# Data Release Description

## Contents of DR3

The 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 Legacy Survey is providing these data in the equatorial region at δ < +30° using the Dark Energy Camera on the Blanco Telescope.

Data Release 3 (DR3) is the third public data release of images and catalogs for the DECam Legacy Survey (DECaLS). Images from DECaLS g,r,z-band observations (NOAO survey program 0404; https://www.noao.edu/perl/abstract?2014B-0404) are included from August 2014 through March 2016. DR3 also includes DECam data from a range of non-DECaLS surveys, including observations that were conducted from September 2012 to March 2016.

In total, the optical data covers a disjoint footprint with 4300 deg² in g-band, 4600 deg² in r-band and 8100 deg² in z-band, of which 4200 deg² has been observed in all three optical filters.

There are approximately 478 million unique sources in DR3 spread over 149,464 bricks.

DR3 includes the stacked images and the Tractor-based catalogs. The size of the DR3 data distribution is:

Size* Directory Description
112 GB calib/ Calibration files.
57 TB coadd/ Co-added images, including χ², depth, image, model, nexp, and Quality Assurance PNG plots
6.7 GB external/ Matches to other catalogs (SDSS, etc.).
437 MB gallery/ Images of notable galaxies (NGC, etc.).
26 GB logs/ Log files generated by Tractor processing.
447 GB metrics/ Metrics.
215 GB sweep/ Repackaged versions of the Tractor catalogs.
663 GB tractor/ 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°. Each brick is defined in terms of a box in RA,Dec coordinates. For the image stacks, we use a simple tangent-plane (WCS TAN) projection around the brick center, with size 3600 × 3600 pixels at a scale of 0.262 arcseconds per pixel. The projections for the g,r,z filters are identical. There are 662174 bricks spread over the sky, meaning that each brick has an average area of 0.0623 deg2. As 36002 × 0.2622 arcsec2 is ~0.0686 deg2, the brick images have some overlap. The co-added images should be used with caution, as noted below in the Image Stacks section.

## Obtaining Images and Raw Data

Images can be viewed directly using the Sky viewer and raw data can be obtained through the NOAO portal (or via ftp; see also the information near the bottom of the files page).

Sections of the Legacy Survey can be obtained as JPEGs or FITS files using the cutout service, as follows:

where "bands" is a string like "grz","gz","g", etc. As of the writing of this documentation the maximum size for cutouts (in number of pixels) is 512. Pixscale=0.262 will return (approximately) the native DECam pixels.

## Source Detection

The source detection uses a PSF- and SED-matched-filter detection on the DECam stacked images, with a 6σ detection limit. The Tractor fitting step is initialized with these positions, although those positions can be changed during the fits and low-S/N sources can be removed.

For source detection, 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 6σ are detected in each of these two SED-matched filters, as well as in each band independently.

## PSF

The Tractor makes use of the PSF on each individual exposure. The PSF for the individual exposures are first computed independently for each CCD using PSFEx, generating spatially-varying pixelized models.

## 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 the mean of what was removed.

Additionally, we compute and remove a spatially varying (spline) sky model, by detecting and masking sources, then computing medians in sliding 512-pixel boxes. 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 without the complication of pixel covariances.

## 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 DR3. These are continuous properties for the object centers, fluxes, and the shape parameters. There is also the discrete choice of which model type to use. In DR3, five morphological types are used: point sources, "simple" galaxies (an exponential profile with a fixed 0.45″ effective radius and round profile), deVaucouleurs profiles (elliptical galaxies), exponential profiles (spiral galaxies), and composite profiles that are deVaucouleurs + exponential (with the same source center). The total numbers of the different morphological types in DR3 are:

Number of Sources Type
478,918,959 Objects in a Primary brick
271,437,526 PSF
121,505,252 SIMP
63,568,420 EXP
20,141,591 DEV
2,266,170 COMP

The decision to retain an object in the catalog and to re-classify it using models more complicated than a point source is made using the penalized changes to χ² in the image after subtracting the models for other sources. The "PSF" and "SIMP" models are computed for every source and the better of these two is used when deciding whether to keep the source. A source is retained if its 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 source is classified as the better of point source or simple galaxy unless the penalized χ² is improved by 9 (i.e., approximately a 3σ improvement) by treating it as a deVaucouleurs or exponential profile. The classification is a composite of deVaucouleurs + exponential if it is 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 galaxy profiles (the exponential and deVaucouleurs profiles mentioned above under Morphological Classification) are approximated with mixture-of-gaussian (MoG) models (http://arxiv.org/abs/1210.6563) and are convolved by the pixelized PSF models using a new Fourier-space method (Lang, in prep). The galaxy profile approximation introduces errors in these models typically at the level of $10^{-4}$ or smaller. The PSF models are treated as pixel-convolved quantities, 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 DR3 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 brightnesses of objects are all stored as linear fluxes in units of nanomaggies. The conversion from linear fluxes to magnitudes is $m = 22.5 - 2.5 \log_{10}(\mathrm{flux})$. 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 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. Namely, $\mathrm{Flux}_{\mathrm{AB}} = \mathrm{Flux}_{\mathrm{Vega}} * 10^{-(\Delta m/2.5)}$ 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. These conversion factors are recorded in the Tractor catalog headers ("WISEAB1", etc).

## 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, so the epoch is implicitly at the time of observation for Pan-STARRS-1. We keep the polynomial distortion model provided by the Community Pipeline, computing a simple RA,Dec offset for each CCD to align it with Pan-STARRS-1. The residuals are typically smaller than ±0.03″.

In the future, the plan is to tie 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. The image stacks are computed using Lanczos-3 interpolation. Stacks should not be used for precision work.

## Depths

As of DR2, the median 5σ point source depths for areas with 3 observations was g=24.65, r=23.61, z=22.84. DR3 should reach similar depths. This is based upon the formal errors in the Tractor catalogs for point sources; those errors need further confirmation. This can be compared to the predicted proposed depths for 2 observations at 1.5″ seeing of g=24.7, r=23.9, z=23.0.

## Code Versions

• LegacyPipe: mixture of versions, ranging from dr3c-21-g3c8a239 to dr3e-255-g1d799e6 (these are git version stings). The version used is documented in the Tractor header card LEGPIPEV.
• NOAO Community Pipeline: mixture of versions; recorded as PLVER.
• SourceExtractor 2.19.5, PSFEx 3.17.1
• Astrometry.net: 0.67
• Tractor: a mixture of versions, all dr3

## Glossary

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; 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.
DR2
DECam Legacy Survey Data Release 2.
DR3
DECam Legacy Survey Data Release 3.
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. A convenient unit is the nanomaggie: a flux of 1 nanomaggie corresponds to an AB magnitude of 22.5.
MoG
Mixture-of-gaussian model to approximate the 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
Point spread function.
PSFEx
Emmanuel Bertin's PSF fitting code.
SDSS
Sloan Digital Sky Survey.
SDSS DR12
Sloan Digital Sky Survey Data Release 12.
SDSS DR13
Sloan Digital Sky Survey Data Release 13.
SED
Spectral energy distribution.
SourceExtractor
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.