SEDS: THE SPITZER EXTENDED DEEP SURVEY. SURVEY DESIGN, PHOTOMETRY, AND DEEP IRAC SOURCE COUNTS

The SEDS observing strategy was governed by the need to maximize the area covered with deep integrations in each of the five fields. It was also necessary to cover each field fully on separate visits so as to enable the planned variability science. Each field was visited three times; the visits (referred to below as epochs) were separated by six months except that the intervals for HDFN were nine and three months. Table 1 lists the epochs for each field. For each field, the coverage was very similar in epochs 1 and 3, but the coverage for epoch 2 differed because of the offset placement of the two IRAC detectors within the Spitzer focal plane and the constraints imposed by the spacecraft roll angle.

Each SEDS epoch accumulated 4 hr integration time per pointing or less when there was pre-existing coverage of a field. Each Astronomical Observation Request (AOR), representing a continuous sequence of Spitzer observations, looked at each pointing position exactly once and covered an entire field.³³ For efficiency, each position in the field was observed for 2–4 frames of 100 s each before moving the telescope to the next position. There was no dithering built into individual AORs, but AOR origins were offset by ∼1' in a Rouleaux pattern. Thus each field required 36–72 observations at each pointing (minus pre-existing coverage), and these were spread over the nearly the entire range of each epoch. Therefore each field was sampled with near-uniform time coverage and point-spread function (PSF). Individual AORs had different spacings between pointings and pointings observed in different time orders. The AORs thus sampled each sky position at a variety of positions on the arrays and also ensured that those positions included both near and far spacings. These characteristics minimize data artifacts.

Two of the fields, EGS and COSMOS, are long and narrow (∼1° × 10'). The map pattern for these was two IRAC FOVs (each 5') in width by a variable number of FOVs in length. Visibility constraints prevented the COSMOS strip from aligning with the IRAC arrays, and the width mapped to full depth in both FOVs was ∼8'. The other fields (UDS, HDFN, ECDFS) are approximately square, and the basic map grid was rectangular but with varying spacings. A few positions in the centers of the HDFN and ECDFS fields already possessed deep coverage (≳23 hr), and pointings that would duplicate this coverage (four in ECDFS, two in HDFN) were omitted. The UDS field has bright stars in its northeast corner, and coverage was designed to exclude these stars.

To the maximum extent possible, identical reduction procedures were applied to all SEDS data so as to facilitate subsequent variability studies and to ensure a uniform data quality throughout the SEDS project. The data reduction was based on version S18.8.0 of the IRAC Corrected Basic Calibrated Data (cBCD) exposures. All 3.6 and 4.5 μm cBCD frames were object-masked and median-stacked on a per-AOR basis; the resulting stacked images (presumed to represent blank sky) were visually inspected and subtracted from individual cBCDs within each AOR to eliminate long-term residual images arising from prior observations of bright sources. The sky-subtracted cBCDs were then examined individually and processed using custom software routines to correct column-pulldown effects associated with bright sources. The code, known as the "Warm-Mission Column Pulldown Corrector," is publicly available at the Spitzer Science Center.³⁴

After these preliminaries, the SEDS exposures and the coincident IRAC imaging from earlier programs (Section 2) were mosaiced together into 3.6 and 4.5 μm mosaics using IRACproc (Schuster et al. 2006). IRACproc implements the standard IRAC reduction software (MOPEX). The standard MOPEX error propagation techniques, which are based on the IRAC uncertainty images, were employed by IRACproc, with one significant exception. IRACproc augments the capabilities of MOPEX by calculating the spatial derivative of each image and adjusting the clipping algorithm accordingly. Pixels where the derivative is low (in the field) are clipped more aggressively than are pixels where the spatial derivative is high (point sources). This avoids downward biasing of point source fluxes in the output mosaics that might otherwise occur because of the slightly undersampled IRAC PSF. The software was configured to automatically flag and reject cosmic ray hits based on pipeline-generated masks together with the adjusted sigma-clipping algorithm for spatially coincident pixels.

In order to take advantage of the subpixel shifts of our mapping strategy, and to facilitate registration of the IRAC mosaics to the coextensive CANDELS imaging (006 pixels; Grogin et al. 2011; Koekemoer et al. 2011), the mosaics were resampled to 06 pixel⁻¹. Thus each SEDS mosaic pixel subtends approximately one-fourth the area of the native IRAC pixel. The final mosaics' tangent-plane projections were likewise aligned to those used by the CANDELS mosaics.

The 40 final mosaics and coverage maps (including three epochs and a total coadd in each of the two IRAC bands for each of the five fields) are all available from the SEDS team Web site.³⁵

A first test of source extraction methods was made in the SEDS EGS field with SExtractor (ver. 2.5.0; Bertin & Arnouts 1996), a standard tool for these purposes (e.g., Lonsdale et al. 2003; Ashby et al. 2009). The software was configured identically to that used by Barmby et al. (2008) to photometer sources in their (shallower) EGS mosaic. Despite the fact that the SEDS EGS mosaics incorporate a factor of four longer integration time per pixel, the resulting SExtractor catalogs improved only marginally upon those of Barmby et al. In effect, source confusion imposed a limit on our ability to identify faint sources that SExtractor could not overcome. This behavior has been remarked on before (e.g., Sanders et al. 2007). We therefore used StarFinder (version 1.6f; Diolaiti et al. 2000) to identify IRAC sources in the SEDS fields. StarFinder is optimized for identification of blended sources in crowded wide-field adaptive-optics observations. StarFinder works by repeatedly fitting and subtracting a PSF to sources it identifies in an image. It begins with the brightest object. After the brightest source has been identified, fitted, and subtracted, the next brightest object is treated in the resulting residual image. StarFinder iterates this process, operating on progressively fainter sources, until a user-specified limiting sensitivity is reached.

The SEDS catalogs were constructed in two steps. First, StarFinder was used to locate sources (even faint, blended ones). Second, a custom code was used to correct biases in the StarFinder photometry.

The source-location step used the full-depth SEDS mosaics masked to exclude regions of shallow coverage. This exclusion of relatively noisy low-coverage regions—virtually all located on the periphery of the SEDS footprints—was done to prevent them from artificially inflating the rms-threshold criteria needed to search deeply for faint objects in the areas of highest signal/noise. The 3.6 and 4.5 μm mosaics were masked separately, i.e., the coverage was not initially required to be coextensive.

The source-location process began with the creation of empirical PSFs for the SEDS fields. Isolated, unsaturated stars (between magnitudes 10 and 15, depending on the field and the coverage) were inspected (to exclude binaries) and then scaled to a common, fiducial intensity. Objects within 64 mosaic pixels (384) of each PSF star were masked, and the resulting scaled images were median stacked to suppress artifacts. The halos of the resulting composite, high-dynamic-range PSFs were then smoothed slightly at large radii to suppress noise. They were also masked at radii beyond 64 pixels. Because the scale factors applied prior to the median stacking can be large for relatively faint stars, the scaling can lead to spurious negative-valued features that create obvious artifacts in the residual images described below. We therefore masked negative-valued pixels in the composite PSFs to zero. All the PSFs were then normalized to unity integrated flux, per standard StarFinder protocol. Correction factors were then estimated by measuring the flux from each PSF star within a series of apertures covering a range of diameters (Table 2).

With the cleaned and normalized PSFs, iterative source identification was carried out as described above on the masked mosaics. To prevent bright sources from distorting the estimates of backgrounds nearby, StarFinder was configured to estimate the backgrounds with a grid spacing equal to 72 times the FWHM of the PSF. It was also set to estimate backgrounds under detected sources. A spacing constraint was imposed, requiring that sources be separated by at least the half of the PSF width (defined as the half-width at half-maximum or HWHM; 09) in order to be counted as separate detections; blended sources lying closer to each other were counted as a single object. StarFinder computes the rms of the source-free pixels to estimate the significance of source detections. In the first StarFinder run, sources were counted as detections if they exceeded 5σ significance relative to the estimated rms variations. After the first run had removed the 5σ sources, StarFinder was run a second time but with a 3σ threshold on the residual images, i.e., a new (lower) rms was computed and then applied to science mosaics from which all previously-detected sources had been removed. Finally, StarFinder was run a third time on the source-subtracted residual from the second iteration, again with a 3σ detection criterion. Figure 23 shows StarFinder residual images for a typical small subregion (in this case, within the EGS). Although bright and extended sources have significant residuals, those for the more abundant faint sources are sufficiently small that the residual image is far from being confused in either band. The SEDS catalogs consist of the source positions and magnitudes determined in all three StarFinder runs, modulo the photometric corrections described below.

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4.1.1. Photometric Corrections

StarFinder is very efficient for identifying sources, but it measures only PSF-fitted photometry. While this is perfectly acceptable for some sources (Milky Way stars, QSOs), it is inadequate for galaxies because they are seldom point sources. It was therefore necessary to convert the PSF-fitted photometry to aperture photometry in order to measure total fluxes for galaxies.

To generate the SEDS aperture photometry we used a custom code that operated on the StarFinder catalogs and residual images. The code first re-created the original appearance of each source in turn by re-inserting the scaled/fitted PSF at the position of that object, effectively adding in the fitted flux to any residuals that remained. Thus each source was re-created at its original position with its original flux, with the PSF fits to all other sources removed. The code then re-measured the flux of this source in a suite of apertures (Table 2). Backgrounds were estimated within annuli centered on the sources but outside the photometric apertures. The procedure was repeated for all detected sources. This approach had two significant advantages. First, it greatly improved the background estimates because to a good approximation all neighboring sources had been removed. Second, it accounted for the fact that galaxies are not generally point sources; aperture photometry requires no assumptions about the surface brightness distributions.

The multiaperture photometry was corrected to total magnitudes using the aperture corrections measured separately for the empirical PSFs in each band and field. All SEDS catalog entries include these aperture corrections, which are given in Table 2 and Figure 24.

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SEDS survey completeness and reliability were assessed with the standard Monte Carlo approach, using photometry of artificial sources. To constrain the properties of the required artificial sources for SEDS, we used a 05 search radius to match the SEDS COSMOS catalog to the coextensive F160W catalog made available by the CANDELS team (Grogin et al. 2011; Koekemoer et al. 2011). Figure 25 shows the measured widths (major axes only) of the CANDELS counterparts in the F160W filter. The great majority of SEDS IRAC-detected objects are significantly smaller than the IRAC PSF; they are in effect point sources at 3.6 μm. At the magnitudes of interest to SEDS, i.e., objects fainter than 23 AB mag, virtually all the IRAC detections are point sources. We therefore used only point sources in our completeness and depth simulations.

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A minimum of 10⁵ artificial point sources were introduced into each SEDS mosaic. The number of artificial sources inserted simultaneously, however, was kept small (less than 2% of the number of detected IRAC sources) so as not to artificially aggravate source confusion effects. Typically, only 50–250 artificial sources were introduced at a time. Approximately the same number of sources was inserted in each 0.5 mag interval between 18 and 27 mag. They were placed at random locations throughout the portions of the science mosaics having at least 10 ks integration time to sample all variations in large-scale structure present. The modified mosaics were then photometered with StarFinder in the same way the original detections had been made.

We followed Barmby et al. (2008) and counted an artificial source as a valid detection if its measured flux was within 50% of its "true" flux and its measured position was within 1'' of its a priori known position. Completeness was thus defined as the fraction of artificial sources over a range of apparent brightnesses in bins of width 0.5 mag extending from 100% completeness (at ∼18 mag) down to zero at 26.5–27.0 mag. The uncertainties in the completeness estimates were inferred from Poisson statistics in each bin. As Figure 26 and Table 3 show, the 3.6 μm SEDS catalog is 80% and 50% complete at roughly 23.5 and 24.75 mag, respectively. The corresponding 4.5 μm limits are 23.8 and 24.8 mag. Thus at magnitudes where the incompleteness correction becomes large (Figure 25), the choice of point sources for the simulations is appropriate. Some field-to-field variation is apparent in both bands.

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Roughly 70% of the faintest 3.6 μm StarFinder detections (25.5–26.0 mag) in the COSMOS field have no F160W counterparts. The CANDELS F160W observations reached approximately 26.5  mag (3σ), so genuine SEDS sources with typical colors ought to have been detected by CANDELS. The comparison suggests that StarFinder generated spurious detections at faint levels. We therefore imposed a requirement that sources must be detected at both 3.6 and 4.5 μm to be included in the SEDS catalogs. Formally, the requirement imposed was that the 3.6 μm detections match a 4.5 μm source within 05. Nearly 100% of the sources brighter than 24.5 mag at 3.6 μm were detected in both SEDS bands. At levels fainter than 24.5 mag, however, the match fraction decreases with magnitude down to the SEDS survey limit. For this reason, Figure 26 and Table 3 report the separate single-band completeness measurements for sources brighter than 24.5 mag but report (identical) two-band completeness estimates for all SEDS sources fainter than this level.

The common practice (e.g., SExtractor) of basing photometric uncertainties on noise estimates made in source-free mosaic pixels can be problematic in some circumstances. The issue of most concern to SEDS is that the supposedly source-free pixels may well fall on faint sources lying just below the detection threshold; their fluxes may then artificially boost the uncertainty estimates. Also, sub-pixel sampling like that used for SEDS introduces correlated noise into the mosaics. To avoid these complications the SEDS error estimates were based solely on photometry of the simulated sources with their known fluxes. We grouped the artificial sources into 0.5 mag bins and measured the offsets from the known fluxes as a function of magnitude. The standard deviations of the offsets were taken as the 1σ measurement uncertainties and the offsets themselves were taken as the measurement biases. The results are shown in Figure 27.

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The uncertainties are much more significant than the biases in all SEDS fields, at least for sources brighter than 26 mag. The uncertainty typically rises smoothly from roughly 0.03 mag for bright sources to about 0.25 mag at 26 AB mag. It combines contributions from three separate sources of uncertainty: (1) the 3% uncertainty in the IRAC absolute calibration (Reach et al. 2005), (2) photon noise, and (3) confusion noise. These are discussed further in Section 6.1. The empirical uncertainties are given in Table 4.

The measurement bias is relatively small for sources brighter than 20 mag. It starts to grow rapidly at roughly the level where SEDS becomes 50% incomplete and becomes greater than 0.1 mag at 26 AB mag. This is consistent with a picture in which faint sources are increasingly difficult to deblend from on-average brighter neighbors. The contamination of the photometric apertures by these neighbors affects the photometry, even though the measurements were made in residual images. The measurement bias is given in Table 5. The photometry reported in the SEDS catalogs has been corrected to remove this bias.

Because SEDS extends to extremely faint levels (by current standards) and must cope with pervasive source confusion, we verified the SEDS measurements by comparing them to previously published catalogs. We estimated the astrometric uncertainties by comparing to the USNOB and 2MASS Point Source Catalog. We verified our photometric calibration by comparing to coextensive surveys including S-COSMOS (Sanders et al. 2007), SpUDS (version DR2), EGS (Barmby et al. 2008), and SIMPLE (Damen et al. 2011).

4.3.1. Astrometric Reliability

To estimate the accuracy of SEDS astrometry, we compared the SEDS positions of bright but unsaturated sources to those in the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) Point Source Catalog. We performed a search within 1'' of the positions of IRAC sources to identify their 2MASS counterparts. The distributions of coordinate offsets for the 3.6 and 4.5 μm sources are shown in Figure 28. The astrometric discrepancies are small compared to the size of a SEDS pixel: at 3.6 μm, the mean difference (SEDS−2MASS) was just −0002 ± 016 in right ascension and 0004  ±  019 in declination. The corresponding mean offsets for the 4.5 μm sources are similar: −0005 ± 016 in right ascension and 003 ± 018 in declination. The radial uncertainties are therefore 024 (1σ) relative to 2MASS, or about 0.4 of a SEDS mosaic pixel.

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We also compared the SEDS positions to their visible-wavelength counterparts in the USNOB1.0 catalog (Monet et al. 2003). We matched the positions in each of the five SEDS fields to those in USNOB1.0 using a 05 search radius. Only USNOB sources having positions known to within 025 were matched. The mean offsets between USNOB and SEDS were insignificant for the UDS, ECDFS, and COSMOS fields. Significant offsets were found for the HDFN and EGS fields. The offsets are quantified for each field in Table 6. Users of the SEDS catalogs should be aware of and account for these offsets when matching to the USNOB positions.

Table 6. Astrometric Offsets (SEDS–USNOB)

Field	ΔR.A.	ΔDecl.	Total
	(arcsec)	(arcsec)	(arcsec)
UDS	0.09 ± 0.19	0.00 ± 0.18	0.24 ± 0.12
ECDFS	0.08 ± 0.20	−0.03 ± 0.19	0.27 ± 0.12
COSMOS	−0.02 ± 0.19	−0.11 ± 0.17	0.25 ± 0.12
HDFN	0.18 ± 0.24	−0.28 ± 0.26	0.44 ± 0.19
EGS	−0.04 ± 0.25	−0.27 ± 0.25	0.39 ± 0.20

Notes. Mean coordinate offsets measured between SEDS sources and their visible-wavelength counterparts in the USNOB1.0 catalog (Monet et al. 2003). Total offsets refer to the mean absolute offsets between SEDS and USNOB positions. The stated uncertainties are the standard deviations of the offset distributions for matched sources.

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4.3.2. SEDS Photometric Verification

To verify the SEDS photometry, we matched the SEDS catalogs to those of the four coextensive surveys mentioned above. In all cases, the matching was done using a 05 search radius, i.e., roughly twice the 1σ astrometric uncertainty established in Section 4.3.1. Only SEDS sources brighter than the detection limits of the respective surveys were used in the comparison. For example, only sources brighter than the SpuDS faint-source detection thresholds (2.0 and 2.7 μJy at 3.6 and 4.5 μm, respectively) were matched to the SpUDS catalog. Only SEDS sources brighter than 1 (1.7) μJy at 3.6 (4.5) μm were matched to S-COSMOS. The limits for the comparisons in the EGS field were set to match the 50% completeness threshold of Barmby et al. (2008), i.e., 1.5 and 1.6 μJy at 3.6 and 4.5 μm, respectively. Only SEDS sources brighter than 24.64 and 24.22 mag (the SIMPLE 5σ sensitivities at 3.6 and 4.5 μm, respectively) were matched to the Damen et al. (2011) SIMPLE catalog. In addition, sources flagged as blended in the SIMPLE DR1 catalog were excluded from the comparison. Because all SIMPLE sources brighter than 18 AB mag were flagged as blended, the comparison could only be carried out for objects fainter than this limit. The results are shown in Figure 29.

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The SEDS photometry is broadly consistent with the previous measurements. The mean offset for faint sources varies from zero in some cases up to a maximum of ∼0.07 mag for the SIMPLE 4.5 μm band. The comparisons for bright SEDS sources show a somewhat different character. With the exception of the EGS 3.6 μm band, SEDS sources brighter than 18 mag show a systematic offset that ranges up to a maximum of 0.1 mag in the worst case (versus SpUDS; Figures 29(a) and (b)) in the sense that these sources are brighter in the SEDS catalog on average. This may be due to the different source types that predominate on opposite sides of the 18 mag threshold. Whereas sources fainter than 18 mag are typically galaxies, objects brighter than 18 mag are much more likely to be Galactic stars, i.e., point sources (Arendt et al. 1998; Fazio et al. 2004a; see also Figure 25). Applying identical aperture corrections to both populations most likely introduced a slight bias to the SEDS 18–21 mag photometry of a few percent. This bias will not be significant for faint sources, because they are pointlike (Figure 25).

Several factors could account for the offsets. Changes in the IRAC calibration during the Spitzer mission could introduce changes no larger than 2%. The discrepancy already noted for the SIMPLE 4.5 μm band may in part be a result of the slightly different flux calibrations applied to the two SIMPLE epochs. However, a more likely cause for the discrepancies is the very different methods used to obtain the photometry in the first place. Whereas SEDS is based on a modified StarFinder approach, the SpUDS, S-COSMOS, EGS, and SIMPLE measurements are all based on SExtractor. In addition, the different surveys measured their photometry in different apertures; the comparisons presented in Figure 29 used aperture diameters of 38 (SpUDS), 28 (S-COSMOS), 42 (EGS), and 40 (SIMPLE). Even small differences in applied aperture corrections could potentially introduce the offsets seen here.

In summary, the comparison to earlier, coextensive surveys shows that SEDS faint-source photometry is generally consistent with previous results even though the SEDS measurements were made using different software and methods and in significantly more crowded mosaics. Given the use of different photometric software with different parameterizations and the different depths of the data sets being compared, we regard the agreement between SEDS and the preexisting surveys as excellent.

The SEDS uncertainties are dominated by the 3% uncertainty in the IRAC absolute calibration for sources brighter than 17 mag. They are likewise dominated by the IRAC sensitivity at the faint limit. At intermediate magnitudes, however, confusion noise is the dominant contributor to the uncertainties (Table 4). This is expected. The SEDS IRAC number counts meet the Rowan-Robinson (2001) criterion for confusion (1 source per 40 beams) at roughly 21.8 mag in both bands. Confusion contributes to the errors even at brighter magnitudes, however. Between 18 and 25 mag, then, the uncertainties plotted in Figure 27 broadly reflect the confusion noise. Future surveys with highly redundant coverage may expect to encounter similar levels of confusion noise if their observations have the same angular resolution as SEDS.

The IRAC colors of the sources give clues to their redshifts and luminosities. Sorba & Sawicki (2010) and Barro et al. (2011) showed that the [3.6] − [4.5] color is a useful photometric redshift indicator, especially for separating galaxies at z ≲ 1.3 from those at z ≳ 1.5. Figure 30 shows a color–magnitude diagram of the SEDS sources. As expected, sources with [3.6] < 19 have [3.6] − [4.5] ≈ −0.4, consistent with late-type stars or low-redshift galaxies. Franceschini et al. (2006) found that galaxies in this magnitude range mostly have redshifts between 0.5 and 1.2. There are many fainter objects with similar color, but starting around [3.6] ≈ 21, another population with [3.6] − [4.5] ≈ 0.1 appears. This is consistent with galaxies at z ≳ 1.3 (Sorba & Sawicki 2010). Helgason et al. (2012) derived galaxy luminosity functions (LFs) at a range of wavelengths as a function of redshift. At z ≈ 1.3, the turnover in the rest 1.63 μm LF, approximately corresponding to observed 3.6 μm, is L* ≈ −24.0. This corresponds to apparent [3.6] ≈ 21.7, roughly a magnitude fainter than the brightest z > 1.3 galaxies. In other words, the brightest observed galaxies with colors consistent with z > 1.3 are roughly a magnitude brighter than L* at that redshift. The color trends are also shown by the histograms in Figure 31. At [3.6] ≳ 23.5, precise color information is largely lost because of photometric uncertainties, but the histogram peak at [3.6] − [4.5] ∼ −0.1 shows that the sources are a mix of low-redshift, low-luminosity galaxies and z ≳ 1.3 galaxies with higher luminosities.

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SEDS detects a total of roughly 300,000 sources in the 1.46 deg² covered by the survey. Figures 32 and 33 and Table 12 present the resulting differential source counts along with Milky Way star counts estimated from the model of Arendt et al. (1998) for the SEDS lines-of-sight. At levels brighter than roughly 18 AB mag in both SEDS bands, the IRAC counts are consistent with the star count models. SEDS contains relatively few galaxies brighter than 18 mag. The vast majority of sources fainter than 18 mag, however, are galaxies: the contributions of Milky Way stars to the faint counts are negligible.

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As shown in Figures 32(e) and 33(e), the SEDS counts agree very well with those of Fazio et al. (2004a) down to the sensitivity limit of the Barmby et al. (2008) EGS survey, despite being based on a different detection/photometry technique. They are also consistent with the deeper counts in the HDFN (Figures 32(d) and 33(d)) compiled by Magdis et al. (2008).

The field-to-field variation in number counts for objects with 21 < [3.6] < 24 is only 3.3% of the area-weighted mean count (Figures 34(a) and (b), and Table 12). This has significant implications for the nature of the source population. Based on tests with the QUICKCV code (Newman & Davis 2002), such a low sample variance (or "cosmic variance" as it is commonly referred to) can only be achieved in one of two ways. One possibility is that the clustering of the sources is intrinsically weak (with a correlation length r₀ ∼ 3 h⁻¹ Mpc comoving, matching low-mass star-forming galaxies at z = 0–1; Zehavi et al. 2011; Coil et al. 2008) and they have a moderately broad redshift distribution spanning Δz ∼ 1.5–2.5. The other possibility is that the sources exhibit strong clustering, e.g., correlation length r₀ ∼ 5–6 h⁻¹ Mpc comoving, matching quiescent galaxies at z = 0–1 (Zehavi et al. 2011; Coil et al. 2008) and Lyman-break-selected samples at z ∼ 4 (Ouchi et al. 2004; Hildebrandt et al. 2009), but that collectively these strongly clustered sources are detected over a very wide redshift range, from z ∼ 0–4. Subpopulations (e.g., color-selected to be at high redshift) show stronger cosmic variance than this, as would be expected if they have stronger clustering and/or span a smaller redshift range.

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If a single field of the same total area as SEDS were observed, errors in the mean number density or number counts of a population due to sample/cosmic variance would be a factor of ∼1.25 times higher than the errors that achieved for SEDS.³⁶ SEDS yields lower variance because a single-field survey observes a correlated volume, which may be dominated by common, large-scale high- or low-density fluctuations, whereas multiple widely separated fields sample statistically independent regions of the universe. This ratio of errors is independent of linear galaxy bias, and hence of the nature of the galaxies observed.

While the ratio of errors between SEDS and a single field covering the total SEDS area is nearly independent of sample properties, the absolute reduction in errors will depend strongly on the source population's bias and redshift range. As an example, we adopt the bias predictions given in Table 4 of Moster et al. (2010) and their assumed power spectrum amplitude (σ₈ = 0.77). In that case, a sample of galaxies with 10^8.5 M_☉<M < 10⁹ M_☉ which spans 0 < z < 2 would have 1.25% scatter in counts/number densities due to cosmic variance in SEDS, but would have a scatter of 1.60% in a single field of the same area. A sample with M > 10¹¹ M_☉ and falling in the range 3.9 < z < 4.1 would have 21.0% scatter from sample variance in SEDS, versus 25.4% in a single-field survey. To achieve the same sample/cosmic variance as SEDS, a single-field survey of the same depth would have to cover ∼2.4 deg², as opposed to the 1.46 deg² surveyed in the five SEDS fields. Of course, for some populations Poisson variance (shot noise) will dominate rather than sample variance; in that case only area surveyed matters. In general, the net errors in counts or number densities for a given sample from a single-field survey must be between 0% (if Poisson-dominated) and ∼25% (if sample-variance-dominated) worse than if the SEDS strategy were used, given that both terms contribute to the overall error. Given that observing time is (to first order) determined by the area surveyed, a multiple-field strategy will always yield errors that are no worse than, and can be significantly better than, a single-field observation at constraining the abundances of galaxy populations.

The mean differential counts, calculated as area-weighted means, are shown in Figures 34(c) and (d). In the aggregate, the counts brighter than 18 mag in both bands very closely follow the Arendt et al. (1998) DIRBE 3.5 and 4.9 μm star count models for the Milky Way. Elsewhere, the SEDS counts correspond closely to the "default model" counts of Helgason et al. (2012), who reconstruct galaxy counts in the IRAC bands from known galaxy populations using an extensive library of multi-wavelength LF measurements extending to z ∼ 4–5.

We fitted a pure power law to the SEDS counts below the break in both bands. Specifically, we performed a χ² minimization fit to the differential counts from 20–26 mag in both SEDS bands. The fitted slopes are 0.17  ±  0.05 and 0.180  ±  0.004 at 3.6 and 4.5 μm, respectively, where the uncertainties are 1σ. This suggests that the dominant contributions to the faint IRAC counts come from galaxies at z = 3–5, with an LF having a faint-end slope of roughly α = −1.5 (Helgason et al. 2012). Although this slope is slightly lower than seen for UV LFs at similar redshifts (α ∼ −1.7; Bouwens et al. 2012; Bouwens et al. 2007), it is consistent with the trends in faint-end slope documented in Helgason et al. (2012) and anchored at low redshifts by the 3.6 and 4.5 μm LFs of Dai et al. (2009) and Babbedge et al. (2006).

The CIB contains the sum of all light from distant galaxies integrated over all of Cosmic time, and therefore is of primary importance for understanding galaxy formation and evolution. Historically, precise measurement of the CIB has been complicated by the difficulties involved in modeling and subtracting the very substantial foreground contaminants (see, e.g., the review by Kashlinsky 2005). However, measurement of the total light from resolved sources, the integrated galaxy light (IGL), provides a strict and robust lower limit on the CIB and is largely unaffected by the foregrounds that complicate direct CIB measurements. Low-background space-based surveys, such as SEDS, have obvious promise for this application.

Fazio et al. (2004a) made the first measurements of the IGL with IRAC: 5.4 and 3.5 nW m⁻² sr⁻¹ at 3.6 and 4.5 μm respectively, down to 23.5 mag. Subsequent analysis by Kashlinsky (2005) revised these estimates respectively to 5.3 ± 1.0 and 4.0 ± 0.8 nW m⁻² sr⁻¹. In other words, the cryogenic IRAC observations resolved somewhat less than half of the estimated CIB at these wavelengths (13.3 ± 2.8 nW m⁻² sr⁻¹; Levenson et al. 2007).

The Fazio et al. (2004a) bright counts are drawn from wide-field observations covering nearly 10 deg², and are therefore unlikely to suffer significantly from cosmic variance. However, as Levenson & Wright (2008) point out, the faint Fazio et al. (2004a) counts are based on only two relatively narrow lines of sight. Levenson & Wright (2008) therefore measured the IRAC counts toward three widely separated fields (DIRBE "Dark Spots") each covering a substantial area (∼1 deg²) to estimate faint IRAC counts relatively free of cosmic variance. On the basis of an extrapolation of their counts to faint levels, Levenson & Wright (2008) arrived at a larger estimate of the contribution of IRAC sources to the CIB: $9.0^{+1.7}_{-0.9}$ nW m⁻² sr⁻¹.

SEDS offers a new opportunity—by virtue of its deep observations spread over five widely-separated fields—to reduce the uncertainties attending the contribution of faint IRAC sources to the CIB. SEDS is of course not optimal for bright-source count estimates. We therefore adopt the Fazio/Kashlinsky measurements for the counts brighter than 23.5 mag. Despite the fact that SEDS reaches 2.5 mag deeper than Fazio et al. (2004a), the incremental contribution of faint SEDS sources (23.5–26.0 mag) to the previous CIB estimate is small, amounting to only ∼10% of the earlier estimates: 0.33  ±  0.03 and 0.36  ±  0.03 nW m⁻² sr⁻¹ at 3.6 and 4.5 μm, respectively. The total contributions to the CIB of detected IRAC sources are therefore 5.6 ± 1.0 and 4.4 ± 0.8 nW m⁻² sr⁻¹ at 3.6 and 4.5 μm, respectively, down to 26 mag. Our results agree with Helgason et al. (2012), whose "default" construction estimated total contributions from IRAC sources to the CIB of $4.9^{+1.7}_{-0.7}$ and $3.3^{+1.2}_{-0.5}$ nW m⁻² sr⁻¹ at 3.6 and 4.5 μm, respectively, where the ranges bracket the two extremes of the faint-end LF extrapolation consistent with the Helgason et al. (2012) LF database.

The SEDS CIB measurement is significantly smaller than that estimated in the three DIRBE "Dark Spots" at 3.6 μm by Levenson & Wright (2008). This may be because the "Dark Spots" estimate is based on an extrapolation to faint levels of relatively bright counts having a significantly steeper slope (∼0.5) than found by SEDS. Figure 12 of Levenson & Wright (2008) nonetheless suggests that the measured SEDS slope is consistent with their analysis at roughly the 90% confidence level.

The faint SEDS IRAC counts impose strong upper limits on the possible contribution of IRAC sources to the CIB. Even if the slopes of the IRAC counts increased immediately below 26 AB mag to the Helgason high faint end case (0.22 in both SEDS bands), the total contributions to the CIB from these undetected sources would be only 0.16 and 0.14 nW m⁻² sr⁻¹ at 3.6 and 4.5 μm, respectively. Thus, discrete IRAC sources appear unable to furnish more than about half of the estimated CIB at 3.6 and 4.5 μm.

SEDS is designed to maximize its impact in fields related to cosmology and high-redshift science. It has already been of some use in this regard. Kashlinsky et al. (2012) used SEDS imaging from two fields (the UDS and EGS) to make new measurements of fluctuations in the CIB; the SEDS data permitted extraction of much fainter sources and analysis of the CIB fluctuations over significantly larger scales than was possible previously at these wavelengths.

SEDS will be of particular interest as a means to identify distant galaxies. High-redshift galaxies have long been identified on the basis of their red colors; historically this has been accomplished in the optical-to-NIR regime (e.g., I − K or R − K) to bracket galaxies' 4000Å break and measure their redshifts out to z ∼ 3 (Roche et al. 2003; Franx et al. 2003; Brown et al. 2005). With Spitzer/IRAC photometry this technique has been extended out beyond z = 3 (e.g., Wang et al. 2009; Huang et al. 2011; Wang et al. 2012). This has begun happening with SEDS photometry as well. Aravena et al. 2010 incorporated SEDS photometry into the spectral energy distribution of a rare submm-selected galaxy in COSMOS to place it at z ∼ 4.8. Caputi et al. (2012) identified and analyzed a sample of very rare, very red objects (H − [4.5] > 4) galaxies in the UDS and found that this color criterion was efficient for identifying sources at 3 < z < 5. At an even more extreme redshift, Capak et al. (2011) used SEDS-COSMOS observations (along with a suite of other data) to identify a massive protocluster at z ∼ 5.3. No doubt the SEDS data will be put to other uses not yet anticipated by the SEDS team, now that they are public.