# Data Release Description

## Contents of DR1

The DECam Legacy Survey will produce an inference model of the 14,000 square degrees of extragalactic sky visible from the northern hemisphere in three optical bands (g,r,z) and four infrared bands. The sky coverage is approximately bounded by -18° < δ < +84° in celestial coordinates and $|b|$ > 18° in Galactic coordinates. The DECam Legacy Survey is providing these data in the equatorial region at δ < +30° using the Dark Energy Camera on the Blanco Telescope.

Data Release 1 (DR1) is the first public data release of images and catalogs for the DECam Legacy Survey. It includes DECam data primarily from z-band observations in August 2013 (http://www.noao.edu/perl/abstract?2013A-0741) and g,r,z-band observations from August 2014 through January 2015 for an NOAO survey program (https://www.noao.edu/perl/abstract?2014B-0404). It also includes public data from other programs near the Fall celestial equator bounded by 315 < α < 360 ° or 0 < α < 5 °, and by -3° < δ < +3°. In total, the optical data covers a disjoint 3100 deg² footprint, with 1200 deg² in g-band, 1300 deg² in r-band and 2700 deg² in z-band, of which 750 deg² of this footprint has been observed in all three optical filters. Only 110 deg² of this footprint is covered to the expected final depth of g=24.0, r=23.6, z=23.0. Non-photometric data have been excluded from this first data release.

There are approximately 140 million unique sources, of which approximately 750,000 have SDSS spectroscopy.

DR1 includes the stacked images and the Tractor-based catalogs. The size of this data distribution is:

Size* Directory Description
238GB tractor Tractor catalogs
15TB coadd Co-added images, including χ², depth, image, model, nexp, and PNG quality-assurance plots
41GB sweep Light-weight versions of the Tractor catalogs.

*Note that although the contents of a directory should be fixed for each Data Release, the size of a directory can change. This is typically due to updated file compression. So, the listed directory sizes should be viewed as (very reasonable) estimates.

The co-added images and Tractor catalogs are presented in bricks of approximate size 0.25° × 0.25°. These images are identical projections for each of the g,r,z filters.

## Source Detection

The source detection relies upon a combination of known SDSS sources and a PSF-matched-filter detection of the DECam stacked images. This should include all detections of sources to near the 5σ detection limit. The Tractor fitting step is initialized with these positions and classifications, although those positions and classifications can be changed during the fits and low-S/N sources are removed.

The existing SDSS DR12 sources are included with the RA,DEC coordinates, classifications, and shape parameters from that catalog.

Each DECam image is convolved by its PSF model, then a weighted stack of these is created in order to optimize the point-source detection efficiency. Next, SED-matched combinations of the three bands are created, for two SEDs: "flat" (a source with AB color zero), and "red", a source with AB color $g-r = 1$, $r-z = 1$. Sources above 5σ are detected in each of these two SED-matched filters. Sources (blobs of significant pixels) containing an SDSS catalog object are removed. Remaining sources are added as point sources in the Tractor fitting.

## PSF

The Tractor makes use of the PSF on each individual exposure. There is no PSF computed for the image stacks, as that would not be used.

The PSF for the individual exposures are first computed independently for each CCD using PSFEx, generating pixelized models. Those PSFs are then re-fit by a spatially-varying mixture of gaussians (MoGs).

## Sky Level

The Community Pipeline removes a sky level that includes a sky pattern, an illumination correction, and a single scaled fringe pattern. These steps are described here: http://www.noao.edu/noao/staff/fvaldes/CPDocPrelim/PL201_3.html . This makes the sky level in the processed images near zero, and removes most pattern artifacts. A constant sky level is then added back to the image that is mean of what was removed.

The Tractor removes a constant sky computed from the median on the object residual image. This value can be found as the SKY_P0 keyword in the calibration files cosmo/work/decam/calib/sky. The stacked images have this sky level removed.

## Tractor Catalogs

The Tractor code runs within the geometrical region of a brick. This fitting is performed on the individual exposures that overlap the brick, without making use of the image stacks. This preserves the full information content of the data set in the fits, handles masked pixels without the need for uncertain interpolation techniques, and fits to data points within the complication of pixel covariances.

To improve the run time for Tractor, each brick is divided into blobs that are collections of contiguous pixels above a detection level and the neighboring pixels. The boundaries of the blobs are made from the stacked detection image. For the high-Galactic latitudes of the DR1, all bricks can be successfully divided into blobs that contain few enough sources to run in a reasonable amount of time. This approach is likely to fail near the Galactic plane, where the high density of stars would be expected to result in a brick appearing as a single blob.

## Morphological classification

The Tractor fitting can allow any of the source properties or image calibration parameters (such as the PSF) to float. Only the source properties were allowed to float in this run. These are continuous properties for the object centers, fluxes, and the shape parameters. The discontinous properties are the choice for each source model: point source, exponential, deVaucouleurs, or a composite exponential+deVauc. In this run, the initialization of sources uses SDSS models where available or otherwise a point source.

Four morphological types are used: point sources, deVauc profiles (elliptical galaxies), exponential profiles (spiral galaxies), and composite profiles that are deVauc + exponential (with the same source center). The decision to retain an object in the catalog and to re-classify as models more complicated than a point source are made using the penalized changes to χ² in the image after subtracting the models for other sources. A source is retained if this penalized χ² is improved by 25; this corresponds to a χ² difference of 27 (because of the penalty of 2 for the source centroid). Sources below this threshold are removed. The classification is as a point source unless the penalized χ² is improved by 9 (i.e., approximately a 3σ improvement) by treating it as a deVauc or exponential profile. The classification is a composite of deVauc + exponential if it both a better fit to a single profile over the point source, and the composite improves the penalized χ² by another 9. These choices implicitly mean that any extended source classifications have to be at least 5.8σ detections and that composite profiles must be at least 6.5σ detections.

The fluxes are not constrained to be positive-valued. This allows the fitting of very low signal-to-noise sources without introducing biases at the faint end. It also allows the stacking of fluxes at the catalog level.

## Tractor Implementation Details

Tractor fundamentally treats the fitting as a χ² minimization problem. The current core routine uses the sparse least squares solver from the scipy (scientific python) package, or the open source Ceres solver (http://ceres-solver.org), originally developed by Google.

The PSF models and the PSF-convolved galaxy profiles are approximated with mixture-of-gaussian (MoG) models (http://arxiv.org/abs/1210.6563). This is not an exact representation, but introduces errors in these models typically at the level of $10^{-4}$ or smaller. The MoGs are treated as the pixel-convolved quantities for the PSF, etc, and are evaluated at the integral pixel coordinates without integrating any functions over the pixels.

The Tractor algorithm could be run with both the source parameters and the calibration parameters allowed to float, at the cost of more compute time and the necessity to use much larger blobs because of the non-locality of the calibrations. A more practical approach would be to iterate between fitting source parameters in brick space, and fitting calibration parameters in exposure space. Such iterations will be considered and tested for future data releases. Another practical issue is that the current PSF models may allow too much freedom.

## Photometry

The flux calibration for the DR1 is on the AB natural system of the DECam instrument. An AB system reports the same flux in any band for a source whose spectrum is constant in units of erg/cm²/Hz. A source with a spectrum of $f = 10^{-(48.6+22.5)/2.5}$ erg/cm²/Hz would be reported to have an integrated flux of 1 nanomaggie in any filter. The natural system means that we have not applied color terms to any of the photometry, but report fluxes as observed in the DECam filters.

Zero point magnitudes for the CP version 2 reductions of the DECam images were computed by comparing 7″ diameter aperture photometry to PS1 photometry, where the latter was modified with color terms to place the PS1 photometry on the DECam system. The same color terms are applied to all CCDs. Zero points are computed separately for each CCD, but not for each amplifier. The color terms to convert from PS1 to DECam were computed for stars in the color range $0.4 < (g-i) < 2.7$ as follows:

\begin{align*} (g-i) & = & g_{\mathrm{PS}} - i_{\mathrm{PS}} \\ g_{\mathrm{DECam}} & = & g_{\mathrm{PS}} + 0.04709 (g-i) + 0.00084 (g-i)^2 - 0.00340 (g-i)^3 \\ r_{\mathrm{DECam}} & = & r_{\mathrm{PS}} - 0.09939 (g-i) + 0.04509 (g-i)^2 - 0.01488 (g-i)^3 \\ z_{\mathrm{DECam}} & = & z_{\mathrm{PS}} - 0.13404 (g-i) + 0.06591 (g-i)^2 - 0.01695 (g-i)^3 \\ \end{align*}

The brightness of objects are all stored as linear fluxes in units of nanomaggies. The conversion from linear fluxes to magnitudes is as follows: $m = 22.5 - 2.5 \log_{10}(\mathrm{flux})$ These linear fluxes are well-defined even at the faint end, and the errors on the linear fluxes should be very close to a normal distribution. The fluxes can be negative for faint objects, and indeed we expect many such cases for the faintest objects.

The SDSS, DECam and WISE fluxes are all within a few percent of being on an AB system. The WISE Level 1 images and the unWISE image stacks are on a Vega system. We have converted these to an AB system using the recommended conversions by the WISE team documented here http://wise2.ipac.caltech.edu/docs/release/allsky/expsup/sec4_4h.html#conv2ab $\mathrm{Flux}_{\mathrm{AB}} = \mathrm{Flux}_{\mathrm{Vega}} * 10^{-(\Delta m/2.5)}$ where $\Delta m$ = 2.699, 3.339, 5.174, and 6.620 mag in the W1, W2, W3 and W4 bands. For example, a WISE W1 image should be multiplied by $10^{-2.699/2.5} = 0.083253$ to give units consistent with the Tractor catalogs.

## Galactic Extinction

Eddie Schlafly has computed the extinction coefficients for the DECam filters through airmass=1.3 Those coefficients are 3.995, 3.214, 2.165, 1.592, 1.211, 1.064 for ugrizY, and are applied to the SFD98 E(B-V) values at the coordinate of each object. The coefficients at different airmasses only have small changes, with the largest effect in g-band where the coefficient would be 3.219 at airmass=1 and 3.202 at airmass=2.

## Astrometry

The astrometry is currently tied to star positions in Pan-STARRS-1, which is implicitly at the time of observation for Pan-STARRS-1.

The Astrometry.net code has been run on SourceExtractor-generated source lists (the same sources used for PSF determination). This yields WCS headers with 2nd-order SIP polynomial distortions. The astrometric reference catalog is from Pan-STARRS-1. This is solved independently on each CCD.

In the DR1 footprint, the SDSS imaging data spans 1998 through 2005, and the SDSS spectroscopic data spans Feb 2000 through April 2014.

Comparison of the astrometric zero point for each image to the PS1 star positions shows systematic differences for individual CCDs in the image. The residuals are shown by the arrows in the attachments below (Offsets*ps*gz). The systematic residuals are typically smaller than ±0.03″.

In the future, the plan is to tied the astrometry to the GAIA astrometry, at which point we will use the predicted stellar positions at the DECam epoch of observation.

## Image Stacks

The image stacks are provided for convenience, but were not used in the Tractor fits. These images are oversized by approximately 260 pixels in each dimension. These are tangent projections centered at each brick center, North up, with dimensions of 3600 × 3600 and a scale of 0.262″/pix.

## Depths

The median 5σ point source depths for areas in the DR1 with 3 observations is g=24.65, r=23.61, z=22.84. This is based upon the formal errors in the Tractor catalogs for point sources; those errors need more confirmation. This can be compared to the depths in the proposal for 2 observations at 1.5″ seeing predicting g=24.7, r=23.9, z=23.0.

## Code Versions

• NOAO Community Pipeline
• Sextractor, PSFEx
• Astrometry.net
• Tractor

## Glossary

Astrometry.net
Dustin Lang's astrometry code.
Blob
Continguous region of pixels above a detection threshold and neighboring pixels; Tractor is optimized within blobs.
Brick
A region bounded by lines of constant RA and DEC; the DR1 reductions are performed within bricks of size approximately 0.25° × 0.25°.
CP
Community Pipeline (DECam reduction pipeline operated by NOAO; http://www.noao.edu/noao/staff/fvaldes/CPDocPrelim/PL201_3.html).
DECaLS
Dark Energy Camera Legacy Survey.
DR1
DECam Legacy Survey Data Release 1, May 2015.
DECam
Dark Energy Camera on the NOAO Blanco 4-meter telescope.
maggie
Linear flux units, where an object with an AB magnitude of 0 has a flux of 1.0 maggie.
MoG
Mixture-of-gaussian model to approximate the PSF and galaxy models (http://arxiv.org/abs/1210.6563).
NOAO
National Optical Astronomy Observatory.
nanomaggie
Linear flux units, where an object with an AB magnitude of 22.5 has a flux of $1 \times 10^{-9}$ maggie or 1.0 nanomaggie.
PSF
PSFEx
Emmanuel Bertin's PSF fitting code.
SDSS
Sloan Digital Sky Survey.
SDSS DR12
Sloan Digital Sky Survey Data Release 12.
SED
Spectral energy distribution.
SExtractor
Source Extractor reduction code.
SFD98
Schlegel, Finkbeiner & Davis 1998 extinction maps (http://adsabs.harvard.edu/abs/1998ApJ...500..525S).
Tractor
Dustin Lang's inference code.
unWISE
New coadds of the WISE imaging, at original full resolution (http://unwise.me, http://arxiv.org/abs/1405.0308).
WISE
Wide Infrared Survey Explorer.