Dark Energy Survey Year 1 Results: Photometric Data Set for Cosmology

I Introduction

Precision measurements of dark energy with DES rely on an unprecedented survey data set and a comprehensive understanding of the survey performance. It is necessary to identify, characterize, and mitigate the influences of variable observing conditions, data processing artifacts, photometric calibration nonuniformity, and astrophysical foregrounds. For example, photometric calibration must be accurate and uniform to avoid introducing noise and bias into photometric redshift estimates. Studies of galaxy clustering depend on a detailed knowledge of survey coverage, galaxy detection efficiency, and the accuracy of recovered galaxy properties. Furthermore, detailed modeling of the point-spread function (PSF) and instrument response is required to perform galaxy shape measurements on objects that are fainter than the the detection limit of a single DES image. The scale and complexity of assembling, characterizing, and validating the DES data motivate a collaborative effort that draws upon and enables a wide range of scientific analyses.

The desired precision of DES cosmological analyses motivates further refinement of Y1A1. The resulting data set, referred to as Y1A1 GOLD, is accompanied by extensive validation and ancillary data products to facilitate cosmological analyses. The primary components of Y1A1 GOLD are (Figure 1): (1) a multi-band photometric object catalog subselected from the Y1A1 COADD object catalog; (2) an adjusted photometric calibration to improve uniformity over the survey footprint; (3) shape and photometry information from a simultaneous multi-epoch, multi-object fit; (4) a set of ancillary maps quantifying survey characteristics using the HEALPix rasterization scheme (Górski et al. 2005); and (5) several value-added quantities for high-level analyses (i.e., a star-galaxy classifier and photo-$z$ estimates). When creating the Y1A1 GOLD object catalog, several classes of non-physical, spurious, or otherwise problematic objects were identified and either flagged or removed. The calibrated magnitudes of objects were also corrected for interstellar extinction using a stellar locus regression (SLR) technique. The ancillary data products associated with Y1A1 GOLD accurately quantify the characteristics of the survey, further mitigating the impact of systematic uncertainties. A high-level summary of the performance of Y1A1 GOLD is tabulated in Table 1.

Our purpose here is to document the production and performance of the Y1A1 GOLD data set in support of upcoming DES cosmology analyses. We start by describing the DES Y1 observations in Section II and briefly reviewing the image reduction pipeline applied to produce the Y1A1 data set in Section III. In Section IV we describe the photometric calibration of the Y1A1 data, and in Section V we describe the image coaddition process. In Section VI we discuss the creation of unique object catalogs, while in Sections VII and VIII we describe the ancillary maps and value-added quantities produced to complement the Y1A1 GOLD catalog. We briefly conclude in Section IX.

II Data Collection

DES has been allocated 105 nights per year on the Blanco telescope starting in 2013. The first year of DES observing spanned from 2013 August 31 to 2014 February 9 and consisted of both full and half nights. Several exposures taken during engineering time earlier in 2013 August were also included in the the Y1A1 data set. Details on DES operation and data collection are provided by Diehl et al. 2014; here we briefly summarize some of the key details relevant to the creation of Y1A1 GOLD.

In addition to the wide-area and SN survey fields, two auxiliary fields outside the DES footprint were observed to aid in the training of photometric redshifts and star-galaxy classification. Fields overlapping with COSMOS (Scoville et al. 2007) and VVDS-14h (Le Fèvre et al. 2005) were observed during the DES Science Verification (SV) period. Data from the DECam Science Verification period is available at: https://des.ncsa.illinois.edu/releases/sva1. These observations are deeper than most of the Y1 wide-area survey.

During DES operation, sets of biases and flat-field calibration exposures were taken in each filter before each night of observing. Standard-star fields were observed at three different airmasses at the beginning and end of each night unless conditions were obviously nonphotometric. On DES half nights only two standard-star fields were observed at the midpoint of the night. Cloud cover was monitored continuously during observing by the RASICAM all-sky infrared camera (Lewis et al. 2010; Reil et al. 2014).

DES images the sky whenever weather allows the Blanco dome to be open, resulting in some exposures being taken in very poor conditions. Thus, data quality monitoring is essential to select exposures that meet the scientific requirements of the survey. The quality of exposures is evaluated based on the PSF, sky brightness, and sky transparency. For each exposure, we define $t_{\rm eff}$ to be the ratio between the actual exposure time and the exposure time necessary to achieve the same signal-to-noise ratio (S/N) for point sources observed in nominal conditions (Neilsen et al. 2015). The effective exposure time is defined as $T_{\rm eff}=t_{\rm eff}T_{\rm exp}$, where $T_{\rm exp}$ is the shutter-open exposure time. To pass preliminary data quality cuts, wide-area survey exposures must have $t_{\rm eff}>0.3$ in $r$, $i$, and $z$ band and $t_{\rm eff}>0.2$ in $g$ and $Y$ band. The median measured $t_{\rm eff}$ for Y1 was $t_{\rm eff}=0.75$ in the $r$, $i$ and $z$ band and $t_{\rm eff}=0.49$ in the $g$ and $Y$ band. In contrast, the preliminary data quality cuts for SN exposures require ${\rm FWHM}<2^{\prime\prime}$ and that a 20th-magnitude simulated source have signal-to-noise ratio $>$20 ($>$80) for the shallow (deep) exposures (Kessler et al. 2015). Of the exposures taken during Y1, 82% of the wide-area exposures and 95% of the SN exposures passed their respective data quality criteria (i.e., did not require re-observation). A number of additional exposures were removed from the Y1 data set due to instrumental artifacts (scattered light and internal reflections from bright stars, contaminating light from airplanes, poor telescope tracking, shutter malfunctions, dome occultations, etc.). In total, the Y1A1 FINALCUT processing consists of 16,857 DECam exposures, including wide field, SN, auxiliary fields, and standard stars.

III Image Processing

The DESDM system is responsible for reducing, cataloging, and distributing DES data. Earlier iterations of the DESDM image processing pipeline are outlined in Sevilla et al. 2011 and Mohr et al. 2012, and a more detailed summary with updates for the forthcoming DES three-year processing is available in Bernstein et al. 2017a and Morganson et al. 2018. Here we briefly summarize the single-epoch image processing steps applied during the DES Y1A1 FINALCUT campaign. The Y1A1 FINALCUT campaign resulted in ${\sim}\,20$ TB of processed images and a catalog of ${\sim}\,740$ million detected objects.

Overscan and Crosstalk: Each DECam CCD has two amplifiers for converting photo-carrier counts to analog-to-digital units (ADU). For each amplifier, the average in the overscan region was calculated and subtracted on a row-by-row basis. Crosstalk is manifested as low-level leakage of electronic signals between different readout amplifiers and is observed at the level of ${\sim}\,10^{-3}$ for pairs of amplifiers on the same CCD and ${\sim}\,10^{-4}-10^{-6}$ for pairs of amplifiers on different CCDs on the same electronic back plane. Crosstalk was corrected by applying a matrix operation to the simultaneous readout of 140 amplifiers (including the amplifiers for the eight focus and alignment CCDs). The elements of the crosstalk correction matrix were derived from the median amplifier output for each “victim” channel as a function of the “source” amplifier signal for a large number of sky images. Crosstalk between the DECam CCDs is found to be nonlinear when the signal on the source amplifier exceeds its saturation level – i.e., the level at which the amplifier response becomes nonlinear (Bernstein et al. 2017a, Figure 2 of). This crosstalk nonlinearity was incorporated into crosstalk correction. There is no evidence for temporal variation in the crosstalk between CCDs on year timescales, and a single crosstalk matrix was used for the Y1A1 processing.

Bias Correction: A master bias frame was constructed from the average of ${\sim}\,100$ zero-second exposures taken during the pre-night calibration sequences over the course of the Y1 observing season. This master bias was subtracted from each CCD to remove any residual fixed pattern noise not incorporated by the overscan correction.

Bad-Pixel Masking: Bad pixel masks were created for each CCD by identifying outliers in sets of biases and $g$-band flat-field calibration exposures. These bad pixels were masked and interpolated based on values in adjacent columns. The Y1A1 processing campaign used a single static bad pixel mask. Two CCDs have failed since commissioning and were removed from Y1 processing (Diehl et al. 2014, Figure 3;). CCD61 failed on 2012 November 7 and data from this CCD were not used in Y1. CCD2 failed on 2013 November 30 and data from this CCD were only included for the early months of Y1. CCD2 subsequently recovered on 2016 December 29.

We corrected for nonlinearity at both low and high light levels using a fixed look-up table derived from calibration exposures obtained during the SV period. One amplifier on CCD31 has a time-variable nonlinear gain at the 20% level, and this CCD was excluded from Y1 processing. The other amplifier on CCD31 is stable and has been recovered in more recent processing. The Y1A1 data processing did not correct for charge-induced pixel shifts (i.e., the “brighter-fatter” effect; Antilogus et al. 2014; Gruen et al. 2015), although corrections have been incorporated into more recent reductions of the DES data (Bernstein et al. 2017a).

Pupil Correction: An additive correction was applied for pupil ghosting in each exposure. As part of this process, “star flats” were created in each filter and CCD by taking multiple dithered exposures of a dense stellar field and fitting a cubic polynomial to variations in the observed brightnesses of stars. The pupil ghost correction was constructed on a CCD by CCD basis for each exposure from the star flat and the level of sky background (including scattered light and the night-sky pupil image). The pupil correction was scaled and subtracted from each CCD individually. This technique can leave gradients of several percent in the sky background level (worst in $z$ and $Y$ band), which propagate into the reduced science images and are corrected during photometric calibration (Appendix A). More recent implementations of the data processing pipeline fit the additive correction over the full focal plane rather than CCD by CCD (Morganson et al. 2018).

Flat Fielding: The response of DECam to the night sky is more stable than nightly variations in the illumination of the flat-field screen taken during pre-night calibrations. Therefore, in Y1A1 we created a single average flat-field frame for each filter from ${\sim}\,100$ individual flat-field exposures. The science exposures were divided by the average flat-field frames normalized on a CCD by CCD basis. The pupil and flat-field corrections used for Y1A1 processing remove small-scale fluctuations in the background due to pixel-size variations, i.e., tree rings, edge brightening, and tape bumps (Plazas et al. 2014). However, this correction is approximate and results in photometric measurement residuals at the level of ${\sim}\,0.5\%$. A more rigorous correction has been applied in subsequent DES data reductions (Bernstein et al. 2017a; Morganson et al. 2018).

Weight Plane Creation: A weight plane image was created containing the inverse variance of the flat-fielded image value in each pixel. The variance estimate summed the expected Poisson noise and read noise. Saturated pixels were flagged and set to zero in the weight plane. The weight plane is used to assign relative weights to images during the coaddition process.

Fringe Frame Correction: Fringing is visible in $z$- and $Y$-band exposures. The fringing pattern is nearly identical in these bands but has a larger amplitude in the $Y$ band. A set of templates was constructed from a stack of ${\sim}\,120$ $z$- and $Y$-band exposures from DES SV. These template images were median filtered and averaged on a pixel-by-pixel level to construct a fringe frame. In the reduction pipeline, each CCD of the $z$- and $Y$-band exposures had its median sky level measured, and this sky level was used to scale the fringe frame, which was then subtracted on a CCD-by-CCD basis. The scaling method was identical to that used to scale and subtract the pupil pattern. The vast majority of exposures have a fringe residual that is $<0.1\%$ of the sky background level. Exposures taken under the brightest conditions accepted for $Y$-band observing can have a fringe residual that is $\sim 0.4\%$ of the sky background level.

Illumination Correction: Light reflected from the flat-field screen fills the telescope pupil differently than the focused light of distant stars. To account for pixel-level differences in the throughput of the flat-field images, we applied a multiplicative correction to the DECam response based on the star flats. After dividing by the star flats the residual difference in response between CCDs is typically $<2\%$ peak to peak (Appendix A.1).

Preliminary Astrometric Solution: A world coordinate system (WCS) was installed in the image header at the time of observation using a fixed distortion map derived from the star flats and an optical axis read from the telescope encoders. The pointing of each image was updated matching the centers of bright stars measured with SExtractor (Bertin & Arnouts 1996; Bertin et al. 2002) to the UCAC-4 catalog using SCAMP (Bertin 2006). This WCS was replaced by a superior one during the coaddition step (Section V), and the astrometric accuracy of the Y1A1 GOLD catalog is described in Section V.1.

Energy deposited from cosmic-ray interactions with the CCDs were detected on single images using the findCosmicRays algorithm adopted from the LSST software stack. https://lsst-web.ncsa.illinois.edu/doxygen/x_masterDoxyDoc/namespacelsst_1_1meas_1_1algorithms.html The cosmic-ray pixels were flagged in the mask plane, zeroed in the weight plane, and interpolated in the image plane.

Long streaks produced by rapidly moving objects (i.e., meteors and Earth-orbiting satellites) were detected using a Hough transform algorithm and were also masked (Melchior et al. 2016).

Single-Epoch Catalog Creation: Object catalogs were produced for each CCD using the AstrOmatic package (Bertin 2006). Photometric fluxes were derived using PSFEx and SExtractor for fixed apertures, the PSF model, and a galaxy model. The local sky background on each CCD was estimated by SExtractor. The single-epoch Y1A1 FINALCUT catalogs served as an input into the photometric calibration described in Section IV.

IV Photometric Calibration

The photometric calibration of Y1A1 was a multistep process largely following the procedure of Tucker et al. 2007. Photometric calibration was performed on the single-epoch Y1A1 FINALCUT images first on a nightly and then on a global basis. An additional calibration adjustment was derived from the stellar locus and applied at catalog level. Below we briefly describe the steps in the photometric calibration of Y1A1; a more detailed discussion of the Y1A1 photometric calibration can be found in Appendix A.

A preliminary photometric calibration of the Y1A1 data was performed on a nightly basis. Standard-star fields were observed at various airmasses at the beginning and end of each night. These images were reduced and the centroids of stars were matched to a set of primary standard stars from Sload Digital Sky Survey (SDSS) DR9 (Smith et al. 2002). The DES secondary standards were then transformed to an initial DES AB photometric system via a set of transformation equations derived from SDSS DR9 and supplemented by UKIDSS DR6 (Appendix A.4). This tied the DES flux calibration of the secondary standards to SDSS and to the AB magnitude system (Padmanabhan et al. 2008, i.e.,).

IV.2 Global Calibration

We implemented a global calibration module (GCM) to derive calibrated zeropoints for all exposures, including those taken under non-photometric conditions, and to improve on the relative calibration accuracy achieved by the nightly photometric solution. The GCM procedure follows that of Glazebrook et al. 1994 and is described in more detail in Appendix A.2. Briefly, the Y1A1 data were split into regions of contiguous, overlapping images where at least one image had been previously calibrated. The calibrated images served as a reference against which other images in the grouping were calibrated. To be calibrated by the GCM, an image needed to either overlap a calibrated image or have an unbroken path of overlapping images to a calibrated image.

IV.3 Photometric Calibration Adjustment

The global calibration is found to be uniform at the ${\sim}\,2\%$ level in each band over the majority of the Y1A1 survey footprint (discussed in Section IV.4). However, non-uniformity in the colors of objects can severely impact DES science by introducing a spatial dependence on object selection and photo-$z$ estimation. The SLR technique uses the distinct shape of the stellar locus in color-color space to provide a relative calibration of exposures in different bands (Ivezić et al. 2004; MacDonald et al. 2004; High et al. 2009; Gilbank et al. 2011; Desai et al. 2012; Coupon et al. 2012; Kelly et al. 2014, e.g.,). To correct for residual spatial non-uniformity in the calibration and account for Galactic reddening (including uncertainties in the amplitude of reddening and possible variations in the effective Milky Way dust law), we have applied a secondary adjustment to the calibration of the coadd object catalogs derived from the stellar locus. Gradients in stellar population are subdominant to other calibration uncertainties in Y1A1 given the DES filter bandpasses and high Galactic latitude of the survey (High et al. 2009; Kelly et al. 2014, e.g.,). We followed the procedure of Drlica-Wagner et al. 2015 and applied a modified version of the BigMACS SLR code (Kelly et al. 2014) https://code.google.com/p/big-macs-calibrate/ coupled with an empirical stellar locus to derive zeropoint adjustments to improve the color uniformity of stars across the Y1A1 footprint. The SLR adjustment was tied to the $i$-band magnitude derived from the GCM, dereddened using the Schlegel et al. 1998 dust map with a reddening law from O’Donnell 1994. The SLR zeropoint adjustments were interpolated to the positions of each object in the catalog and were applied directly to the magnitudes of objects derived from the coadded images. In this way, the calibrated magnitudes of the Y1A1 GOLD catalog are already corrected for interstellar extinction. After the SLR adjustment, the color of stars was found to be uniform at the ${\sim}\,1\%$ level across the footprint, which was verified using the red sequence of galaxies. More detail on the SLR calibration adjustment can be found in Appendix A.3.

IV.4 Photometric Calibration Accuracy

To quantify the accuracy of photometric calibration, we would like to characterize the statistical distribution of $\Delta m=m_{\rm meas}-m_{\rm true}$, where $m_{\rm meas}$ and $m_{\rm true}$ are the measured and true magnitude of catalog objects, respectively. The characterization of the $\Delta m$ distribution can be split into two components: (1) an “absolute” calibration accuracy that represents a linear shift of the $\Delta m$ distribution (e.g., the mean of the distribution), and (2) a “relative” calibration accuracy that represents the spread of the $\Delta m$ distribution (e.g., standard deviation of the distribution). In reality, values of $m_{\rm true}$ are not available, and we must make use of the calibrated magnitudes from other surveys or synthetic models, which have their own associated uncertainties. We describe several calibration validation studies below and summarize the results in Table 2.

The absolute calibration of the Y1A1 GOLD is tied to SDSS through the DES secondary standard stars. As an independent cross-check on the absolute photometric calibration, we examined the CALSPEC standard star, C26202 (Bohlin et al. 2014). We calculated synthetic magnitudes for C26206 by convolving Hubble Space Telescope (HST) spectra (stisnic_006) http://www.stsci.edu/hst/observatory/crds/calspec.html with the focal-plane-averaged DECam filter throughput including atmospheric attenuation at an airmass of 1.3 (Berk et al. 1999). The predicted magnitude of C26202 in each of the DES $grizY$ bands is $g=16.695$, $r=16.340$, $i=16.257$, $z=16.245$, and $Y=16.268$. These predicted magnitudes were then compared against the pre-SLR corrected magnitudes measured by the GCM to give a “top-of-the-atmosphere” estimate of the absolute calibration uncertainty. We derive an absolute offset (in mag) of $\delta g=0.014$, $\delta r=0.004$, $\delta i=0.002$, $\delta z=0.015$, and $\delta Y=0.032$, which we quote as the absolute photometric calibration uncertainty in Table 1.

Our primary technique for quantifying the relative photometric accuracy of Y1A1 GOLD is by comparing the calibrated magnitudes of stars against those derived from a combination of APASS (Henden & Munari 2014) and 2MASS (Skrutskie et al. 2006) (Figure 5). We perform a “top-of-the-atmosphere” comparison by calculating the difference between the GCM calibrated magnitude and the APASS/2MASS magnitude transformed to the DES system (Appendix A.4). We derive the relative calibration uncertainty as the half-width between the 16th and 84th percentiles of the difference in magnitude over the footprint: $\sigma_{68}(g)=0.019$, $\sigma_{68}(r)=0.022$, $\sigma_{68}(i)=0.020$, $\sigma_{68}(z)=0.020$, and $\sigma_{68}(Y)=0.018$ (Table 1). These values include calibration uncertainties from both DES and APASS/2MASS, and are thus a conservative upper bound on the Y1A1 GCM accuracy. We further compare the SLR-adjusted Y1A1 GOLD photometry to the transformed APASS/2MASS photometry dereddened using the SFD maps and reddening law of O’Donnell 1994. We find a dispersion of $\sigma_{68}(g)=0.025$, $\sigma_{68}(r)=0.024$, $\sigma_{68}(i)=0.020$, $\sigma_{68}(z)=0.018$, and $\sigma_{68}(Y)=0.015$. These values include an additional contribution from differences in the reddening correction derived from the SLR and the SFD dust maps, which results in larger uncertainty in the bluer filters where interstellar reddening is more extreme. These comparisons are shown in more detail in Appendix A.5.

As an additional cross-check, we compared the “top-of-the-atmosphere” Y1A1 GCM calibration against a global calibration of the contiguous DES three-year data set (Y3A1). The absolute calibration of the Y3A1 data set was also tied to C26202, but made use of additional observations of this object. From comparisons against other CALSPEC standards (LDS749B and WD0308-565), the absolute calibration of Y3 is believed to be accurate at the ${\sim}\,1\%$ level. The relative calibration of Y3 was performed over the contiguous Y3A1 footprint using an independent forward global calibration method (FGCM) and is found to be uniform at the $0.7\%$ level (Burke et al. 2018). We checked the absolute calibration of Y1A1 GOLD by matching stars against their Y3 counterparts over the Y1A1 GOLD footprint. We found that the absolute offset between Y1A1 GCM and Y3A1 FGCM was $\delta g=0.023$, $\delta r<0.001$, $\delta i=0.004$, $\delta z=0.011$, and $\delta Y=0.05$, while the relative calibration spread was $\sigma_{68}(g)=0.014$, $\sigma_{68}(r)=0.007$, $\sigma_{68}(i)=0.008$, $\sigma_{68}(z)=0.013$, and $\sigma_{68}(Y)=0.015$. These numbers are in good agreement with those quoted above, and support the expectation that the relative calibration uncertainty in Table 1 is a conservative estimate.

V Image Coaddition

Image coaddition allows DES to detect fainter objects and mitigates the impact of residual transient imaging artifacts (e.g., unmasked cosmic rays, satellite streaks, etc.). Combining multiple dithered exposures also positions objects at different points on the focal plane, mitigating systematics associated with the non-uniform response of the instrument.

Before performing image coaddition, several image quality checks were run to identify and blacklist CCD images with severe imaging artifacts. CCD images affected by strong scattered light artifacts were identified by a ray tracing algorithm using the Yale bright star catalog (Hoffleit & Jaschek 1991), the telescope pointing, and a detailed model of the DECam optics, filter changer, and shutter assemblies. Several exposures have excess noise in one or more of the DECam CCD backplanes. These CCD images were identified through visual inspection and through the detection of a large number of spurious catalog objects. In addition, CCD images that were affected by bright meteor trails and airplanes were identified through visual inspection. Less than $1\%$ of CCD images were blacklisted and removed from the coadd process.

When DESDM created coadded images, the PSFs of the individual input images were not homogenized. This decision was motivated by studies of SV data where PSF homogenization was found to produce correlated sky noise, which made it difficult to properly estimate the photometric uncertainties of galaxies. While non-homogenized PSF coaddition yields better-behaved photometric uncertainties, it can introduce sharp PSF discontinuities on the ${\sim}\,0\fdg 1$ scale that are difficult to model with conventional polynomial approximation techniques (Bertin 2006, i.e., PSFEx;). Some of these issues can be addressed by using quantities measured in the Y1A1 FINALCUT catalog (Section VI); however, studies that depend sensitively on morphological characterization (i.e., weak lensing analyses) perform their own simultaneous fit of the individual single-epoch images (Section VI.3). Studies with PSF homogenization are ongoing, and PSF-homogenized coadds have been used for several DES science analyses using SV data (Hennig et al. 2017; Klein et al. 2017).

In addition to the main survey, there are several regions where the DES Y1 imaging is considerably deeper than the nominal three to four tilings. Coadds have been created in these regions using different numbers of input images to achieve different photometric depths. The Y1A1 GOLD coadd catalog thus contains four different samples:

WIDE: The WIDE coadd data sample is built from exposures in the S82 and SPT regions of the Y1 wide-area survey footprint and has a depth of three to four tilings. One of the SN fields, SN-E, resides within the SPT region; however, to maintain uniformity the WIDE data set only includes images that were taken as part of the DES wide-area survey (the SN-E exposures are included in the other data sets that follow).

D10: The D10 sample is constructed in the SN, COSMOS, and VVDS-14h fields by coadding images to an effective depth of 10 exposures. The 10-exposure depth is intended to mimic the expected main survey depth at the end of DES. Similar to D04, general criteria requiring survey quality, ${\rm FWHM}<1\farcs 3$ in $riz$ and ${\rm FWHM}<1\farcs 4$ in $gY$ were applied. The median MAG_AUTO $10\sigma$ limiting magnitude for galaxies (Section VII.1) in the D10 sample is $g=24.2$, $r=24.0$, $i=23.5$, $z=22.7$, $Y=20.9$.

DFULL: The DFULL sample uses all high-quality images in the SN, COSMOS, and VVDS-14h fields. The DFULL coadd applies a requirement of ${\rm FWHM}<1\farcs 3$ in $riz$-band and ${\rm FWHM}<1\farcs 4$ in $g$-band (no FWHM requirement is placed on $Y$-band). Exposures are still required to pass the survey quality cuts, but no restriction is placed on the number of exposures that go into the coadd. The median MAG_AUTO $10\sigma$ limiting magnitude for galaxies (Section VII.1) in the DFULL sample is $g=24.2$, $r=23.9$, $i=23.8$, $z=23.7$, $Y=21.2$, with $\sim 10\%$ of the area having a limiting magnitude greater than 25 in $griz$. The median depth of the DFULL sample in $g$- and $r$-band is comparable to that of D10 owing to the fact that few additional exposures passed the survey quality and FWHM requirements outside of the deep SN fields. The $r$-band depth is $0.05$ mag shallower in DFULL owing to a slightly larger area with more varied data quality.

Astrometric calibration places the DES exposures onto a consistent reference frame with each other and with external catalogs. We used SCAMP (Bertin 2006) to find an astrometric solution including corrections for optical distortion towards the edges of the focal plane. During Y1A1 FINALCUT processing, initial astrometric calibration was performed on individual exposures. Starting with an approximate initial solution provided by the telescope control system, the SExtractor windowed image coordinates of bright stars in the DES exposures were extracted and matched against the UCAC-4 stellar catalog (Zacharias et al. 2013).

VI Object Catalogs

Catalogs of unique astrophysical sources were assembled from the coadded images. The goal of the DESDM catalog production was to assemble the most inclusive catalog of sources while maintaining a low contamination fraction. The production of catalog subsamples that are complete to a given threshold is left to subsequent science analyses. Source detection, morphological characterization, and multi-band photometric flux measurements were performed using SExtractor (Bertin & Arnouts 1996; Bertin et al. 2002). Source detection used a CHI-MEAN combination of the coadded images in $r+i+z$ (Szalay et al. 1999; Bertin 2010). The CHI-MEAN detection image was designed to minimize discontinuities between regions with different numbers of exposures (see Appendix B). In contrast, flux and shape measurements were performed on each band individually using SExtractor in dual mode (i.e., analyzing the image for an individual band simultaneously with the detection image). The local background was estimated via $16\times 16$ pixel boxes with $3\sigma$ clipping of bright pixels and median filtering of the boxes. The image was convolved with a $3\times 3$ pixel structuring element of the form []. An S/N threshold of $1.5\sigma$ per pixel was applied over the convolved image to detect objects. Source localization was derived from the barycenter of the object in the $i,z,Y,r,g$ single-band coadd images (in order). Coadd object positions in world coordinates (J2000 epoch) were computed using the astrometric solution found during image coaddition (Section V.1).

The depth and PSF of the DES imaging result in overlapping isophotes for objects in crowded regions, e.g., galaxy clusters, star clusters, and dense stellar regions around the LMC. Incomplete deblending of overlapping objects affects the measured shapes and photometric properties of cluster galaxies, which impacts weak lensing and cluster cosmology science. SExtractor attempts to deblend each detected object into sub-components using a multi-thresholding algorithm (Bertin & Arnouts 1996). An object is separated into two (or more) new objects if the intensity of the new object is greater than a fraction of the total intensity set by the DEBLEND_MINCONT parameter, while the number of deblending thresholds is set by the DEBLEND_NTHRESH parameter. The Y1A1 processing campaign adopts 0.001 and 32, respectively, for the two parameters. These values were optimized based on SV data to balance completeness and purity for cluster galaxies. More aggressive deblending techniques for the DES data have been explored in Zhang et al. 2015.

SExtractor was used to measure object photometry via several methods (Sevilla et al. 2011, see).

Fixed aperture fluxes (FLUX_APER) were measured for 12 circular apertures with different radii from $0\farcs 25$ to $9\arcsec$.

Elliptical aperture fluxes (FLUX_AUTO) were calculated using the second-order moments of each object to derive the elongation and orientation of the best-fit ellipse (Kron 1980). The ellipse scaling factor was derived from the first-order moment of the radial distribution.

PSF model fluxes (FLUX_PSF) suitable for point-like sources were fit to the measured PSF shape. As mentioned in Section V, PSF discontinuities in the Y1A1 coadd images can degrade the quality of the PSF model fluxes.

Exponential model fluxes (FLUX_MODEL) suitable for galaxies were fit by convolving a one component exponential model with a local model of the PSF. These fluxes were fit both individually in each band and by fixing the model shape based on the detection image (FLUX_DETMODEL).

Among the morphological measurements performed by SExtractor, two are designed to separate point-like objects (i.e., stars) from spatially extended sources (i.e., galaxies). The first is the CLASS_STAR variable which uses a neural network to assess the “stellarity” of an object (Bertin & Arnouts 1996). The second variable, SPREAD_MODEL, is derived from the Fisher’s linear discriminant between a model of the PSF and an extended source model convolved with the PSF (Desai et al. 2012; Bouy et al. 2013; Soumagnac et al. 2015). The application of these variables to star-galaxy separation is detailed in Section VIII.1.

As stated previously, catalog quantities were also derived for individual single-epoch exposures that compose the coadded images. Objects detected on the individual exposures were associated with sources in the coadd catalog using a $1\arcsec$ matching radius. While shallower, the single-epoch catalogs are important for probing the temporal domain. Additionally, the photometry of the single-epoch catalogs is not subject to the PSF discontinuities present in the coadds. For this reason, we calculated a number of photometric and morphological quantities from the average of single-epoch measurements weighted by their associated statistical uncertainties (the names of these quantities are prefixed by “WAVG”). In particular, the weighted-average spread-model quantity (WAVG_SPREAD_MODEL) has been shown to yield better star-galaxy separation (Drlica-Wagner et al. 2015) for stellar objects, and the weighted-average PSF magnitudes (WAVGCALIB_MAG_PSF) have been found to yield more precise stellar photometry than the corresponding coadd quantities. In addition, uncertainties for the WAVG quantities are calculated directly from the variance in the measurements from individual exposures and thus avoid any systematics introduced in the coaddition process.

VI.2 Y1A1 GOLD Catalog Selection

We assembled the Y1A1 GOLD object catalog as a high-quality subselection of the objects extracted from the Y1A1 coadd images. When selecting the Y1A1 GOLD catalog, we sought to remove spurious, non-physical objects while minimally decreasing the statistical power of any scientific investigation (Table 3). Specifically, we required that objects be observed, but not necessarily detected, at least once in each of the $g$, $r$, $i$, and $z$ bands. We also required that all objects have $\texttt{{SPREADERR\_MODEL}}>0$ for the $g$, $r$, $i$, and $z$ bands to eliminate objects with unphysical SPREADERR_MODEL values indicative of a failure in the SExtractor photometric fit. Objects that are not detected in a specific band have a sentinel value of $\texttt{{SPREADERR\_MODEL}}=1$. We also identify several classes of objects that are extremely unusual and flag them for exclusion from most cosmological analyses (Table 4). In addition to objects flagged by SExtractor, we specifically identify (1) objects with extremely blue ($\{g-r,r-i,i-z\}<-1$) or extremely red ($\{g-r,r-i,i-z\}>4$) colors, (2) bright stars that saturate some of the single-epoch inputs to the coadd image, (3) objects that have a large ($>1\arcsec$) offset in the windowed centroid derived from the $g$ and $i$ bands. Finally, we require that objects reside within the Y1A1 GOLD footprint (Section VII.3) and flag any objects that reside in poor-quality or potentially problematic (“bad”) regions (Section VII.4).

VI.3 Multi-Epoch, Multi-Object Fitting

The Y1A1 coadded images provide deeper and more sensitive object detection than individual single-epoch images. However, the coaddition process averages across multiple images, resulting in a discontinuous PSF and correlated noise properties. Precision measurements that rely on an accurate PSF determination, such as galaxy shape measurements for cosmic shear, require a joint fit of pixel-level data from multiple single-epoch images.

We used the ngmix https://github.com/esheldon/ngmix code (Sheldon 2014; Sheldon & Huff 2017; Jarvis et al. 2016) to reanalyze pixel-level data from multi-epoch postage stamps of each object in the Y1A1 GOLD coadd catalog. We used PSFEx (Bertin 2011) to model and interpolate the PSF at the location of each object, and then we generated an image of the PSF using the python package, psfex https://github.com/esheldon/psfex. We then used the ngmix code to fit this reconstructed PSF image to a set of three free, independent Gaussians.

We used ngmix in “multi-epoch” mode to simultaneously fit a model to all available epochs and bands. In this mode, a model is convolved by the local PSF in each single-epoch image, and a $\chi^{2}$ sum is calculated over all pixels in a postage stamp. This is repeated for each epoch and band, and a total $\chi^{2}$ sum is calculated. We then find the parameters of the model that maximize the likelihood.

We took this procedure one step further, performing simultaneous multi-epoch, multi-band, and multi-object fit, which we call “MOF”. We first identified groups of objects using a friends-of-friends algorithm (Huchra & Geller 1982; Berlind et al. 2006, e.g.,). We then fit the members of the group using the following procedure:

Perform an initial model fit to each object, masking the light from neighbors using the überseg algorithm (Jarvis et al. 2016).

Fit the model to each object again, this time subtracting the light from neighbors using the models from the previous fit.

Repeat the previous step until all fits converge, or a maximum of 15 iterations was reached.

This fit was performed simultaneously in the $g,r,i,z$ bands using all available imaging epochs and assuming the same spatial model for all bands and epochs. An example of this procedure is shown in Figure 7.

We found that fitting a galaxy model with fully free bulge and disk components was highly unstable, so we adopted the following approach, inspired by the ‘‘composite’’ model used in the SDSS. http://www.sdss.org/dr12/algorithms/magnitudes/#cmodel We first fit the disk and bulge models separately, represented by an exponential and De Vaucouleurs’ profile (de Vaucouleurs 1948), respectively. We then determined the linear combination of these models that best fit the data,

where $M_{\rm dev}$ is the bulge model, $M_{\rm exp}$ is the disk model, and $f_{\rm dev}$ represents the fraction of light in the bulge component. This total model is unlikely to be a good fit of the data, and we only use it as a starting point for a more refined model. We formed a new model that has the best $f_{\rm dev}$ determined as above, as well as the same ratio of scale lengths for the bulge and disk components. This new model has free parameters for the center, ellipticity, overall scale, and fluxes. A common center, scale, and ellipticity were used for all bands, but the flux for each band was left free.

For computational efficiency, each component of this model was approximated by a sum of Gaussians (Hogg & Lang 2013). This choice made convolution with the triple-Gaussian PSF model very fast. A fast approximation for the exponential function was also used to speed up computations (Sheldon 2014).

We imposed uninformative priors on all parameters except for the ellipticity and the fraction of light present in the bulge, $f_{\rm dev}$. For both of these parameters, we applied priors based on fits to deep COSMOS imaging data, provided as postage stamps with the GalSim project https://github.com/GalSim-developers/GalSim. We defined convergence to be when the flux from subsequent fits to objects did not change more than one part in a thousand, and structural parameters such as scale and ellipticity did not change by more than a part in a million. For incorporation into the Y1A1 GOLD catalog, we converted MOF fluxes to magnitudes and applied the SLR adjustment discussed in Section IV.3.

VI.4 Catalog Completeness

VII Ancillary Maps

Several ancillary maps were produced to characterize the coverage, sensitivity, observing conditions, and potentially problematic regions of Y1A1 GOLD as a function of sky position. Generating ancillary maps for Y1A1 GOLD was a multi-step process: we created a vectorized representation of the survey coverage and limiting magnitude using mangle (Hamilton & Tegmark 2004; Swanson et al. 2008), we rasterized the mangle maps with HEALPix for ease of use, we estimated observing conditions over the survey footprint, and we subselected a nominal high-quality footprint. Finally, we flagged sky regions where the true survey performance deviates from that estimated by the ancillary data products (i.e., the regions around bright stars, astrometric failures, etc.). Each of these steps is described in more detail below.

Quantifying survey coverage and limiting magnitude as a function of sky position is essential for statistically rigorous cosmological analyses. To accurately track characteristics of the DES survey at the sub-CCD level, DESDM produces mangle masks (Hamilton & Tegmark 2004; Swanson et al. 2008) as part of the Y1A1 COADD pipeline. These masks are an accurate representation of the coverage, sensitivity, and overlap of DECam exposures including dead CCDs, gaps between CCDs, masked regions around bright stars, and bright streaks from Earth-orbiting satellites.

During coadd production, mangle masks were created at the level of coadd tiles (Figure 9). The steps are the following:

Polygons were created using the four corners of each input CCD image and assigned a weight equal to the median value of pixels in the CCD weight plane.

Satellite streaks were represented by polygons, and the area of these polygons was removed from the single-epoch CCD polygon.

Polygons were trimmed to fit the tile boundaries.

Polygons were subdivided into disjoint regions with the balkanize command. Following the weighted-average scheme chosen for image coaddition, the total weight of a balkanized polygon is the sum of the weights of the individual polygons.

Regions around bright stars and bleed trails are removed from the mangle mask. While the precise location of these artifacts is image dependent, it is computationally simpler to mask the stacked map with the largest shape covering a bright star or bleed trail rather than removing these regions from each single-epoch polygon.

The mangle coadd weight map was converted into a $10\sigma$ limiting magnitude map for a $2\arcsec$ diameter aperture:

where $m_{\rm ZP}=30$, is the tile zero-point, $D=2\arcsec$, $\omega_{\rm pix}=0\farcs 263$ is the pixel size, and $w_{\rm tot}$ is the total weight of the polygon. This definition of the magnitude limit corresponds to the MAG_APER_4 quantity measured by SExtractor.

We followed the prescription of Rykoff et al. 2015 to convert the mangle coverage and depth maps into $10\sigma$ limiting magnitude maps for galaxy photometry. We selected galaxies using the MODEST_CLASS star-galaxy classifier (Section VIII.1) and trained a random forest model to predict the $10\sigma$ limiting magnitude as a function of observing conditions. The input vector for the random forest included the PSF FWHM, sky brightness, airmass, and exposure time for each band being fit (Section VII.2). The training was performed on coarse HEALPix pixels (nside = 1024) that contained more than 100 galaxies. Once trained, the model was applied to the pixels at the full mask resolution of nside = 4096. We derived magnitude limits for both coadd AUTO magnitudes and the multi-epoch composite model magnitudes derived by the MOF (Section VI.3). We applied the SLR calibration adjustment (Section IV.3) to the resulting depth maps to correct for interstellar extinction and zeropoint non-uniformity. The median $10\sigma$ limiting magnitudes for MAG_AUTO are $g=23.4^{+0.14}_{-0.40}$, $r=23.2^{+0.13}_{-0.37}$, $i=22.5^{+0.14}_{-0.34}$, $z=21.8^{+0.12}_{-0.37}$, $Y=20.1^{+0.18}_{-0.33}$, where the uncertainties represent the 16th and 84th percentiles of the distribution. In comparison, the median $10\sigma$ limiting magnitudes for the MOF CM_MAG magnitudes are $g=23.7^{+0.07}_{-0.40}$, $r=23.5^{+0.16}_{-0.29}$, $i=22.9^{+0.14}_{-0.30}$, and $z=22.2^{+0.14}_{-0.32}$. We find that the depth estimates are accurate at the level of 6%-7%, but that 3%-4% of this measured uncertainty is due to “pixelization noise” resulting from averaging over a range of depths when fitting the model on coarse pixels. An example of the resulting depth maps for $r$ band can be found in Figure 10, and figures for the other bands can be found in Appendix C.

VII.2 Maps of Survey Characteristics

Variations in observing conditions can be a significant source of systematic uncertainty in cosmological analyses. In a wide-area optical survey such as DES, variable observing conditions can imprint spurious spatial correlations, noise, and depth fluctuations on the object catalogs that are used for galaxy clustering and cosmic shear analyses. By identifying and characterizing these systematic effects, it becomes possible to quantify and minimize their impact on scientific results. We followed the procedure developed by Leistedt et al. 2016 to construct survey characteristic and coverage fraction maps for the Y1A1 GOLD data set using QuickSip. https://github.com/ixkael/QuickSip Since the nonlinear transfer function between the stack of images at any position on the sky and the final galaxy catalog is largely unknown, we created maps of many different survey observables. For each band, we created maps of both weighted- and unweighted-average quantities of each image. The main quantities expected to be used for null tests in cosmological analyses with the Y1A1 GOLD catalog are the total exposure time, the mean PSF FWHM, the mean airmass, and the sky background. The inverse variance weighted averages of these quantities are shown in Figure 11. Further modeling of the survey transfer function is important for DES cosmology analyses, and several approaches have already been developed (Chang et al. 2015; Suchyta et al. 2016, e.g.).

VII.3 Footprint Map

The nominal footprint for the Y1A1 GOLD catalog is defined using an $\texttt{nside}=4096$ HEALPix map. For a pixel to be included in the Y1A1 GOLD footprint, it must meet the following criteria simultaneously in the $g,r,i,z$ bands:

A mangle coverage fraction $\geq 0.5$ implying that at least half of the pixel area has been observed or is unmasked according to mangle (Section VII.1).

A coverage fraction of $\geq 0.5$ from the survey characteristics maps (Section VII.2).

A valid solution from the SLR calibration adjustment (Section IV.3).

VII.4 Bad Region Mask

VII.4.2 Bright Stars

Regions around saturated stars were masked at the pixel level as part of the image processing pipeline described in Section III. However, catalog-level investigation revealed a residual increase in the number density of objects surrounding the brightest stars. To avoid contamination from spurious objects in the halos of bright stars, we designed radial masks based on the brightness of the contaminating stars and the number density of surrounding objects. These masks were developed for two bright star catalogs as described below.

Yale bright star regions (bit=32): Masked regions were determined from the positions and magnitudes of stars in the Yale Bright Star Catalog (Hoffleit & Jaschek 1991). The masking radius was determined from the $V$-band magnitude of each star, following the equation:

2MASS bright stars (bit=2,8): We mask regions around bright stars from the 2MASS catalog (Skrutskie et al. 2006) within a radius of

VII.4.3 Large Foreground Objects

Bright galaxies (bit=4): The Third Reference Catalog of Bright Galaxies (Corwin et al. 1994, RC3;) contains galaxies subtending $\gtrsim 1\arcmin$. Since galaxy size is highly correlated with magnitude, we continue to use a magnitude-dependent masking formulation similar to that applied to bright stars. We masked a circular region around RC3 galaxies with $10<B<16$ with a magnitude-dependent selection:

VIII Value-Added Quantities

The astrometric, photometric, and morphological parameters derived for each object are supplemented with additional information important for astrophysical and cosmological analyses. These “value-added quantities” are built from the calibrated coadd object catalog and provide additional information on an object-by-object basis. The two primary value-added quantities provided with Y1A1 GOLD are: (1) a simple star-galaxy classifier, and (2) a set of photo-$z$ estimates.

As part of the Y1A1 GOLD catalog, we produced a “MODEST_CLASS” object classification with the primary goal of selecting high-quality galaxy samples. MODEST_CLASS is based on the $i$-band coadd quantity SPREAD_MODEL_I and its associated error, SPREADERR_MODEL_I. SPREAD_MODEL is a morphological variable defined as a normalized linear discriminant between the best-fit local PSF model and a slightly more extended model composed of a circular exponential disk convolved with the PSF (Desai et al. 2012; Soumagnac et al. 2015). The $i$ band was chosen as the reference band for object classification owing to its depth and superior PSF. Image-level simulations of the DES data support the conclusion that $i$ band yields the best overall performance for object classification, and this result was verified using deep HST imaging on the COSMOS field.

We used space-based imaging of COSMOS (Leauthaud et al. 2007) and GOODS-S (Giavalisco et al. 2004) along with spectroscopic observations from VVDS (Le Fèvre et al. 2005) that overlapped the Y1A1 GOLD footprint as a truth sample for developing MODEST_CLASS. We defined star and galaxy samples optimized for “high completeness” and “high purity” by applying thresholds on the combination of SPREAD_MODEL_I and SPREADERR_MODEL_I. The high-completeness and high-purity samples differ in the classification assigned to ambiguous objects. The object classification scheme is defined in Table 6 and shown graphically in Figure 12.

Following Drlica-Wagner et al. 2015, we validated the performance of the MODEST_CLASS star-galaxy classifier on data from CFHTLenS (Erben et al. 2013; Hildebrandt et al. 2012). We matched CFHTLenS catalog objects to the Y1A1 GOLD data (Section VI) and selected high-quality samples of stars and galaxies using the CLASS_STAR and FITCLASS measurements by CFHTLenS (Heymans et al. 2012). Specifically, our CFHTLenS stellar selection was $(\texttt{{FITCLASS}}=1){\rm\,OR\,}(\texttt{{CLASS\_STAR}}>0.98)$ and our galaxy selection was $(\texttt{{FITCLASS}}=0){\rm\,OR\,}(\texttt{{CLASS\_STAR}}<0.2)$. Note that ${\sim}\,7\%$ of matched CFHTLenS objects are unclassified according to this prescription, and these objects are not used for assessing the performance of MODEST_CLASS.

We define the “efficiency” of a galaxy sample as the number of true galaxies that are also classified as galaxies divided by the total number of true galaxies in the sample (i.e., the true positive rate). Conversely, the “contamination” of a galaxy sample is defined as the number of galaxies that are misclassified divided by the total number of objects classified as galaxies (i.e., the false discovery rate). Similar definitions apply to the stellar selections, and the performance of the MODEST_CLASS galaxy and star selections are shown in Figure 13. We find that a high-purity galaxy selection has an efficiency $\gtrsim 98\%$ and a contamination rate $\lesssim 3\%$ for $i<22$. In contrast, the high-completeness stellar selection has an efficiency of $\gtrsim 86\%$ with a contamination of $\lesssim 6\%$ for $i<22$. We estimate similar performance for MODEST_CLASS through a comparison against the DEEP2-3 field in the first public data release of Hyper Suprime Camera (Aihara et al. 2018).

The MODEST_CLASS selection provides an initial baseline for object classification and is found to be sufficient for characterizing the distributions of stars and galaxies in Y1A1 GOLD (Figures 14 and 15). Multi-variate machine-learning techniques and template-fitting algorithms have the potential to provide much better object classification (e.g. Fadely et al. 2012; Soumagnac et al. 2015, etc.). Several advanced object classification techniques are currently being explored within DES and will be detailed in future publications (Sevilla-Noarbe et al. 2018). We emphasize that MODEST_CLASS has been optimized for galaxy selection. Several alternative selections have been suggested for more complete samples of stars (Bechtol et al. 2015; Drlica-Wagner et al. 2015, e.g.).

VIII.2 Photometric Redshift Estimation

In this section we briefly summarize the approach to photo-$z$ estimation and validation for DES Y1 science analyses. While photo-$z$ estimates were provided as part of the initial Y1A1 GOLD data set, it was realized that individual cosmology analyses benefit from photo-$z$ estimation and validation customized to their distinct science samples. Therefore, we present a general overview of the photo-$z$ estimation and validation procedures, and we refer the reader to upcoming publications dedicated to photo-$z$ estimation for distinct DES analyses (Hoyle et al. 2017; Gatti et al. 2018; Davis et al. 2017; Cawthon et al. 2017, e.g.,).

Photo-$z$ estimates were generated with two distinct algorithms: the machine-learning code DNF (De Vicente et al. 2016), and a modified version of the template code BPZ (Benítez 2000; Hoyle et al. 2017). These two codes are representative of common machine learning and template fitting photo-$z$ estimation techniques. Both algorithms utilized spectroscopic data for training, and a detailed discussion of the spectroscopic sample can be found in Gschwend et al. 2017.

For many cosmological analyses, we are interested in accurately characterizing the statistical distribution of galaxies in tomographic bins of redshift and less interested in predicting the redshift of any individual galaxy. Thus, we applied two independent techniques targeted at validating the statistical properties of our predicted photo-$z$ distributions (Hoyle et al. 2017; Davis et al. 2017).

A second, independent indirect validation technique relies on the clustering-redshift technique (Newman 2008; Ménard et al. 2013; Schmidt et al. 2013). We selected a luminous red galaxy sample (Rozo et al. 2016, redMaGiC;), which has well-determined photo-$z$ estimates, as a reference and divided this sample into redshift bins of width $\Delta z=0.02$. We then divided the full sample of DES objects into tomographic redshift bins based on predicted photo-$z$ and cross correlated the data in each tomographic bin with each of the more finely binned redMaGiC reference samples. We measured the excess angular cross-correlation signal, which is proportional to the redshift distribution. We calibrated a constant redshift offset in each tomographic bin between the photo-$z$ predictions and the clustering signal. We estimated the errors arising from the evolution of galaxy-dark matter halo bias and discrepancies in the shape of the clustering reshift distribution by repeating the same analysis using the Buzzard simulations (Gatti et al. 2018; Cawthon et al. 2017).

The most important photo-$z$ performance metric for cosmic shear analyses is the bias of the estimated mean of a redshift distribution in a tomographic bin with respect to the unknown true mean redshift in that bin (Bonnett et al. 2016). We characterized the photo-$z$ accuracy from the photo-$z$ bias distribution, defined as the difference between the average measured photometric redshift and the average true redshift distribution, $\Delta z=\langle z_{\rm true}\rangle-\langle z_{\rm phot}\rangle$. Since the true redshift distribution is unknown, we employed the direct and indirect validation techniques described above to estimate $\langle z_{\rm true}\rangle$ and $\Delta z$ in four tomographic bins with $0.2<z<1.3$. We find that both techniques yield $|\Delta z|\lesssim 0.02$ with an uncertainty of comparable magnitude when applied to the BPZ estimates for the primary subsample of the Y1A1 GOLD catalog used for cosmic shear analyses (Hoyle et al. 2017; Zuntz et al. 2017).

We present several other results from the validation of the BPZ template code optimized over the redshift range $0.2<z<1.3$ for the primary Y1 weak-lensing shear catalog (Zuntz et al. 2017). In Figure 16, we show the $n(z)$ distribution for the weak-lensing shear catalog derived from Y1A1 GOLD. The $n(z)$ distribution is found to be in good agreement with the $n(z)$ predicted from COSMOS when cosmic variance and other associated systematic uncertainties are accounted for (Hoyle et al. 2017). We also show a comparison between the redshift estimate from a random sampling of the 30-band COSMOS $P(z)$ (Laigle et al. 2016) and the median photo-$z$ derived from DES Y1 using BPZ. Structure along the line of sight is visible in the higher-resolution COSMOS redshifts but is not resolved by DES. For the full weak-lensing subsample, the normalized median absolute deviation (NMAD) of the quantity $(z_{\rm DES}-z_{\rm COSMOS})/(1+z_{\rm COSMOS})$ is $0.08-0.09$, depending on the point estimate used to determine the DES BPZ redshift. When restricted to $i\leq 22$, the photo-$z$ NMAD decreases to $0.06-0.07$. Due to the strict selection requirements of the weak-lensing subsample, the NMAD for the full Y1A1 GOLD galaxy sample is slightly larger (${\sim}\,0.12$). The photometric redshift accuracy for forthcoming DES Y1 cosmology analyses will be documented in more detail in Hoyle et al. 2017; Cawthon et al. 2017; Davis et al. 2017; Gatti et al. 2018.

IX Conclusion

Acknowledgments

Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey.

The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas A&M University, and the OzDES Membership Consortium.

Based in part on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

The DES data management system is supported by the National Science Foundation under Grant Numbers AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-88861, FPA2015-68048, SEV-2012-0234, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013) including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020.

This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

Support for DG was provided by NASA through Einstein Postdoctoral Fellowship grant number PF5-160138 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. ACR is supported by CNPq process 157684/2015-6.

This work is based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/IRFU, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency. CFHTLenS data processing was made possible thanks to significant computing support from the NSERC Research Tools and Instruments grant program.

This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.

This research was made possible through the use of the AAVSO Photometric All-Sky Survey (APASS), funded by the Robert Martin Ayers Sciences Fund.

The UKIDSS project is defined in Lawrence et al. 2007. UKIDSS uses the UKIRT Wide Field Camera (Casali et al. 2007, WFCAM;). The photometric system is described in Hewett et al. 2006, and the calibration is described in Hodgkin et al. 2009. The pipeline processing and science archive are described in Irwin et al (2009, in prep) and Hambly et al. 2008.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/.

SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

Appendix A Photometric Calibration

In this Appendix, we provide more details on the photometric calibration of Y1A1, including nightly calibration (Appendix A.1), global calibration (Appendix A.2), and a SLR adjustment (Appendix A.3). We note that the nightly and global calibration steps followed on the procedure of Tucker et al. 2007 and were performed on the single-epoch catalog data before coaddition. In contrast, the SLR adjustment was performed on the weighted-average magnitudes of multiple single-epoch catalogs and is applied directly to the coadded object catalogs. A collection of transformation equations between DES and several other surveys is provided in Appendix A.4.

The first step in DES Y1 photometric calibration used observations of standard-star fields to derive a set of calibration coefficients for each photometric night. A subset of the standard-star fields listed in Table A.1 were observed at different airmasses at the beginning and end of each DES night or half night (Section II). The DES nightly standard-star fields are predominantly located in the equatorial fields of SDSS Data Release 9 (Ahn et al. 2012, DR9;), with the addition of several fields from the Southern $u^{\prime}g^{\prime}r^{\prime}i^{\prime}z^{\prime}$ Standard Network (Smith et al. 2017). http://www-star.fnal.gov Devoted observations of these standard-star fields were supplemented by DES survey observations that overlapped the standard-star fields. For $Y$ band, we used stars from the equatorial fields of the UKIRT Infrared Deep Sky Survey Data Release 6 (Lawrence et al. 2007, UKIDSS DR6; ) matched against SDSS stars. All nightly standard stars were transformed to an initial DES AB photometric system via matching to objects in SDSS and UKIDSS (Appendix A.4). The spatial distribution of the DES standard-star fields is shown in Figure A.1.

Due to its provenance, primarily from SDSS DR9, we refer to the set of DES nightly standards as secondary standards. The fundamental standard for SDSS was the F subdwarf star BD$+$17∘ 4708, which was used for calibrating the set of SDSS primary standards (Smith et al. 2002). These primary standards were in turn used (indirectly) in the ubercalibration of SDSS (Padmanabhan et al. 2008). Thus, the DES secondary standards tie the absolute flux calibration of DES to the SDSS primary standards, to BD$+$17∘ 4708, and ultimately to the AB magnitude system.

Nightly observations of the secondary standards were used to fit a set of photometric equations. These photometric equations, which are based on those used by SDSS (Tucker et al. 2006), have the form

where $\lambda_{0}$ ($\lambda={g,r,i,z,Y})$ is the calibrated standard-star magnitude in the DES system, $F_{\lambda}$ is the observed PSF flux (counts/sec), $a$ is the photometric zeropoint for the night, $b$ is the instrumental color term coefficient, $(g-r)_{0}$, $(i-z)_{0}$, $(z-Y)_{0}$ are the calibrated standard-star colors, $(g-r)_{\rm fid}$, $(i-z)_{\rm fid}$, and $(z-Y)_{\rm fid}$ are fiducial reference colors (chosen so that the effects of $b$ are relatively small for a star of typical color within the DES footprint), $k$ is the first-order extinction coefficient, and $X$ is the airmass of the observation. The values for the fiducial colors are $(g-r)_{\rm fid}=0.53$, $(i-z)_{\rm fid}=0.09$, and $(z-Y)_{\rm fid}=0.05$.

Separate $a$ and $b$ coefficients were determined for each functioning science CCD, while a single value of $k$ was assumed for the full focal plane. The nightly values of $a$ track the overall throughput of the DECam instrument at the location of each CCD, and variations in $a$ mostly track the gradual accumulation of dust on the Blanco primary mirror. The nightly values of $b$ track variations in the shape of the total filter response curve at the location of each CCD (including atmospheric transmission). Under photometric conditions, the value of $k$ should not vary across the focal plane, and a single value of $k$ was fit for the full focal plane. Variations in the nightly values of $k$ track the relative throughput of the atmosphere at CTIO. The median values of $a$ and $b$ are shown for each science CCD in Figure A.2, and the nightly variations of $a$, $b$, and $k$ are shown in Figure A.3. The site-average values for the $a$, $b$, and $k$ coefficients are tabulated in Table A.2.

We note that, despite the use of star flats and pupil corrections, there are still minor variations in the zeropoints across the focal plane in Figure A.2. These variations can be attributed to two main sources: (1) the DES starflat procedure is subject to small flat/planar gradients across the focal plane, with the understanding that the photometric calibration procedure will remove such gradients; and (2) CCD-to-CCD variations in quantum efficiency have not been fully accounted for in the Y1A1 image processing, and this is also reflected in the smaller scale between-CCD variations in the zeropoints. The DES Y3 processing has largely corrected for variations in quantum efficiency while Burke et al. 2018 show that gradients in the star flats can be successfully removed by the photometric calibration.

A.2 Global Calibration

The global calibration was implemented as a Global Calibrations Module (GCM). https://github.com/DarkEnergySurvey/GCM The GCM generalizes the procedure of Glazebrook et al. 1994 by replacing overlapping image “frames” with arbitrarily shaped overlapping catalog data sets (these are still conventionally referred to as “images”). The procedure is summarized briefly as follows.

For each filter, consider $n$ data sets for which $(1,\ldots,m)$ are uncalibrated and $(m+1,\ldots,n)$ are calibrated. In most cases these data sets represent object catalogs from individual exposures or CCD images. However, the calibrated data set consists of standard stars spanning the entire Y1A1 footprint (Figure A.1).

Compile a list of all unique pairs of observations of a common star on two data sets.

where $m_{i}$ is the magnitude of a star in image $i$, $m_{j}$ is the magnitude of the same star in image $j$, and the median is calculated over matched pairs of stars. Note that $\Delta_{ij}=-\Delta_{ji}$.

Let $ZP_{i}$ be a floating zero-point that can be applied to the data set from image $i$ to produce calibrated magnitudes. For images that are already calibrated ($i>m$), we fix $ZP_{i}=0$.

Let $\theta_{ij}$ define a function that selects overlapping image pairs. We define $\theta_{ij}=1$ if $i=j$ or if $i$ and $j$ overlap; otherwise $\theta_{ij}=0$.

To find calibrated zeropoints for each image, we minimize the sum of squares,

We derive a calibrated magnitude for each object detected on image $i$ (where $i<m$) by adding $ZP_{i}$ to the raw instrumental magnitudes.

In Figure A.4, we show a simple example of the GCM algorithm on two disconnected groups of three overlapping data sets (i.e., images). In each group, one of the overlapping images has been previously calibrated and serves as the reference against which the other images in its grouping are calibrated. To be calibrated, an uncalibrated image needs either to overlap a calibrated image (e.g., the left group in Figure A.4) or to have an unbroken path of overlapping images to a calibrated image (e.g., image 3 in the right group of Figure A.4). In the right panel of Figure A.4 we show the matrix equation that minimizes Equation (A7) for this particular set of images (Glazebrook et al. 1994). Note that, via this matrix equation, the zeropoints for the two calibrated images (images 5 and 6) have been fixed to a value of zero ($1\times ZP_{5}=0$ and $1\times ZP_{6}=0$), since no offset is applied to these previously calibrated images.

Following the prescription of Glazebrook et al. 1994, we estimate the rms magnitude residual for each CCD image, $i$, from overlap with other CCD images, $j$, as

The rms distribution over all CCD images is a measure of the internal (reproducibility) errors on small scales (the scales of overlapping CCD images) and is a measure of the precision of the overall GCM solution.

The GCM algorithm relies on having at least one calibrated image or data set to anchor each isolated image group. To identify isolated groups of exposures, we employed a group-finding algorithm developed for studies of galaxy clusters and large-scale structure (Huchra & Geller 1982). For Y1A1 FINALCUT, there were several disconnected image groups – in particular, the SPT region, the S82 region, the four SN fields (SN-E was treated as an isolated group even though it overlaps the SPT area), the COSMOS field, and the VVDS-14h field (see Figure 2). We therefore ran GCM separately on each of these eight regions. The S82, COSMOS, and VVDS-14h fields overlap with the equatorial region of SDSS and were anchored by the secondary standards (mostly derived from SDSS). SPT was anchored by the aforementioned gridwork of tertiaries, supplemented with individual fields from DES SV. The SN fields also used individual standard-star fields from SV for their calibrators. As with the gridwork of tertiary standards, the individual SV fields had been previously calibrated using nightly results from the PSM code (Wyatt et al. 2014).

The S82 region and the smaller individual fields (COSMOS, VVDS-14h, and the SN fields) were each calibrated with a single pass of the GCM. This run treated the catalog from each individual CCD image as the unit to be calibrated and yielded zeropoint offsets for each CCD directly. Due to its large area, the SPT region was calibrated from multiple iterations of the GCM. The first pass treated the full catalog from each exposure (59 or 60 functioning science CCDs) as the unit to be calibrated. This could be done because, due to the star flat procedure, all the CCDs on a given exposure have very nearly the same zeropoint (at least for exposures taken under photometric conditions). In this pass, small (2–3%) variations in the relative zeropoint across the focal plane were temporarily removed using the median $a$ coefficients for each CCD (Figure A.2). In this manner, each exposure was temporarily flat-fielded across the focal plane to reduce exposure-scale photometric gradients. For the first pass, only exposures that were classified as having been observed under photometric conditions – as determined by RASICAM – were allowed in the GCM fit. The first pass yielded a set of zeropoint offsets – one per exposure – for all the (apparently) photometric exposures in the SPT region. The second run of GCM was essentially identical to the first, but it removed outlier exposures – ones with particularly “noisy” or discrepant zeropoints. For both the first and second runs, the sparse gridwork of tertiaries and the handful of individual calibrated SV fields (Figure A.1) were used as the calibrated data set for the Glazebrook et al. 1994 algorithm. Again, this yielded a set of zeropoint offsets – one per exposure – for all the photometric exposures in the SPT region. These individual CCD zeropoint offsets were applied to all the CCD images in the set of photometric exposures included in the second-pass run of GCM, creating a set of “quaternary” standard stars covering nearly all of the SPT region. In the third and final run of the GCM for the SPT region, the catalog from each individual CCD image was treated – as in the case of GCM runs for S82, COSMOS, VVDS-14h, and the SN fields – as the unit to be calibrated. Furthermore, all CCD images from the SPT region – those from photometric exposures and those from non-photometric exposures – were included in the GCM fit. For this third pass of the GCM, the newly created quaternary standard stars were used as the calibrated data set. This third pass of the GCM for the SPT region yielded a set of zeropoint offsets for each CCD image, which was used to calibrate the Y1A1 GOLD single-epoch CCD images in advance of the image coaddition process.

A.3 Photometric Calibration Adjustment

Variations in the average metallicity of the stellar populations used for the SLR will introduce systematic shifts that are not due to photometric variation or Galactic reddening (High et al. 2009, e.g.,). For DES Y1A1, these shifts are largest for the $g$ band, where they can have a 1-2% effect on the calibration. A larger effect can be found in the vicinity of the LMC, which we avoid for extragalactic science. The effect of metallicity variations can be much worse at lower Galactic latitudes and in bluer filters (i.e., $u$ band).

The final product was an SLR correction map at a resolution of $\texttt{nside}=512$ that we implemented with a bi-linear interpolation to obtain magnitude and flux corrections for the full Y1A1 GOLD catalog. The resulting SLR-adjusted magnitudes used in the Y1A1 GOLD catalog are thus already corrected for Galactic reddening.

A.4 Photometric Transformation Equations

We have derived transformation equations between various surveys and the DES system. We document these transformation equations here for reference.

We define a transformation from SDSS/UKIDSS to the DES system to place the nightly standard star exposures on an initial DES AB photometric system (Section IV.1):

To validate the completeness and contamination of the Y1A1 GOLD catalog, we perform a comparison with the CFHTLenS data in the W4 field. In this case, we are interested in the transformed magnitude of all objects, so we perform no stellar selection. We use matched objects to derive a set of transformation equations from the CFHTLenS $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ filters to the DES $g,r,i,z$ system:

We find that these equations should be valid for objects with $g-r<1.2$ and $i-z<1.0$.

A.5 Calibration Validation

In this section we show ancillary plots of the performance and validation of the Y1A1 photometric calibration (Figures A.6 – A.9).

Appendix B Co-add Source Detection

The Y1A1 COADD source detection was performed on a normalized “detection image” formed from a nonlinear combination of the $r$, $i$, and $z$ coadded images. The original SWarp combination formula for computing the value of a pixel of the detection image is (Bertin 2010):

where $f_{c}$ is the background-subtracted pixel value, $w_{c}$ is the weight of the pixel in channel $c$, and $n$ is the number of valid inputs. Compared to the standard $\chi^{2}$ combination proposed by Szalay et al. 1999, $\chi$ leads to a less skewed noise distribution (if one assumes that input noise follows a Gaussian distribution), while maintaining identical detection capabilities. However, both estimators have a bias that depends on $n$, which leads to visible seams between regions with a different number of input images. This motivated the implementation of two new normalized image combination schemes in SWarp, with a variable offset applied to the original (still assuming that the inputs are normally and independently distributed). CHI-MEAN is recentered on the mean (Evans et al. 2000, e.g.,):

while CHI-MODE is recentered on the mode of the distribution:

The left panel of Figure B.1 shows a comparison of the distributions obtained from the original $\chi$, CHI-MODE and CHI-MEAN estimators for Gaussian input noise. The right panel of Figure B.1 shows that the CHI-MEAN estimator generates the most seamless stacking results, and it was used to produce the Y1A1 COADD detection images.

Appendix C Catalog Depth Maps

In this appendix we collect a set of figures documenting the $10\sigma$ limiting magnitude of the Y1A1 GOLD catalog as described in Section VII.1. We include depth maps both for the MAG_AUTO values derived from the coadded images (Figure C.1) and for the CM_MAG values derived from multi-epoch, multi-object fitting (Figure C.2).

References