric redshifts are well fitted within the formal 1σand 2σconfidence MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from ALHAMBRA Survey: Bayesian photometric redshifts 2907 Figure 25. Photometric redshift accuracy. The figures show the comparison between the ALHAMBRA photometric redshift zband the spectroscopic redshift zs, along with the error distribution z/(1 +z), for two different magnitude ranges. The left plot shows the accuracy obtained for the bright sample (mF814W<22.5) with σz<0.0106 and a fraction of catastrophic outliers η1∼2.7 per cent, while the right plot shows σz<0.0134 and a fraction of catastrophic outliers η1∼4.0 per cent when including the entire sample. In both cases, the fraction of catastrophic outliers (defined in Section 4.1) decreases dramatically when selecting galaxies with higher Odds, as indicated in Table 7. Figure 26. Photometric redshift accuracy as a function of apparent magnitude F814W(left panel) and spectroscopic redshift (right panel). We explored the expected accuracy for our photometric redshifts in terms of a specific magnitude range and redshift range, applying different Odds intervals. intervals, respectively. This indicates that the uncertainties in zbare quite realistic. Applying the same approach explained in Section 3.8, we performed internal photometric redshifts checks to compare our results between contiguous CCDs. As illustrated in Fig. 28, the statistical results were consistent between CCDs, showing a scatter within the intrinsic variance for the sample observed by each CCD. 4.2 Photometric zero-point recalibration 4.2.1 Photometric ZP calibrations using spectroscopic redshifts As was shown in Coe et al. (2006), by comparing the observed colours of galaxies with spectroscopic redshifts against those expected from an empirically defined photo-zlibrary, it is possible to calibrate photometric zero-points to within a few per cent, an accuracy similar to or better than that reached by standard, stellar-based calibration techniques. This capability has been included in the BPZ software package from its initial release (Ben´ ıtez 2000) and has been applied successfully to several data sets (Capak et al. 2007; Hildebrandt, Wolf & Ben´ ıtez 2008). To calibrate the ALHAMBRA zero-points, we followed this procedure for each individual CCD. First, we selected the spectroscopic redshift galaxies detected in all 24 bands with S/N>10, and chose the BPZ template that best fits its colours at their redshift. We then calculated the ratios between the fluxes predicted in each band by the templates and those observed; the median ratio, converted to a magnitude, represents the zero-point offset (ZPO) required to match the observed magnitudes to the expected ones. We then corrected the fluxes by this value and iterated until the process converged and MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2908 A. Molino et al. Table 5. Photometric redshift quality versus spectroscopic redshifts. Spectroscopic σz#η1η2σz#η1η2σz#η1η2 Redshift (Odds >0.0) (per cent) (per cent) (per cent) (Odds >0.5) (per cent) (per cent) (per cent) (Odds >0.9) (per cent) (per cent) (per cent) 0.00 <z<0.25 0.0115 10.8 0.4 0.8 0.0086 3.8 0.1 0.2 0.0056 0.3 0.0 0.0 0.25 <z<0.50 0.0101 21.0 0.6 1.5 0.0087 10.5 0.2 0.4 0.0062 1.6 0.0 0.1 0.50 <z<0.75 0.0136 19.6 1.0 2.4 0.0107 11.5 0.3 0.8 0.0061 1.2 0.1 0.1 0.75 <z<1.00 0.0135 21.4 0.7 2.3 0.0104 12.7 0.2 0.7 0.0066 1.4 0.0 0.1 1.00 <z<1.25 0.0171 13.2 0.4 1.3 0.0125 7.0 0.1 0.4 0.0070 0.3 0.0 0.0 1.25 <z<1.50 0.0194 7.2 0.3 0.9 0.0132 2.3 0.1 0.3 – – – – 1.50 <z<1.75 0.0988 3.4 0.1 0.2 0.0567 0.3 0.0 0.0 – – – – 1.75 <z<2.00 0.1078 1.4 0.2 0.4 0.1620 0.0 0.0 0.1 – – – – Table 6. Photometric redshift quality versus F814Wmagnitude. Magnitude σz#η1η2σz#η1η2σz#η1η2 F814W (Odds >0.0) (per cent) (per cent) (per cent) (Odds >0.5) (per cent) (per cent) (per cent) (Odds >0.9) (per cent) (per cent) (per cent) 18.0 <m<19.0 0.0081 0.8 0.0 0.1 0.0073 0.6 0.0 0.0 0.0055 0.1 0.0 0.0 19.0 <m<20.0 0.0083 2.2 0.1 0.3 0.0077 1.7 0.1 0.1 0.0056 0.3 0.1 0.1 20.0 <m<21.0 0.0095 5.3 0.3 0.7 0.0085 4.1 0.1 0.3 0.0059 0.7 0.0 0.0 21.0 <m<22.0 0.0101 11.9 0.4 1.1 0.0093 9.0 0.2 0.5 0.0058 1.3 0.0 0.0 22.0 <m<23.0 0.0140 26.0 0.7 2.1 0.0111 16.0 0.3 0.9 0.0065 1.5 0.0 0.0 23.0 <m<23.5 0.0182 22.8 0.6 2.1 0.0129 9.4 0.2 0.6 0.0045 0.5 0.0 0.0 23.5 <m<24.0 0.0263 30.7 0.9 2.3 0.0118 7.4 0.2 0.4 0.0038 0.3 0.0 0.0 Table 7. Photometric redshift accuracy versus Odds for the global sample. Interval Sampleaσzη1η2 (per cent) (per cent) (per cent) Odds >0.00 1.00 0.0137 3.04 8.64 Odds >0.10 0.91 0.0131 2.56 7.36 Odds >0.20 0.80 0.0123 2.13 6.01 Odds >0.30 0.71 0.0116 1.71 5.00 Odds >0.40 0.61 0.0109 1.46 4.09 Odds >0.50 0.50 0.0102 1.08 2.89 Odds >0.60 0.36 0.0093 0.72 1.86 Odds >0.70 0.24 0.0082 0.51 1.13 Odds >0.80 0.14 0.0069 0.30 0.57 Odds >0.90 0.07 0.0062 0.15 0.23 Odds >0.95 0.03 0.0057 0.08 0.14 amF814W<24. the calculated correction was below 1 per cent in all filters. Since all these changes are relative by nature, the synthetic F814Wimages were taken as anchor of the whole system. Another useful quantity calculated by BPZ is the excess photometric scatter over the expected photometric error, what we call zeropoint error (ZPE). This noise excess could be due to two sources: a systematic mismatch between the templates and real galaxy colours or a systematic error in the photometry. As Ben´ ıtez (2014)shows, if enough spectroscopic redshifts are present, averaging over many templates and different SED rest-frame locations ensures that such residuals are typically due to flaws in the photometry. Including this factor allows for a much more realistic estimate of the error and significantly improves the photo-zprecision. We explored the dependence of the amplitude of these zero-point corrections on several observational variables. Looking for possible systematic effects in the reduction, in Fig. 29 we plot globally the zero-point corrections for the ∼1100 individual images as a function of the airmass (top left panel), stellar symmetry (top right panel; defined as the ratio of a/bparameters (Table C1), FWHM scatter Figure 27. Cumulative distribution of the ratio |δz|/1σ. We observed that ∼64 and ∼90 per cent of the photometric redshifts are well fitted within the formal 1σ(magenta vertical line) and 2σconfidence intervals, respectively. This indicates that the photometric redshift uncertainties have been reliably established. (bottom left panel) and the differences between PSF models and stars (top left panel). The procedure was repeated using three different photometric apertures (SEXTRACTOR ISOphotal as red circles, SEXTRACTOR AUTO as blue circles and SEXTRACTOR APER (3 arcsec) as magenta circles) to discard any dependence on the sampled area. As indicated by the mean value of the distributions (dashed black lines), we did not observe any clear correlations, with typical fluctuations smaller than 1 per cent. We explored whether zero-point offsets depended on the magnitude.Forthat, we split the spectroscopic sample into twoequal-sized groups with galaxies brighter and fainter than mF814W=22.5. As seen in Fig. 30 (blue dots) the corrections derived for both samples are the same, within the typical level of photometric uncertainties. Even though filter F954Wshowed a clear disagreement among MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from ALHAMBRA Survey: Bayesian photometric redshifts 2909 Figure 28. Internal photometric redshift checks. Following the same approach as explained in Section 3.8, we systematically compared the Odds (left panel) and photometric redshift zb(right panel) distributions among contiguous CCDs. The statistical results were consistent between each other, with a scatter within the expected intrinsic variance for the sample imaged by each detector. These tests served to ascertain the homogeneity within the different fields. Figure 29. Photometric zero-point validations. We studied the source of the photometric zero-point corrections (derived using SED-fitting algorithms) by comparing these quantities with several observational variables. Considering the possibility of a systematic effect during the data reduction, we represented the corrections for the ∼1100 individual images globally as a function of AIRMASS (top left panel), Stellar Symmetry (top right panel), FWHM scatter (bottom left panel) and the differences between PSF models and stars (top left panel). The procedure was repeated using three different photometric apertures (SEXTRACTOR ISOphotal as red circles, SEXTRACTOR AUTO as blue circles and SEXTRACTOR APER (3 arcsec) as magenta circles) to discard any systematic effect due to the galaxy sampling regions. As indicated by the mean value of the distributions (dashed black lines), no clear correlations were observed, with fluctuations smaller than 1 per cent. samples, its scatter was as large as ∼0.3 mag, indicating other sort of problems, perhaps related to the reductions. To look for a dependence on the photometric aperture size due to some effect related to the PSF corrections, we again divided the spectroscopic sample into two equal-sized groups with photometric areas smaller (and larger, respectively) than 125 pixels. As seen in Fig. 30 (green dots), differences among samples were smaller than 1 per cent. Finally, the dependence between redshift range and zero-point offsets was also considered, assuming a possible effect due to evolution in the galaxy populations (since the BPZ templates do not include any evolution). As seen in Fig. 30 (magenta dots), the differences obtained from both samples were smaller than 1 per cent and so within the error-bar regime. We therefore conclude that the zero-point offsets do not depend on the photometric treatment and MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2910 A. Molino et al. Figure 30. Photometric zero-point validations II. We also studied the robustness of the photometric zero-point corrections using different samples of galaxies. We split the spectroscopic sample into equal-sized groups based on its magnitude (mF814W<22.5 and mF814W>22.5), aperture size (area <125 pixels and area >125 pixels) and redshift (z<0.81 and z>0.81) and derive new photometric zero-point corrections using BPZ. As observed in the figure, for all three cases, the differences among samples (δZP)are quite small. This result shows that the zero-point corrections we derive do not depend strongly on the redshift range or spectral type and therefore are indicative of true offsets in the zero-points, most likely due to the differences between the calibrations obtained from traditional colour transformations based on stars and the average colours of galaxies as defined by the BPZ template set, calibrated with Hubble Space Telescope (HST) observations. represent real offsets between the zero-points defined by the colours of the BPZ templates calibrated with the FIREWORKS HST photometry and those defined by the stellar-based colour calibrations used for the primary ALHAMBRA photometric calibration. 4.2.2 Photometric zero-point calibrations using photometric redshifts AlthoughALHAMBRAwasdesigned to overlapwithotherspectroscopic surveys, only ∼40 per cent of its fields had enough galaxies with spectroscopic redshifts to derive zero-point corrections, as described above. As discussed in Section 4.2.1, the absence of any clear dependence on the observational parameters made infeasible any extrapolations between different fields. Given the obvious improvement resulting from the zero-point corrections, this lack of calibration spectroscopy created a serious source of inhomogeneity across the survey. We realized that the photometric redshifts obtained for emissionline galaxies were quite robust to changes in the zero-point calibration and therefore, statistically, we could treat those redshifts as spectroscopic for calibration purposes, obtaining an automatic source of zero-point corrections for all our fields. Thus, we ran BPZ on the photometric catalogues with the original, stellar-based zero-point estimations. Then we selected a sample formed by those galaxies observed in all 24 filters, with large S/N (mF814W<23.0), good fit to the SED (Odds ≥0.9 and χ2≤1) and classified by BPZ.2 as late-type galaxies (Tb>7). We apply the procedure described in Section 4.2.1, using the photometric redshifts as spectroscopic values and iterating until convergence is reached. This is basically equivalent to calibrating the ZP using the continuum of ELGs as defined by the BPZ.2 templates. In the top panel of Fig. 31, we show the photometric redshift accuracy obtained with three different calibration methods: the original zero-points (red line), corrections derived from photometric redshifts (blue line) and corrections from spectroscopic redshifts (green line). The results indicate that the methodology presented here improves the photometric redshift accuracy successfully almost up to the level provided by the spectroscopic sample and also dramatically reduces the fraction of catastrophic outliers. The bottom panel of Fig. 31 shows how the corrections derived with late-type galaxies worked very well for early-type galaxies, proving that they are independent of the particular choice of templates in the library. It is worth noting that even if the accuracy reached by this method was always slightly worse than that provided by a real spectroscopic sample, it was always much better than the standard stellar-based calibration. Therefore, we decided to apply this kind of zero-point calibration for all fields without spectroscopy, which significantly improved the overall homogeneity of the ALHAMBRA sample. This kind of calibration promises to have wide application to future narrow-band surveys such as Javalambre Physics of the Accelerating Universe (JPAS: Ben´ ıtez et al. 2009;Ben ´ ıtez et al. 2014). 4.3 Photometric redshift distributions Despite having a relatively small field of view (FOV) compared with other, much larger surveys, one of the main virtues of ALHAMBRA is that it includes eight different lines of sight widely separated, which provides a realistic estimation of both the typical redshift distribution of galaxies across cosmic time and its inherent variability (cosmic variance). Photometric redshifts are probabilistic by nature and the shape of the probability distribution is usually far from a well-behaved Gaussian. Therefore point estimates of the redshift and other parameters have limited value and it is much safer to work with the full probability distribution p(z,T|C)(Ben ´ ıtez 2000; Coe et al. 2006; Mandelbaum et al. 2008; Cunha et al. 2009; Wittman 2009; Bordoloi, Lilly &Amara2010; Abrahamse et al. 2011; Sheldon et al. 2012). This is specially true for most faint galaxies, with noisy photometric information, where probability distributions usually become multimodal and completely asymmetric. Even in those cases, the distribution p(z,T|C) obtained with a properly calibrated library and prior can be relied upon to produce accurate population properties like the redshift distribution. We therefore define the global photometric redshift distribution P(z) as follows: P(z)= Ng  i=1 Pi(z)= Ng  i=1dz T pi(z, T |C),(15) where pi(z,T) represents the redshift/type probability distribution function for the ith galaxy. We also ran BPZ on the photometric catalogue used by Ilbert et al. (2009) to derive the global redshift probability distribution function P(z) for the COSMOS field and compare it consistently with our results. We first looked at the P(z) derived using the ALHAMBRA-4/COSMOS data (red line) with the P(z) derived using the COSMOS data (blue line), as seen in the left panel of Fig. 32, where both distributions consistently reproduce a double peak at redshifts z∼0.3 and z∼0.9, respectively. However, MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from ALHAMBRA Survey: Bayesian photometric redshifts 2911 Figure 31. We compare the spectroscopic redshifts with photo-zobtained after applying zero-point corrections with three different approaches: using the standard stellar-based method (red line), photometric redshifts derived from emission-line galaxies (blue line) and a spectroscopic redshift sample (green line). As seen in the top left panel, photometric redshifts using emission-line galaxies not only are a vast improvement with respect to the stellar-based method but also get quite close, in terms of accuracy, to the level of precision achieved by using the highest quality spectroscopic redshifts (Odds >0.3). In addition, the fraction of catastrophic outliers with high Odds was also significantly reduced, as shown in the top right panel. In the two bottom panels we compare how the zero-point corrections derived with the emission-line galaxies (late-type) affect both main galaxy types. We show the dependence of both the accuracy (left scale) and the outlier rate (right scale) before (left bottom panel) and after (bottom right panel) applying the zero-point corrections. Not only has the accuracy for the late-type galaxies (solid blue line) improved significantly with the corrections but also that of the early-type galaxies (solid red line). Meanwhile, the fraction of galaxies per Odds interval (vertical bars) increased homogeneously among spectral types, indicating that the calibration also produced more galaxies with high quality photo-z. whereas the ALHAMBRA-4 field shows a mean redshift z=0.60 for mF814W<22.5 and z=0.87 for mF814W<25.5, the COSMOS field shows a mean redshift z=0.66 for mF814W<22.5 and z=0.96 for mF814W<25.5, as seen in the right panel of Fig. 32. Meanwhile, the global photometric redshift distribution derived for all seven ALHAMBRA fields (excluding stars) shows a mean redshift z=0.56 for mF814W<22.5 and z=0.85 for mF814W<25.5, as seen in the right panel of Fig. 33. This result indicates that, as is known, the COSMOS field shows a clear overdensity with respect to the mean value derived by averaging the seven ALHAMBRA fields. In fact, the average galaxy number in COSMOS goes up by 60 per cent between z=0.4 and z=0.7, whereas no such effect is observed in our average. To study the evolution of the number counts as a function of the magnitude F814Wand redshift, we derived the averaged redshift probability distribution function for the ALHAMBRA fields. As seen in the left panel of Fig. 34, the solid red line corresponding to the mean redshift distribution (per bins of 0.5 mag) indicates a clear evolution moving from z∼0.2 for mF814W<20.5 to z∼0.8 for mF814W>23.0. Inversely, the right panel of Fig. 34 shows how the peak of the averaged distribution of galaxies increases as a function of the redshift for different magnitude ranges. We explored the variance in the redshift–magnitude distribution of galaxies as a function of the absolute Bmagnitude and spectral type. As seen in Fig. 35, we split the sample into early-type galaxies (top panel, defined as 1 <Tb<5) and late-type galaxies (bottom panel, defined as 7 <Tb<11). We plot the redshift distribution for each of the seven individual ALHAMBRA fields (Ai) and one averaged (Global) sample. As observed from the figure, where the logarithmic density was colour-coded, individual structures clearly seen in each individual field are smoothed over in the global distribution. In particular, the well-known bimodal distribution in the COSMOS field (A4) is not systematically observed in the other fields. MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2912 A. Molino et al. Figure 32. Comparison of the redshift probability distribution function P(z) for ALHAMBRA and the COSMOS field. We run BPZ on the Ilbert et al. (2009) catalogue in the same way we did for our ALHAMBRA fields and generate the corresponding P(z). As seen in the left panel, the P(z) for ALHAMBRA- 04/COSMOS (red line) and COSMOS (blue line) are quite similar: both distributions consistently reproduce a double peak at redshifts z∼0.3 and z∼0.9. The average redshifts are also similar: ALHAMBRA-4 has z=0.60 for mF814W<22.5 and z=0.87 for mF814W<25.5, whereas the COSMOS field shows a mean redshift z=0.66 for mF814W<22.5 and z=0.96 for mF814W<25.5. The global P(z) derived averaging the seven ALHAMBRA fields shows a mean redshift z=0.56 for mF814W<22.5 and z=0.85 for mF814W<25.5, as seen in the right panel. It is obvious that the COSMOS field has a peculiar distribution, with a peak-through-peak structure that mimics a large evolution effect between z=0.4 and z=0.9. Figure 33. Effect of the cosmic variance on P(z). The left panel shows the redshift probability distribution function P(z) for all the seven ALHAMBRA fields, using a range of magnitudes 19.0 <mF814W<23.5. The different ALHAMBRA fields are colour-coded as indicated in the legend. Once again, the ALHAMBRA-04 field associated with the COSMOS fields (green line) shows a peculiar distribution with a prominent peak at redshift z∼0.86. The right panel shows the cumulative number counts for the seven fields. Again, the ALHAMBRA-4 field (green line) shows a clear excess in the number of galaxies detected per magnitude range with respect to the other fields. Figure 34. Evolution of the redshift distribution. The left panel shows the evolution of the averaged redshift distribution for the ALHAMBRA fields, as a function of the magnitude F814W. The mean redshift distribution (solid red line) indicates a clear evolution moving from z∼0.2 for mF814W<20.5 to z∼0.86 for mF814W>23.0. The right panel shows the averaged distribution of galaxies for the ALHAMBRA fields, as a function of redshift for different ranges in magnitude. MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from ALHAMBRA Survey: Bayesian photometric redshifts 2913 Figure 35. Redshift distribution in the rest frame per ALHAMBRA field. We explored the variance in the redshift–magnitude distribution of galaxies as a function of the absolute Bmagnitude and spectral type. After splitting the sample into early-type galaxies (top panel, defined as 1 <Tb<5) and late-type galaxies (bottom panel, defined as 7 <Tb<11), we compared the resulting distributions among the seven individual ALHAMBRA fields (Ai)+one averaged sample (Global). As observed from the panels, where the logarithmic density is colour-coded, whereas each individual field shows clear and identifiable structures at different redshifts, the global samples show a more smooth distribution. In particular, we find that the well-known bimodal distribution in the COSMOS field (A4) is not systematically observed along the other fields, emphasizing the effects of cosmic variance on galaxy evolution studies. 4.4 Photometric redshift depth Due to the colour/redshift degeneracies, it is possible to have galaxies that are detected at high S/N in many filters but for which no unambiguous redshifts can be derived. One of the main practical ways of characterizing the effective completeness and depth of a photometric redshift catalogue is by using the number of galaxies with Odds above a certain threshold, which basically tells us how manygalaxies we can expecttohavewithmeaningful,unambiguous photometric redshifts (Ben´ ıtez 2000;Ben ´ ıtez et al. 2009b). We therefore took into account Odds to carry out a set of analyses and evaluate the completeness and accuracy of our sample. For this, we set the interval to compute the Odds parameter to DZ =2×0.0125 ×(1 +z), since this quantity corresponds to MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2914 A. Molino et al. Figure 36. Photometric redshift depth. In order to characterize the photometric redshift depth for the ALHAMBRA catalogues, we quantified the number of galaxies per Odds interval, which is equivalent to estimating the fraction and distribution of galaxies with a certain expected photometric redshift accuracy. As seen in the left panel, we explored the expected completeness factor as a function of the magnitude F814Wand Odds interval. The total fraction of galaxies within each interval is specified in the legend. Similarly, the right panel shows the cumulative distribution of galaxies as a function of the F814Wmagnitude for different Odds intervals. The expected accuracy for photometric redshift δzand the fraction of catastrophic outliers no(according to the spectroscopic sample) are indicated in the legend. twice the expected σ. The completeness factor (fraction of galaxies per Odds interval) as a function of F814Wmagnitude is presented in Fig. 36. Forsources detected only inthe F814Wdetection image,an upper limit (defined as 1σabove the background) is provided. These limiting magnitudes represent the deepest magnitudes extractable from an image, providing useful information for the SED-fitting analysis. Limiting magnitudes are applied whenever measured fluxes, inside a fixed aperture, are equal to or lower than the estimation of the background signal. Since limiting magnitudes depend directly on photometric errors, we computed limiting magnitudes after reestimating photometric errors, via empirical sigma estimation (Section 3.7). Derived limiting magnitudes for each band can be found within the photometric catalogues. In Fig. 37,werepresenttheaveraged 5σlimiting magnitudes for all 23 bands using fixed circular apertures of 3 arcsec. 4.5 Emission-line galaxies When plotting the Odds distribution as a function of F814Wmag- nitude for all galaxies (Fig. 38), we find a concentration of objects with low odds at magnitudes between 18 <mF814W<23 and 0.0 <Odds <0.1. When plotting the logarithmic χ2distribution for those objects, it immediately reveals those detections to have very high χ2values (since BPZ.2 will automatically assign low odds to those objects) indicative of a poor fit, as the right panel in Fig. 38 illustrates. Detections with unexpected poor χ2fitting (given its magnitude) could be due to incorrect photometry or to an incomplete library of templates. After purging the sample from objects with high SEXTRACTOR flags, we saw that the remaining galaxies in that locus could be classified into two different groups: (1) unresolved stellar pairs (identified as a single detection by SEXTRACTOR) with clearly asymmetric morphologies (despite their photometric colours) and (2) very strong broad emission-line objects. As mentioned in Sec- Figure 37. Limiting magnitudes. We derived limiting magnitudes for every image, as they represent a very useful piece of information during the SED- fitting procedure. As required by BPZ, we replaced galaxies with measured fluxes equal to or lower than the estimation of the background signal by an upper limit defined as 1σabove the background. Since limiting magnitudes depend on the photometric uncertainties, we computed limiting magnitudes after re-estimating the photometric errors empirically. Meanwhile, we calculated the expected limiting magnitude using fixed apertures of 3 arcsec and 5σ, as seen in the figure. These magnitudes correspond to the averaged values for the complete set of images. tion 4, neither AGN nor QSO templates were included in the BPZ library and therefore these sources might be expected to show poor fits to any BPZ template. In fact, this is a good way of finding active galaxies, as illustrated in the left panel of Fig. 38. Given the high value of χ2, the new version of BPZ generates for them a redshift distribution that is (in most cases) assigned by the prior probability, MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from ALHAMBRA Survey: Bayesian photometric redshifts 2915 Figure 38. Emission-line galaxy identification. The left panel shows the Odds distribution as a function of magnitude F814Wfor the complete catalogue (stars excluded). As expected, there is a clear dependence between Odds and magnitude, indicating how the photometric redshift confidence decreases with S/N. We observed an unexpected locus for magnitudes in range 18 <mF814W<24 and Odds in range 0.0 <Odds <0.1. When plotting the logarithmic χ2 distribution, it revealed those detections to have extremely high χ2values when SED-fitting the BPZ galaxy templates. We observed that those sources were mostly composed of very strong broad emission-line objects, AGNs and QSOs, galaxy types not included in the BPZ library of templates. The right panel shows an example of an intense emission-line galaxy within that horizontal sequence. favouring solutions near the prior mode zb∼0.4 for intermediate spectral types Tb(E0/Scd/Sbc). 5 PHOTOMETRIC CATALOGUES As explained in Section 3.5, we have generated homogeneous F814W-based catalogues across ∼3.0 deg2, combining the available information from our 23 +1 photometric filters. The full area is then divided into 48 individual catalogues containing the information listed in Appendix C1 and C2. Unique IDs are given to every detection according to the following criteria: ID =81442100119 stands for 814 (detection image) +4 (field) +2 (pointing) +1 (CCD) +00119 (ColorPro_ID). Both astrometric and geometrical information are therefore derived from the corresponding F814Wdetection image: f04p02_F814W_1.swp.fits (following the former example). SEXTRACTOR detection parameters were chosen differently for every detection image, as discussed in Section 3.5.2. Kron apertures (RK) and fraction-of-light radii (RF) were settled according to the aperture parameters defined in Table D1. Total magnitudes and empirically corrected uncertainties (Section 3.7) are given by all 24 filters. Along with this, F814W_3arc represents F814Wmag- nitudes measured on a 3-arcsec circular apertures and likewise F814W_3arc_corr, but corrected to match COSMOS/F814Wpho- tometry (Section 3.5). As every detection in the ALHAMBRA fields was covered by all 24 filters, nfd indicates the number of filters in which a source was detected. Whenever a source was not detected, its magnitude was set to 99. and its photometric uncertainty replaced by a 1σupper limit (Section 4.4) suitable for BPZ. The final catalogues contain several quality flags. PhotoFlag corresponds to the standard SEXTRACTOR photometric flag (Bertin & Arnouts 1996), Satur_Flag indicates a possible saturated source (typically stars with magnitudes brighter than mF814W=16), Stellar_Flag represents a source-by-source statistical classification among stars and galaxies (Section 3.6) and irms_OPT_Flag and irms_NIR_Flag indicate the number of optical and NIR bands in which a detection was observed with a normalized exposure time below 80 per cent, respectively. The DupliDet_Flag indicates that a source was detected twice (within the overlapping area among consecutive detectors). If so, the detection with the poorest S/N is set to a value DupliDet_Flag =1. Therefore, selecting detections with DupliDet_Flag =0 removes all duplicated detections when combining catalogues. The best photometric redshift estimate for every source is zb. Additionally, zmin band zmax brepresent the lower and upper limits for the first peak within a 1σinterval. Spectral type classification is given by Tb, where its number refers to the selected template as indicated in Fig. 21.Odds gives the amount of redshift probability enclosed around the main peak (see Section 4) and χ2is the reduced squared chi from the comparison between observed and predicted fluxes according to the selected template and redshift. An estimation of each detection stellar mass content (in units of log10(M)) is given by Stell Mass.MABS corresponds to the absolute (AB) magnitude for the Johnson B band (Johnson & Morgan 1953). MagPrior corresponds to the F814Wmagnitude used to derived the BPZ prior. Finally, zml and tml represent respectively the maximum-likelihood photometric redshift and spectral type. 6 THE ALHAMBRA ‘GOLD’ CATALOGUE The ALHAMBRA gold catalogue corresponds to a subsample of ∼100k galaxies (17 <mF814W<23) with very accurate and reliable photometric redshifts, an expected error σz<0.012 and redshift probabilitydistribution functions P(z) well-defined by a single peak. The catalogue also includes PSF-corrected photometry for ∼20 000 stars in the Galactic halo (identified according to the methodology described in Section 3.6), along with ∼1000 AGN candidates found with the method discussed in Section 4.5. The ALHAMBRA gold catalogue can be downloaded from the website http://cosmo.iaa.es/content/alhambra-gold-catalog. MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from 2922 A. Molino et al. Table D2. Effective surveyed area. The definition of the effective area is provided in Section 3.5.3. Field Eff. area Field Eff. area name [deg2]name[deg 2] ALHAMBRA_F02P01C01 0.0580 ALHAMBRA_F06P01C01 0.0593 ALHAMBRA_F02P01C02 0.0584 ALHAMBRA_F06P01C02 0.0583 ALHAMBRA_F02P01C03 0.0540 ALHAMBRA_F06P01C03 0.0585 ALHAMBRA_F02P01C04 0.0582 ALHAMBRA_F06P01C04 0.0582 ALHAMBRA_F02P02C01 0.0596 ALHAMBRA_F06P02C01 0.0587 ALHAMBRA_F02P02C02 0.0506 ALHAMBRA_F06P02C02 0.0587 ALHAMBRA_F02P02C03 0.0538 ALHAMBRA_F06P02C03 0.0572 ALHAMBRA_F02P02C04 0.0586 ALHAMBRA_F06P02C04 0.0589 ALHAMBRA_F03P01C01 0.0586 ALHAMBRA_F07P03C01 0.0587 ALHAMBRA_F03P01C02 0.0589 ALHAMBRA_F07P03C02 0.0590 ALHAMBRA_F03P01C03 0.0578 ALHAMBRA_F07P03C03 0.0576 ALHAMBRA_F03P01C04 0.0592 ALHAMBRA_F07P03C04 0.0587 ALHAMBRA_F03P02C01 0.0592 ALHAMBRA_F07P04C01 0.0589 ALHAMBRA_F03P02C02 0.0577 ALHAMBRA_F07P04C02 0.0566 ALHAMBRA_F03P02C03 0.0569 ALHAMBRA_F07P04C03 0.0580 ALHAMBRA_F03P02C04 0.0590 ALHAMBRA_F07P04C04 0.0590 ALHAMBRA_F04P01C01 0.0589 ALHAMBRA_F08P01C01 0.0588 ALHAMBRA_F04P01C02 0.0590 ALHAMBRA_F08P01C02 0.0590 ALHAMBRA_F04P01C03 0.0569 ALHAMBRA_F08P01C03 0.0577 ALHAMBRA_F04P01C04 0.0589 ALHAMBRA_F08P01C04 0.0587 ALHAMBRA_F05P01C01 0.0595 ALHAMBRA_F08P02C01 0.0585 ALHAMBRA_F05P01C02 0.0594 ALHAMBRA_F08P02C02 0.0583 ALHAMBRA_F05P01C03 0.0588 ALHAMBRA_F08P02C03 0.0558 ALHAMBRA_F05P01C04 0.0594 ALHAMBRA_F08P02C04 0.0576 1IAA–CSIC, Glorieta de la astronom´ ıa S/N. E-18008, Granada, Spain 2Centro de Estudios de F´ ısica del Cosmos de Arag´ on (CEFCA), Plaza San Juan 1, E-44001 Teruel, Spain 3Instituto de F´ ısica de Cantabria (CSIC–UC), E-39005 Santander, Spain 4Unidad Asociada Observatori Astron´ omic (IFCA – Universitat de Val ´ encia), Valencia, Spain 5Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK 6Space Telescope Science Institute, Baltimore, MD, USA 7Physics and Astronomy Department, University of Missouri, Columbia, MO 65211, USA 8Observat´ orio Nacional–MCT, Rua Jos´ e Cristino 77, CEP 20921-400, Rio de Janeiro–RJ, Brazil 9Instituto de Astrof´ ısica de Canarias, V´ ıa L´ actea s/n, La Laguna, Tenerife 38200, Spain 10GEPI, Paris Observatory, 77 av. Denfert Rochereau, F-75014 Paris, France 11University Denis Diderot, 4 Rue Thomas Mann, F-75205 Paris, France 12Department of Theoretical Physics, University of the Basque Country UPV/EHU, Bilbao, Spain 13Departamento de F´ ısica At´ omica, Molecular y Nuclear, Facultad de F´ ısica, Universidad de Sevilla, Spain 14Departamento de Astrof´ ısica, Facultad de F´ ısica, Universidad de la Laguna, Spain 15Departamento de Astronom´ ıa, Pontificia Universidad Cat´ olica, Santiago, Chile 16Departament d’Astronom´ ıa i Astrof´ ısica, Universitat de Valencia, E-46100 Valencia, Spain 17Observatori Astronomic de la Universitat de Valencia, E-46071 Valencia, Spain This paper has been typeset from a T EX/L A TEX file prepared by the author. MNRAS 441, 2891–2922 (2014) at CSIC on February 2, 2015http://mnras.oxfordjournals.org/Downloaded from