Tractor Catalog Format

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

FITS binary table containing Tractor photometry. Before using these catalogs, note that there may be known issues regarding their content and derivation. Note that all flux-based quantities in the catalogs are on the AB system (we specify that WISE fluxes are AB in the table for clarity, as such quantities are often quoted on the Vega system).

Name	Type	Units	Description
`release`	int16		Integer denoting the camera and filter set used, which will be unique for a given processing run of the data (as documented here)
`brickid`	int32		Brick ID [1,662174]
`brickname`	char[8]		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 `release,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
`maskbits`	int16		Bitwise mask indicating that an object touches a pixel in the `coadd///maskbits` maps, as cataloged on the DR9 bitmasks page
`fitbits`	int16		Bitwise mask detailing pecularities of how an object was fit, as cataloged on the DR9 bitmasks page
`type`	char[3]		Morphological model: "PSF"=stellar, "REX"="round exponential galaxy", "DEV"=deVauc, "EXP"=exponential, "SER"=Sersic, "DUP"=Gaia source fit by different model.
`ra`	float64	deg	Right ascension at equinox J2000
`dec`	float64	deg	Declination at equinox J2000
`ra_ivar`	float32	1/deg²	Inverse variance of RA (no cosine term!), excluding astrometric calibration errors
`dec_ivar`	float32	1/deg²	Inverse variance of DEC, excluding astrometric calibration errors
`bx`	float32	pix	X position (0-indexed) of coordinates in the brick image stack (i.e. in the e.g. legacysurvey-<brick>-image-g.fits.fz coadd file)
`by`	float32	pix	Y position (0-indexed) of coordinates in brick image stack
`dchisq`	float32[5]		Difference in χ² between successively more-complex model fits: PSF, REX, DEV, EXP, SER. The difference is versus no source.
`ebv`	float32	mag	Galactic extinction E(B-V) reddening from SFD98, used to compute the `mw_transmission_` columns
`mjd_min`	float64	days	Minimum Modified Julian Date of observations used to construct the model of this object
`mjd_max`	float64	days	Maximum Modified Julian Date of observations used to construct the model of this object
`ref_cat`	char[2]		Reference catalog source for this star: "T2" for Tycho-2, "G2" for Gaia DR2, "L3" for the SGA, empty otherwise
`ref_id`	int64		Reference catalog identifier for this star; Tyc11,000,000+Tyc210+Tyc3 for Tycho2; "sourceid" for Gaia DR2 and SGA
`pmra`	float32	mas/yr	Reference catalog proper motion in RA direction (\(\mu_\alpha^*\equiv\mu_\alpha\cos\delta\)) in the ICRS at `ref_epoch`
`pmdec`	float32	mas/yr	Reference catalog proper motion in Dec direction (\(\mu_\delta\)) in the ICRS at `ref_epoch`
`parallax`	float32	mas	Reference catalog parallax
`pmra_ivar`	float32	1/(mas/yr)²	Reference catalog inverse-variance on `pmra`
`pmdec_ivar`	float32	1/(mas/yr)²	Reference catalog inverse-variance on `pmdec`
`parallax_ivar`	float32	1/mas²	Reference catalog inverse-variance on `parallax`
`ref_epoch`	float32	yr	Reference catalog reference epoch (eg, 2015.5 for Gaia DR2)
`gaia_phot_g_mean_mag`	float32	mag	Gaia G band mag
`gaia_phot_g_mean_flux_over_error`	float32		Gaia G band signal-to-noise
`gaia_phot_g_n_obs`	int16		Gaia G band number of observations
`gaia_phot_bp_mean_mag`	float32	mag	Gaia BP mag
`gaia_phot_bp_mean_flux_over_error`	float32		Gaia BP signal-to-noise
`gaia_phot_bp_n_obs`	int16		Gaia BP number of observations
`gaia_phot_rp_mean_mag`	float32	mag	Gaia RP mag
`gaia_phot_rp_mean_flux_over_error`	float32		Gaia RP signal-to-noise
`gaia_phot_rp_n_obs`	int16		Gaia RP number of observations
`gaia_phot_variable_flag`	bool		Gaia photometric variable flag
`gaia_astrometric_excess_noise`	float32		Gaia astrometric excess noise
`gaia_astrometric_excess_noise_sig`	float32		Gaia astrometric excess noise uncertainty
`gaia_astrometric_n_obs_al`	int16		Gaia number of astrometric observations along scan direction
`gaia_astrometric_n_good_obs_al`	int16		Gaia number of good astrometric observations along scan direction
`gaia_astrometric_weight_al`	float32		Gaia astrometric weight along scan direction
`gaia_duplicated_source`	bool		Gaia duplicated source flag
`gaia_a_g_val`	float32	magnitudes	Gaia line-of-sight extinction in the G band
`gaia_e_bp_min_rp_val`	float32	magnitudes	Gaia line-of-sight reddening E(BP-RP)
`gaia_phot_bp_rp_excess_factor`	float32		Gaia BP/RP excess factor
`gaia_astrometric_sigma5d_max`	float32	mas	Gaia longest semi-major axis of the 5-d error ellipsoid
`gaia_astrometric_params_solved`	uint8		which astrometric parameters were estimated for a Gaia source
`flux_g`	float32	nanomaggy	model flux in \(g\)
`flux_r`	float32	nanomaggy	model flux in \(r\)
`flux_z`	float32	nanomaggy	model flux in \(z\)
`flux_w1`	float32	nanomaggy	WISE model flux in \(W1\) (AB system)
`flux_w2`	float32	nanomaggy	WISE model flux in \(W2\) (AB)
`flux_w3`	float32	nanomaggy	WISE model flux in \(W3\) (AB)
`flux_w4`	float32	nanomaggy	WISE model flux in \(W4\) (AB)
`flux_ivar_g`	float32	1/nanomaggy²	Inverse variance of `flux_g`
`flux_ivar_r`	float32	1/nanomaggy²	Inverse variance of `flux_r`
`flux_ivar_z`	float32	1/nanomaggy²	Inverse variance of `flux_z`
`flux_ivar_w1`	float32	1/nanomaggy²	Inverse variance of `flux_w1` (AB system)
`flux_ivar_w2`	float32	1/nanomaggy²	Inverse variance of `flux_w2` (AB)
`flux_ivar_w3`	float32	1/nanomaggy²	Inverse variance of `flux_w3` (AB)
`flux_ivar_w4`	float32	1/nanomaggy²	Inverse variance of `flux_w4` (AB)
`fiberflux_g`	float32	nanomaggy	Predicted \(g\)-band flux within a fiber of diameter 1.5 arcsec from this object in 1 arcsec Gaussian seeing
`fiberflux_r`	float32	nanomaggy	Predicted \(r\)-band flux within a fiber of diameter 1.5 arcsec from this object in 1 arcsec Gaussian seeing
`fiberflux_z`	float32	nanomaggy	Predicted \(z\)-band flux within a fiber of diameter 1.5 arcsec from this object in 1 arcsec Gaussian seeing
`fibertotflux_g`	float32	nanomaggy	Predicted \(g\)-band flux within a fiber of diameter 1.5 arcsec from all sources at this location in 1 arcsec Gaussian seeing
`fibertotflux_r`	float32	nanomaggy	Predicted \(r\)-band flux within a fiber of diameter 1.5 arcsec from all sources at this location in 1 arcsec Gaussian seeing
`fibertotflux_z`	float32	nanomaggy	Predicted \(z\)-band flux within a fiber of diameter 1.5 arcsec from all sources at this location in 1 arcsec Gaussian seeing
`apflux_g`	float32[8]	nanomaggy	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 \(g\), masked by \(invvar=0\) (inverse variance of zero [1])
`apflux_r`	float32[8]	nanomaggy	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 \(r\), masked by \(invvar=0\)
`apflux_z`	float32[8]	nanomaggy	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 \(z\), masked by \(invvar=0\)
`apflux_resid_g`	float32[8]	nanomaggy	Aperture fluxes on the co-added residual images in \(g\), masked by \(invvar=0\)
`apflux_resid_r`	float32[8]	nanomaggy	Aperture fluxes on the co-added residual images in \(r\), masked by \(invvar=0\)
`apflux_resid_z`	float32[8]	nanomaggy	Aperture fluxes on the co-added residual images in \(z\), masked by \(invvar=0\)
`apflux_blobresid_g`	float32[8]	nanomaggy	Aperture fluxes on \(image-blobmodel\) residual maps in \(g\) [2], masked by \(invvar=0\)
`apflux_blobresid_r`	float32[8]	nanomaggy	Aperture fluxes on \(image-blobmodel\) residual maps in \(r\), masked by \(invvar=0\)
`apflux_blobresid_z`	float32[8]	nanomaggy	Aperture fluxes on \(image-blobmodel\) residual maps in \(z\), masked by \(invvar=0\)
`apflux_ivar_g`	float32[8]	1/nanomaggy²	Inverse variance of `apflux_resid_g`, masked by \(invvar=0\)
`apflux_ivar_r`	float32[8]	1/nanomaggy²	Inverse variance of `apflux_resid_r`, masked by \(invvar=0\)
`apflux_ivar_z`	float32[8]	1/nanomaggy²	Inverse variance of `apflux_resid_z`, masked by \(invvar=0\)
`apflux_masked_g`	float32[8]		Fraction of pixels masked in \(g\)-band aperture flux measurements; 1 means fully masked (ie, fully ignored; contributing zero to the measurement)
`apflux_masked_r`	float32[8]		Fraction of pixels masked in \(r\)-band aperture flux measurements; 1 means fully masked (ie, fully ignored; contributing zero to the measurement)
`apflux_masked_z`	float32[8]		Fraction of pixels masked in \(z\)-band aperture flux measurements; 1 means fully masked (ie, fully ignored; contributing zero to the measurement)
`apflux_w1`	float32[5]	nanomaggy	Aperture fluxes on the co-added images in apertures of radius [3, 5, 7, 9, 11] [3] arcsec in \(W1\), masked by \(invvar=0\)
`apflux_w2`	float32[5]	nanomaggy	Aperture fluxes on the co-added images in apertures of radius [3, 5, 7, 9, 11] arcsec in \(W2\), masked by \(invvar=0\)
`apflux_w3`	float32[5]	nanomaggy	Aperture fluxes on the co-added images in apertures of radius [3, 5, 7, 9, 11] arcsec in \(W3\), masked by \(invvar=0\)
`apflux_w4`	float32[5]	nanomaggy	Aperture fluxes on the co-added images in apertures of radius [3, 5, 7, 9, 11] arcsec in \(W4\), masked by \(invvar=0\)
`apflux_resid_w1`	float32[5]	nanomaggy	Aperture fluxes on the co-added residual images in \(W1\), masked by \(invvar=0\)
`apflux_resid_w2`	float32[5]	nanomaggy	Aperture fluxes on the co-added residual images in \(W2\), masked by \(invvar=0\)
`apflux_resid_w3`	float32[5]	nanomaggy	Aperture fluxes on the co-added residual images in \(W3\), masked by \(invvar=0\)
`apflux_resid_w4`	float32[5]	nanomaggy	Aperture fluxes on the co-added residual images in \(W4\), masked by \(invvar=0\)
`apflux_ivar_w1`	float32[5]	1/nanomaggy²	Inverse variance of `apflux_resid_w1`, masked by \(invvar=0\)
`apflux_ivar_w2`	float32[5]	1/nanomaggy²	Inverse variance of `apflux_resid_w2`, masked by \(invvar=0\)
`apflux_ivar_w3`	float32[5]	1/nanomaggy²	Inverse variance of `apflux_resid_w3`, masked by \(invvar=0\)
`apflux_ivar_w4`	float32[5]	1/nanomaggy²	Inverse variance of `apflux_resid_w4`, masked by \(invvar=0\)
`mw_transmission_g`	float32		Galactic transmission in \(g\) filter in linear units [0, 1]
`mw_transmission_r`	float32		Galactic transmission in \(r\) filter in linear units [0, 1]
`mw_transmission_z`	float32		Galactic transmission in \(z\) filter in linear units [0, 1]
`mw_transmission_w1`	float32		Galactic transmission in \(W1\) filter in linear units [0, 1]
`mw_transmission_w2`	float32		Galactic transmission in \(W2\) filter in linear units [0, 1]
`mw_transmission_w3`	float32		Galactic transmission in \(W3\) filter in linear units [0, 1]
`mw_transmission_w4`	float32		Galactic transmission in \(W4\) filter in linear units [0, 1]
`nobs_g`	int16		Number of images that contribute to the central pixel in \(g\) filter for this object (not profile-weighted)
`nobs_r`	int16		Number of images that contribute to the central pixel in \(r\) filter for this object (not profile-weighted)
`nobs_z`	int16		Number of images that contribute to the central pixel in \(z\) filter for this object (not profile-weighted)
`nobs_w1`	int16		Number of images that contribute to the central pixel in \(W1\) filter for this object (not profile-weighted)
`nobs_w2`	int16		Number of images that contribute to the central pixel in \(W2\) filter for this object (not profile-weighted)
`nobs_w3`	int16		Number of images that contribute to the central pixel in \(W3\) filter for this object (not profile-weighted)
`nobs_w4`	int16		Number of images that contribute to the central pixel in \(W4\) filter for this object (not profile-weighted)
`rchisq_g`	float32		Profile-weighted χ² of model fit normalized by the number of pixels in \(g\)
`rchisq_r`	float32		Profile-weighted χ² of model fit normalized by the number of pixels in \(r\)
`rchisq_z`	float32		Profile-weighted χ² of model fit normalized by the number of pixels in \(z\)
`rchisq_w1`	float32		Profile-weighted χ² of model fit normalized by the number of pixels in \(W1\)
`rchisq_w2`	float32		Profile-weighted χ² of model fit normalized by the number of pixels in \(W2\)
`rchisq_w3`	float32		Profile-weighted χ² of model fit normalized by the number of pixels in \(W3\)
`rchisq_w4`	float32		Profile-weighted χ² of model fit normalized by the number of pixels in \(W4\)
`fracflux_g`	float32		Profile-weighted fraction of the flux from other sources divided by the total flux in \(g\) (typically [0,1])
`fracflux_r`	float32		Profile-weighted fraction of the flux from other sources divided by the total flux in \(r\) (typically [0,1])
`fracflux_z`	float32		Profile-weighted fraction of the flux from other sources divided by the total flux in \(z\) (typically [0,1])
`fracflux_w1`	float32		Profile-weighted fraction of the flux from other sources divided by the total flux in \(W1\) (typically [0,1])
`fracflux_w2`	float32		Profile-weighted fraction of the flux from other sources divided by the total flux in \(W2\) (typically [0,1])
`fracflux_w3`	float32		Profile-weighted fraction of the flux from other sources divided by the total flux in \(W3\) (typically [0,1])
`fracflux_w4`	float32		Profile-weighted fraction of the flux from other sources divided by the total flux in \(W4\) (typically [0,1])
`fracmasked_g`	float32		Profile-weighted fraction of pixels masked from all observations of this object in \(g\), strictly between [0,1]
`fracmasked_r`	float32		Profile-weighted fraction of pixels masked from all observations of this object in \(r\), strictly between [0,1]
`fracmasked_z`	float32		Profile-weighted fraction of pixels masked from all observations of this object in \(z\), strictly between [0,1]
`fracin_g`	float32		Fraction of a source's flux within the blob in \(g\), near unity for real sources
`fracin_r`	float32		Fraction of a source's flux within the blob in \(r\), near unity for real sources
`fracin_z`	float32		Fraction of a source's flux within the blob in \(z\), near unity for real sources
`anymask_g`	int16		Bitwise mask set if the central pixel from any image satisfies each condition in \(g\) as cataloged on the DR9 bitmasks page
`anymask_r`	int16		Bitwise mask set if the central pixel from any image satisfies each condition in \(r\) as cataloged on the DR9 bitmasks page
`anymask_z`	int16		Bitwise mask set if the central pixel from any image satisfies each condition in \(z\) as cataloged on the DR9 bitmasks page
`allmask_g`	int16		Bitwise mask set if the central pixel from all images satisfy each condition in \(g\) as cataloged on the DR9 bitmasks page
`allmask_r`	int16		Bitwise mask set if the central pixel from all images satisfy each condition in \(r\) as cataloged on the DR9 bitmasks page
`allmask_z`	int16		Bitwise mask set if the central pixel from all images satisfy each condition in \(z\) as cataloged on the DR9 bitmasks page
`wisemask_w1`	uint8		W1 bitmask as cataloged on the DR9 bitmasks page
`wisemask_w2`	uint8		W2 bitmask as cataloged on the DR9 bitmasks page
`psfsize_g`	float32	arcsec	Weighted average PSF FWHM in the \(g\) band
`psfsize_r`	float32	arcsec	Weighted average PSF FWHM in the \(r\) band
`psfsize_z`	float32	arcsec	Weighted average PSF FWHM in the \(z\) band
`psfdepth_g`	float32	1/nanomaggy²	For a \(5\sigma\) point source detection limit in \(g\), \(5/\sqrt(\mathrm{psfdepth\_g})\) gives flux in nanomaggies and \(-2.5[\log_{10}(5 / \sqrt(\mathrm{psfdepth\_g})) - 9]\) gives corresponding AB magnitude
`psfdepth_r`	float32	1/nanomaggy²	For a \(5\sigma\) point source detection limit in \(r\), \(5/\sqrt(\mathrm{psfdepth\_r})\) gives flux in nanomaggies and \(-2.5[\log_{10}(5 / \sqrt(\mathrm{psfdepth\_r})) - 9]\) gives corresponding AB magnitude
`psfdepth_z`	float32	1/nanomaggy²	For a \(5\sigma\) point source detection limit in \(z\), \(5/\sqrt(\mathrm{psfdepth\_z})\) gives flux in nanomaggies and \(-2.5[\log_{10}(5 / \sqrt(\mathrm{psfdepth\_z})) - 9]\) gives corresponding AB magnitude
`galdepth_g`	float32	1/nanomaggy²	As for `psfdepth_g` but for a galaxy (0.45" exp, round) detection sensitivity
`galdepth_r`	float32	1/nanomaggy²	As for `psfdepth_r` but for a galaxy (0.45" exp, round) detection sensitivity
`galdepth_z`	float32	1/nanomaggy²	As for `psfdepth_z` but for a galaxy (0.45" exp, round) detection sensitivity
`nea_g`	float32	arcsec²	Noise equivalent area in \(g\).
`nea_r`	float32	arcsec²	Noise equivalent area in \(r\).
`nea_z`	float32	arcsec²	Noise equivalent area in \(z\).
`blob_nea_g`	float32	arcsec²	Blob-masked noise equivalent area in \(g\).
`blob_nea_r`	float32	arcsec²	Blob-masked noise equivalent area in \(r\).
`blob_nea_z`	float32	arcsec²	Blob-masked noise equivalent area in \(z\).
`psfdepth_w1`	float32	1/nanomaggy²	As for `psfdepth_g` (and also on the AB system) but for WISE W1
`psfdepth_w2`	float32	1/nanomaggy²	As for `psfdepth_g` (and also on the AB system) but for WISE W2
`psfdepth_w3`	float32	1/nanomaggy²	As for `psfdepth_g` (and also on the AB system) but for WISE W3
`psfdepth_w4`	float32	1/nanomaggy²	As for `psfdepth_g` (and also on the AB system) but for WISE W4
`wise_coadd_id`	char[8]		unWISE coadd brick name (corresponding to the, e.g., legacysurvey-<brick>-image-W1.fits.fz coadd file) for the center of each object
`wise_x`	float32	pix	X position of coordinates in the brick image stack that corresponds to `wise_coadd_id` (see the DR9 updates page for transformations between `wise_x` and `bx`)
`wise_y`	float32	pix	Y position of coordinates in the brick image stack that corresponds to `wise_coadd_id` (see the DR9 updates page for transformations between `wise_y` and `by`)
`lc_flux_w1`	float32[15]	nanomaggy	`flux_w1` in each of up to fifteen unWISE coadd epochs (AB system; defaults to zero for unused entries)
`lc_flux_w2`	float32[15]	nanomaggy	`flux_w2` in each of up to fifteen unWISE coadd epochs (AB; defaults to zero for unused entries)
`lc_flux_ivar_w1`	float32[15]	1/nanomaggy²	Inverse variance of `lc_flux_w1` (AB system; defaults to zero for unused entries)
`lc_flux_ivar_w2`	float32[15]	1/nanomaggy²	Inverse variance of `lc_flux_w2` (AB; defaults to zero for unused entries)
`lc_nobs_w1`	int16[15]		`nobs_w1` in each of up to fifteen unWISE coadd epochs
`lc_nobs_w2`	int16[15]		`nobs_w2` in each of up to fifteen unWISE coadd epochs
`lc_fracflux_w1`	float32[15]		`fracflux_w1` in each of up to fifteen unWISE coadd epochs (defaults to zero for unused entries)
`lc_fracflux_w2`	float32[15]		`fracflux_w2` in each of up to fifteen unWISE coadd epochs (defaults to zero for unused entries)
`lc_rchisq_w1`	float32[15]		`rchisq_w1` in each of up to fifteen unWISE coadd epochs (defaults to zero for unused entries)
`lc_rchisq_w2`	float32[15]		`rchisq_w2` in each of up to fifteen unWISE coadd epochs (defaults to zero for unused entries)
`lc_mjd_w1`	float64[15]		`mjd_w1` in each of up to fifteen unWISE coadd epochs (defaults to zero for unused entries)
`lc_mjd_w2`	float64[15]		`mjd_w2` in each of up to fifteen unWISE coadd epochs (defaults to zero for unused entries)
`lc_epoch_index_w1`	int16[15]		Index number of unWISE epoch for W1 (defaults to -1 for unused entries)
`lc_epoch_index_w2`	int16[15]		Index number of unWISE epoch for W2 (defaults to -1 for unused entries)
`sersic`	float32		Power-law index for the Sersic profile model (`type="SER"`)
`sersic_ivar`	float32		Inverse variance of `sersic`
`shape_r`	float32	arcsec	Half-light radius of galaxy model for galaxy type `type` (>0)
`shape_r_ivar`	float32	1/arcsec²	Inverse variance of `shape_r`
`shape_e1`	float32		Ellipticity component 1 of galaxy model for galaxy type `type`
`shape_e1_ivar`	float32		Inverse variance of `shape_e1`
`shape_e2`	float32		Ellipticity component 2 of galaxy model for galaxy type `type`
`shape_e2_ivar`	float32		Inverse variance of `shape_e2`

Goodness-of-Fits and Morphological `type`

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"), round exponential galaxy model ("REX"), de Vaucouleurs model ("DEV"), exponential model ("EXP"), and a Sersic model ("SER"), in that order. Note that the Sersic model replaces the composite ("COMP") model used in DR8 (and before). The "REX" model is a round exponential galaxy profile with a variable radius 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 rchisq 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, and can be negative-valued for sources that have a flux measured as negative in some bands where they are not detected.

The final, additional moropholigical type is "DUP." This type is set for Gaia sources that are coincident with, and so have been fit by, an extended source. No optical flux is assigned to DUP sources, but they are retained to ensure that all Gaia sources appear in the catalogs even if Tractor prefers an alternate fit.

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.

Eddie Schlafly has computed the extinction coefficients for the DECam filters through airmass=1.3, computed for a 7000K source spectrum as was done in the Appendix of Schlafly & Finkbeiner (2011). 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 are multiplied by the SFD98 E(B-V) values at the coordinates of each object to derive the \(g\), \(r\) and \(z\) mw_transmission values in the Legacy Surveys catalogs. The coefficients at different airmasses only change by a small amount, with the largest effect in \(g\)-band where the coefficient would be 3.219 at airmass=1 and 3.202 at airmass=2.

We calculate Galactic extinction for BASS and MzLS as if they are on the DECam filter system.

The coefficients for the four WISE filters are derived from Fitzpatrick (1999), as recommended by Schlafly & Finkbeiner (2011), considered better than either the Cardelli et al. (1989) curves or the newer Fitzpatrick & Massa (2009) NIR curve (which is not vetted beyond 2 microns). These coefficients are A / E(B-V) = 0.184, 0.113, 0.0241, 0.00910.

Ellipticities

The ellipticities for each galaxy type (i.e. shape_e1, shape_e2) are 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*}

Footnotes