# Data Release Description

The Legacy Surveys are producing 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. To achieve this goal, the Legacy Surveys are conducting 3 imaging projects on different telescopes, described in more depth at the following links:

 The Beijing-Arizona Sky Survey (BASS) The DECam Legacy Survey (DECaLS) The Mayall z-band Legacy Survey (MzLS)

## Contents of DR4

Data Release 4 (DR4) is the fourth public data release of the Legacy Surveys. It consists of the first release of data from BASS and MzLS reduced using the Tractor. Each of the imaging datasets is first reduced through the NOAO Community Pipeline before being processed using the Tractor.

DR4 includes BASS images taken prior to July 13, 2016 and MzLS images taken prior to June 6, 2016. For the latest DECaLS images, see DR3 of the Legacy Surveys. The BASS and MzLS data in DR4 are reduced in a manner that is largely consistent with DECaLS reductions in prior Legacy Survey Data Releases.

In total, the BASS imaging included in DR4 covers 58,341 bricks in either $g$-band or $r$-band. The MzLS imaging in DR4 covers 57,943 bricks in $z$-band. Bricks average 0.0623 deg² in size. Both BASS and MzLS therefore cover about 3600 deg² in unique area, although they do not necessarily cover the same area. There are approximately 183 million unique sources in DR4.

DR4 includes the Right Ascension (RA) range of 55 to 301 degrees, and Declination (Dec) range of +29 to +82 degrees. There are two small regions near RA,Dec = (56, +33) and RA,Dec = (66, +68), plus the main contiguous Northern Galactic Cap region, which lies within RA of 87 to 301 degrees.

DR4 includes the stacked images and the Tractor-based catalogs. The size of the DR4 data distribution is:

Size* Directory Description
6.2 GB calib/ Calibration files.
30 TB coadd/ Co-added images, including χ², depth, image, model, nexp, and Quality Assurance PNG plots
7.1 GB external/ Matches to other catalogs (SDSS, etc.).
437 MB gallery/ Images of notable galaxies (NGC, etc.).
11 GB logs/ Log files generated by Tractor processing.
117 GB metrics/ Metrics.
63 GB sweep/ Repackaged versions of the Tractor catalogs.
256 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.

For all of the Legacy Surveys, including BASS and MzLS, 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. The projections for the $g,r,z$ filters are identical. There are 662,174 bricks spread over the sky, meaning that each brick has an average area of 0.0623 deg2. The brick images have some overlap. The co-added images should be used with caution, as noted below in the Image Stacks section.

For DESI members with access to DocDB, a further overview of DR4 is available in Kaylan Burleigh's presentation from the June, 2017 DESI collaboration meeting.

## Obtaining Images and Raw Data

Images, for all 3 of the Legacy Surveys 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 BASS and MzLS for DR4 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 pixels used by the Tractor. For information on how to recover DECaLS cutouts, see the DR3 description page.

## Source Detection

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

For source detection, each 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. The same pixelized PSF from PSFex is used for BASS and MzLS in order to match the PSF used to extract DECaLS sources for DR3.

For DECaLS and MzLS we adopt a 63 x 63 pixel image size and a 0.262 pixel scale and use a 7″ diameter aperture for normalization. For BASS we adopt a 31 x 31 pixel image size and a 0.470 pixel scale and use a 7″ diameter aperture for normalization The configuaration files for SExtractor and PSFex are available on our github page.

## 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 on the NOAO Community Pipeline page. 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 DR4. 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 DR4, 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 DR4 are:

Number of Sources Type
183,489,859 Objects in a Primary brick
90,683,489 PSF
58,829,887 SIMP
22,653,067 EXP
10,492,773 DEV
830,643 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 (PSF)" or "simple galaxy (SIMP)" 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 package, or the open source Ceres solver, 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 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 BASS and MzLS are on the AB natural system of the 90Prime and Mosaic-3 cameras, respectively. 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 90Prime and Mosaic-3 filter systems.

Zero point magnitudes for the CP version 2 reductions of the 90Prime and Mosaic-3 images were computed by comparing 7″ diameter aperture photometry to Pan-STARRS-1 (PS1) photometry, where the latter was modified with color terms to place the PS1 photometry on the 90Prime and Mosaic-3 camera systems. The same color terms are applied to all CCDs. Zero points are computed separately for each CCD, but not for each amplifier. The average color terms to convert from PS1 to 90Prime (for BASS) and Mosaic-3 (for MzLS) 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{BASS}} & = & g_{\mathrm{PS}} + 0.06630 (g-i) + 0.00958 (g-i)^2 - 0.00672 (g-i)^3 \\ r_{\mathrm{BASS}} & = & r_{\mathrm{PS}} - 0.04836 (g-i) + 0.01100 (g-i)^2 - 0.00563 (g-i)^3 \\ z_{\mathrm{MzLS}} & = & z_{\mathrm{PS}} - 0.12315 (g-i) + 0.04608 (g-i)^2 - 0.01164 (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 filter curves are available for BASS g-band, BASS r-band, MzLS z-band and MzLS z-band with corrections for the telescope, corrector, camera and atmosphere (at airmass=1.0). The derivation of the BASS filter responses is described on the BASS website.

DR4 also contains WISE fluxes force-photometered at the position of Legacy Survey sources. 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. 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

For DR4, we calculate Galactic extinction for BASS and MzLS as if they are on the DECam filter system (e.g., see DR3).

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

As of DR4, astrometry uses the Gaia Data Release 1 system. Positions of sources are tied to predicted Gaia positions at the epoch of the corresponding Legacy Survey observation. The residuals are typically smaller than ±0.03″.

Astrometric calibration of MzLS data is conducted using Gaia astrometric positions of stars matched to Pan-STARRS-1 (PS1). The same matched objects are used for both astrometric and photometric calibration. There are some areas of sky where Gaia has "holes," i.e., where stars brighter than the Gaia magnitude limit are missing from the Gaia catalog. As a result, in some regions of the survey there are fewer matches to a given bright magnitude limit in the PS1-Gaia catalog than there are in the PS1 catalog that was used for astrometric calibration in, e.g., DR3 of the Legacy Surveys.

## 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. These stacks should not be used for "precision" work.

## Depths

As of DR2 of the Legacy Surveys, the median 5σ point source (AB) depths for areas with 3 observations in DECaLS was $g=24.65$, $r=23.61$, $z=22.84$. DR4 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 $g=24.7$, $r=23.9$, $z=23.0$.

For MzLS, the median 5σ point source (AB) depth for areas with 3 observations is $z=23.04$. 90% of the individual CCDs are deeper than $z=22.81$.

## Code Versions

• LegacyPipe: mixture of versions, ranging from dr3e-834-g419c0ff to dr3e-887-g068df7a (these are git version strings). The version used is documented in the Tractor header card LEGPIPEV. The date range of the versions is 3/15/2017 to 4/19/2017.
• Astrometry.net: 0.67, git versions 0.67-188-gfcdd3c0 to 0.67-152-gfa03658 (dates 3/6/2017 to 4/15/2017).
• Tractor: dr4, git versions dr4.1-9-gc73f1ab to dr4.1-9-ga5cfaa3 (dates 2/22/2017 to 3/31/2017).
• NOAO Community Pipeline: mixture of versions; recorded as PLVER.

## Glossary

BASS
Beijing-Arizona Sky Survey.
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 (reduction pipeline operated by NOAO; http://www.noao.edu/noao/staff/fvaldes/CPDocPrelim/PL201_3.html).
DECaLS
Dark Energy Camera Legacy Survey.
DR2
Legacy Survey Data Release 2.
DR3
Legacy Survey Data Release 3.
DR4
Legacy Survey Data Release 4.
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).
MzLS
Mayall z-band Legacy Survey.
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.
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.