# Tractor Catalog Format

## tractor/<AAA>/tractor-<brick>.fits

FITS binary table containing Tractor photometry. Before using these catalogs, note that there are known issues regarding their content and derivation.

Name

Type

Units

Description

BRICKID

int32

Brick ID [1,662174]

BRICKNAME

char

Name of brick, encoding the brick sky position, eg "1126p222" near RA=112.6, Dec=+22.2

OBJID

int32

Catalog object number within this brick; a unique identifier hash is BRICKID,OBJID; OBJID spans [0,N-1] and is contiguously enumerated within each brick

BRICK_PRIMARY

boolean

True if the object is within the brick boundary

BLOB

int32

Blend family; objects with the same [BRICKID,BLOB] identifier were modeled (deblended) together; contiguously numbered from 0

NINBLOB

int16

Number of sources in this BLOB (blend family); isolated objects have value 1.

TYCHO2INBLOB

boolean

Is there a Tycho-2 (very bright) star in this blob?

TYPE

char[4]

Morphological model: "PSF"=stellar, "SIMP"="simple galaxy" = 0.45" round EXP galaxy, "DEV"=deVauc, "EXP"=exponential, "COMP"=composite. Note that in some FITS readers, a trailing space may be appended for "PSF ", "DEV " and "EXP " since the column data type is a 4-character string

RA

float64

deg

Right ascension at equinox J2000

RA_IVAR

float32

1/deg²

Inverse variance of RA (no cosine term!), excluding astrometric calibration errors

DEC

float64

deg

Declination at equinox J2000

DEC_IVAR

float32

1/deg²

Inverse variance of DEC, excluding astrometric calibration errors

BX

float32

pix

X position (0-indexed) of coordinates in brick image stack

BY

float32

pix

Y position (0-indexed) of coordinates in brick image stack

BX0

float32

pix

Initialized X position (0-indexed) of coordinates in brick image stack

BY0

float32

pix

Initialized Y position (0-indexed) of coordinates in brick image stack

LEFT_BLOB

boolean

True if an object center has been optimized to be outside the fitting pixel area

OUT_OF_BOUNDS

boolean

True for objects whose center is on the brick; less strong of a cut than BRICK_PRIMARY

DCHISQ

float32[5]

Difference in χ² between successively more-complex model fits: PSF, SIMPle, DEV, EXP, COMP. The difference is versus no source.

EBV

float32

mag

Galactic extinction E(B-V) reddening from SFD98, used to compute DECAM_MW_TRANSMISSION and WISE_MW_TRANSMISSION

CPU_SOURCE

float32

seconds

CPU time used for fitting this source

CPU_BLOB

float32

seconds

CPU time used for fitting this blob of sources (all sources in this brick with the same blob number)

BLOB_WIDTH

int16

size of this blob of pixels in brick coordinates, bounding box width

BLOB_HEIGHT

int16

size of this blob of pixels in brick coordinates, bounding box height

BLOB_NPIX

int32

size of this blob of pixels in brick coordinates, number of brick pixels

BLOB_NIMAGES

int16

number of images overlapping this blob

BLOB_TOTALPIX

int32

total number of pixels from all the images overlapping this blob

DECAM_FLUX

float32[6]

nanomaggies

DECam model flux in ugrizY

DECAM_FLUX_IVAR

float32[6]

1/nanomaggies²

Inverse variance oF DECAM_FLUX

DECAM_APFLUX

float32[8,6]

nanomaggies

DECam aperture fluxes on the co-added images in apertures of radius [0.5,0.75,1.0,1.5,2.0,3.5,5.0,7.0] arcsec in ugrizY

DECAM_APFLUX_RESID

float32[8,6]

nanomaggies

DECam aperture fluxes on the co-added residual images

DECAM_APFLUX_IVAR

float32[8,6]

1/nanomaggies²

Inverse variance oF DECAM_APFLUX

DECAM_MW_TRANSMISSION

float32[6]

Galactic transmission in ugrizY filters in linear units [0,1]

DECAM_NOBS

uint8[6]

Number of images that contribute to the central pixel in each filter for this object (not profile-weighted)

DECAM_RCHI2

float32[6]

Profile-weighted χ² of model fit normalized by the number of pixels

DECAM_FRACFLUX

float32[6]

Profile-weight fraction of the flux from other sources divided by the total flux (typically [0,1])

float32[6]

Profile-weighted fraction of pixels masked from all observations of this object, strictly between [0,1]

DECAM_FRACIN

float32[6]

Fraction of a source's flux within the blob, near unity for real sources

int16[6]

Bitwise mask set if the central pixel from any image satisfy each condition

int16[6]

Bitwise mask set if the central pixel from all images satisfy each condition

DECAM_PSFSIZE

float32[6]

arcsec

Weighted average PSF FWHM per band

WISE_FLUX

float32[4]

nanomaggies

WISE model flux in W1,W2,W3,W4

WISE_FLUX_IVAR

float32[4]

1/nanomaggies²

Inverse variance of WISE_FLUX

WISE_MW_TRANSMISSION

float32[4]

Galactic transmission in W1,W2,W3,W4 filters in linear units [0,1]

WISE_NOBS

int16[4]

Number of images that contribute to the central pixel in each filter for this object (not profile-weighted)

WISE_FRACFLUX

float32[4]

Profile-weight fraction of the flux from other sources divided by the total flux (typically [0,1])

WISE_RCHI2

float32[4]

Profile-weighted χ² of model fit normalized by the number of pixels

WISE_LC_FLUX

float32[5,2]

nanomaggies

analog of WISE_FLUX, for each of up to five unWISE coadd epochs; W1 and W2 only

WISE_LC_FLUX_IVAR

float32[5,2]

1/nanomaggies²

analog of WISE_FLUX_IVAR, for each of up to five unWISE coadd epochs; W1 and W2 only

WISE_LC_NOBS

int16[5,2]

analog of WISE_NOBS, for each of up to five unWISE coadd epochs; W1 and W2 only

WISE_LC_FRACFLUX

float32[5,2]

analog of WISE_FRACFLUX, for each of up to five unWISE coadd epochs; W1 and W2 only

WISE_LC_RCHI2

float32[5,2]

analog of WISE_RCHI2, for each of up to five unWISE coadd epochs; W1 and W2 only

WISE_LC_MJD

float32[5,2]

mean MJD in W1 and W2, for up to five unWISE coadd epochs; 0 means epoch unavailable

FRACDEV

float32

Fraction of model in deVauc [0,1]

FRACDEV_IVAR

float32

Inverse variance of FRACDEV

SHAPEEXP_R

float32

arcsec

Half-light radius of exponential model (>0)

SHAPEEXP_R_IVAR

float32

1/arcsec²

Inverse variance of R_EXP

SHAPEEXP_E1

float32

Ellipticity component 1

SHAPEEXP_E1_IVAR

float32

Inverse variance of SHAPEEXP_E1

SHAPEEXP_E2

float32

Ellipticity component 2

SHAPEEXP_E2_IVAR

float32

Inverse variance of SHAPEEXP_E2

SHAPEDEV_R

float32

arcsec

Half-light radius of deVaucouleurs model (>0)

SHAPEDEV_R_IVAR

float32

1/arcsec²

Inverse variance of R_DEV

SHAPEDEV_E1

float32

Ellipticity component 1

SHAPEDEV_E1_IVAR

float32

Inverse variance of SHAPEDEV_E1

SHAPEDEV_E2

float32

Ellipticity component 2

SHAPEDEV_E2_IVAR

float32

Inverse variance of SHAPEDEV_E2

DECAM_DEPTH

float32[6]

1/nanomaggies²

For a $5\sigma$ point source detection limit, $5/\sqrt(\mathrm{DECAM\_DEPTH})$ gives flux in nanomaggies and $-2.5[\log_{10}(5 / \sqrt(\mathrm{DECAM\_DEPTH})) - 9]$ gives corresponding magnitude

DECAM_GALDEPTH

float32[6]

1/nanomaggies²

As for DECAM_DEPTH but for a galaxy (0.45" exp, round) detection sensitivity

Bit

Value

Name

Description

0

1

See the CP Data Quality bit description.

1

2

saturated

See the CP Data Quality bit description.

2

4

interpolated

See the CP Data Quality bit description.

4

16

single exposure cosmic ray

See the CP Data Quality bit description.

6

64

bleed trail

See the CP Data Quality bit description.

7

128

multi-exposure transient

See the CP Data Quality bit description.

8

256

edge

See the CP Data Quality bit description.

9

512

edge2

See the CP Data Quality bit description.

10

1024

longthin

$\gt 5\sigma$ connected components with major axis $\gt 200$ pixels and major/minor axis $\gt 0.1$. To mask, e.g., satellite trails.

## Goodness-of-Fits

The DCHISQ values represent the χ² sum of all pixels in the source's blob for various models. This 5-element vector contains the χ² difference between the best-fit point source (type="PSF"), simple galaxy model ("SIMP"), de Vaucouleurs model ("DEV"), exponential model ("EXP"), and a composite model ("COMP"), in that order. The "simple galaxy" model is an exponential galaxy with fixed shape of 0.45″ and zero ellipticity (round) and is meant to capture slightly-extended but low signal-to-noise objects. The DCHISQ values are the χ² difference versus no source in this location---that is, it is the improvement from adding the given source to our model of the sky. The first element (for PSF) corresponds to a traditional notion of detection significance. Note that the DCHISQ values are negated so that positive values indicate better fits. We penalize models with negative flux in a band by subtracting rather than adding its χ² improvement in that band.

The DECAM_RCHI2 values are interpreted as the reduced χ² pixel-weighted by the model fit, computed as the following sum over pixels in the blob for each object:

\begin{equation*} \chi^2 = \frac{\sum \left[ \left(\mathrm{image} - \mathrm{model}\right)^2 \times \mathrm{model} \times \mathrm{inverse\, variance}\right]}{\sum \left[ \mathrm{model} \right]} \end{equation*}

The above sum is over all images contributing to a particular filter. The above can be negative-valued for sources that have a flux measured as negative in some bands where they are not detected.

## Galactic Extinction Coefficients

The Galactic extinction values are derived from the SFD98 maps, but with updated coefficients to convert E(B-V) to the extinction in each filter. These are reported in linear units of transmission, with 1 representing a fully transparent region of the Milky Way and 0 representing a fully opaque region. The value can slightly exceed unity owing to noise in the SFD98 maps, although it is never below 0.

Extinction coefficients for the SDSS filters have been changed to the values recommended by Schlafly & Finkbeiner (2011; Table 4) using the Fizpatrick 1999 extinction curve at R_V = 3.1 and their improved overall calibration of the SFD98 maps. These coefficients are A / E(B-V) = 4.239, 3.303, 2.285, 1.698, 1.263 in ugriz, which are different from those used in SDSS-I,II,III, but are the values used for SDSS-IV/eBOSS target selection.

Extinction coefficients for the DECam filters also use the Schlafly & Finkbeiner (2011) values, with u-band computed using the same formulae and code at airmass 1.3 (Schlafly, priv. comm. decam-data list on 11/13/14). These coefficients are $A / E(B-V)$ = 3.995, 3.214, 2.165, 1.592, 1.211, 1.064 for the DECam $u$, $g$, $r$, $i$, $z$, $Y$ filters, respectively. Note that these are slightly different from the coefficients in Schlafly & Finkbeiner (2011).

The coefficients for the four WISE filters are derived from Fitzpatrick 1999, as recommended by Schafly & Finkbeiner, considered better than either the Cardelli et al 1989 curves or the newer Fitzpatrick & Massa 2009 NIR curve not vetted beyond 2 micron). These coefficients are A / E(B-V) = 0.184, 0.113, 0.0241, 0.00910.

## Ellipticities

The ellipticity, ε, is different from the usual eccentricity, $e \equiv \sqrt{1 - (b/a)^2}$. In gravitational lensing studies, the ellipticity is taken to be a complex number:

\begin{equation*} \epsilon = \frac{a-b}{a+b} \exp( 2i\phi ) = \epsilon_1 + i \epsilon_2 \end{equation*}

Where ϕ is the position angle with a range of 180°, due to the ellipse's symmetry. Going between $r, \epsilon_1, \epsilon_2$ and $r, b/a, \phi$:

\begin{align*} r & = & r \\ |\epsilon| & = & \sqrt{\epsilon_1^2 + \epsilon_2^2} \\ \frac{b}{a} & = & \frac{1 - |\epsilon|}{1 + |\epsilon|} \\ \phi & = & \frac{1}{2} \arctan \frac{\epsilon_2}{\epsilon_1} \\ |\epsilon| & = & \frac{1 - b/a}{1 + b/a} \\ \epsilon_1 & = & |\epsilon| \cos(2 \phi) \\ \epsilon_2 & = & |\epsilon| \sin(2 \phi) \\ \end{align*}