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VI. Analysis of Release Products

2. Sky Coverage


a. All-Sky Release Data Area
b. Sky Coverage Statistics
c. Caveats About Low Coverage

In this section we describe the depth-of-coverage of the All-Sky Data Release area and explain some of the issues with the pathologies of low coverage areas. For the purposes of this section, the term "Sky Coverage" refers generically to the topic of the WISE dataset spatial surveying features; when appropriate, the term "depth-of-coverage" is used to refer specifically to the number of observations at a specific point on the celestial sphere, and the term "Catalog source density" is used to refer to the number density of Catalog sources extracted in a small region.

The WISE survey strategy was designed to provide at least 8 frames of coverage on at least 99% of the sky in the 6-month minimum all-sky survey interval. This minimum coverage was required in order to achieve sensitivity limits, and includes coverages lost due to proximity to the Moon and the SAA, and further allows for recovery period in the event of satellite anomaly (although no such anomalies caused the loss of any data). As a result, the expected whole-mission data downlink produce an ab initio depth-of-coverage as shown in Figure 1; the cryogenic portion of the mission produces the coverage shown in Figure 2 for bands W1 and W2. Because of the gradual degradation of performance at cryogen loss, the depths-of-coverage of W3 and W4 vary slightly from that shown in Figure 2; these are shown in Figure 3 and Figure 4.

Figure 1 - During the entire WISE operations period, covering more than a year, a total of 2,784,184 framesets were taken and downloaded. The depth of coverage across the whole sky in Galactic coordinates shows the buildup near the ecliptic poles. Figure 2 - The cryogenic portion of the mission, those framesets which will be included in the Final Data Release, lasted until cryogen depletion in October 2010. Up to that time, all W1 and W2 data cover the sky at a depth of more than 8 using 18,844,474 framesets.

Figure 3 - As WISE approached cryogen loss, the telescope began to warm up. W3 integration times were reduced to prevent saturation once the telescope had reached 45 K. The actual coverage at full integration time is somewhat shallower for W1 and W2. Figure 4 - As WISE approached cryogen loss, the telescope began to warm up and the W4 detectors saturated. The actual a priori coverage at 22 microns is therefore shallowest of all the WISE bands. Even so, the usable survey coverage allowed 99.71% of the sky to be seen 8 times or more.

a. All-Sky Release Data Area

WISE imaged the entire sky with multiple, independent exposures in all four bands obtained simultaneously for the duration of its full cryogenic survey. The All-Sky Release includes data taken from 7 January 2010 to 6 August 2010, processed with improved calibrations and reduction algorithms as compared to the Preliminary Data Release. WISE completed its first all-sky coverage on 17 July 2010 and surveyed approximately 20% of the sky a second time before the end of the full cryogenic mission phase. Because of WISE's survey scanning strategy, the depth of coverage ranges from 12 to 13 exposures of each point on the ecliptic plane, increasing to over 3000 exposures at the ecliptic poles (see Figure 5 and Figure 6.

The WISE All-Sky Data Release area is comprised of 18,240 Atlas Tiles, each Tile spanning 1.564° × 1.564° in 4095 × 4095 pixels at a resolution of 1.375″ per pixel. These Tiles are delivered in FITS format image sets, consisting of an intensity image, the corresponding uncertainty image, and a depth-of-coverage map at each of the four WISE bands. The celestial sphere is tessellated with the grid of 18,240 such Tiles on an equatorial projection for the purpose of combining the WISE single-exposure images and extracting final source information. The Tiles are distributed in 119 iso-declination bands with 238 Tiles on the celestial equator decreasing to six Tiles in the |δ|=89.35° declination band. Tiles are designed to overlap by 180″ in RA and Dec on the equator, increasing in RA overlap towards the equatorial poles (see Figure 2 of section IV.4.f.1). This overlap means that the total image content of the tiles corresponds to 44,620.357 deg2, or roughly 108.163% of the sky. The extra 8.163% represents the overlap regions, but for the purpose of quantifying the sky coverage below we have renormalized to 100% of the celestial sphere of 41,252.961 deg2.

Figure 5 - Ecliptic Hammer-Aitoff projection sky map showing the area covered by the WISE All-Sky Data Release; the survey scan pattern is most evident in this projection. The colors encode the average number of single 7.7/8.8 sec WISE exposure frames covering 15´ × 15´ bins. The legend on the left gives the cumulative area in square degrees as a function of frame coverage depth. (Galactic and Equatorial projections are available in III.4). Figure 6 - Differential area as a function of average frame depth-of-coverage in the All-Sky Data Release, computed in 15´ × 15´ bins. The peak at ≈12 is the 'typical' coverage; the secondary peak at ≈24 is the coverage for the ≈10% of the sky that was seen a second time; the peak at ≈160 is the constant-viewing area near the Ecliptic poles.

The post facto coverage is shown in Figure 7, computed in 15´ × 15´ bins and shown in Galactic coordinates in order to match the images following.

Figure 7 - Hamer-Aitoff equal-area projection of the WISE All-Sky Data Release depth of coverage in each band in Galactic coordinates.

Below in Figures 8 and 9 are full-sky Hammer-Aitoff equal-area projection images of the WISE All-Sky Data Release Atlas Tiles oriented in Galactic coordinates. The slight differences in coverage at the four wavelengths can be seen, as can the strips of enhanced background due to the proximity of the Moon (seen as segments running slightly clockwise of vertical). The plane of the galaxy runs prominently throughout, as does a diffuse zodiacal light component. Those with sharp eyes will be able to discern banding in the zodiacal light running along Ecliptic longitude.

Figure 8 - Hammer-Aitoff equal-area projection of the WISE All-Sky Data Release intensity images, manufactured by direct addition of the 44,620.357 deg2 in all 18,240 Atlas Tiles. A large (36MB) version of this image is available for download. This and the following images are in Galactic coordinates centered on the Galactic center; the plane of the Milky Way runs horizontally. The Ecliptic can be seen as the gold-toned swath running across the center, with strips of elevated background due to residual Moon glow visible as white bars perpendicular to the Ecliptic.

Figure 9 - Hamer-Aitoff equal-area projection of the WISE All-Sky Data Release intensity images in each band.

b. Sky Coverage Statistics

WISE survey depth-of-coverage varies across the sky because of the survey scanning strategy, as described in III.4. There are typically 12 independent exposure frames contributing to each point on the sky near the ecliptic plane. The depth increases towards the ecliptic poles, reaching a maximum of ~260 frames at the highest ecliptic latitudes in the All-Sky Data Release (Figure 5). Visible in Figure 5 are some small patches with decreases in frame coverage caused by filtering out exposures considered to be of lower quality because of contamination by scattered moonlight (within 20° of the ecliptic), image quality degradation due to flight system motion, or other events. Pixel-level frame coverage information is provided in the WISE Atlas Tile Depth-of-Coverage Maps. Here we present ensemble statistics of the coverage achieved for this data release.

Each Atlas FITS image contains in the header some high-level quantification of the depth-of-coverage for that Tile. This information may also be accessed in the Atlas Inventory metadata table. (Full depth-of-coverage information can readily be derived from the Atlas Depth-of-Coverage maps, for those who wish to determine this on a per-pixel level). The header keywords are listed in Table 1.

Table 1 - Atlas Image FITS Keywords Describing Depth-of-Coverage
KeywordMeaningData Type
MEDCOVMedian depth-of-coveragefloat
MINCOVMinimum depth-of-coveragefloat
MAXCOVMaximum depth-of-coveragefloat
LOWCOVPCPercent of pixels with depth ≤4¥float
LOWCOPCPercent of pixels with depth ≤6float
NOMCOVPCPercent of pixels with depth ≤8float

¥ Coverage of 4 was the metric used as the WISE mission's Level 1 requirements for sky coverage, specifically that at least 95% of the sky should be covered to this depth or greater.
† Coverage ≤5 implies pixels that are at or below the threshold for statistically viable outlier detection and rejection (see below), and so can be contaminated by random pixel variations such as cosmic rays.
‡ Coverage ≤8 implies regions where the coverage is less than the nominal coverage required for the desired minimum sensitivity goals.

The median depth-of-coverage across the full Preliminary Data Release Area is 15.645±0.003 in W1, 15.552±0.004 in W2, 14.845±0.002 in W3, and 14.842±0.003 in W4. (The reason for the uncertainty is that the median is determined by fitting to a histogram of the 305,867,016,000 image pixels per band, a process that necessarily results in some imprecision.) Below, we show more complete statistics of the depth-of-coverage distributions in this data release.

Figure 10 - Calculated pixel-level depth-of-coverage vs. ecliptic latitude for each band, plotted on a per-Tile basis; the yellow region indicates the dispersion of the distribution in each Tile, calculated via an outlier-resistant variance estimator. The typical Tile coverage can be seen as the heavy convex band; the doubling of coverage in certain areas is visible at twice this value. Higher coverage near the Ecliptic poles is clipped for clarity.

Figure 11 - FITS header values of the median coverage (MEDCOV) in each band vs. ecliptic latitude; the yellow region indicates the minimum (MINCOV) and maximum (MAXCOV) coverage in each Tile.

Figure 12 - Histogram of per-pixel depth-of-coverage in each Tile for each band for the entire All-Sky Data Release. Note that this is summed over Tiles, and so there is a slight overlap resulting in a double-counting of certain spatial pixels on the sky as described above. The bin width is in units of 1/8th of a coverage, which can be non-integral (see section II.3.d).

Figure 13 - Cumulative histogram of the area in square degrees resulting from integrating the curves in Figure 12, above.

Figure 14 - Same as Figure 13, but in a linear scale.

Figure 15 - The ordinate shows the percentage of the sky covered in the All-Sky Data Release Tiles to a depth of at least that indicated on the abscissa, for each band.

Figure 16 - Same as Figure 15, but in log-linear scale to highlight the small area covered to high depth.

i. Tabulated Statistics

Here we provide statistics calculated across the WISE All-Sky Atlas Tiles on a per-pixel basis. Table 2 lists the pixel-level depth of coverage for each WISE band as a function of fraction of sky covered. For example, in band W3 (12 microns),
50% of the sky has been covered at a depth of ≥14.84; in band W2 (4.6 microns), 1% of the sky has been covered at a depth of ≥74.15.

Table 2 - Depth of coverage for each WISE band as a function of fraction of sky covered. For example, in band W1 (3.4 microns),
50% of the sky has been covered at a depth of ≥15.65; in band W3 (12 microns), 95% of the sky has been covered at a depth of ≥9.78.

As can be seen below in Table 3, there are several square degree areas — a small percentage of the sky, but not negligible — where the coverage is zero. While WISE imaged every point on the sky multiple times during the full cryogenic mission, not every Single-exposure image was of sufficient quality to incorporate in the Multiframe Pipeline processing (cf. V.2.c). Because of the many factors that impact the usable depth-of-coverage, these are regions within the footprints of the 18,240 Atlas Tiles that cover the full sky for which the effective depth-of-coverage is very low or even zero (see VI.2.c). If there is insufficient coverage in these regions, the corresponding pixels in the Atlas Images may have "NaN" values, and no sources can be detected in those locations. We provide Table 3 to illustrate the scope of the low coverage regions in the Atlas Tiles. The most important rows are those that show the fraction of sky the is not covered at all (COV=0) or covered at a low enough level that outlier rejection is invalidated (COV<5), hence detection reliability will be significantly impacted.

Consequently, although WISE observed every point on the sky multiple times, there may be insufficient usable Single-exposure data to have corresponding Atlas Image or Source Catalog data. Viewing the Atlas Depth-of-Coverage maps is the best way to determine if a region of interest to you may have reduced coverage, and therefore lower sensitivity, and/or missing detections in the Source Catalog.

All of the Single-exposure Images and Single-exposure Source Database, regardless of image and data quality, are available among the All-Sky Release Ancillary products. Therefore, you may find image and extracted source information in those archives for regions with low and/or no coverage in the All-Sky Release Atlas and Source Catalog.

Table 3 - A selection of area of sky covered (in both percentile and square degrees) for a selection of depth-of-coverages
near the low coverage end. This can provide some guidance as to the fraction of sky the is not covered (COV=0) or
covered at a low enough level that pixel outlier rejection is invalidated (COV<5).

The median depth-of-coverage can be calculated for portions of the sky to highlight the effect of spatial selections. In each of Ecliptic, Galactic, and Equatorial coordinates, Table 4 shows the median depth-of-coverage as a function of latitude cuts. In this case, the pixel-level median is calculated on a per-Tile basis and the Tile central latitude is used; hence, there is some inaccuracy in the highest latitude cuts where the depth-of-coverage changes rapidly with latitude on scales smaller than a Tile (1.564°)

Table 4 - The median depth-of-coverage as a function of cuts in Ecliptic latitude, Galactic latitude, and Equatorial latitude (declination).
|lat|≥ 5°20.820.320.7

ii. Sensitivity and Depth of Coverage

It is expected that, since depth of coverage is linearly related to the amount of time spent collecting photons from each position on the sky, the sensitivity should improve approximately as the square root of the depth of coverage. One of the Atlas products is the UNCertainty data in the same spatial format as the INTensity and COVerage data. A description of the uncertainty maps is found in section Section II.3.E. The uncertainty map stores the 1-σ uncertainty per pixel corresponding to the co-added intensity values in the primary Atlas Image, in the same units of DN (cf. section II.3.f on the use of uncertainty maps in aperture photometry). These uncertainty maps are based solely on prior knowledge of the instrument response (as opposed to a posteriori data-derived estimates), and hence do not include any component of confusion noise, which may be significant in regions with high source density and/or complex background emission.

Figure 17 shows a plot of the per-pixel uncertainty map vs. the depth-of-coverage. Since each plot consists of all 305,867,016,000 pixels, the intensity has been logarithmically scaled better to highlight the scatter in the distribution. The lower boundary, which contains a large fraction of the total pixels in each band, shows that the uncertainty at pixel j scales very closely to σj ∝ 1/√Nj, where Nj is the depth-of-coverage at pixel j.

Figure 17 - Uncertainty vs. depth of coverage evaluated on a per-pixel basis for each band.

c. Caveats About Low Coverage

The WISE scan strategy was designed to allow for repeat viewings of at least 8 times on every point on the sky, with accommodations allotted for planned survey motions and margins for unplanned survey interruptions. The achieved characteristic coverage is slightly higher than this because the survey was not interrupted. However, there are some regions that have anomalously low effective coverage in the Atlas Images and Source Catalog because some Single-exposure framesets were rejected from Multiframe processing due to poor assessed quality (i.e. see V.2). Some of the reasons for low coverage are summarized below. The All-Sky Data Release Atlas Tiles consist of three products per band: an INTensity image, a COVerage image, and an UNCertainty image. An example of these three products, combined into a 4-color image, is shown in Figure 16.

W1-4 INTW1-4 COVW1-4 UNC
Figure 18 - An image of 1061m107_ab41, a single Atlas tile in the area of IC2177, the Seagull Nebula, showing the direct image, the depth of coverage of the image, and the uncertainty of the image. The depth of coverage shows its inverse effect on the uncertainty and hence implicitly on the significance of detection of sources in the direct image. Where there is lower coverage, there will be higher uncertainty and poorer source extraction will arise.

i. Torque Rod Gashes

Comparison of the achieved Atlas tile coverage (Figures 5, 7, 8, and 9) with the survey frame coverage (Figures 1-4, also via interactive comparison) illustrates several areas with a notable loss of coverage within the general boundaries of the release. Most significant are the horizontal bands at Ecliptic λ,β= 100°,+45° and 290°,-45° (Equatorial α, δ= 110°,+70° and 310°,-70°). Early in the survey, the spacecrafts' magnetic torque rods were enabled to dump accumulated momentum when scans approached within 45° of the ecliptic poles. Activating the torque rods resulted in a small jump in the telescope pointing and smearing of the resulting images. Because the smearing occurred near the same point on each orbit, and the smeared images were flagged as having degraded image quality in the QA process, low-coverage "holes" developed at those locations. Later in the survey (2010 May 02), torque rod enabling was staggered between 45, 57.5 and 70° latitude on alternating orbits so that any image smearing would not occur at the same point on the sky on each orbit. It was hoped that the WISE cryogenic mission would last long enough to enable a repeat visit of the affected areas, but some small portions of sky were never revisited and so the gaps remain. A multi-Atlas Tile region around one such gap is shown in Figure 16.

W1-4 INTW1-4 COV
Figure 19 - A mosaic of 16 Atlas Images near (95,+45) Ecliptic, showing a clear gap in coverage spanning across portions of several Tiles at one of the torque rod gashes. The coverage is very similar at all wavelengths, since it was induced by a common-mode issue at the spacecraft level. However, the qualitative appearance of the nearby effect is wavelength dependent, as can be seen in the background level shift in W3 across the boundary (stretched to accentuate the change).

ii. Moon Contamination

When WISE observes near the moon, stray light can contaminate images significantly enough that source detection sensitivity is degraded and spurious detections are triggered by the structured scatter light. Moreover, spatially-varying scattered light artifacts are problematic for the background-matching portion of the Multiframe pipeline image coaddition process.

The Moon crosses the scan circle twice a month. This would imply that a large amount of data would be corrupted; this would leave gaps in the sky coverage. To counter this, the WISE survey strategy uses a modified scan pattern where the scan circle gets slightly ahead before the Moon interferes and then drops slightly behind to recover the region the Moon obscured. The Moon moves 13° per day in ecliptic longitude, so with a 15° nominal exclusion zone (30° diameter) WISE needs to be 1.2° ahead just before the Moon crosses the scan circle, and then drops back to 1.2° behind just after the Moon crosses the scan circle. This "Moon avoidance" maneuver produces the "spokes" of enhanced coverage that are visible in the nominal sky coverage maps seen in Figures 1-4, for example.

Moon avoidance helps to fill in the coverage, but does not solve the problem fully because scattered light artifacts affected frames taken as far as ~30° away in W3 and W4, and ~20° in W1 and W2. (e.g. see II.4.a.ii). To minimize the impact of scattered moonlight in Single-exposure images on the coadded Atlas Images, frames suspected to be contaminated are flagged if they fall within the area of a static "moon-mask", and filtered out from the coadding if the spatially-varying portion of the moonlight produces a pixel RMS in excess of a threshold defined by frames not within the static moon-mask area, as described in IV.4.f.

There are a few cases where most or even all of the available input frames touching parts of an Atlas Tile are within the masked region resulting in incomplete rejection of the scattered light artifacts, or, in the worst cases, zero-coverage holes in the Atlas Images and Catalog. An example of such an Atlas Image, 3165m137_ab41, is shown in Figures 20 and 21. Because the extent of scattered moonlight is larger in W3 and W4, the loss of coverage is more severe in those bands, and gaps where no valid data can be found are evident. In this particular case, the coverage in W2 is low enough that the outlier detection threshold is not surpassed, and so spurious features such as cosmic rays can be seen contaminating the image.

Figure 20 - Atlas Intensity Images for Tile 3165m137_ab41, showing residual scattered light and loss of coverage because of Moon contamination. The extent of scattered moonlight is larger at longer wavelengths, so the resulting loss of coverage is greater.

Figure 21 - Corresponding square-root-scaled depth-of-coverage map for Atlas Image 3165m137_ab41 showing obvious Moon contamination; the depth-of-coverage ranges from zero near the left/right edges left to (Dominic, find this!) near the center.

To assist in the proper identification of moon-contaminated Tiles, there are FITS keywords in the Atlas Image headers that describe the Moon contamination mitigation process. These are detailed in Table 5. These parameters are also available in the Atlas Inventory metadata tables. As an example, for Tile 3165m137_ab41 in W1/W2/W3/W4, the value of MOONINP indicates that 114/139/165/165 frames (out of 191 initial frames per band) are flagged as "suspect" for moon-glow; of these, MOONREJ=72/116/153/145 were rejected, leaving only NUMFRMS=119/75/38/46 frames to make up the final Tiles. With such extreme ratios, care should be taken with the portions of the Tile nearest to the uncovered area. The WISE outlier detection relies on median absolute deviation as a robust measure of the dispersion of the pixel intensity distributions at any particular location. This technique becomes unreliable below a depth-of-coverage of five, so outliers may be incorrectly flagged and removed.

Table 5 - Atlas Image FITS Keywords Describing Moon Contamination
KeywordMeaningData Type
MOONREJNumber of frames rejected due to moon-glowint
MOONINPInitial number of frames with suspect moon-glowint
NUMFRMSFinal number of frames touching footprintint

iii. Source Density Suppression Around Bright Stars

Bright stars have a noticeable impact on depth-of-coverage, but also a more subtle change in sky coverage as measured by the Catalog. Very bright stars effectively obscure background sources with their their scattered light halos and diffractions spikes, and they elevate the surrounding background, thus increasing the source detection limits. This can be illustrated visually in an extreme case for a very bright star, Betelgeuse. As a roughly -4th mag star, Betelgeuse saturates thoroughly in each of the WISE bands, making it an easy example for the effect. A by-eye inspection reveals the suppression of source density in the vicinity of bright stars down to a magnitude of ~5, and it is likely that this effect would be statistically significant down to fainter levels.

We show in Figure 22a the intensity in W1-4 for Betelgeuse from Tile 0884p075_ab41. The corresponding depth-of-coverage image in W1-4 is shown in Figure 22b.

Overlaid on this are all the Catalog sources selected in W1 (Figure 23, top) and W3 (Figure 23, bottom), including those flagged as being contaminated by diffraction spike objects, halo objects, etc. It is clear that the the distribution of sources is spatially nonuniform. One can infer that the source distribution is the result of a high density of potentially spurious sources within the halo area, a suppression of real sources in the halo near the bright star, and the more-or-less-uniformly distributed real sources at a greater distance from the star. The suppression of Catalog source density is a subtle effect of bright stars that can lead to, for example, incorrect two-point correlation function determination due to an unknown windowing. This lack of sky coverage is not reflected in the depth-of-coverage information provided in the Atlas Image sets.

The example in Figure 23, (right) shows the distribution of all Catalog sources, but many of them are flagged to enable Catalog-query-based removal of potentially contaminated sources. If one removes these potentially contaminated and spurious sources by selecting only those with cc_flags="0000," the entire region is denuded of sources, as shown in Figure 23 (left).

Figure 22a - Atlas Intensity Image in W1-4 for Betelgeuse from Tile 0884p075_ab41. For this very bright source, many causes of spurious or potentially spurious sources can be seen: ghosts and latents, diffraction spike objects, halo objects, etc. Figure 22b - Atlas depth-of-coverage in W1-4 for Betelgeuse.

Refined selection criteria can be used to eliminate the spurious sources without filtering our all real objects. One way is to also use the multiple-band detection bit flag, det_bit, since spurious sources should not necessarily be associated with the same Catalog entry. Taking the above field and selecting according to:

(det_bit=3 or det_bit=7 or det_bit=11 or det_bit=15) and w1cc_map_str not like "d%" and w1cc_map_str not like "D%"

results in an improved likelihood of the reliability of sources (Figure 20), which makes it more evident that the Catalog source density is low in the region of bright stars.

W1, cc_flags="0000" W1, cc_flags="????"
W3, cc_flags="0000" W3, cc_flags="????"
Figure 23 - Intensity images in W1-W4 for Betelgeuse from Tile 0884p075_ab41, with catalog sources overlaid selected from W1 (top) and W3 (bottom). With cc_flags="0000" (left pair), a draconian selection in that it removes any suspect source for any reason whatsoever, a significant region of order a degree in diameter is source-free; smaller regions are seen around fainter stars and the latent images of Betelgeuse. With the extremely lax selection criterion of cc_flags="????" (right pair), when no sources are flagged, it is still seen that the source density is suppressed near the very bright star, and many sources are clearly spurious.

As one final note, we mention that the depth-of-coverage is low in the immediate vicinity of bright stars. This is reflected in the Atlas Image Depth-of-Coverage Maps files and is visible in the depth-of-coverage histograms as the regions of anomalously low coverage. It should be noted there are also low depth-of-coverage groups of pixels associated with the ghosts and latents of bright stars, as is shown for W2, W3, and W4 in Figure 24. This shows the intensity and coverage images near Betelgeuse for bands W2 (top), W3 (middle), and W4 (bottom). The ~zero depth-of-coverage right at the position of the star is evident in all bands, as are the ~zero depth-of-coverage latent images in W3 and W4 that extend for several degrees.

Figure 24 - (Top) W1-W4 intensity image for an approximately 9′ field around a star in near the upper edge of Tile 0884p075_ab41, designated J055309.18+081445.7. Superposed on the image are the catalog sources selected with cc_flags="0000" (green) and cc_flags="????" (red). This star is around 4th magnitude in all bands, and hence saturates in W1 and W2, but not in W3 or W4. The depth-of-coverage maps for each band are shown in the middle and lower rows, illustrating the very low coverage right at the location of a saturating star.

A quantitative analysis of the Catalog source density suppression has been done for a large set of sources. For each source, the areal density of other secondary sources at a given radius r from the primary source. has been calculated and normalized to the areal density at very large distances (r→∞). This is then averaged over every source and tracked as a function of the flux ratio of the two sources.

In Figure 25 a plot for W1 is shown, where the color scale is calculated for log(<ρ(r)/ρ(r→∞)>) in a range of 0.01x to 100x. A very strong suppression is seen at close radii (r<10″) due to deblending of sources; this is covered in Section VI.2.c.iv. on Suppression of Close-Separation Sources. Some additional perturbations to a uniform density can be seen as 'real correlations' for nearby sources and over/underdensities due to artifacts (for example, diffraction spike sources). In the upper left, corresponding to separations of typically 10″-100″ or more, there is an additional suppression of sources as shown qualitatively above. In W1, the boundary of this region corresponds approximately to the combination of a Gaussian and an Airy profile of the bright source, such that even in the very far wings (≈250″) of a very bright source (≈106 brighter), there is a pronounced underdensity of secondary sources. The same holds true for W2, as shown in Figure 26, but is less the case for W3 and W4. In fact, in those bands there is an overdensity of sources at the wings of bright sources.

Figure 25 - Source density suppression quantified: the color scale represents the over- or underdensity of sources as a function of radius, as compared to its asymptotic behavior as r→∞. Regions identified as 'blended' and 'suppressed source density' indicate an underdensity of sources that depends on the relative brightness of sources nearby; see text for details.

Figure 26 - Source density suppression quantified; see caption of Figure 25 or text for details.

iv. Suppression of Close-Separation Sources

WISE's angular resolution and sensitivity combine to provide a noticeable frequency of blended sources. While the WISE source extraction and photometry pipeline does attempt to deblend modestly extended structure into multiple sources, it cannot do this for objects at very close separations. This produces an effective limit to the window function of spatial correlations in the Catalog at very small distances. To characterize this, an autocorrelation of a region of the Catalog in Bootes was produced. This produces points in a spatial-offset plane wherein the source density should be nearly uniform for uncorrelated sources, dropping significantly within some radius of deblending. Shown in Figure 27, this effect is quite clear; a circle of radius 10″ (green dots) and 7.5″ (red dash) show that the onset occurs quickly at an angular scale roughly 1.5 times the WISE PSF FWHM.

Figure 27 - The source autocorrelation shows the likelihood of finding two catalog sources as a function of their α, δ offsets. Few sources are found at a distance of <9″, setting the lower bound on close-separation pairs in the WISE Catalog source extraction.

v. High Flux/Source Density Regions

In regions with a large number of sources or particularly bright sources (either diffuse or point-like), the depth-of-coverage can vary between wavelengths in a spatially-varying way dependent on the intensity structure. Hence, performing tasks such as aperture photometry on extended sources must take into account these variations across the source. As an example of the coverage variations, the four-color composite intensity and depth-of-coverage maps for Tile 0835m061_ab41, the Orion IRC2 region, are shown in Figure 28. There is a pronounced decrease in coverage (in blue and magenta color) across a several arcminute-wide region around the brightest portion of the nebula near the top, but also in broader swaths just north of center. Similarly, some regions to the east of center exhibit low coverage in W4 (cyan). These decreases are not severe; the total stretch depth-of-coverage is 0 to roughly 16, while the low coverage areas in those bands amount to a change in depth of only a few. What is interesting about the spatial variations is that the low depth-of-coverage nearer to the center of the Tile is not coincident with the brightest regions in the relevant bands, nor in the region of highest flux density. Such decreased depths-of-coverage are to be anticipated and do feature in this Tile.

Intensity ImageDepth-of-Coverage Map
Figure 28 - Four-color composite intensity and depth-of-coverage images for Atlas Tile 0835m061_ab41, showing the reduced coverage in regions with very high background. Also note the low coverage near the bright stars, e.g. one near the lower left corner of the image.

Last update: 2013 January 14

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