The CatWISE Preliminary Catalog: Motions from WISE and NEOWISE Data

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Published 2020 April 14 © 2020. The American Astronomical Society. All rights reserved.
, , Citation Peter R. M. Eisenhardt et al 2020 ApJS 247 69 DOI 10.3847/1538-4365/ab7f2a

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Abstract

CatWISE is a program to catalog sources selected from combined WISE and NEOWISE all-sky survey data at 3.4 and 4.6 μm (W1 and W2). The CatWISE Preliminary Catalog consists of 900,849,014 sources measured in data collected from 2010 to 2016. This data set represents four times as many exposures and spans over 10 times as large a time baseline as that used for the AllWISE Catalog. CatWISE adapts AllWISE software to measure the sources in coadded images created from six-month subsets of these data, each representing one coverage of the inertial sky, or epoch. The catalog includes the measured motion of sources in eight epochs over the 6.5 yr span of the data. From comparison to Spitzer, signal-to-noise ratio = 5 limits in magnitudes in the Vega system are W1 = 17.67 and W2 = 16.47, compared to W1 = 16.96 and W2 = 16.02 for AllWISE. From comparison to Gaia, CatWISE positions have typical accuracies of 50 mas for stars at W1 = 10 mag and 275 mas for stars at W1 = 15.5 mag. Proper motions have typical accuracies of 10 mas yr−1 and 30 mas yr−1 for stars with these brightnesses, an order of magnitude better than from AllWISE. The catalog is available in the WISE/NEOWISE Enhanced and Contributed Products area of the NASA/IPAC Infrared Science Archive.

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1. Introduction

NASA's Wide-field Infrared Survey Explorer mission (WISE; Wright et al. 2010) revealed iconic objects, including the first Earth Trojan asteroid (Connors et al. 2011), the closest and coolest brown dwarfs (Luhman 2013, 2014), and the most luminous galaxy yet found in the universe (Tsai et al. 2015). These discoveries were made using two or more infrared coverages of the sky (or epochs) obtained from 2010 January to 2011 February. Each epoch typically consists of a dozen exposures per band taken within two days at a given position. The satellite was reactivated as NEOWISE and resumed searching for near-Earth objects in 2013 December (Mainzer et al. 2014), and has continued to cover the sky every six months since then.

In 2013 November, the AllWISE release (Cutri et al. 2013) made available to the community an atlas from coadding the two dozen exposures per position from the initial year of WISE surveying, and a catalog of source fluxes and positions measured from those exposures. With at least two epochs per inertial position, AllWISE also provided motion estimates and became the definitive catalog in the WISE bandpasses. Each year, NEOWISE releases the individual exposures from the reactivated survey (Cutri et al. 2015), corresponding to two additional epochs. With the 2020 March 26 NEOWISE release, exposures from 14 epochs are now available. Meisner et al. (2018b) used unWISE processing (Lang 2014) to produce an image atlas which combines the 2010 and 2011 data used for AllWISE with the 2013 through 2016 NEOWISE data. An obvious next step is to catalog the sources revealed in these combined exposures.

The unWISE Catalog (Schlafly et al. 2019) uses a crowded-field point-source photometry code called "crowdsource" to do this, measuring source fluxes and positions in the coadded image, with the measurements at 3.4 μm (W1) and 4.6 μm (W2) carried out independently. In contrast, CatWISE has adapted AllWISE software to produce a full-sky catalog of sources selected simultaneously in both W1 and W2, and also provides motion estimates. For the CatWISE Preliminary Catalog described in this paper, sources were selected from the ensemble of eight epochs of WISE and NEOWISE data from (Meisner et al. 2018b, the "full coadd"), and the least-squares best-fit solution for point-source flux, position, and motion was determined from measurements on the individual "epoch coadd" images (Meisner et al. 2018c) rather than individual exposures, to reduce computational cost. Because the total time spanned by CatWISE epochs at a given inertial position is over 6 yr, compared to a typical value of six months for AllWISE, the CatWISE motion estimates are far more accurate. This, in addition to the greater depth of the CatWISE catalog relative to AllWISE, is being used to extend the census of the coldest brown dwarfs in the solar neighborhood and enable definitive measurement of the form of the low-mass end of the star formation process (Kirkpatrick et al. 2019). Figure 1 illustrates an example of the potential of CatWISE to progress in this area.

Figure 1.

Figure 1. (Top) Proper motions that are insignificant in AllWISE become obvious with the increased time baseline of CatWISE. Discovered via its color in WISE data (Gelino et al. 2011; Kirkpatrick et al. 2011), WISEA J161441.47+173935.4 is a T9 brown dwarf at 10 pc with a proper motion of μα = 554.5 ± 1.2 mas yr−1, μδ = −476.7 ± 1.2 mas yr−1 as determined by Spitzer (Kirkpatrick et al. 2019). With a six-month baseline, AllWISE (top left and center) measures a motion consistent with zero (μα = 352 ± 412 mas yr−1, μδ = −69 ± 452 mas yr−1; bottom center), while with the inclusion of NEOWISE data from 2016 (top right), the corresponding source in the CatWISE Preliminary Catalog (CWISEP J161441.63+173933.7) has a highly significant motion (${\mu }_{\alpha }=583.6\pm 23.5$ mas yr−1, μδ = −442.0 ± 25.0 mas yr−1; bottom right) consistent with the Spitzer values. The top panels show 2' × 2' cutouts in W2 centered on the WISE position of the source at the first epoch, marked in all three epochs by a red circle.

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In Section 2 of this paper, we summarize relevant aspects of the WISE and NEOWISE mission phases. Section 3 describes the CatWISE processing steps. Section 4 assesses the astrometric and photometric performance of CatWISE using comparisons to Gaia and Spitzer data. Section 5 provides some initial examples of science results enabled by CatWISE, and Section 6 provides information on accessing CatWISE data products. Appendices provide additional information on CatWISE column entries, cautions on known issues in the CatWISE Preliminary Catalog, and details on how positions were combined from alternating survey scan directions (Section 2). The CatWISE website is https://catwise.github.io.

2. Observations

WISE was launched on 2009 December 14, with its 40 cm telescope cooled to 12 K by an outer cryostat tank, and the W1 and W2 detectors operated at 32 K. The 12 and 22 μm (W3 and W4) detectors were cooled to 7.8 K by an inner cryostat tank. Both tanks were filled with frozen hydrogen. The cryostat cover was ejected and the first images obtained on 2009 December 31, and science survey data were taken starting on 2010 January 7.

WISE uses dichroics to image the same 47' × 47' region of sky simultaneously in all bands using 1024 × 1024 pixel arrays with 2farcs75 pixels, and obtaining exposures every 11 s. The duration of each W1 and W2 exposure is 7.7 s, due to readout time and scan mirror settling, and discarding the initial readout.

The Sun-synchronous polar WISE orbit was designed to precess so that the satellite stays over Earth's terminator. The basic WISE survey strategy is to point near the zenith, scanning at the orbital rate along lines of ecliptic longitude, with the image motion compensated by a scan mirror that flies back for the start of each exposure. The precession rate sweeps across the imaging field of view in approximately 12 orbits (less than one day) near the ecliptic, although the detailed survey strategy extends this time to more than a day. Because images are obtained on both sides of the orbit, the same region of inertial sky is covered every six months, with the direction of the survey scans alternating between ascending and descending in ecliptic latitude. CatWISE processes ascending and descending scans separately for source measurement.

The fully cryogenic survey continued until the hydrogen in the outer tank evaporated on 2010 August 6, exceeding the seven-month cryogen lifetime requirement and covering the sky 1.2 times (Figure 2). WISE then surveyed an additional 30% of the sky during its 3-Band (W1, W2, and W3) cryogenic phase, with the W3 detector operating at reduced sensitivity. After the cryogen in both tanks was exhausted on 2010 September 29, the post-cryogenic NEOWISE survey (Mainzer et al. 2011) in W1 and W2 began, as the telescope and detectors warmed to ∼73 K. Surveying continued until 2011 February 1, completing a second pass over the sky in W1 and W2, after which the satellite was placed into hibernation. In 2013 September, the spacecraft was brought out of hibernation, where it had equilibrated at ∼200 K due to thermal radiation from Earth, and renamed NEOWISE. On 2013 December 13, with the telescope and detectors passively cooled below 76 K, NEOWISE resumed surveying the sky every six months in W1 and W2 (Mainzer et al. 2014).

Figure 2.

Figure 2. Temperature of the WISE beamsplitter assembly vs. date. This temperature is close to that of the telescope and W1 and W2 detectors. Dashed lines indicate the transitions from full cryogenic to 3-Band cryogenic phases, to the post-cryogenic phase, and to the start of hibernation and reactivation. Gray shading indicates the date ranges of data used for the CatWISE Preliminary Catalog. AllWISE included only the left portion of the shaded range.

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The CatWISE Preliminary Catalog is based on the combination of W1 and W2 exposures in the two sky coverages used for the AllWISE data release (Cutri et al. 2013) and in the six additional sky coverages from the 2017 NEOWISE data release. For point-spread function (PSF) purposes (Section 3.2), we use MJD 55480 (2010 October 11) as the dividing point between cryogenic and post-cryogenic data. The average observation date is closer to MJD 56700 (2014 February 12), which we adopt as the epoch for reporting positions when solving for source motion in the Preliminary Catalog. Source positions, whether or not incorporating source motion, are given in the equinox J2000 coordinate frame. Magnitudes in the catalog and throughout this paper are on the Vega system.

3. CatWISE Processing

CatWISE adapts the AllWISE pipeline to detect and measure source fluxes in the combined WISE and NEOWISE images provided by unWISE. A full description of the AllWISE pipeline is provided in Cutri et al. (2013).

CatWISE processing works in the atlas tile footprint established by the WISE All-Sky Release, dividing the inertial sky into 18,240 overlapping square images (tiles), each approximately 1fdg56 on a side, aligned with the local R.A. and decl. Except for the "primary flagging" step (Section 3.6), processing steps were carried out independently on each tile. For the Preliminary Catalog, CatWISE uses the full-depth unWISE coaddition of eight epochs (Meisner et al. 2018b) and the eight individual unWISE epoch coadds (Meisner et al. 2018c; after astrometric modifications described in Section 3.1). The full-depth coadds and the PSF (Section 3.2) were used to create detection images. Sources were detected in these images (Section 3.3), while source properties were determined from measurements on the epoch coadds, treating ascending and descending epochs (Section 2) separately for most tiles and then merging the results (Section 3.4). Potential artifacts affecting the sources were identified (Section 3.5), and sources with multiple measurements because they were in the tile overlap region were flagged to indicate which set of measurements should be used (Section 3.6). Finally, sources were selected for inclusion in the catalog or reject files (Section 3.7). We describe these steps in more detail below.

3.1. unWISE Coadds

The coadded images in the atlas released with the AllWISE (and All-Sky) Catalogs were primarily intended to facilitate source detection, and for this reason they are convolved with the WISE PSF. The unWISE coadds retain the resolution of individual WISE exposures. To reduce differences from the AllWISE processing approach, for source detection (Section 3.3) in the CatWISE Preliminary Catalog, we convolved the masked version (Lang 2014) of the full-depth unWISE coadds (Meisner et al. 2018b) with the PSF (Section 3.2). For source measurement (Section 3.4), we used the masked version of the unWISE epoch coadds (Meisner et al. 2018c) without convolution.

An adjustment was made to the world coordinate system (WCS) for the pre-hibernation unWISE epoch coadds. Although all of the released individual exposures are tied to 2MASS (Skrutskie et al. 2006), the individual pre-hibernation exposures released for AllWISE are not on the same astrometric system as the individual post-hibernation exposures released for NEOWISE. The NEOWISE images include corrections for the motions of the 2MASS reference stars, as does the AllWISE Catalog (see Section V.2.b of the AllWISE Explanatory Supplement; Cutri et al. 2013), but the released pre-hibernation images do not include those corrections. A table of corrections for these images exists, however,17 and these corrections were applied to the unWISE input, making the astrometric system of the pre-hibernation epoch coadds consistent with those from the post-hibernation epoch coadds.

3.2. Point-spread Function

The WISE and NEOWISE PSFs have been well characterized at the individual exposure level, but CatWISE works with coadded images rather than individual exposures, so PSFs appropriate for these coadded images are needed. The W1 and W2 PSFs vary with position in the focal plane, and changed somewhat between the cryogenic and post-cryogenic phases of the mission, particularly for W1. The PSFs are also asymmetric, with an orientation that is fixed with respect to the focal plane, but the focal plane orientation with respect to equatorial coordinates varies between exposures. The focal plane orientation also flips every six months because at a given inertial location, the survey scan direction alternates between ascending and descending in ecliptic latitude (Section 2). CatWISE addressed these issues as follows.

A 9 × 9 grid over the focal plane of cryogenic phase model PSFs and their uncertainties, 8× oversampled relative to WISE pixels and covering 220'' on a side, is provided in Section IV.4.c.iii.1 of the WISE All-Sky Explanatory Supplement (Cutri et al. 2012). The post-cryogenic PSFs used for NEOWISE are given in Section IV.2.b.i of the NEOWISE Explanatory Supplement (Cutri et al. 2015). Because many focal plane positions contribute to each source in the coadded images, CatWISE averaged these model PSFs, weighted only by their partition sizes in the 9 × 9 grid. The uncertainty in the averaged PSF was taken to be the root sum square of two terms: the rms of the individual grid PSF uncertainties divided by $\sqrt{N-1}$, where N is the 81 PSFs, and the standard deviation of the grid PSFs about the averaged PSF. Figure 3 (left) shows the resulting focal plane average post-cryogenic PSF model for W1. An analogous focal plane average cryogenic PSF was created for W1, as well as average cryogenic and post-cryogenic PSFs for W2. These are referred to below as the "basic" PSFs.

Figure 3.

Figure 3. Left: the "basic" (averaged over focal plane position) post-cryogenic PSF model for W1. The grayscale uses a log stretch from 1% to 99% of the peak value. The model extends to ±110''. Center: the ascending scan W1 PSF for tile 1497p015 after averaging over cryogenic and post-cryogenic epochs, and a PA range from 199fdg93 to 200fdg56. This is illustrative of the type of PSF used by CatWISE for source measurement, with the exception of 50 tiles near the ecliptic poles. Right: the W1 PSF averaged over all scans for tile 0890m667, which includes the south ecliptic pole and all PAs. This is illustrative of the type of PSF used by CatWISE for source measurement for 50 tiles near the ecliptic poles.

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As can also be seen in the AllWISE PSF's plotted in Figure 1 of Lang et al. (2016), the PSFs contain fine structure in the core that is qualitatively consistent with the expected diffraction pattern for WISE. This structure is not rotationally symmetric. Figure 4 shows the difference between ascending and descending orientations of the W1 post-cryogenic PSF. The bright and dark stripes in and around the core correspond to variations of roughly 25% of the peak of the PSF. The center of the PSF is the most crucial region for position estimation, so inaccuracies in this part of the PSF have serious consequences for astrometry, as well as photometry.

Figure 4.

Figure 4. Difference image of W1 post-cryogenic PSFs in ascending vs. descending scans. The image extends to ±110''.

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These structures are not due to misalignment of the ascending and descending PSFs, which would need to be ∼1farcs0 to account for the features—far greater than the difference in astrometry from the ascending versus descending PSFs. For example, the median difference in source astrometry for tile 0895p227 (where ecliptic longitude and R.A. align) was 26.5 mas in ecliptic longitude, and 0.0 mas in ecliptic latitude. With the PSFs intentionally swapped, these values became −1216.0 mas in longitude and 633.6 mas in latitude. Over the sky, the tile median differences using the correct PSFs are distributed with a median value of 78.1 mas and σ = 33 mas in ecliptic longitude, and −14.4 mas and σ = 16 mas in ecliptic latitude.

The structure revealed here has no impact on the measurements carried out by the WISE and NEOWISE projects, because those measurements were made (and continue to be made) on individual exposures. The PSF structure is captured in the models, and the PSF orientation is always the same in the focal plane. This is not the case for CatWISE, which uses coadds in place of individual WISE exposures. The coadded image tile orientation is aligned with the local equatorial coordinates. Therefore, CatWISE rotated the basic PSFs by an appropriate set of position angles (PAs) between focal plane and equatorial coordinates for each image tile.

The coadded images were assembled from individual exposures with a range of PA values, so histograms of exposure PA values were constructed for each tile, using a bin width of 0fdg1. Separate histograms were constructed for ascending versus descending and cryogenic versus post-cryogenic exposures. The basic PSF was rotated by each PA bin center value, and these rotated PSFs averaged together with weights equal to the histogram bin count. Those averages were then combined for each tile with weights given by the number of corresponding cryogenic and post-cryogenic exposures to make ascending and descending PSFs for each tile.

Tiles in the vicinity of the ecliptic poles have large PA ranges, and so the tile PSF becomes very smeared (see Figure 3, right). For the 50 tiles nearest the ecliptic poles (listed in Table 1), the ascending and descending PSFs were averaged together, weighted by the number of ascending and descending exposures.

Table 1.  Tiles Processed Using a Single PSF per Band

R.A. Range in Decimal Degrees of Tiles in Column
79.1:87.9 89.0:95.7 96.2:264.2 265.0:272.1 272.6:280.8
0791m682 0890m667 0962m697 2650p681 2726p651
0803m652 0891m637 0964m667 2656p651 2729p681
0830m682 0908m652 0978m652 2672p666 2741p636
0837m697 0909m682 0988m682 2675p636 2746p666
0838m652 0920m697 1002m667 2679p696 2761p651
0853m667 0924m637 2610p681 2690p681 2762p696
0858m637 0927m667 2621p651 2691p651 2769p681
0870m682 0943m652 2635p666 2708p636 2783p666
0873m652 0949m682 2637p696 2709p666 2796p651
0879m697 0957m637 2642p636 2721p696 2808p681

Download table as:  ASCIITypeset image

The description above applies to the PSFs used by CatWISE for source measurement. For the detection step in the Preliminary Catalog (Section 3.3), PSFs analogous to the measurement PSFs of the 50 tiles nearest the ecliptic poles were created for every tile, but with 4× oversampling relative to the unWISE images, rather than the 8× oversampling of the measurement PSFs. These detection PSFs were made by resampling the central portion of the weighted average of ascending and descending PSFs for that tile. The detection PSFs have 27 × 27 pixels with each pixel spanning 0farcs6875, i.e., covering an area of 18farcs5625 on a side (6.75 native WISE pixels).

3.3. Detection

Source detection for the CatWISE Preliminary Catalog was done simultaneously in W1 and W2 with the Multiband Detection (MDET; Marsh & Jarrett 2012) and Image Co-addition with Optional Resolution Enhancement (ICORE) software18 (Masci & Fowler 2009) used in the WISE pipeline, following the process described in Section IV.4.b.iii.1 of the WISE All-Sky Explanatory Supplement (Cutri et al. 2012). The detection PSFs in each band were used as matched filters to generate images which are optimal for detection of isolated point sources in that band. ICORE generated the convolution (or more accurately, the cross-covariance) of the PSF with the full-depth unWISE coadd, resampling the 2048 × 2048 2farcs75 pixel unWISE coadds to the 4095 × 4095 1farcs375 pixel detection image format employed by MDET for WISE. The resampling was done using nearest-neighbor interpolation into a temporary finer grid matching the PSF grid, before being downsampled to the output pixel size. Similarly, ICORE created uncertainty images from the detection PSFs and the unWISE "std" images, which are the standard deviation of the individual exposures that comprise the unWISE full-depth coadds. MDET then subtracted a local background from each ICORE image using a 21 × 21 pixel median filter, normalizing the result by the ICORE uncertainty image. To account for confusion noise, the uncertainties were augmented by the root sum square of the estimated variance of the ICORE image from the local background. Finally, MDET generated a detection image from these normalized and background-subtracted ICORE images by summing the two bands in quadrature, identifying as the sources' local maxima (pixels with larger values than their neighbors) that exceeded a specified detection threshold.

As was done for WISE, the detection threshold was set at an estimated source reliability of ∼50%. AllWISE, with two sky coverages, selected a threshold of 2.4, compared to 3.5 used for the single-coverage WISE All-Sky Release. For CatWISE, we estimated the threshold based on comparison to deeper Spitzer data from the SERVS (Mauduit et al. 2012) and S-COSMOS (Sanders et al. 2007) programs. These programs have a source density of ∼100,000 deg−2, so with the matching radius of 2farcs5, the chance of a spurious match is not trivial (15%), but still well below the 50% criterion for the detection threshold. The estimated threshold varied from 1.7 in the COSMOS field to 2.6 in the Lockman Hole, and a value of 1.8 was selected for the Preliminary Catalog.

At the high source densities typical for CatWISE in coadds of ∼100 or more individual WISE exposures, this matched filter detection methodology yields an asymptotic number of ∼60,000 detected sources per tile for the Preliminary Catalog (or ∼25,000 deg−2, Figure 5) and hence becomes incomplete, particularly in W1. The detected source density declines slightly in the Galactic plane, for reasons not well understood at present. The limiting source density corresponds to an exclusion radius of 13''. This is similar to the decline in sources separated by less than 10'' shown in Figure 27 of Section VI.2.c.iv in the WISE All-Sky Explanatory Supplement (Cutri et al. 2012), and so is likely a consequence of the source-detection methodology used in the WISE pipeline. Schlafly et al. (2019) present an alternative approach ("crowdsource"), which results in higher detected source densities, but does not provide motion estimates. We are using the Schlafly et al. (2019) catalog as the detection list for an updated version of the CatWISE catalog (CatWISE2020). The completeness and reliability of the CatWISE Preliminary Catalog are discussed further in Section 4.1.

Figure 5.

Figure 5. Map of CatWISE Preliminary Catalog source density in Galactic coordinates.

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3.4. Source Measurement

Source photometry, astrometry, and motion estimation for CatWISE use an adapted version of the WPHOT software developed for the AllWISE pipeline. WPHOT carries out point-source extraction, solving for both photometry and astrometry simultaneously. Source positions detected in each coadded tile image were propagated to individual exposures, and the flux and χ2 evaluated from fitting the PSF. The source position and flux were refined by searching for a local minimum in χ2. For AllWISE, a linear motion was also solved for, based on the observation time of the images.

CatWISE did not have the computational resources to perform the source fitting on all of the many hundreds of individual exposures that contribute to a coadded tile image. Because the  12 exposures for a given inertial position in each sky coverage are obtained within less than two days, the motions of sources beyond the solar system can be assumed to be fixed for each sky coverage (or epoch). Therefore, CatWISE ran WPHOT treating unWISE epoch coadd images as the individual images.

The other significant modification to the AllWISE WPHOT process implemented by CatWISE addressed the alternating scan direction of each epoch and hence varying PSF orientation. WPHOT was not designed to use a time-dependent PSF, but with eight or more epoch coadd images per position, CatWISE elected to measure source properties with WPHOT separately for the groups of four or more epoch coadds in each of the two scan directions, and then merge the two results. This methodology was used for all but the 50 tiles nearest the ecliptic poles, listed in Table 1. For those tiles, a tile-specific average PSF over all epochs was used for both scan directions, and all epochs were processed together with WPHOT.

WPHOT performs PSF-fit photometry and astrometry assuming sources are inertially fixed (the "stationary fit"), and also searches for a solution assuming a linear motion with time (the "motion fit"). The χ2 minimization fit can be performed at any location in the flux image. The goal of astrometry is to find the location at which χ2 has a local minimum.

The stationary fit uses the gradient descent method to minimize the total χ2 (i.e., the combined W1 and W2 χ2) in the two-dimensional space of R.A. (α) and decl. (δ). As one moves around in the space, χ2 decreases and increases as the local flux distribution appears more or less like a point source. The (α, δ) where χ2 is estimated to be minimal is the position assigned to the source, and the scale factor on the PSF that minimizes χ2 there is the flux estimate. The value of χ2 is recorded, as are the individual χ2 for the W1 and W2 flux fits. Under certain conditions such as low coverage or negative fluxes, the gradient descent algorithm may be unable to compute estimates, in which case nulls are reported. Standard Gaussian error analysis provides uncertainties for (α, δ) and flux. The error model includes both PSF error and image flux error, and is discussed further in Section 3.4.1. More details on WPHOT are given in Section IV.4.c.iii of the WISE All-Sky Explanatory Supplement (Cutri et al. 2012).

The model used for the motion solution replaces the single location of the stationary solution with locations along a linear function of time. The slopes of this line in the (α, δ) directions are the angular motion rates (μα, μδ) in (α, δ). The motion fit minimizes the total χ2 over the four-dimensional space of $(\alpha ,\delta ,{\mu }_{\alpha },{\mu }_{\delta })$. When the motion fit is based on both ascending and descending epochs, the motions will include parallax effects (see Kirkpatrick et al. 2014), and so they are not true proper motions. However, except for the 50 tiles near the ecliptic poles, CatWISE processed ascending and descending scans separately, so that the measured motions are close to true proper motions.

3.4.1. Uncertainties

WPHOT estimates uncertainties in photometry, position, and motion based on error propagation from uncertainty images corresponding to the PSF and exposure images. The PSF uncertainty images from WISE and NEOWISE appropriate to each PSF were combined using the methodology described in Section 3.2, and these dominate the uncertainties estimated for brighter stars (≲12 mag). For fainter sources (≳15 mag), the exposure image (or for CatWISE, epoch image) uncertainties dominate. For these, the "std" unWISE images were used, which are the sample standard deviation at each pixel of the individual WISE exposures divided by $\sqrt{N-1}$, where N is the number of exposures.

Reduced χ2 values from the CatWISE PSF-fitting measurements showed that the uncertainties needed adjustment. The PSF uncertainties were scaled down by 0.9 in W1 and 0.64 in W2 based on bright star reduced χ2 values. Cryogenic PSF uncertainties for W1 were scaled down by an additional factor of 0.58. Based on faint star reduced χ2 values, the image uncertainties were scaled up by 1.4 in W1 and 1.15 in W2, and those for pre-hibernation epochs were scaled up by additional factors of 1.1 in W1 and 1.05 in W2. The units of the unWISE images are Vega nanomaggies (nMgy), i.e., 0.306681μJy for W1 and 0.170663μJy for W2 (Wright et al. 2010), and a minimum value of 1 nMgy in W1 and 10 nMgy in W2 was also imposed on the image uncertainties.

The uncertainties for the 50 tiles near the ecliptic poles, which used averages of ascending and descending PSFs (Section 3.2) had somewhat different adjustments. For these tiles, the PSF uncertainties were scaled up by 1.3 in W1, with no further adjustment for cryogenic values, and were left unchanged for W2. The image uncertainties were scaled up by 1.75 in W1 and 1.25 in W2, and those for pre-hibernation epochs were scaled up further by 1.1 in W1 and 1.05 in W2. A minimum value of 1 nMgy in W1 and 5 nMgy in W2 was imposed on the image uncertainties.

3.4.2. Merging Measurements from Ascending and Descending Scans

As noted earlier, for nearly all tiles, two independent measurements were made, one extracted from epoch coadds constructed from ascending scans and one from descending-scan epochs. These were merged into a single source list as follows.

Sources were matched based on their identifier in the detected source list (Section 3.3). A small number of mismatches occurred because of active deblending in WPHOT. Active deblending inserts a new source (not from the detection program) into the fitting region if the χ2 value exceeds a threshold and is reduced by the insertion by a minimum required amount. Full details may be found in Section IV.4.c of the WISE All-Sky Explanatory Supplement (Cutri et al. 2012). Actively deblended sources have the same identifier as the parent source in the detection list. Because active deblending may proceed differently in the ascending and descending data, when the identifier was not unique, a nearest-match criterion was also applied. If the number of ascending sources did not equal the number of descending sources, the leftover sources were discarded, leaving a one-to-one association list.

Corresponding parameters for each matched ascending–descending source pair were combined when the ascending and descending apparitions have non-null values (Section 3.4), otherwise the single non-null values (if any) were retained. Aperture magnitudes for the ascending and descending scans were measured from the same full-depth coadd, differing only slightly in the position of the aperture centers. Hence, the fluxes and flux uncertainties corresponding to the aperture magnitudes and their uncertainties were simply averaged without weighting. Positions were averaged using inverse-covariance weighting, with the averaging done in a local Cartesian projection consistent with the uncertainty representation. Additional details are provided in Appendix C. PSF-fit photometry was combined by averaging the flux values using inverse-variance weighting. This yields refined flux values and reduced uncertainties that are used to recompute the magnitudes, magnitude uncertainties, and signal-to-noise ratios.

3.5. Artifact Flagging

Bright stars create a variety of scattered-light effects and electronic charge issues that require special handling by the software. These effects include scattered-light halos, diffraction spikes, glints from off-frame bright stars, optical ghosting from internal reflections within the optical system, and charge persistence on the arrays. These can create false detections, hereafter called artifacts, or can contaminate detections of real, astrophysical sources. The goal of artifact flagging is to label spurious or affected sources so that the user can easily create source lists for which most of these problems are eliminated.

The CatWISE Preliminary Catalog employs two types of artifact flagging. One is the cc_flags values copied directly from AllWISE processing. If a source was found in either the AllWISE Catalog or Reject Table within 2farcs75 of a CatWISE source, its cc_flag was included in the entry for the CatWISE source; if no AllWISE source was found within this radius, then cc_flags contains a null value. For a CatWISE source having multiple AllWISE sources within the $2\buildrel{\prime\prime}\over{.} 75$ radius, the most pessimistic value per band was retained, as described in Section 3.5.1. These cc_flags values indicate whether a source is likely to be spurious because it is dominated by an artifact (encoded as an upper-case letter) or is a real source contaminated by an artifact (encoded as a lower-case letter). Each of the four characters in cc_flags corresponds to artifacts in one of the four WISE bands, so the first two characters are most relevant for CatWISE, which does not include W3 or W4 data. The possibilities are "0" for no artifact or contamination, "D" or "d" for a diffraction spike, "H" or "h" for a scattered-light halo, "O" or "o" for an optical ghost, or "P" or "p" for charge persistence. The cc_flags field conveys only the main features of the full artifact flag information contained in the AllWISE $w1{cc}\_{map}$, $w1{cc}\_{map}\_{str}$, $w2{cc}\_{map}$, and $w2{cc}\_{map}\_{str}$ fields,19 which are also provided in the CatWISE source entry. A more detailed description can be found in Section IV.4.g of the WISE All-Sky Explanatory Supplement (Cutri et al. 2012).

The second type of artifact flag is called ab_flags, which was determined for every CatWISE source and is based on artifact flagging images provided by unWISE (unWISE bit masks; Meisner et al. 2019b). The ab_flags do not attempt to distinguish between an outright artifact and a real astrophysical source that suffers from some level of artifact contamination, but are set so that only egregious artifacts more likely to be spurious detections are flagged. By analogy with cc_flags, the ab_flags thus contain only upper-case letters "D," "H,""O," or "P" or the value "0." Furthermore, because the CatWISE data deal only with W1 and W2 data, the ab_flags values are only two characters long. Additional details are given in Section 3.5.2.

Figure 6 shows examples of both types of artifact flags. These cc_flags and ab_flags values should be regarded as two different yet complementary methods for tagging sources of special concern to the user. As described in Section IV.4.g of the WISE All-Sky Explanatory Supplement (Cutri et al. 2012), the cc_flags are known to overflag; their purpose is to produce a reliable catalog of source extractions free of contamination by artifacts, but they do so at the expense of completeness. AllWISE cc_flags are not available for sources detected only in CatWISE, so requiring a source to have "0" in its cc_flags entry again emphasizes reliability over completeness. In contrast, the ab_flags, which are available for every CatWISE source, are used to tag only the more egregious artifacts, thereby emphasizing completeness, albeit at the expense of reliability. Users of the CatWISE data products can thus query against these two sets of artifact flags to best fit their needs.

Figure 6.

Figure 6. Example artifact flags for 16farcm× 13farcm0 cutouts in W1 (top) and W2 (bottom) from the tile 1497p015. Detected CatWISE sources are shown by the small cyan circles. Sources with upper-case cc_flags are marked with large red circles, and sources labeled as artifacts by ab_flags are marked in medium-sized blue circles.

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3.5.1. Setting the cc_flags Values when there Are Multiple Matches

The values of cc_flags were taken directly from the AllWISE Point Source Catalog and Reject Table. When more than one of these AllWISE sources matched to within 2farcs75 of a CatWISE source, the band-by-band cc_flags value of the CatWISE source was determined as follows. If there was an upper-case letter for any matching source, it took precedence over any lower-case letter. The letter "D" is the highest priority followed, in order, by "P," "H," and "O." If there were no upper-case letters for any matching source, lower-case letters had the next highest priority, in the same order ("d," "p," "h," and "o"). If all matching sources had a value of "0" in that band, then "0" was used.

For the binary bit encoding of AllWISE artifacts given by ${\rm{w}}1{\rm{cc}}{\rm{\_}}{\rm{map}}$ and ${\rm{w}}2{\rm{cc}}{\rm{\_}}{\rm{map}}$, when there was more than one AllWISE match to a CatWISE source, a logical "OR" was performed over all the matches for each bit. The ${\rm{w}}1{\rm{cc}}{\rm{\_}}{\rm{map}}{\rm{\_}}{\rm{str}}$ and ${\rm{w}}2{\rm{cc}}{\rm{\_}}{\rm{map}}{\rm{\_}}{\rm{str}}$ values were then constructed using the priority rules given in the previous paragraph.

3.5.2. Translating the unWISE Bit Mask Values to ab_flags

The unWISE bit mask values at the (x, y) pixel location of the source were used to set the value of ab_flags, as shown in Table 2, where we use the prefix "b" to indicate specific unWISE mask bits in column 3. Bits 0–3 and 7–8 are related to a nearby bright star; bits 11, 12, 25, and 26 indicate optical ghosts; bits 13–20 flag charge persistence; bits 23 and 24 mark halos; and bits 27–30 are for diffraction spikes. The checks against bits 21 and 22 are to ensure that the bright star is not flagged by its own diffraction spikes or scattered-light halo. A complete description of the unWISE mask bits is given in Meisner et al. (2019).

Table 2.  Logic Used in Converting unWISE Bit Mask Values to ab_flags Values

Value Band Logic
"D" W1 b0 or b1 or b7 or b27 or b29 but only if not b21
W2 b2 or b3 or b8 or b28 or b30 but only if not b22
"H" W1 b23 but only if not b21
W2 b24 but only if not b22
"O" W1 b25 or b26
W2 b11 or b12
"P" W1 b13 or b14 or b17 or b18
W2 b15 or b16 or b19 or b20

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In addition to the ab_flags field, the CatWISE catalog includes fields with detailed artifact flag information (${\rm{w}}1{\rm{ab}}{\rm{\_}}{\rm{map}}$, ${\rm{w}}1{\rm{ab}}{\rm{\_}}{\rm{map}}{\rm{\_}}{\rm{str}}$, ${\rm{w}}2{\rm{ab}}{\rm{\_}}{\rm{map}}$, and ${\rm{w}}2{\rm{ab}}{\rm{\_}}{\rm{map}}{\rm{\_}}{\rm{str}}$) for each source, analogous to the similar fields providing detailed artifact information related to cc_flags.

3.6. Duplicate Source Measurements

WISE tiles, and, therefore, unWISE coadds, overlap each other by ∼3' on the equator. As a result, sources appearing near the edge of a tile will also be measured in neighboring tiles. To remove these duplicate measurements, we adopted the approach used by Schlafly et al. (2019). For each source in a tile, its coordinates were used to calculate the minimum distance to the edge of the tile. The same coordinates were used to calculate the minimum distance to the edge for all neighboring tiles, and the source was flagged as "primary" if these other minimum distances were all smaller.

3.7. The CatWISE Preliminary Catalog

With the necessary flagging in place, catalog generation could proceed. CatWISE Preliminary Catalog sources are required to:

  • (1)  
    be from the tile where that source is farthest from the tile edge (i.e., flagged as "primary," Section 3.6) and
  • (2)  
    have W1 signal-to-noise ratio (S/N) ≥ 5 with no identified artifacts (a value of 0 in the left character of ab_flags) or
  • (3)  
    have W2 S/N ≥ 5 with no identified artifacts (a value of 0 in the right character of ab_flags).

There are 900,849,014 sources that meet these criteria. The 167,831,546 sources that fail to meet these criteria go into the reject file for their tile. Individual tile reject files typically contain 8000 sources, although near the celestial poles, they can contain over 30,000 sources due to large tile overlap. There are 186 formatted columns of information about each source in the tile catalog files. Reject files have one additional column, indicating if the source is primary in its tile. Descriptions of most of the columns are available in Section II.1.a of the AllWISE Explanatory Supplement (Cutri et al. 2013), and Appendix A provides additional information about CatWISE columns.

The individual Preliminary Catalog and reject files for the 18,240 tiles were transferred to the NASA Infrared Science Archive (IRSA), where they were merged into the IRSA database. Four columns (with names in italics in Table A1) were removed from view by IRSA, for reasons explained in that table. Information regarding access to the catalog is provided in Section 6.

CatWISE source designations should have the prefix CWISEP for objects in the CatWISE Preliminary Catalog and CWISEPR for objects in the CatWISE Preliminary Reject Table. The designation for each source, based on its coordinates for the J2000 equinox following the IAU truncation convention and without the leading CWISEP or CWISEPR prefix, is given by the field source_name, which is the first column in the files. For example, the quasar 3C 273 is CWISEP J122906.70+020308.6.20

4. Performance Characterization

The greatest potential for improvement of the CatWISE Preliminary Catalog over existing WISE catalogs is in providing more accurate motion measurements, due to the much longer time baseline compared to AllWISE. Hence, characterization has focused on astrometric properties of the Preliminary Catalog. Photometric depth is also improved due to the four times larger number of exposures than AllWISE. Characterization has emphasized comparison to external truth sets, using Spitzer for photometric comparisons including completeness and reliability, and Gaia for astrometric comparisons. We begin with the photometric assessments.

4.1. Completeness and Reliability

4.1.1. Bright Sources

CatWISE completeness and reliability for sources with W1 or W2 < 8 mag were assessed using an updated version of the WISE Bright Star List (BSL) as a truth set. The list was generated by the WISE team for artifact flagging (see Section 4.4.g.vi in the WISE All-Sky Release Explanatory Supplement; Cutri et al. 2012). To avoid degradation of completeness or reliability due to missed matches for fast-moving sources, astrometric information for sources moving faster than 0farcs275 yr−1 was added to the BSL to propagate the positions of such stars to the CatWISE epoch. Astrometric information was taken from Gaia DR2 (Gaia Collaboration et al. 2018; Lindegren et al. 2018) or, when not available (given Gaia's known incompleteness for bright stars) from the Hipparcos main catalog (van Leeuwen 2007), the Luyten Half-Second catalog (Bakos et al. 2002), or the Gliese–Jahreiß catalog (Stauffer et al. 2010).

CatWISE completeness was determined as the percentage of sources that have astrometric matches in CatWISE as a function of BSL magnitude. Differential CatWISE reliability was determined as the percentage of sources that have astrometric matches in the BSL as a function of CatWISE magnitude. We used a relatively large matching radius of 5farcs5 (corresponding to two WISE pixels) to account for the poorer centroiding accuracy expected for highly saturated sources.

Figure 7 shows the results for completeness, compared to those from AllWISE. CatWISE achieves ∼99% completeness in the BSL W1 ∼ 5.5–8 mag and BSL W2 ∼ 5–8 mag ranges, slightly lower than AllWISE. For reasons that we have not investigated, CatWISE completeness drops for brighter stars, falling to ∼50% by W1 ∼ 4.3 mag and W2 ∼ 3.6 mag. AllWISE completeness remains above 90% even for stars as bright as 0.25 mag, making it preferable to CatWISE for investigations of the brightest stars.

Figure 7.

Figure 7. Differential completeness of the CatWISE Preliminary Catalog as a function of the Bright Star List's W1 (left) and W2 (right), compared to AllWISE.

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CatWISE reliability is ∼99% for W1 ∼ 4.8–8 mag and W2 ∼ 4.5–8 mag, somewhat better than AllWISE, as can be seen in Figure 8. (For sources without artifacts in either CatWISE or AllWISE, the median (CatWISE – AllWISE) value over the 2.5–8 mag range is 0.17 mag in W1 and 0.02 mag in W2, and the median absolute deviation from the median is 0.08 mag in W1 and 0.02 mag in W2). Even though completeness falls rapidly for brighter stars, CatWISE reliability is ∼90% or better down to 2.5 mag. For the brightest stars, CatWISE completeness is poor, and CatWISE reliability shows large fluctuations due in part to the resulting small number statistics.

Figure 8.

Figure 8. Differential reliability of the CatWISE Preliminary Catalog as a function of the Bright Star List's W1 (left) and W2 (right), compared to AllWISE. Not shown are points at W2 = −0.75 mag and +0.75 mag with reliabilities of 0 and 0.5 respectively.

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4.1.2. Faint Sources

Completeness and reliability were assessed for faint sources using the Spitzer South Pole Telescope Deep Field (SSDF) survey (Ashby et al. 2013) as a truth set. The SSDF covers ∼94 deg2 with 2 minutes of integration per position with Spitzer. WISE survey depth increases toward the ecliptic poles, and for the SSDF, with β ∼ −46°, the typical number of CatWISE exposures is 125, or 16 minutes. Nevertheless, the larger Spitzer mirror diameter (85 cm versus 40 cm for WISE) and better image quality (2'' versus 6'') make the SSDF data more sensitive than CatWISE.

The radius used to match Spitzer SSDF sources with CatWISE sources was 2farcs5; otherwise, the methodology to determine completeness and reliability was the same as in Section 4.1.1. The results are shown in Figures 9 and 10.

Figure 9.

Figure 9. Completeness of the CatWISE Preliminary Catalog vs. Spitzer 3.6 μm (left) and 4.5 μm (right) magnitude for sources in the SSDF.

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Figure 10.

Figure 10. Reliability of the CatWISE Preliminary Catalog as a function of W1 (left) and W2 (right), for sources in the SSDF.

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At this coverage depth, the CatWISE Preliminary Catalog completeness is ∼98% for sources brighter than 13th mag, consistent with the performance seen from comparisons to the Bright Star List (Section 4.1.1), and remains above 90% for sources brighter than [3.6] = 16 mag or [4.5] = 15.5 mag, dropping to 50% at [3.6] = 17.8 mag and [4.5] = 17.4 mag. The SSDF achieves 55% completeness at [3.6] = 18.5 mag and [4.5] = 18.0 mag (Ashby et al. 2013).

CatWISE reliability at this coverage depth is better than 99% for sources brighter than 15th mag in both W1 and W2, again consistent with the Bright Star List results. CatWISE reliability remains above 90% to W1 = 18.2 and W2 = 17.6 for this ecliptic latitude and coverage depth. Reliability at fainter magnitudes is not well determined because the SSDF data are not deep enough.

4.2. Photometric Properties

We assessed CatWISE photometric depth using both the SSDF (Section 4.1.2) and the COSMOS field. The COSMOS field is an important benchmark for assessing CatWISE performance, because it has been intensively observed, is near the ecliptic (β = −11°), and is at fairly high Galactic latitude (b = 41°). Although confusion effects are reduced by the high Galactic latitude, the ecliptic has the highest zodiacal emission and lowest survey coverage from WISE, making COSMOS a representative base for performance estimates.

Figure 11 compares the CatWISE Preliminary Catalog PSF-fitting photometry to the 2farcs9 radius aperture photometry from the Spitzer S-COSMOS program (Sanders et al. 2007). These observations were obtained using longer integration times (20 minutes) than for the SSDF, while the CatWISE integration is lower (12 minutes) than in the SSDF, so the S-COSMOS data are much deeper than CatWISE. The closest CatWISE source within 2farcs75 was taken as the match to the S-COSMOS source. Because the CatWISE photometry is point-source fitting, S-COSMOS sources were required to have <10% flux increase between the 1farcs9 and 2farcs9 radius apertures. In addition, because the W1 band is significantly bluer than the [3.6] band, S-COSMOS sources at [3.6] were required to have −0.1 ≤ [3.6] – [4.5] ≤ 0 (see Figures 2 and 3 in Section VI.3.a of the All-Sky Explanatory Supplement; Cutri et al. 2012). While necessary for comparing W1 and [3.6] photometry, the color cut significantly reduces the numbers of sources for comparison. Figure 12 gives the analogous comparison to photometry from the SSDF survey.

Figure 11.

Figure 11. Comparison of CatWISE photometry to Spitzer photometry for COSMOS. Left: difference between CatWISE W1 PSF and Spitzer S-COSMOS 2farcs9 radius aperture photometry at [3.6], for sources with −0.1 < [3.6] – [4.5] < 0 and < 10% flux increase from the 1farcs9 to 2farcs9 aperture. Median differences and standard deviations in 0.5 mag bins are shown by the red points and error bars. Right: the analogous comparison for CatWISE W2 and Spitzer [4.5] photometry, but without the restriction on Spitzer source color.

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Figure 12.

Figure 12. Comparison of CatWISE photometry to Spitzer photometry for the SSDF, using the same methodology as in Figure 11. The outer contour represents a source density of 10 sources per 0.05 × 0.05 mag bin, with each additional contour showing a factor of 2 increase in source density. Note the three additional contour levels on the right, due to the lack of the color cut used on the left.

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The comparison between the CatWISE and Spitzer photometry is consistent for both fields, in both bands. CatWISE photometry becomes ∼0.1 mag fainter than Spitzer beyond 16th mag, possibly due to the increasing incidence of extragalactic sources at faint magnitudes. The measured scatter in the SSDF reaches 0.217 mag, equivalent to an S/N of 5, at [3.6] = 17.64 mag and [4.5] = 16.49 mag. Adjusting for the mean offsets in W1 – [3.6] and W2 – [4.5] at these magnitudes, and subtracting 0.14 mag to adjust the SSDF 125 exposure depth to the 96 exposure depth that we take as the baseline for the CatWISE Preliminary Catalog, we find that the S/N = 5 limits for CatWISE are W1 = 17.67 mag and W2 = 16.47 mag.

4.3. Astrometric Properties

4.3.1. Full-sky Astrometric Assessments

The astrometric performance of CatWISE was assessed by comparing to Gaia DR2 (Gaia Collaboration et al. 2018; Lindegren et al. 2018). Within each tile, the 10 brightest sources in bins of 0.5 mag over the 10 < W1 < 17.5 mag range were selected, providing a sample of 150 sources per tile, uniformly distributed on the sky. At low Galactic latitudes, CatWISE does not reach to W1 = 17.5 mag, and therefore the faintest bins are empty. The sample for astrometric comparison consists of 2,699,315 sources. These sources were cross-matched with Gaia DR2 using a 5farcs5 radius (corresponding to two WISE pixels), requiring the Gaia counterpart to have measured proper motions. This returned 2,148,274 unique matches. The completeness of the match approaches 100% for sources brighter than W1 = 14 mag and drops to ∼25% at the faintest magnitudes. Gaia astrometry was used to propagate the Gaia counterparts to the CatWISE epoch, and the standard deviation21 between the CatWISE motion fit and Gaia position and motion values was computed.

Figure 13 summarizes the results of the full-sky comparison. The positional accuracy floor for bright sources approaches ∼50 mas and remains approximately constant until W1 ∼ 12.5 mag. At fainter magnitudes, the dispersion increases to 275 mas (1/10 of a pixel) at W1 ∼ 15.5 mag, while in the faintest magnitude bin, the dispersion is ∼700 mas, with the dispersion in α being slightly better than in δ. This is expected because the scan direction is closer to δ, and the PSF is more elongated in the scan direction. At the bright end, however, the accuracy in δ is better than in α, an effect not fully understood.

Figure 13.

Figure 13. CatWISE astrometric performance with respect to Gaia DR2. Left: the 1σ dispersion between CatWISE and Gaia R.A. (specifically, Δα cos(δ)) and decl. (top) and proper motion (bottom), for a subsample of ∼2.1 million sources in the 10 < W1 < 17.5 mag range, uniformly distributed over the entire sky. Right: the median χ2 computed taking into account CatWISE catalog uncertainties, Gaia catalog uncertainties, and the uncertainty introduced by the translation of Gaia's positions to the CatWISE epoch.

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The motion accuracy floor for bright stars is just under 10 mas yr−1, consistent with the positional accuracy floor—given CatWISE's 6 yr baseline, and because the motion accuracy scales linearly with time, one would expect ${\sigma }_{\mu }\sim {\sigma }_{\mathrm{pos}}/6$. At W1 ∼ 15.5 mag, the motion accuracy is ∼30 mas yr−1, a factor of 10 better than AllWISE (Kirkpatrick et al. 2014). At the faint end, CatWISE is sensitive to proper motion of 100 mas yr−1 until W1 ∼ 17 mag.

The two panels on the right of Figure 13 show the χ2 computed using the CatWISE catalog uncertainties, the Gaia catalog uncertainties, and the uncertainty introduced by the translation of the Gaia position to the CatWISE epoch. Because the total uncertainty is dominated by CatWISE, these χ2 values are essentially a measurement of how accurate the CatWISE Preliminary Catalog uncertainties are. The expected value of the median χ2 with one degree of freedom is ∼0.45, so the top-right panel of Figure 13 indicates that the catalog position uncertainties underestimate the actual errors by a factor of 2.5–3. In contrast, the motion uncertainties are consistent with the expected value. We have not investigated the reason for this, although it suggests an additional error in position that is stable for a given source. Confusion is one possible explanation. Although the uncertainties are underestimated, the actual CatWISE position errors are comparable to those for AllWISE (see Section II.5.c of the AllWISE Explanatory Supplement; Cutri et al. 2013).

The astrometric performance is, however, not uniform over the sky. Figures 1417 show the 1σ dispersion in each tile with respect to Gaia positions and motion components for the full magnitude range considered (Figures 14 and 16) and in three smaller magnitude intervals (Figures 15 and 17). The maps for the full magnitude range are smooth overall, indicating a fairly constant astrometric performance for CatWISE over the majority of the sky. The main features can be easily identified—the Galactic plane (and in particular the bulge), and the Small and Large Magellanic Clouds (SMC and LMC). In those denser regions, the astrometric accuracy for the bright stars deteriorates to ∼500 mas for positions and ∼30 mas yr−1 for motions, and to ∼1000 mas and ∼200 mas yr−1 (or worse) for the faint stars.

Figure 14.

Figure 14. 1σ dispersion of the CatWISE α (left) and δ (right) with respect to Gaia DR2, for sources in the 10 < W1 < 17.5 mag range.

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Figure 15.

Figure 15. Same as Figure 14, but for three W1 magnitude ranges. Gray tiles are those where there were no sources in CatWISE in the given magnitude bin.

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Figure 16.

Figure 16. Same as Figure 14, but for the proper motion components.

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Figure 17.

Figure 17. Same as Figure 16, but for three W1 magnitude ranges. Gray tiles are those where there were no sources in CatWISE in the given magnitude bin.

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The motion accuracy maps show additional features that appear to be related to the WISE survey strategy and to the transition between the cryogenic and post-cryogenic phases of the mission. In particular, one can see better motion performance approaching the ecliptic poles (at l = 96°; b = 30° and l = 276°; b = −30°, respectively) compared to regions of similar Galactic latitude. This is a result of the increased coverage of the sky by WISE at higher ecliptic latitude. Conversely, there are two strips of slightly poorer motion performance, which are coincident with the transition between cryogenic and post-cryogenic phases, where the PSF was changing rapidly as the telescope was warming up.

The maps for the faintest magnitude interval appear noisy. This is partly intrinsic, and partly an effect of statistical fluctuations due to the low number of sources with a Gaia counterpart in each tile (as discussed above, the completeness for the Gaia match drops to ∼25% at the faint end). Moreover, at lower Galactic latitudes, CatWISE detects only brighter sources because of confusion noise.

4.3.2. Astrometric Assessments in Selected Tiles

We next consider the astrometric performance in more detail by focusing on four tiles:

  • 1.  
    the North Ecliptic Pole tile (NEP, tile 2709p666), a field with maximal WISE coverage and average source density;
  • 2.  
    the South Ecliptic Pole tile (SEP, tile 0890m667), a field with maximal WISE coverage and high source density (the SEP tile contains part of the LMC);
  • 3.  
    the Galactic Center tile (GC, tile 2657m288), a field with average WISE coverage and maximal source density; and
  • 4.  
    the COSMOS tile (tile ID 1497p015), representative of most of the sky, i.e., a field with average WISE coverage and source density.

The analysis of Section 4.3.1 was repeated for these four tiles, but using all of the sources in each tile. The results are shown in Figures 18 and 19. We then defined 10 metrics to characterize the astrometric performance of CatWISE:

  • 1.  
    σmin and σμ,min are the accuracy floor for positions and motions, respectively. These accuracy floors are determined as the median dispersion with respect to Gaia in the 8 < W1, W2 < 10 mag interval, except in the GC where we restrict to 8 < W1, W2 < 9 mag because the astrometric accuracy starts deteriorating significantly beyond W1, W2 ∼ 9 mag (see Figures 1819).
  • 2.  
    W1min, W2min, W1μ,min, and W2μ,min are the W1 and W2 mag at which σmin and σμ,min are exceeded by no more than 20 mas and 5 mas yr−1, respectively.
  • 3.  
    W1500 and W2500 are the W1 and W2 mag at which the accuracy on positions reaches 500 mas.
  • 4.  
    W1μ,100 and W2μ,100 are the W1 and W2 mag at which the accuracy on motion reaches 100 mas yr−1.

Figure 18.

Figure 18. Same as Figure 13, but for four tiles: the SEP (0890m667), COSMOS (1497p015), the GC (2657m288), and the NEP (2709p666). The standard deviation between CatWISE position measurements and Gaia DR2 position measurements, and the corresponding χ2 in 0.5 mag bins, is shown in red (R.A.) and blue (decl.).

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Figure 19.

Figure 19. Same as Figure 18, but for motion measurements.

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The results for the four representative tiles are summarized in Table 3.

Table 3.  CatWISE Astrometric Performance Evaluation Fields

  0890m667 1497p015 2657m288 2709p666
  SEP, LMC COSMOS GC NEP
l (deg) 276.5 237.3 359.8 96.4
b (deg) −30.2 41.4 0.6 29.5
β (deg) −89.6 −10.2 −5.4 89.6
Exp. 7154 90 86 7839
# 71462 58961 63368 61702
σmin (mas) 52.9 27.3 526.4 37.7
W1min (mas) 11.0 12.5 8.0 12.0
W1500 (mag) 15.1 17.0 8.4 18.5
W2min (mag) 11.0 12.5 8.0 12.0
W2500 (mag) 15.0 16.8 8.3 19.0
σμ,min (mas yr−1) 7.4 8.5 22.2 7.3
W1μ,min (mag) 14.5 13.5 9.0 15.5
W1μ,100 (mag) 18.2 16.8 >11.0 >19.0
W2μ,min (mag) 14.5 13.5 9.0 15.5
W2μ,100 (mag) >20.5 16.7 >11.5 >20.0

Note. l, b, and β are the Galactic longitude, Galactic latitude, and ecliptic latitude for the center of the tile, in degrees. Exp. indicates the number of exposures for the tile, # the number of sources (combining catalog and reject entries). The subsequent metrics are described in detail in Section 4.3.

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For brighter sources, σmin and σμmin are encouragingly small, on the order of 40 mas and 8 mas yr−1, respectively. W1min and W2min are ∼12 mag while W1μ,min and W2μ,min are ∼14.5 mag. All the above metrics show little dependence on coverage and source density, except for the GC tile, where they are degraded to σmin ∼ 530 mas, ${\sigma }_{\mu ,\min }\sim 20$ mas, at a limiting depth of only ∼8 mag and ∼9 mag, respectively. This is consistent with the uniformity of the maps in Figures 1417.

For fainter sources, W1500, W2500, W1μ,100 and W2μ,100 show a clearer dependence on source density and coverage. For COSMOS (i.e., a typical CatWISE tile), these metrics are ∼17 mag. W1500 and W2500 become ∼9 mag shallower in the GC, while W1μ,100 and W2μ,100 measurements are upper limits only. This is again a consequence of the fact that at lower Galactic latitudes, CatWISE only detects brighter sources because of confusion noise, and for sources this bright, the motion accuracy never degrades to the 100 mas yr−1 level.

W1μ,100 and W2μ,100 become ∼2 mag deeper (∼19 mag) at the ecliptic poles, thanks to the higher coverage. W1500 and W2500 are much deeper at the NEP than the SEP, most likely an effect of the much higher source density at the SEP, and therefore the higher confusion noise. However, this does not seem to affect the motion metrics.

4.3.3. Fast Movers

We compared the astrometric performance using merged results from the ascending and descending scans processed with separate PSFs to that using a single PSF per band for all scans processed together (see Section 3.4) on a set of 19 known ultracool dwarfs, chosen from the literature. Our test set included extremely cold, very fast-moving objects (e.g., WISE J085510.83–071442.5, μtot ∼ 8 arcsec yr−1; Luhman 2014), as well as warmer, slower M dwarfs (e.g., WISE J072003.20–084651.2, μtot ∼ 0.12 arcsec yr−1; Scholz 2014). Results using separate PSFs proved superior, delivering good motion measurements for 17 out of the 19 test objects, while the single PSF option only recovered 13 out of the 19 test objects, with a clear drop in performance for objects with μtot ≳ 2farcs5 yr−1. Only one out of the five fastest moving objects in our test sample is correctly measured using the single PSF method, while using separate ascending- and descending-scan PSFs and merging the results measures four out of these five.

The two objects that our pipeline is unable to correctly measure—WISE J163940.83–684738.6 and WISEPC J205628.90+145953.3—are missed at the detection stage (Section 3.3) because they are partly blended with brighter nearby sources. These two sources were recovered when the detection step was run without the PSF convolution (Sections 3.1 and 3.3), yielding reasonable motions, but they are not present in the CatWISE Preliminary Catalog.

The fastest movers in our test set have larger parallaxes (up to 502 mas for WISE J104915.57–531906.1; Lazorenko & Sahlmann 2018), which will affect motion measurements when measuring ascending and descending scans together. To test this, we also processed the fastest movers using a single PSF but measuring ascending and descending scans separately and merging them. This gave better performance than processing scans together, recovering motions correctly for three of the five fastest movers.

Comparing astrometry to Gaia for all sources in these tiles showed that even when measuring ascending and descending scans separately and merging them, using separate PSFs further improves performance. The position sigmas were 10% to 20% better at all magnitudes when using separate PSFs than when using a single PSF. For brighter sources (<12 mag), motion sigmas improved by ∼20% using separate PSFs, while at fainter magnitudes, the single and separate PSFs yielded similar motion sigmas. Processing ascending and descending scans separately was beneficial both because it allowed the PSF asymmetry to be addressed, and because it removed the effect of parallax on measured motions.

5. Example Science Applications

An initial application of the CatWISE catalog was the first secure W2 detection for the Y dwarf WD0806–661 B (Meisner et al. 2018a), leading to a [4.5] – W2 color consistent with the population of known Y dwarfs. CatWISE represents a major hunting ground for cold brown dwarfs. The improved depth (Section 4.2) and motion sensitivity (Section 4.3) allow for a deeper, more complete search for the coldest constituents of the solar neighborhood, a crucial population if we wish to constrain the low-mass end of the mass function (see e.g., Kirkpatrick et al. 2019).

Toward this goal, we are mining CatWISE using both a "classical" and a "machine learning based" approach. Here, "classical" means a search based on color and motion cuts applied to the catalog data to select cold brown dwarf candidates, while machine learning uses the previously known population of cold brown dwarfs as a training set to develop a classifier that is then applied to the CatWISE catalog.

Early results include the discoveries of CWISEP J193518.59–154620.3 (Marocco et al. 2019) and WISEP J144606.62–231717.8 (Marocco et al. 2020), two of the coldest brown dwarfs identified to date, with infrared colors comparable with those of the coldest brown dwarf known, WISE J085510.83–071442.5 (Luhman 2014). Spitzer follow-up of additional cold brown dwarf candidates is presented in Meisner et al. (2020).

Prospects are also good for discovering distant galaxy clusters using CatWISE. Gonzalez et al. (2019) used the AllWISE Catalog together with Pan-STARRS to carry out the Massive and Distant Clusters of WISE Survey (MaDCoWS), identifying over 2000 galaxy cluster candidates with photometric redshifts in the 0.7–1.5 range. The additional depth of CatWISE compared to AllWISE increases the W1 detection limit for L* galaxies from z ∼ 0.8 to z ∼ 2. Figure 20 illustrates the increase in the number of distant galaxies with substantial photometric redshifts in the COSMOS field (Laigle et al. 2016) detected by CatWISE compared to AllWISE. Between z = 1.5 and 1, clusters transition from being more actively star-forming than the field to being mainly quiescent in terms of star formation (e.g., Brodwin et al. 2013), so CatWISE offers the potential of reaching the era where the major formation and assembly of clusters is underway.

Figure 20.

Figure 20. CatWISE detects sources ∼0.5 mag fainter than AllWISE, providing many times more sources at z > 1.5. The vertical axis is the number of COSMOS sources that were detected by CatWISE and AllWISE in the 1497p015 tile and had matches within 2farcs5 of sources with the indicated photometric redshifts from Laigle et al. (2016).

Standard image High-resolution image

Finally, the AllWISE Catalog played an important role in the discovery of ULAS J1342+0928, at z = 7.54 the most distant quasar known (Bañados et al. 2018). The additional depth of CatWISE may enable extending this to redshifts as large as 9, when the seeds of reionization were emerging in the overwhelmingly neutral universe. With over 3000 refereed papers making use of the existing WISE catalogs, many other uses for CatWISE can be anticipated.

6. Data Access

Current information about CatWISE data products is provided at https://catwise.github.io.

The merged Preliminary Catalog and reject files are available from IRSA (https://irsa.ipac.caltech.edu) in the WISE/NEOWISE Enhanced and Contributed Products area. IRSA's catalog search tools allow for complex search queries. IRSA also hosts the AllWISE Explanatory Supplement (Cutri et al. 2013), which provides full details on the AllWISE processing algorithms and includes descriptions of the AllWISE Catalog columns, many of which are applicable to CatWISE. Appendix A provides additional information about CatWISE columns.

The individual tile files have also been transferred to a data repository at the National Energy Research Scientific Computing Center (NERSC) and are available at https://portal.nersc.gov/project/cosmo/data/CatWISE/prelim in 18,240 pairs of gzipped ASCII files (one catalog and one reject file per tile) in IPAC table format, organized into 359 directories, one for each decimal degree of R.A. from 0° to 358° (there are no tiles beginning with 359). Text files providing the format and a brief description of the columns in the catalog and reject files are also provided there. The catalog and reject files for the 50 tiles near the ecliptic poles (Table 1), where a single PSF per band was used for processing, include the string "opt0" in their names. Files for tiles where different PSFs were used for ascending and descending scans (Section 3.2) include the string "opt1" in their names.

CatWISE was only possible because it uses and adapts software developed at IPAC for WISE to the maximum extent practical. We thank Tim Conrow, Frank Masci, and Ken Marsh for many helpful discussions and assistance in developing CatWISE. We also thank the anonymous referee for a careful reading and numerous suggestions which improved this paper. CatWISE uses data products from WISE, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory (JPL)/California Institute of Technology (Caltech), funded by the National Aeronautics and Space Administration (NASA), and from NEOWISE, which is a JPL/Caltech project funded by NASA. Characterization of CatWISE performance uses data from Gaia and from Spitzer. CatWISE is led by JPL/Caltech, with funding from NASA's Astrophysics Data Analysis Program (ADAP), and is also supported in part by ADAP grant NNH17AE75I at Lawrence Berkeley Laboratory. CatWISE is also supported by the Fellowships and Internships in Extremely Large Data Sets (FIELDS) program funded by NASA at UC Riverside. F.M. acknowledges support from the NASA Postdoctoral Program at the Jet Propulsion Laboratory, administered by Universities Space Research Association under a contract with NASA.

Appendix A: CatWISE Preliminary Catalog Column Descriptions

We adopt MJD 56700 (2014 February 12) as the epoch for reporting positions when solving for source motion in the Preliminary Catalog. Source positions, whether or not incorporating source motion, are given in the equinox J2000 coordinate frame. Column entries involving R.A. that are in units of arcseconds have the cos(decl.) term applied. The convention for designating sources from the CatWISE Preliminary Catalog and Reject Table is specified in Section 3.7.

There are 186 formatted columns of information about each source in the CatWISE Preliminary Catalog. The CatWISE Preliminary Reject Table adds a column to indicate whether the source is "primary" (see Section 3.6). Descriptions of nearly all the columns can be obtained from IRSA at https://irsa.ipac.caltech.edu/data/WISE/CatWISE/gator_docs/catwise_colDescriptions.html. Most of the columns have the same names as in the AllWISE Catalog and are described in Section II.1.a of the AllWISE Explanatory Supplement (Cutri et al. 2013). Table A1 provides information about selected columns in the CatWISE Preliminary Catalog that augments or supersedes the information provided by IRSA. Four columns (w1fitr, w2fitr, glon, glat) in the NERSC release are hidden in the IRSA release, and their names are shown in parentheses in Table A1. Table A2 provides the corrected version of the contamination and confusion binary bit map referenced in the entry for w1cc_map in Table A1.

Table A1.  Additional Information on CatWISE Preliminary Catalog Columns

Name Units Type Format Description
(w1fitr) arcsec R*4 f7.2 Fitting radius for W1. In the CatWISE Preliminary Catalog, w1fitr and w2fitr are always −99.99, 7.5, or 13.2. Both are hidden in the IRSA release because they do not appear to follow the prescription given in http://wise2.ipac.caltech.edu/docs/release/allsky/expsup/sec4_4c.html#wpro, where rfit = 1.25 FWHM (7farcs5 for W1 and W2) or 2rsat (saturation radius), whichever is larger.
(w2fitr) arcsec R*4 f7.2 Fitting radius for W2. See w1fitr.
dist_ad arcsec R*4 f9.3 Radial distance between ascending and descending apparitions. The field name in the IRSA release is dist_ad, but in the NERSC release, this field is called dist.
elon_avg deg R*8 f11.6 Averaged ecliptic longitude between ascending and descending apparitions
elat_avg deg R*8 f11.6 Averaged ecliptic latitude between ascending and descending apparitions
chi2pmra R*4 1pE10.3 χ2 for difference between PMRA for ascending and descending apparitions (one degree of freedom)
chi2pmdec R*4 1pE10.3 χ2 for difference between PMDec for ascending and descending apparitions (one degree of freedom)
par_pm arcsec R*4 f11.3 Parallax estimate from motion solution. Computed using PMRA and PMDec to propagate ascending and descending motion solution positions to MJD 56700, then dividing ecliptic longitude difference by 2. Because scan longitudes on opposite sides of the orbit had a 5° bias from a great circle until the end of 2014, gradually increasing to 18° by the end of 2017, the actual baseline is < 2 au, declining from 1.996 to 1.951 au over this period, although the difference is negligible given the uncertainty in parallax. Will be null unless both ascending and descending apparitions provided motion solutions (km = 3).
par_stat arcsec R*4 f11.3 Parallax estimate from stationary solution. Computed using PMRA and PMDec to propagate ascending stationary-solution position from ascending observation epoch to descending observation epoch, then dividing ecliptic longitude difference by 2 (see entry for par_pm regarding dividing by 2). Will be null unless both ascending and descending apparitions provided photometric solutions (ka = 3) and at least one motion solution (ka > 0), and all w?mjdmin/max/mean values are non-null in both ascending and descending WPHOT output.
dist_cc arcsec R*4 f13.3 Maximum distance between CatWISE and AllWISE sources providing cc_flags. See Section 3.5.1. In the NERSC release, this field is called dist_x.
cc_flags char a16 Worst-case character cc_flag from AllWISE. See Section 3.5.1.
w1cc_map int i13 The description in the AllWISE Explanatory Supplement is incorrect, so an updated description is provided here. Worst-case contamination and confusion map in W1 for matching AllWISE sources. Contains integer equivalent of a 12-bit binary number specifying if W1 measurement in AllWISE is believed to be contaminated by or a spurious detection of an image artifact. Elements of the binary array (with bit number indicated below each code) are given in Table A2. Bits 0, 1, 3 and 4 indicate whether band-detection is contaminated by an artifact. If brightness of detection is less than expected for artifact, source is regarded as spurious, and bits 7, 8, 10, and 11 are also set accordingly. Letters denote contamination by different types of artifacts (see Section 3.5). For example, a measurement believed to be a spurious detection of a scattered-light halo and contaminated by a diffraction spike has a binary bit map value of "010000001001" and w1cc_map = 1033. When there is more than one AllWISE match to a CatWISE source, a logical "OR" is performed over all the matches for each bit.
w1cc_map_str char a20 The w1cc_map_str description in the AllWISE Explanatory Supplement is incorrect, so an updated description is provided here. Worst-case contamination and confusion string in W1 for matching AllWISE sources. This character string denotes all artifacts that may contaminate the AllWISE W1 measurement of this source, in the priority order D,d,P,p,H,h,O,o. For example, a real detection contaminated by a diffraction spike and a latent (persistent) image has w1cc_map_str = "dp." A spurious detection of a diffraction spike also contaminated by a latent image has w1cc_map_str = "Dp." This string is "null" if there are no artifacts that affect the measurement in this band. The value that appears in first element of the cc_flags string is the leftmost character in w1cc_map_str. If w1cc_map_str is "null," then the corresponding cc_flags entry is "0."
w2cc_map int i13 Worst-case w2cc_map from AllWISE. See w1cc_map.
w2cc_map_str char a20 Worst-case w2cc_map_str from AllWISE. See w1cc_map_str.
ab_flags char a9 Two-character (W1 W2) artifact flag. See Section 3.5.2.
w1ab_map int i9 W1 artifact code value. See Section 3.5.2.
w1ab_map_str char a13 W1 artifact string. See Section 3.5.2.
w2ab_map int i9 W2 artifact code value. See Section 3.5.2.
w2ab_map_str char a13 W2 artifact string. See Section 3.5.2.
(glon) deg R*8 f12.6 Galactic longitude, calculated using a pole of α = 192fdg85 δ = 27fdg13, and a zero of longitude of α = 266fdg4 δ = −28fdg94 (both in J2000). Hidden in IRSA. See Appendix B for details.
(glat) deg R*8 f12.6 Galactic latitude. Hidden in IRSA. See glon.
p int i6 Flag to indicate if source is "primary" in tile. See Section 3.6.

Download table as:  ASCIITypeset image

Table A2.  cc_map Bit Definitions

O H 0 P D 0 0 o h 0 p d
11 10 9 8 7 6 5 4 3 2 1 0

Download table as:  ASCIITypeset image

Appendix B: Caveats

The CatWISE Preliminary Catalog contains a number of features that users should be aware of. Among these are:

  • 1.  
    The number of sources per square degree has relatively small variation over the sky (Figure 5).
  • 2.  
    Catalog performance is not as good in high source density regions (the Galactic plane and the ecliptic poles). Figures 1419 and Table 3 illustrate this.

These issues appear to arise in the detection step. Relatively few deblended sources are added in the measurement step. We are using the unWISE Catalog (which contains many more sources in high-density regions; Schlafly et al. 2019) as a detection list for an updated version of the CatWISE catalog (CatWISE2020) that is now available via NERSC and will soon become available via IRSA.

  • 3.  
    The completeness and reliability for bright sources is low (Figure 7).

As an example, the two brightest catalog sources in W2 (CWISEP J005153.01–235140.3 and CWISEP J223327.80+060246.2) are spurious, and it is likely that other spurious bright sources are present in the catalog. Users should visually inspect interesting sources selected from the catalog using AllWISE or unWISE images before devoting significant resources to follow-up observations.

Additional features present in the CatWISE Preliminary Catalog include:

  • 4.  
    Tabulated position uncertainties are significantly smaller than the measured position scatter with respect to Gaia, as illustrated in Figure 13 (upper right) and Figure 18 (right).
  • 5.  
    A floor of 10 mas yr−1 was imposed on the tabulated motion uncertainties, making them significantly larger than the measured scatter with respect to Gaia motion, as illustrated in Figure 19 (right).
  • 6.  
    The Galactic coordinates in the CatWISE Preliminary Catalog were calculated using a pole of α = 192fdg85 δ = 27fdg13, and a zero of longitude of α = 266fdg4 δ = −28fdg94 (both in J2000). These directions are not perpendicular by 22farcs663, and consequently yielded "nan" entries for the Galactic coordinates of the 31 catalog sources and 6 reject sources within 88farcs3 of the north Galactic pole, and the 39 catalog sources and 5 reject sources within 87farcs8 of the south Galactic pole. The discrepancy in the glon and glat Galactic coordinates of the sources compared to coordinates calculated using the IAU-defined system (Blaauw et al. 1960) increases with absolute Galactic latitude from <1'' in the Galactic plane to 88'' near the Galactic poles. These glon and glat values (including the 81 with glat = "nan") appear in the NERSC release of the CatWISE Preliminary Catalog and reject table files. In the IRSA release, these columns are hidden, and in addition the 81 glat "nan" values have been replaced with +90° or −90° as appropriate.

Appendix C: Combining Ascending- and Descending-scan Positions

Here we provide additional details on how ascending- and descending-scan positions are combined for the CatWISE Preliminary Catalog. Positions are averaged using inverse-covariance weighting. The averaging is done in a local Cartesian projection consistent with the uncertainty representation.

A transformation matrix T is defined as follows: starting with a Cartesian (x, y, z) system whose z-axis points to the celestial north pole and whose x-axis points to the vernal equinox, we perform two Euler rotations that place the z'-axis of the rotated system on the ascending celestial (α, δ) position with the y'-axis aligned with the local north–south direction, and the x'-axis aligned with the local east–west direction. First, rotate about the z-axis by ϕ1 = α − 90°, then rotate about the x'-axis by ϕ2 = δ − 90°. Then, T is given by

Equation (C1)

with elements

Equation (C2)

This corresponds to a z'-axis that looks outward from the origin, so any nearby α', δ' position will have an (x', y', z') vector in the rotated system whose z' component will be positive and close to 1. By "nearby" we mean within a few arcseconds of the origin, because it is very rare for an extracted source's position to vary between the ascending and descending solutions by more than that. This justifies our Cartesian approximation.

The coordinate system is computed for the ascending position, so that the ascending position of the source has coordinates (0, 0, 1). The descending position $(\alpha ^{\prime} ,\delta ^{\prime} )$ is mapped into that system as follows. We construct the vector v to the descending position in the original celestial coordinate system:

Equation (C3)

and transform it into the new system,

Equation (C4)

wherein its x' and y' coordinates are the offsets of the descending position from the ascending position.

The (x', y') coordinates are averaged with (0, 0) using inverse-covariance weighting. We construct 2 × 2 error covariance matrices Ωa and Ωd for the ascending and descending vectors using the corresponding σα, σδ, and σαδ:

Equation (C5)

A minimum value of 10−8 is enforced along the diagonal. The merged (i.e., inverse-covariance-weighted average) vector (xm, ym, zm) and associated covariance matrix are computed as follows:

Equation (C6)

Equation (C7)

Equation (C8)

Equation (C9)

The celestial coordinates corresponding to the (xm, ym, zm) vector are obtained using the inverse of the transformation matrix T described above, which is the transpose because T is orthonormal:

Equation (C10)

Equation (C11)

The image pixel coordinates are then computed for the merged position using the coadd WCS information.

Footnotes

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10.3847/1538-4365/ab7f2a