# Data Release Description

## Contents of DR2

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 2 (DR2) is the second public data release of images and catalogs for the DECam Legacy Survey. DR2 includes DECam data primarily from z-band observations in August 2013 (https://legacy.noirlab.edu/perl/abstract?2013A-0741) and g,r,z-band observations from August 2014 through June 2015 for an NOAO survey program (https://legacy.noirlab.edu/perl/abstract?2014B-0404). It also includes public data from other programs with the footprint, including data taken by the Dark Energy Survey that are now public, in the "stripe 82" region bounded by 315 < α < 360 ° or 0 < α < 5 °, and by -3° < δ < +3°.

In total, the optical data covers a disjoint footprint with 2078 deg² in g-band, 2141 deg² in r-band and 5322 deg² in z-band, of which 1807 deg² has been observed in all three optical filters.

There are approximately 260 million unique sources in DR2 spread over 97,554 bricks.

DR2 includes the stacked images and the Tractor-based catalogs. The size of the DR2 data distribution is:

Size*

Directory

Description

36 GB

calib/

Calibration files

33 TB

Co-added images, including χ², depth, image, model, nexp, and PNG quality-assurance plots

5.1 GB

external/

Matches to other catalogs (SDSS, etc.)

437 MB

gallery/

Images of notable galaxies (NGC, etc.)

16 GB

logs/

Log files generated by Tractor processing

211 GB

metrics/

Metrics

108 GB

sweep/

Repackaged versions of the Tractor catalogs

301 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. The brick images have some overlap.

## Obtaining Images and Raw Data

Images can be viewed directly using the Sky viewer and raw data can be obtained through the NOIRLab portal (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. 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 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: https://legacy.noirlab.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 DR2. 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 DR2, 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 DR2 are:

Number of Sources

Type

288,347,865

All objects

262,426,862

Objects in a Primary brick

149,084,610

PSF objects in a Primary brick

69,164,070

SIMP objects in a Primary brick

31,300,725

EXP objects in a Primary brick

11,610,513

DEV objects in a Primary brick

1,266,944

COMP objects in a Primary brick

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 are approximated with mixture-of-gaussian (MoG) models (https://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 DR2 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

The most recent values of the Galactic extinction coefficients are available on the DR8 catalogs page.

## 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. Note that the image stacks are computed using nearest-neighbor interpolation, so should not be used for precision work.

## Depths

The median 5σ point source depths for areas in DR2 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 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 starting with "dr2p" tag; documented in all file headers.

• NOAO Community Pipeline: mixture of versions; recorded as PLVER.

• SourceExtractor 2.19.5, PSFEx 3.17.1

• Astrometry.net: 0.64

• Tractor: dr2.2

## 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; the DR2 reductions are performed within bricks of size approximately 0.25° × 0.25°.

CP

Community Pipeline (DECam reduction pipeline operated by NOAO; https://legacy.noirlab.edu/noao/staff/fvaldes/CPDocPrelim/PL201_3.html).

DECaLS
DR2

DECam Legacy Survey Data Release 2, January 2016.

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 (https://arxiv.org/abs/1210.6563).

NOAO
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
SDSS
SDSS DR12
SED

Spectral energy distribution.

SourceExtractor
SFD98

Schlegel, Finkbeiner & Davis 1998 extinction maps (https://ui.adsabs.harvard.edu/abs/1998ApJ...500..525S/abstract).

Tractor
unWISE

New coadds of the WISE imaging, at original full resolution (http://unwise.me, https://arxiv.org/abs/1405.0308).

WISE