The Massive and Distant Clusters of WISE Survey. I. Survey Overview and a Catalog of >2000 Galaxy Clusters at z ≃ 1

WISE W1 and W2 data are the foundation for the MaDCoWS cluster search. For a description of the WISE satellite and survey strategy, we refer the reader to Wright et al. (2010). Our cluster search uses the WISE project data products created and distributed by NASA/IPAC, available at the Infrared Science Archive. Initial work to develop the MaDCoWS algorithm was based upon the WISE All-Sky Data Release of 2012 March 14 (Cutri et al. 2012). The first MaDCoWS clusters were discovered using the All-Sky Data Release (e.g., Gettings et al. 2012; Stanford et al. 2014). For this data release, the survey scanning strategy yielded approximately 12 exposures at positions along the ecliptic plane, and a published 5σ photometric sensitivity in the ecliptic plane of 68 and 111 μJy (16.63 and 15.47 mag Vega) in the W1 and W2 bands, respectively. Sensitivity improves toward the ecliptic poles due to the denser coverage and lower zodiacal background (Wright et al. 2010).

The current search is based upon the updated AllWISE Data Release from 2013 November 13, with approximately twice the coverage depth in W1 and W2 (Cutri et al. 2013). Full descriptions of the data processing and catalog constructions for each are contained in the Explanatory Supplements (Cutri et al. 2012, 2013). The AllWISE release yields both improved sensitivity and uniformity of coverage relative to the earlier All-Sky release, and also significantly reduces the flux underestimation bias that impacted the All-Sky release. The 5σ depths for the AllWISE release are 54 and 71 μJy (16.96 and 15.95 mag Vega) in the W1 and W2 bands, respectively, for low-coverage sky regions (23 exposures) along the ecliptic plane (Cutri et al. 2013). For regions away from the Galactic plane that are not confusion-limited, the AllWISE release enables uniform selection down to these magnitudes.

The primary data used in the cluster search come from the AllWISE source catalog, which provides positions and profile-fitting-derived fluxes for over 747 million sources over the full sky. In the public catalogs provided by IPAC, the position and flux information are derived from a combination of the deep coadds in the AllWISE Image Atlas and the single-exposure (L1b) frames. The initial source positions for the catalog are derived from the deep coadds using a multiwavelength χ² technique that combines information from all four bands simultaneously (Marsh & Jarrett 2012). Based on this initial list, procedures for profile-fitting photometry and source deblending are performed on the L1b frames at each source position. We note that the resolution of WISE (61 in W1 and 64 in W2) effectively suppresses the detection of sources within 10'' of one another due to blending. As shown in section VI.2.c.iv (Figure 27) of the All-Sky Explanatory Supplement (Cutri et al. 2012), few sources are detected within 10'' of another source. We discuss the impact of blending on the search in Section 3.1.

In addition to the WISE photometry, we also use data from ground-based optical surveys to reject foreground galaxies (as described below). For the initial phase of this program, including clusters published in Gettings et al. (2012) and Stanford et al. (2014), we used the SDSS (York et al. 2000), which restricted our search to the SDSS footprint. The SDSS data set has now been superseded by the Pan-STARRS 3π survey (Chambers et al. 2016), which extends to δ = −30°. At more southern declinations, we have also investigated use of the SuperCOSMOS Sky Survey (Hambly et al. 2001b, 2001c). Although we present details of all three surveys here, Pan-STARRS provides the primary optical data for the current MaDCoWS search.

2.2.1. The SDSS Eighth Data Release

2.2.2. Pan-STARRS

2.2.3. The SuperCOSMOS Sky Survey

The DES is in the process of mapping ∼5000 deg² in the region of the southern Galactic cap in the grizY passbands (Abbott et al. 2018). Over half of the DES footprint lies south of δ = −30° and hence outside the Pan-STARRS area, thus providing complementary optical imaging. The photometric depths for the first data release (DES DR1) are g = 24.33, r = 24.08, i = 23.44, z = 22.69, and Y = 21.44 (10σ; Abbott et al. 2018). Although the DES DR1 was not available in time to be incorporated into the current MaDCoWS cluster search, we use the i-band photometry in Section 6.1 to derive photometric redshifts for the subset of cluster candidates that lie within the DES footprint but outside the Pan-STARRS survey area.

Our team was awarded Spitzer time during Cycles 9, 11, and 12 to obtain [3.6] and [4.5] imaging for 1959 cluster candidates (PI: Gonzalez, PIDs 90177 and 11080), enabling photometric redshift and richness estimates. For the Cycle 9 program, we targeted 200 candidates from a preliminary WISE–SDSS search. We targeted an additional 1759 clusters in the Cycle 11–12 snapshot program. These clusters were selected by peak amplitude in the WISE–Pan-STARRS and WISE–SuperCOSMOS searches (see Section 4.5) and include only clusters that were not previously observed in Cycle 9. We obtain total exposure times of 180 s in each band using a 6 × 30 s cycling dither pattern. These two programs, both conducted during the Spitzer "warm" mission, and existing archival data together yield IRAC [3.6] and [4.5] imaging for 1967 MaDCoWS clusters. Of these, 1723 are in the WISE–Pan-STARRS catalog presented in this paper, and 86 are in the WISE–SuperCOSMOS catalog. The remainder are within the WISE–Pan-STARRS footprint, but are detected at lower significance.

Data were reduced using the MOPEX (Makovoz & Khan 2005) package and source extraction was performed using SExtractor (Bertin & Arnouts 1996) in dual image mode, with the [4.5] image serving as the detection image. During the Spitzer warm mission, the FWHM values for the PSF are 195 and 202 for [3.6] and [4.5], respectively, providing a factor of 3 improvement in spatial resolution relative to WISE. Following the methodology of Wylezalek et al. (2013), we determine that at 10 μJy, the recovered source density in our fields is 95% that of SpUDS at the same threshold. For subsequent analysis, we include only sources with f_4.5 > 10 μJy. We measure our completeness by comparing the MaDCoWS Spitzer number counts with number counts from the Spitzer UKIDSS Ultra Deep Survey (SpUDS; PI: J. Dunlop) survey. The SpUDS survey is a Spitzer Cycle 4 legacy program that observed ∼1 deg² in the UKIDSS UDS field with IRAC and the Multiband Imaging Spectrometer (Rieke et al. 2004), reaching 5σ depths of ∼1 μJy at 3.6 μm.

We were awarded time with the Combined Array for Research in Millimeter-wave Astronomy (CARMA)²⁶ between 2012 and 2014 (PIDs c0884, c1128, c1197, c1272, c1303) to observe a selection of the richest cluster candidates at 31 GHz. We were also awarded time in 2014 September (PID c1272) to target ∼150 cluster candidates with very short exposures to identify very massive clusters. Most of the observations were made with the array in the 23 element CARMA-23 mode, with the exception of the 2012 observations from c0884 and c1128, which used only the eight-element SZA. Detections from the pilot run in 2012 and 2013 are presented in Brodwin et al. (2015), and MOO J1142+1527, observed in 2014, is presented in Gonzalez et al. (2015). In the present work, the data were re-reduced using a new version of the SZA MATLAB pipeline (Muchovej et al. 2007) updated to handle 23 element data and produce uv fits files, and the CLIMAX software was used to fit pressure profiles from Arnaud et al. (2010) to the data. The spherically integrated Comptonization was measured from the Arnaud model, and M₅₀₀, r₅₀₀, and Y₅₀₀ were calculated by forcing consistency with the Andersson et al. (2011) scaling relation. A more detailed description of the observations and analysis is given in Brodwin et al. (2015) and Decker et al. (2019).

A number of authors have demonstrated that the stellar mass content of cluster galaxies is tightly correlated with the total cluster mass (e.g., Lin et al. 2004, 2012; Mulroy et al. 2014, and references therein). Mulroy et al. (2014) for example found an intrinsic scatter of only ∼10% between the K-band luminosity and weak-lensing mass for nearby clusters. The W1 and W2 WISE bands, which probe approximately rest-frame H and K_s at z ≃ 1, trace the total stellar mass content, while being relatively insensitive to the age of the stellar population. In the WISE bands, the apparent magnitude of an L* galaxy is only weakly dependent on redshift at z ≳ 0.7 due to e+k corrections that offset the impact of increasing luminosity distance (Figure 1). Consequently, a magnitude-limited galaxy sample selected with WISE has a roughly uniform luminosity limit within this redshift range. Photometry from WISE therefore provides a proxy for stellar mass that is relatively unbiased by star formation history, and the uniform luminosity limit translates to a uniform selection in stellar mass.

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The primary observable for galaxy-based cluster searches is the projected overdensity of galaxies. The luminosity function of cluster galaxies is well parameterized by the Schechter function (Schechter 1976), and recent papers have demonstrated that high-redshift galaxy clusters have relatively flat faint-end slopes at WISE wavelengths (e.g., Mancone et al. 2012). Combined with the rising number counts of the field population at faint magnitudes, a cluster will have the greatest density contrast relative to the background population when the limiting magnitude of the input galaxy catalog is slightly below L*. Thus, while W2 offers the more uniform stellar mass limit with redshift, for MaDCoWS we use a W1-selected galaxy sample due to the greater depth relative to L* in this band. For z ≃ 1, the W1 AllWISE imaging reaches 1.1L* at 5σ, while the [4.6] imaging only reaches approximately 2.1L* at 5σ (M* − 0.8), or 0.85L* at 2σ (M* + 0.2; Figure 1). With MaDCoWS, we are therefore effectively searching for z ∼ 1 galaxy clusters via overdensities of galaxies with luminosities of approximately L* or greater.

In practice, one additional consideration that impacts the effective depth is source blending in WISE due to the large PSF. Blending affects the number of observed galaxies in two competing ways. First, blending decreases the number of individual detections for galaxies brighter than the apparent magnitude limit. Second, blending leads to detections arising from blends of galaxies that are individually fainter than the detection limit. For the general field population, the net impact of these two factors will be a uniform shift in the number counts as a function of magnitude, which does not impact our cluster search. For clusters, both factors will have the greatest effect in the core region where the projected density is highest. For MaDCoWS, because the magnitude limit is close to L*, the second effect will generally dominate due to the higher surface density of galaxies with L < L* compared to super-L* galaxies. The MaDCoWS search therefore ends up benefiting from the inclusion of blended galaxies that are individually somewhat fainter than the nominal WISE detection limit. For illustration, we show WISE and Spitzer imaging for one of the spectroscopically confirmed MaDCoWS clusters in Figure 2.

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The concept for the MaDCoWS algorithm, though different in detail, is in the spirit of previous cluster searches using Spitzer data. The basic idea is to first isolate the distant galaxy population, using color and magnitude cuts to minimize foreground contamination, and then use wavelet filtering to identify the most significant overdensities on cluster scales. The color and magnitude selections, as described below, are similar to those employed by Papovich (2008) and Muzzin et al. (2013), while the wavelet technique draws upon the legacy of the ISCS and IDCS (Eisenhardt et al. 2008; Stanford et al. 2012).

3.2.1. Galaxy Selection

For the MaDCoWS cluster search, we start with the full WISE catalog of all sources detected at 5σ in W1. We then impose a magnitude cut W1 < 16.9 to enforce uniformity of depth for the galaxy catalog.²⁷

The optical magnitude criterion is applied next. Within the Pan-STARRS region, we reject sources with i < 21.3 (i < 20.93 Vega). In Figure 3, we cross-match WISE sources within the NOAO Deep Wide-Field (NDWFS) region with a photometric redshift catalog for IRAC-selected sources from Brodwin et al. (2006) to illustrate the impact of our cuts. As can been seen in this figure, the optical rejection effectively removes galaxies at z ≲ 0.8. In Figure 3, we also show the redshift distribution in the WISE bands of all sources surviving this cut. The i-band magnitude of this cut is predominantly empirical based upon the data shown in Figure 3, but set at a physical level where no cluster galaxies, except potentially BCGs, at z ≃ 0.8 are removed. For the same evolutionary model as in Figure 1, this magnitude limit corresponds to a 1.8 L* galaxy at z = 0.8. The use of a brighter magnitude cut increases foreground contamination, while using a significantly fainter cut would diminish the cluster signal. Outside the Pan-STARRS region, we reject sources with R_F < 20.5 from SuperCOSMOS, a shallower cut that is less effective at removing low-redshift interloper galaxies. In Figure 4, we illustrate the approximate impact of this cut by applying an R > 20.5 cut within NDWFS. These interlopers decrease the density contrast between clusters and the field—and hence larger scatter between detection amplitude and richness—and also result in higher contamination of the sample by low-redshift clusters (see Section 6.2).

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Subsequent to the optical cut, we impose a WISE color cut, rejecting objects with W1 − W2 < 0.2. As a precaution at this stage, we also reject galaxies not detected at 2σ in W2. The WISE color cut preferentially removes galaxies at z < 0.8 from the galaxy population remaining after the optical rejection. For the WISE–Pan-STARRS region, the median redshift increases from 0.93 to 1.01 with the addition of the WISE color cut (see the redshift distributions in the rightmost panel of Figure 3). As a result, clusters at z ≲ 1 are downweighted in the WISE–Pan-STARRS search. Outside the Pan-STARRS region, because of the shallower SuperCOSMOS optical cut, this color cut is vital for reducing contamination from galaxies at 0.5 ≲ z ≲ 0.8. This can be seen in the center and right panels of Figure 4. It is worth emphasizing that even with the WISE color cut, the lack of SDSS- or Pan-STARRS-quality optical data has a detrimental impact on the search at δ < −30°. We discuss in Section 6.6 prospects for an improved southern search.

3.2.2. Identifying Galaxy Overdensities

From the filtered galaxy catalogs, we construct density maps with a resolution of 15''. These density maps are filtered with a difference-of-Gaussians kernel (similar to a Mexican hat kernel) to identify cluster-scale overdensities. The functional form for this kernel is

$$\begin{eqnarray}&&K=\displaystyle \frac{1}{2\pi {\sigma }_{1}^{2}{\sigma }_{2}^{2}}\left({\sigma }_{2}^{2}\exp \left(-\displaystyle \frac{{r}^{2}}{2{\sigma }_{1}^{2}}\right)-{\sigma }_{1}^{2}\exp \left(-\displaystyle \frac{{r}^{2}}{2{\sigma }_{2}^{2}}\right)\right),\end{eqnarray} \tag{ 1 }$$

where σ₁ and σ₂ are the scales of the inner and outer Gaussians, respectively. This kernel functions as a bandpass filter (much like the filters in the SZ surveys), removing contributions to the density map from large-scale structure and other sources of gradients in the projected galaxy density on large scales. The form of the kernel is shown in Figure 5. Details regarding the specific scales set for the kernel are presented in Section 4.4.

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Both the WISE and optical catalogs contain quality flags for each source. For WISE, the catalog contains information on sources that are flagged as contaminants in cc_flags, which can arise from optical ghosts, diffraction spikes, persistence effects, or scattered light. We reject sources with ${\mathtt{cc}}\_{\mathtt{flags}}\ne 0$ in W1 or W2, as non-zero flags are indicative that the source detection may be unreliable or measurements for that source may be contaminated. We also reject sources that are flagged as optical ghosts in either W3 or W4 as a precaution. Although we are not using W3 and W4 photometry, the detection of an optical ghost in these bands is indicative of potential contamination from ghosts at shorter wavelengths—which might not always be flagged.

The above criteria are designed to maximize the purity of the WISE catalog, and hence minimize spurious cluster detections. For the optical catalogs, the more important factor is completeness because the optical photometry is used to reject low-redshift interlopers. Put simply, it is better to be able to use the existence of an optically bright source with some quality issues to identify a WISE source as low redshift than to allow that interloper to contribute to the density map. We therefore minimize the rejection due to flagging in the optical catalogs to the extent possible. For the SDSS catalog, we require that all sources are primary for the initial SQL query when downloading the data from CASJobs, but apply no additional filters. For Pan-STARRS, we apply no filters to the source catalog. For SuperCOSMOS, we reject sources for which the R_F-band quality flag indicates a severe defect.

To match the optical and WISE catalogs, we perform a nearest neighbor match for each WISE detection. We consider a match to be a true physical association if the separation is less than 15 from each WISE detection. This matching radius was set empirically to be sufficiently large to robustly identify true matches while minimizing the rate of spurious associations. In Figure 6, we show the distribution of nearest neighbor matches for WISE sources. For associations within 3'', 90% of matches have separations less than our 15 threshold. The AllWISE Explanatory Supplement (Section II.5.b) quantifies the distribution of astrometric offsets between WISE and UCAC4 (Zacharias et al. 2013), accounting for proper motions, finding a standard deviation σ ≃ 055 at W1 = 16. Our matching radius is thus slightly less than the 3σ astrometric uncertainty.

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Once the WISE and optical catalogs have been cross-matched, we apply the magnitude and color cuts described in Section 3.2.1 and construct density maps from the remaining sources. For existing Spitzer searches for high-redshift galaxy clusters, which typically cover <100 deg², there is generally no need to subdivide the survey region. In contrast, it is necessary for MaDCoWS to develop a tiling strategy to subdivide the search region, enabling efficient handling of the catalogs and generation of density maps. The chosen approach is to conduct the search within 10° × 10° tiles, each of which overlaps with neighboring tiles by approximately 1°. The overlap regions are used for validation in assessing the robustness of the search results.

For each tile, we generate a raw density map with a resolution of 15'' pix⁻¹. Each galaxy that passes the color, magnitude, and quality cuts described above is then inserted into the raw density map, using a smoothing kernel that assigns uniform weight over a width of two pixels. The result is a number-weighted projected galaxy density map. We note that one could instead attempt to use a flux-weighted map given the weak dependence of W1 on redshift at z ≳ 0.7 (Figure 1). Such a flux-weighted approach has the advantage of giving greater weighting to blended galaxies in cluster cores that are undercounted in number-weighted maps; however, flux-weighted maps also amplify the impact of bright contamination from low-redshift interlopers. Moreover, increasing the importance of individual bright cluster galaxies for cluster detection is not necessarily desirable, as detection becomes more sensitive to omission of a single galaxy from the density map due to the photometric quality cuts.

An important element of generating the density maps is the construction of corresponding masks to properly account for survey boundaries, regions around bright stars, and low-coverage regions. For masking, we use a two-stage approach. First, we generate masks directly from the WISE catalog data in parallel with the construction of the density maps. For every source that passes the quality cuts, the value for the coverage at that location is used as input to generate an initial coverage map at the same resolution as the density map. A smoothing kernel is applied to the map to interpolate the coverage map over pixels lacking sources. These smoothed coverage maps are then converted into binary masks associated with each raw density map, effectively masking regions of low coverage. For coverage, we define a location as having low coverage if there are fewer than 20 single-frame exposures in either W1 or W2. For reference, the standard two-epoch coverage from AllWISE corresponds to 22 observations (Cutri et al. 2013). In practice, our low-coverage restriction has little impact on MaDCoWS because the AllWISE coverage in our survey region rarely falls below 20 exposures (see Figure 7 in Section 4.2 of the AllWISE Explanatory Supplement; Cutri et al. 2013). At this stage, we also mask regions that lie outside the footprint of the associated optical data set.

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Second, we use the WISE source catalog to mask regions near bright stars. Within the region of the scattered-light halo for bright stars, the photometry for fainter objects can be contaminated. It is therefore best to avoid these sources in the survey. Table 11 in Section 4.4g.ii.1.a of the All-Sky Explanatory Supplement provides coefficients relating the halo radius for scattered-light halos to the magnitude of the source. Using this relation, we mask all sources with halo radii larger than 1' (W1 < 6.8) out to the halo radius.

Once the raw density map and mask are generated, we next convolve both with the difference-of-Gaussians kernel (Equation (1)). For the inner and outer Gaussians, we use a 6:1 ratio of outer to inner radii, setting σ₁ = 382 and σ₂ = 382 (320 kpc and 1.9 Mpc at z = 1, respectively).²⁸ The value of σ₁ is similar to that used for the ISCS and IDCS surveys (400 kpc and 300 kpc, respectively), while σ₂ is larger for MaDCoWS than for those surveys (1.6 Mpc and 1.2 Mpc, respectively). Physically, the larger σ₂ is designed to avoid oversubtraction for the most massive clusters, for which the signal can extend to larger radii. Dividing the convolved density map by the convolved mask properly removes gradients in the smoothed images that arise from the masking.

Within the smoothed density maps, we use Source Extractor (Bertin & Arnouts 1996) to identify candidate clusters. Source Extractor is run on each tile with no background subtraction. Only a single pixel is required to exceed the detection threshold for a source to be selected. Specifically, we define the peak amplitude for a source to be the maximum pixel value associated with a detection in the smoothed density maps (which is equivalent to FLUX_MAX in SExtractor), and only this peak amplitude must exceed the threshold for a source to be detected. Detections from all tiles are then combined to form a single catalog; detections are merged within overlap regions to eliminate duplicates. For all cluster candidates, we also calculate the signal-to-noise ratio (S/N) based on the peak amplitude and the rms noise in the tile within which a cluster is detected.

From the remaining candidate list, we then search through the 2MASS Extended Source Catalog (Jarrett et al. 2000) and remove all candidates that lie within twice the total magnitude extrapolation radii (r_ext) of the 2MASS extended sources. This cut, which is designed to remove peaks that may be associated with substructure in nearby galaxies, eliminates 8% of candidates. We next impose the Galactic latitude restrictions mentioned in Section 2. We restrict our search to $| b| \gt 25^\circ$ for the WISE–Pan-STARRS and WISE–SDSS data sets, increasing the Galactic zone of avoidance to $| b| \gt 30^\circ$ for cluster candidates at 300° < l < 360° and 0° < l < 60°. For the WISE–SuperCOSMOS search, we opt to maintain a $| b| \gt 30^\circ$ Galactic zone of avoidance at all l. For the SuperCOSMOS search we also apply avoidance regions near the Magellanic Clouds. We impose the restriction that candidates cannot lie within 3° of the Small Magellanic Cloud, or within an ellipse with semimajor axes of 13° and 45 for the Large Magellanic Cloud. In practice, this exclusion cut did not remove any candidates from the catalog presented below.

At this stage, we also apply an automated rejection of all cluster candidates for which the peak flux lies in a pixel adjacent to a masked region (12% of detections). Although the majority of these sources are expected to be true clusters, these sources have an enhanced likelihood of being spurious due to contamination near diffraction spikes of bright stars or other subtle image artifacts. Moreover, the peak fluxes for clusters on mask edges will often be underestimated due to the masking. For these reasons, we opt for a modest sacrifice in area for increased catalog fidelity and uniformity.

Finally, our team visually inspects WISE cutouts of each candidate in W1 and W2 to identify any non-cluster sources of peaks in the wavelet maps. There are three main sources of such contamination, examples of which are shown in Figure 7. The first source is optical ghosts, which for WISE appear as ring-like structures at a fixed position from the parent star. While optical ghosts are flagged as artifacts during generation of the WISE catalog, we have found that there exist some instances where these sources are not flagged, resulting in clusters of sources that in catalog space mimic a cluster detection. Additional examples of WISE optical ghosts can be seen in Figures 19–21 of Section II.4.b.ii of the All-Sky Explanatory Supplement. The second source of contamination arises from scattered light. Scattered light can yield anomalously red sources and can induce spurious sources of a common color in the images. The third main source of contamination consists of local galaxies not present in the 2MASS Extended Source catalog. All of the above sources of contamination are easily identifiable visually. In addition to these three main contributors, we also remove a small number of detections associated with satellite trails and other rare anomalies. In total, visual inspection removes 6% of the candidates that remain after automated rejection.

Because of the difference-of-Gaussians filtering, the MaDCoWS cluster search is relatively insensitive to larger scale variations in the source counts, which can arise from a variety of observational (sensitivity gradients) and astrophysical (foreground extinction, large-scale structure) effects. In Figure 8, we show the projected distribution of the 2433 highest amplitude detections in the WISE–Pan-STARRS region and the 250 highest amplitude detections over the rest of the extragalactic sky. The effective area of the WISE–Pan-STARRS region after accounting for masking (17,668 deg²) constitutes 82% of the combined area covered by the WISE–Pan-STARRS and WISE–SuperCOSMOS searches. As discussed in Section 4.5, we avoid $| b| \leqslant 25^\circ$ over the full sky and widen our Galactic zone of avoidance both for the SuperCOSMOS search and toward the Galactic center.

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The measured peak amplitude of an overdensity in the smoothed maps, as defined in Section 4.5, is the observable quantity used to select clusters for the MaDCoWS catalog. The distribution of peak amplitudes for the WISE–Pan-STARRS search, normalized such that the most significant peak has an amplitude of 1, is shown in Figure 9. It is approximately a power law in number versus peak amplitude. For a given detection, the amplitude of a peak is determined by the number of galaxies associated with the cluster core and the physical size of the smoothing kernel.

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Although this quantity provides the best direct observable for identifying clusters in the MaDCoWS search, it is important to understand that peak amplitude is only a coarse tracer of the true cluster richness. We therefore expect broad dispersions in cluster richness and mass for a given observed peak amplitude. There are several reasons for this scatter. First, the number of galaxies contributing to a given overdensity in the smoothed maps will be dependent on the redshift of the cluster (due to both the optical magnitude and WISE color cuts, which have the greatest impact at lower redshifts, and the fixed limiting apparent magnitude). Second, the observed number of galaxies is affected by blending in the WISE data, which will be most pronounced for the richest and most centrally concentrated clusters. Third, the observed peak amplitude will also be affected by physically associated structures along the line of sight, such as filaments. The net impact of this scatter is that for a catalog selected at a fixed peak amplitude threshold, the completeness at a fixed mass threshold is expected to be relatively low—put succinctly, we detect massive clusters, but not in a statistically complete sense as would be needed for the derivation of cosmological constraints.

Keeping this limitation in mind, as an initial validation of our approach we use IRAC photometry to confirm that the WISE candidates selected via peak amplitude correspond to overdensities of red galaxies. We directly counted the number of red galaxies (defined as [3.6] − [4.5] > 0.1 Vega) within 1' of the cluster centroid defined by the IRAC data (see Section 5.3) for the 1723 clusters from the Pan-STARRS region with IRAC photometry.²⁹ For comparison, we applied the same criteria to derive the equivalent density of red galaxies for 50 massive clusters from the SPT (0.9 < z_phot < 1.3) and for a distribution of random locations from SpUDS (Kim et al. 2011). We show the results of this comparison in Figure 10. By this IRAC-based measure, both the South Pole Telescope Sunyaez–Zel'dovich effect survey (SPT–SZ) and MaDCoWS clusters have distributions with significantly higher median values of ${N}_{\mathrm{gal},{1}^{{\prime} }}$ (43 and 44, respectively) than the random field locations from SpUDS (6.6). This figure indicates that MaDCoWS is identifying true overdensities, but should be taken only to be illustrative. In Section 6.3, we derive a higher fidelity richness estimator incorporating background subtraction, and we revisit the topic of the mass distribution of MaDCoWS clusters in Section 6.4.

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There are two factors that limit the astrometric precision of the locations presented for the cluster candidates. The first is the resolution of the smoothed density maps. The coordinates presented correspond to the central value for the pixel with the peak flux associated with each detection, with no subpixel interpolation. The precision of these coordinates is therefore limited by the 15'' pixel scale of the density maps. Second, the shot noise associated with each detection is significant, given that the detections are typically based on only the L ≳ L* galaxy population in the presence of both source confusion and foreground and background contamination. To quantitatively estimate the centering uncertainty associated with these positions, we use the IRAC photometry to calculate the centroid of the galaxy distribution as defined by the deeper Spitzer data for the subset of galaxy clusters in the WISE–Pan-STARRS catalog with existing IRAC imaging.

Details of the Spitzer centroiding will be described in an upcoming paper focused on the Spitzer catalogs; most pertinent for the current discussion is that the centroids are number-weighted and defined using galaxies detected at 3.6 μm down to the completeness limit of 10 μJy, which corresponds to roughly a 0.3 L* galaxy at z = 1 (Mancone et al. 2010). Centroids correspond to the most significant density peaks of galaxies within 1' of the MaDCoWS location. This matching radius corresponds to 500 kpc at z = 1 and is set to be substantially larger than the expected centroiding error. For this centering comparison, we apply no [3.6] − [4.5] color cut to the IRAC photometry. This choice maximizes the signal for centroiding and avoids spurious centroids for any low-redshift clusters in the sample. We include in Table 3 both the original detection coordinates and the Spitzer-derived centroids.

In Figure 11, we show the distribution of offsets. The average catalog and centroid coordinates are co-centric to within 1'', with standard deviations σ_α = 143 and σ_δ = 15'' (∼1 pixel). For clusters at z = 1, the two-dimensional positional uncertainty of 21'' corresponds to a physical uncertainty of 175 kpc in the cluster position relative to the peak of the galaxy density distribution derived from Spitzer data.

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We have previously reported spectroscopic redshifts for MaDCoWS clusters in Gettings et al. (2012), Stanford et al. (2014), Brodwin et al. (2015), Gonzalez et al. (2015), and Decker et al. (2019). In this paper, we provide spectroscopic confirmation for one additional cluster, MOO J1229+6521, which also appears in the Planck cluster catalog as PSZ2 G126.57+5161 (Planck Collaboration et al. 2016b). Observational details and individual redshifts for newly confirmed members of this cluster are reported in Appendix B. Literature redshifts also exist for several known clusters (Hilton et al. 2007, 2018). The full spectroscopic sample includes 39; the subset of 38 clusters that have both spectroscopic data and IRAC photometry serves as the validation set for our photometric redshifts.

We derive photometric redshifts based upon the [3.6] − [4.5] colors of cluster galaxies, augmented by the i – [3.6] color information. This approach is similar to that of Muzzin et al. (2013), who used a combination of z-band and IRAC photometry to derive photometric redshifts. Figure 12 shows the i – [3.6] versus [3.6] − [4.5] color of galaxies in the field of one of our spectroscopically confirmed clusters, MOO J1142+1527 (z = 1.189). Also shown is a curve tracing the expected colors as a function of redshift for a passively evolving galaxy with solar metallicity formed via a single stellar burst at z_f = 3, using EzGal (Mancone et al. 2012, www.baryons.org/ezgal) and the Flexible Stellar Population Synthesis code (FSPS; Conroy et al. 2009; Conroy & Gunn 2010).

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To compute the effective color of the ensemble of cluster galaxies, we first select all galaxies with f_4.5 > 15 μJy that lie within 1' of the cluster centroid.³⁰ We then construct a smoothed density distribution using a kernel density estimation algorithm. The peak of this smoothed density distribution is taken as the representative color of cluster galaxies. For the subset of candidates with multiple color peaks, we associate the brightest peak with the cluster but also calculate the colors of any secondary or tertiary peaks. We report the redshifts of these peaks only if the derived richnesses (see Section 6.3) exceed that of the primary peak. In principle, the peak of the smoothed density distribution associated with the cluster should lie close to the model curve for passive cluster populations, and blueward of the curve in i – [3.6] for star-forming galaxies. In practice, the i – [3.6] peak color is not well constrained because many cluster galaxies are non-detections in Pan-STARRS. Inclusion of galaxies with only magnitude limits in the i-band results in the peak of the distribution being biased toward bluer i – [3.6].

To infer redshifts from the color distribution, we rely primarily on the more robust [3.6] − [4.5] color. This color increases monotonically at 0.7 < z < 1.7. Within this redshift range, we calculate the photometric redshift by determining the model redshift, which yields the [3.6] − [4.5] color closest to that of the peak of the smoothed density distribution. While the IRAC photometry alone is sufficient to derive low-scatter photometric redshifts for clusters at z > 0.7,³¹ the expected [3.6] − [4.5] colors of cluster galaxies at 0.7 < z < 1.15 are degenerate with those of galaxies at z < 0.7. We use the i – [3.6] color to break this degeneracy. For low-redshift structures, the galaxies are brighter and the i – [3.6] colors bluer, yielding detections rather than upper limits, and enabling robust determination of the low-redshift solution.

The strongest peaks in the smoothed density maps correspond to z < 0.7 for ∼2% of the full ensemble of candidates with Spitzer/IRAC photometry. Using data from the Legacy Surveys (Dey et al. 2018), we visually inspected the subset of these 2% that lies within the Dark Energy Camera Legacy Survey DR7 footprint.³² In all cases, we find that the low-redshift peak in color space is a foreground cluster unassociated with the galaxies that contributed to the MaDCoWS detection. For this reason, we impose a prior on the photometric redshift estimates, requiring that the solution lie at z ≥ 0.6 for the WISE–Pan-STARRS and WISE–SDSS catalogs. In cases where there is a strong peak in the color distribution corresponding to a low-redshift cluster, we note in the tables the presence of a foreground structure. There are a total of six clusters in the two catalogs (0.3% of the Spitzer sample) for which it is not possible to recover a redshift and richness for the background cluster. In these cases, we simply note the presence of the foreground structure. For the WISE–SuperCOSMOS catalog, which lies outside the DR7 footprint and has less robust removal of foreground galaxies (see Figure 4), we impose no prior.

Comparing with the 38 spectroscopic redshifts (Figure 13), we find two outliers for which the photometric redshifts are >5σ from the spectroscopic redshift.³³ For the rest of the sample, the scatter is σ_z/(1 + z) = 0.036. For all clusters with Spitzer/IRAC photometry, which is essential for achieving this fidelity in the redshift estimates, we include in Table 3 the photometric redshifts and associated uncertainties.

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In Figure 14, we show the photometric redshift distribution for MaDCoWS cluster candidates within the Pan-STARRS region with Spitzer photometry (blue solid curve). We also show the redshift distribution for all MaDCoWS clusters within the Pan-STARRS region with spectroscopic redshifts (red dashed). The curves shown are derived using Gaussian kernel density estimation, applying Scott's rule (Scott 1992) to calculate the estimator bandwidth. The general similarity of the curves illustrates the robustness of the estimated redshift distribution. The low-redshift cutoff seen in the full sample arises primarily from the magnitude and color cuts used in the initial galaxy selection for the cluster search,³⁴ while the high-redshift decline is due to a combination of a decrease in the number density of massive clusters and the W1 band not quite reaching constant stellar mass with increasing redshift.

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In Figure 14, we also plot the photometric redshift distribution for MaDCoWS clusters within the SuperCOSMOS footprint with Spitzer photometry (green dotted–dashed line). As expected, the redshift distribution is shifted to slightly lower redshifts relative to the Pan-STARRS sample, with median redshifts of 0.98 and 1.06 for the two samples. For the WISE–SuperCOSMOS sample, 6% of the clusters have z_phot < 0.7, compared to 0% for the WISE–Pan-STARRS sample. This difference is due to the combination of the weaker optical color cut, which retains more low-redshift galaxies during the cluster search, and the fact that we do not impose a z ≥ 0.6 prior on the photometric redshifts. The prior is omitted to reflect the fact that with the weaker color cut, these low-redshift solutions may correspond to the cluster detections.

At a fundamental level, there are strong indications that robust cluster mass estimates are attainable directly from observations of the stellar content. Authors including Girardi et al. (2000) and Lin et al. (2003) provided early demonstrations that the total baryon content scales with cluster mass. Lin et al. (2003), for example, found that the scatter in the relation between K-band luminosity (L_K) and M₅₀₀ from X-ray data was ∼45%, with this scatter dominated by observational uncertainties. More recently, studies with much higher fidelity data and membership information have demonstrated convincingly that the intrinsic scatter is quite low. For example, Mulroy et al. (2014) determined that for the LoCuSS cluster sample the intrinsic scatter in the L_K−M₅₀₀ relation is ∼10%. Consistent with these observations, multiple groups have also shown at a fixed halo mass that the ratio of gas mass in the ICM to stellar mass displays a remarkably small intrinsic scatter, indicative of the baryons being partitioned between these two phases with little variation between clusters at fixed M₅₀₀ (Laganá et al. 2008; Zhang et al. 2011; Gonzalez et al. 2013).

The challenge, however, lies in the reality that in contrast with the LoCuSS sample, membership information is not available for existing cluster surveys directly from the searches. As a result, interlopers can significantly degrade the fidelity of luminosity-based mass estimators. Cluster richnesses, defined based upon number counts rather than total luminosity, are more robust to such contamination. In recent years, multiple groups have shown that it is possible to define richness measures that are robust mass proxies with low scatter (e.g., Rykoff et al. 2012; Rozo & Rykoff 2014; Andreon 2015, 2016; Old et al. 2015, and references therein). Using mock galaxy catalogs to compare a suite of richness estimators, Old et al. (2015) found a scatter of 0.18 dex in the M₂₀₀−richness relation for the best proxy. For samples of real, low-redshift clusters, Andreon (2015) and Rozo & Rykoff (2014) defined the richness measures n₂₀₀ and λ, for which they find scatters of 0.16 dex and ∼0.11 dex, respectively.

Our practical goal for MaDCoWS is to develop a similarly low-scatter mass proxy that can be applied to the full catalog. A limitation, as discussed in the previous section, is that the WISE data alone lack the spatial resolution and depth necessary for such a low-scatter estimator. We have therefore proceeded with the alternate approach of calibrating a Spitzer-based richness estimator that can be applied to the large fraction of the sample with IRAC data from either the archive or our programs in Cycles 9, 11, and 12.

6.3.1. Richness Definition

For MaDCoWS, we explored the use of multiple richness measures to identify a suitable estimator for use with IRAC data. Similar to Rettura et al. (2018), we settled on the use of a fixed aperture for defining the richness. In contrast with that study, we employ a physical rather than angular aperture and incorporate optical data to minimize contamination and reduce scatter in the mass–richness relation.

Our first step in establishing a richness definition for MaDCoWS is to set a uniform limiting [4.5] flux density for the IRAC input galaxy catalog of 15 μJy (m = 17.7 Vega). This 4.5 μm selection is designed to yield an approximately constant stellar mass threshold at 0.7 < z < 1.5 and hence minimize the redshift dependence of the richness measure. For this redshift range, 15 μJy corresponds to a stellar mass of ∼5 × 10¹⁰ M_⊙ assuming an FSPS model with a Chabrier IMF normalized to Coma, with only a modest dependence on star formation history. We also match all 4.5 μm selected sources to the Pan-STARRS PV2 catalog to obtain i-band magnitudes or upper limits for each galaxy.

A challenge that one encounters when using Spitzer imaging for this analysis is that the IRAC field of view extends to only ∼1.3 Mpc from the center of the cluster for a galaxy cluster at z ≃ 1. One consequence is that the total galaxy density does not necessarily reach the field level within the IRAC field of view (for example, see Wylezalek et al. 2013), precluding robust local background subtraction. For this reason, when calculating richnesses, we use color cuts to minimize foreground contamination, and then use data from the Spitzer Deep, Wide-Field Survey (SDWFS; Ashby et al. 2009) to estimate the background density. We isolate galaxies near the cluster redshift by combining an i – [3.6] criteria with a second color cut in [3.6] − [4.5]. This additional cut helps compensate for the fact that the Pan-STARRS imaging is not deep enough to detect all IRAC-selected cluster galaxies at z = 1.

Starting with the redshift for a given cluster, we use EzGal to calculate the expected i – [3.6] and [3.6] − [4.5] color for a cluster galaxy. We calculate this color using the same passively evolving model as in Section 6.1. We then consider galaxies to be possible cluster members if they are either detected in i and less than one mag bluer in i – [3.6] than the fiducial color, or else are non-detections in i and the lower limit on i – [3.6] is no more than one mag redder than the fiducial color. We additionally require that a galaxy have a [3.6] − [4.5] color within ±0.15 mag of the fiducial. The i – [3.6] color threshold is set such that this threshold will retain not only passive galaxies, but also star-forming galaxies with exponentially declining star formation histories (τ = 1 Gyr) and initial formation redshifts z_f ≳ 3. The width of the color window in [3.6] − [4.5] minimizes the exclusion of cluster members due to either photometric uncertainty or redder colors arising from moderate AGN contributions to the photometry, while still providing a meaningful reduction of the background contribution. Examples of the implemented color cuts are shown in Figure 15 for two confirmed MaDCoWS clusters at z = 0.99 and z = 1.189, respectively. The boxes in Figure 15 illustrate the color windows used for galaxies with i-band detections.

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A second consequence of the field-of-view constraint is that the data do not uniformly reach to sufficiently large radii for us to use richness estimators extending to r₂₀₀—motivating our use of a fixed, 1 Mpc radius metric aperture. Green points in Figure 12 denote galaxies that lie within 1 Mpc of the WISE-based cluster centroid and satisfy the color criteria. In defining the color cuts and apertures size, we use the photometric redshifts described in Section 6.1.

We define the richness λ = N − N_field, where N is the total number of color-selected galaxies within the metric aperture. In quoting values of λ, we also include as a subscript the threshold flux density, such that λ₁₅ denotes the richness calculated for sources f_4.5 > 15 μJy. We calculate the expected field density, N_field, for each cluster by computing the average density of galaxies found in SDWFS for the same magnitude and color cuts and scaling to the appropriate aperture area. In cases where the IRAC data are incomplete within the metric aperture, we apply a correction to account for the fractional area lost. We refrain, however, from quoting richnesses for clusters at z < 0.7. A 1 Mpc radius extends beyond the field of the IRAC imaging for these clsuters, and a fractional area correction would generally lead to a poor estimate of the true richness. For clusters with archival Spitzer data, we also avoid quoting richnesses for systems with low partial IRAC coverage. Richnesses are included in the catalog in Table 3.

The caveat with this approach is that photometric redshift scatter will increase the scatter between richness and mass, and a catastrophic failure on the photometric redshift will result in a spurious richness estimate. We find that the former effect is minor. Based upon our spectroscopic confirmation, catastrophic outliers are also rare (at the few percent level). When they do occur, the impact will be a misestimation of the richness due to shifting of the color-selection window away from the appropriate cluster color.

6.3.2. The Relation between Richness and Mass

To provide an initial calibration of the mass–richness relation, we consider a subset of MaDCoWS clusters imaged with Spitzer with derived SZ mass estimates from CARMA. The M₅₀₀ measurements are for a total of 14 clusters, five of which have previously reported SZ detections in Brodwin et al. (2015) and Gonzalez et al. (2015). For previously reported clusters, we use updated mass estimates from Decker et al. (2019), which will provide a homogeneous analysis for the full sample. The list of clusters used for this analysis is presented in Table 2.

Table 2.  Clusters in the Mass–Richness Calibration

Name	z	λ15	M500
			(1014 M⊙)
MOO J0037+3306	1.139	54 ± 8	${2.34}_{-0.63}^{+0.65}$
MOO J0105+1324	1.143	87±10	${4.03}_{-0.45}^{+0.48}$
MOO J0123+2545	1.229	41±7	${3.90}_{-0.81}^{+0.89}$
MOO J0319–0025	1.194	34 ± 6	${3.11}_{-0.47}^{+0.53}$
MOO J1014+0038	1.230	44 ± 7	${3.26}_{-0.30}^{+0.32}$
MOO J1111+1503	1.36a	33 ± 6	${2.08}_{-0.31}^{+0.30}$
MOO J1142+1527	1.189	58 ± 8	${5.45}_{-0.51}^{+0.58}$
MOO J1155+3901	1.009	33 ± 6	${2.61}_{-0.55}^{+0.56}$
MOO J1231+6533	0.99a	50 ± 8	${4.69}_{-1.00}^{+1.24}$
MOO J1335+3004	0.984	30 ± 6	${1.38}_{-0.74}^{+0.75}$
MOO J1514+1346	1.059	73 ± 9	${1.89}_{-0.79}^{+0.68}$
MOO J1521+0452	1.312	47 ± 7	${3.65}_{-0.94}^{+1.03}$
MOO J2206+0906	0.951	54 ± 8	${2.66}_{-0.74}^{+0.93}$
MOO J2231+1130	0.80a	49 ± 8	${4.38}_{-1.37}^{+1.51}$

Note. We list in this table all clusters that are included in determination of the mass–richness calibration. All M₅₀₀ measurements are derived from CARMA SZ observations.

^aPhotometric redshift.

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We derive a best-fit mass–richness relation, which we parameterize as

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{500}}{{10}^{14}{M}_{\odot }}=\alpha \mathrm{log}{\lambda }_{15}+\beta ,\end{eqnarray} \tag{ 2 }$$

using the Python implementation³⁵ of the Bayesian code linmix (Kelly 2007). For the sake of uniformity, the richnesses used in this fit are calculated using the photometric redshifts to define the appropriate color window for selecting cluster members. We show the data, with richness calculated within a 1 Mpc diameter aperture, in the left panel of Figure 16. The scatter between mass and richness is large for the full ensemble; however, we note that two of these clusters, MOO J0105+1323 and MOO J2206+0906, are clearly early-stage major mergers based on Chandra observations that will be presented in a forthcoming paper. These two clusters are plotted as red open circles in the right panel of this figure. A third cluster, MOO J1514+1346 (red filled circle), which has the second highest Spitzer-derived richness of the clusters in the Figure, also shows tentative evidence of major merger activity. In the right panel, we additionally plot in blue the clusters with existing Chandra data that exhibit no evidence for early-stage major merger activity. Overlaid, we show a best-fit mass–richness relation derived excluding the red points. The best-fit relation is plotted as a solid line, with the shaded region indicating the 1σ confidence interval.

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The best-fit values, which are not well-constrained given the limited dynamic range in mass and small sample size, are formally $\alpha ={1.65}_{-0.96}^{+1.45}$ and $\beta =-{2.16}_{-2.38}^{+1.57}$. The scatter in mass about the relation is 36% ± 11% (${\sigma }_{\mathrm{log}M| \lambda }=0.12$), where the quoted uncertainty is derived via a bootstrap resampling of the data. It is clear from the right panel of Figure 16 that a single cluster, MOO J0037+3306, is a significant contributor to this scatter. If we assume that this cluster, for which we currently lack Chandra data, is also a merging cluster, then we can re-fit the data and obtain a refined estimate of the scatter for the other systems that lack similar evidence of ongoing major mergers. Doing so, the best-fit parameters change minimally ($\alpha ={1.86}_{-0.88}^{+1.53}$ and $\beta =-{2.49}_{-2.50}^{+1.43}$), while the scatter is reduced to 16% ± 6% (${\sigma }_{\mathrm{log}M| \lambda }=0.07$).

We repeat the above analysis to assess the sensitivity of this relation to photometric redshift uncertainties, positional offsets, and flux density thresholds, varying these quantities. First, we use spectroscopic redshifts, which are available for all but three of these clusters. The change in the richnesses is minimal, and hence the fit and ${\sigma }_{\mathrm{log}M| \lambda }$ remain essentially unchanged. Second, we use the Spitzer-derived centers instead of the WISE cluster centers, again finding negligible change in ${\sigma }_{\mathrm{log}M| \lambda }$. Finally, we also test the use of a 10 μJy rather than 15 μJy threshold for the richness. This again does not appreciably alter the scatter, though by definition it does change the normalization of the relation.

It thus appears, perhaps not surprisingly, that there may exist a relatively tight underlying relation between mass and richness for non-merging clusters, while a subset of merging systems are offset to lower SZ mass (or higher richness) than one would expect from this relation. Multiple studies (e.g., Poole et al. 2007; Krause et al. 2012; Yu et al. 2015) find in simulations that major mergers can systematically bias downward the masses inferred from Y_SZ. This bias is on average ∼10%–15% for M₂₀₀ in Krause et al. (2012), but in some cases can be significantly larger. Physically, this bias is due to the time required for the temperature to increase to the equilibrium level corresponding to the mass of the merged cluster. If the richness measure approaches the new level more quickly than the temperature, which is expected given the large 1 Mpc radius metric aperture used in this paper, then there will also be an offset of merging systems in the λ₁₅−M₅₀₀ plane.³⁶

The MaDCoWS clusters with the highest Spitzer richnesses will therefore be comprised of a combination of the most massive clusters and those undergoing major mergers. ICM observations are necessary to discriminate between these two scenarios. It should also thus be expected that as major mergers become an increasing fraction of the total cluster population with increasing redshift, the observed scatter between SZ mass and richness will increase commensurately unless one identifies and exclude mergers.

We caution that the above is preliminary, being based upon a small number of clusters and not including CARMA non-detections. It therefore should be taken as indicative of the general trend rather than a definitive measure of the mass−richness relation. Ongoing SZ programs with ALMA (PI: Brodwin, programs #2016.2.00014.S and #2017.1.00961.S), MUSTANG-2 (PI: Brodwin, programs GBT 18A-272 and GBT 18B-215), and NIKA2 (PI: Brodwin, programs 095-17 and 095-18), plus a more thorough analysis of the CARMA observations including non-detections and stacking, are forthcoming. These efforts should yield a superior calibration and a better assessment of the total scatter.

In Figure 17, we plot the observed richness distribution for all clusters with IRAC photometry from both the WISE–Pan-STARRS and southern WISE–SuperCOSMOS searches. In both instances, these histograms correspond to peak amplitude-limited subsamples, modulo the inclusion of a small number of clusters added from the Spitzer archive. As is evident from the figure, both samples have similar median richnesses and approximately power-law distributions at higher richness, as might be expected if the distribution is probing the halo mass function at the high richness end with the survey selection function yielding a turnover in the number of clusters below λ₁₅ ∼ 25. Using the mass–richness calibration derived in Section 6.3, the median richness for the WISE–Pan-STARRS sample corresponds to a mass ${M}_{500}={1.6}_{-0.8}^{+0.7}\times {10}^{14}\,{M}_{\odot }$. The equivalent number for the WISE–SuperCOSMOS sample is M₅₀₀ = (1.4 ± 0.7) × 10¹⁴ M_⊙.

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We also present in Figure 18 the current distribution in the mass–redshift plane of all MaDCoWS clusters with masses from CARMA or the literature (Fassbender et al. 2011b; Bleem et al. 2015; Hilton et al. 2018), comparing to existing wide-area SZ and X-ray surveys. We denote with open circles clusters for which we currently lack a spectroscopic redshift. These clusters are placed at their estimated photometric redshift. It is apparent from Figure 18 that the MaDCoWS sample includes clusters that span the mass range probed by the combination of existing SZ and X-ray surveys at this epoch, including several of the most massive clusters known at z > 1. For comparison, we also plot contours showing the inferred distribution for all MaDCoWS clusters with IRAC photometry, where we use the photometric redshifts from Section 6.2 and richness-based mass estimates from Section 6.3. The density contours are spaced by powers of 2, illustrating that the distribution is strongly peaked at z ≃ 1 and M ≃ (1–2) × 10¹⁴ M_⊙. We caution against overinterpretation of these contours, particularly outside the range over which the mass–richness relation is calibrated (M₅₀₀∼(1.5–5.4) × 10¹⁴ M_⊙). These contours should be considered illustrative rather than definitive.

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As a test of our ability to recover known massive, high-redshift clusters, we compare our MaDCoWS–Pan-STARRS results with the two-season ACTPol Sunyaev–Zel'dovich catalog (Hilton et al. 2018). ACTPol, which covers 987.5 deg², is the only published high-redshift SZ survey that overlaps with the WISE–Pan-STARRS region. The ACTPol catalog includes 19 clusters at z > 0.9, four of which have spectroscopic redshifts, with weak-lensing calibrated masses ${M}_{500}^{\mathrm{Cal}}\gtrsim 2.5\times {10}^{14}\,{M}_{\odot }$. Of these 19 ACTPol clusters, only one (ACT-CL J0125.2–0802) is in the MaDCoWS catalog in Table 3. We investigate the cause of this minimal overlap, finding that it can be attributed to several factors. A minor factor is the masking of bright stars in the MaDCoWS search, which removes one of the 19 clusters (ACT-CL J0248.7–0019). The other two more significant factors are the high threshold for our catalog and the large scatter between peak amplitude and mass—the latter also being the reason that IRAC imaging is required for determining richnesses. Two additional clusters are detected at S/N > 8, but just below our peak amplitude threshold, and a total of 8 (12) out of the 18 unmasked clusters are detected at S/N > 5 (>3). From a practical perspective, it would not be possible with the current approach to identify these clusters as the most massive among the larger ensemble of MaDCoWS clusters in this region without deeper mid-infrared imaging such as what we have obtained with Spitzer/IRAC for a subset of the MaDCoWS clusters.

Table 3.  Top 2433 Candidate Clusters in the WISE–Pan-STARRS Region

Cluster	α	δ	Peak	S/N	zphot	z (Members)	λ15	M500	Spitzer	Literature Names	Reference
	[J2000]	[J2000]	Height					[1014M⊙]		and Comments
MOO J0001+1428	00h01m091	14d28m57s	0.59	9.0	${1.14}_{-0.10}^{+0.13}$	⋯	15 ± 4	⋯	C11	⋯
MOO J0001+3644	00h01m098	36d44m38s	0.56	9.9	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0001+3440	00h01m385	34d40m50s	0.56	9.3	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0001−2447	00h01m494	−24d47m32s	0.58	8.4	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0001−2533	00h01m547	−25d33m35s	0.69	10.6	${1.17}_{-0.05}^{+0.06}$	⋯	43 ± 6	⋯	C11	⋯
MOO J0002−0820	00h02m062	−08d20m50s	0.56	8.5	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0002+1751	00h02m295	17d51m30s	0.60	9.5	${1.33}_{-0.06}^{+0.04}$	⋯	26 ± 5	⋯	C11	⋯
MOO J0003−0903	00h03m012	−09d03m24s	0.66	10.0	${0.94}_{-0.06}^{+0.07}$	⋯	18 ± 5	⋯	C11	⋯
MOO J0003−2925	00h03m283	−29d25m58s	0.84	12.9	${1.05}_{-0.10}^{+0.10}$	⋯	22 ± 5	⋯	C11	⋯
MOO J0003−1341	00h03m373	−13d41m16s	0.69	10.5	${0.85}_{-0.05}^{+0.06}$	⋯	32 ± 6	⋯	C11	⋯
MOO J0004−0232	00h04m267	−02d32m44s	0.56	8.5	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0004+0024	00h04m428	00d24m00s	0.57	8.7	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0004+0108	00h04m521	01d08m36s	0.61	9.3	${0.94}_{-0.09}^{+0.09}$	⋯	21 ± 5	⋯	C11	⋯
MOO J0005+1329	00h05m286	13d29m32s	0.58	8.8	${0.94}_{-0.08}^{+0.08}$	⋯	34 ± 6	⋯	C11	⋯
MOO J0005+0024	00h05m292	00d24m00s	0.56	8.6	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0005+1408	00h05m378	14d08m10s	0.69	10.4	${0.98}_{-0.06}^{+0.06}$	⋯	17 ± 5	⋯	C11	⋯
MOO J0005−0443	00h05m401	−04d43m26s	0.57	8.6	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0006+3050	00h06m293	30d50m55s	0.65	10.9	${1.02}_{-0.06}^{+0.06}$	⋯	42 ± 7	⋯	C11	⋯
MOO J0006−0244	00h06m343	−02d44m42s	0.57	8.7	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0006−0751	00h06m363	−07d51m39s	0.57	8.6	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0007−2108	00h07m136	−21d08m36s	0.56	8.4	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0008−1703	00h08m164	−17d03m40s	0.56	8.4	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0009−0750	00h09m343	−07d50m12s	0.62	9.4	${1.14}_{-0.15}^{+0.17}$	⋯	22 ± 5	⋯	C11	⋯
MOO J0010+2027	00h10m189	20d27m28s	0.63	10.0	${0.88}_{-0.10}^{+0.12}$	⋯	14 ± 5	⋯	C11	⋯
					${1.48}_{-0.10}^{+0.26}$	⋯	18 ± 5	⋯
MOO J0010+3142	00h10m477	31d42m14s	0.66	10.9	${1.41}_{-0.05}^{+0.05}$	⋯	33 ± 5	⋯	C11	⋯
MOO J0010+2751	00h10m541	27d51m10s	0.58	9.7	${0.98}_{-0.09}^{+0.10}$	⋯	20 ± 5	⋯	C11	⋯
MOO J0011−1414	00h11m144	−14d14m46s	0.60	9.0	${1.03}_{-0.06}^{+0.08}$	⋯	35 ± 6	⋯	C11	⋯
MOO J0011−2530	00h11m313	−25d30m55s	0.56	8.7	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0012−0218	00h12m544	−02d18m10s	0.60	9.1	${1.19}_{-0.07}^{+0.08}$	⋯	35 ± 6	⋯	C11	⋯
MOO J0012−1941	00h12m595	−19d41m38s	0.57	8.5	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0013+0700	00h13m481	07d00m52s	0.59	8.9	${1.09}_{-0.07}^{+0.07}$	⋯	33 ± 6	⋯	C11	⋯
MOO J0014−0909	00h14m333	−09d09m23s	0.61	9.2	${0.89}_{-0.04}^{+0.05}$	⋯	16 ± 6	⋯	C11	⋯
MOO J0014−0459	00h14m405	−04d59m23s	0.62	9.5	${1.02}_{-0.04}^{+0.04}$	⋯	32 ± 6	⋯	C9	⋯
MOO J0015+2059	00h15m062	20d59m58s	0.57	9.1	⋯	⋯	⋯	⋯	⋯	⋯
MOO J0015+2822	00h15m063	28d22m16s	0.59	9.9	${0.98}_{-0.09}^{+0.10}$	⋯	27 ± 5	⋯	C11	⋯

Note. The 2433 highest significance galaxy cluster candidates in the MaDCoWS catalog drawn from the Pan-STARRS region. The detection peak height is normalized such that the highest significance detection has a value of 1. The signal-to-noise ratio corresponding to each detection is also given in column 5. Column 6 lists the photometric redshifts from Spitzer when available, and column 7 provides spectroscopic redshifts and the number of confirmed members for clusters with spectroscopic data. For clusters with Spitzer data, we also present the derived richness in column 8 and indicate in column 10 whether this data was from the Cycle 9 or Cycle 11 programs, or from the archive. We also include masses for clusters with SZ observations in Column 9. A "†" in the reference column indicates that there is a foreground cluster along the line of sight.

References. [1] Postman et al. (1996), [2] Olsen et al. (1999), [3] Gonzalez et al. (2001), [4] Andreon et al. (2005), [5] Hilton et al. (2007), [6] Pacaud et al. (2007), [7] Andreon et al. (2008), [8] Muzzin et al. (2009), [9] Stern et al. (2010), [10] Durret et al. (2011), [11] Fassbender et al. (2011a), [12] Gettings et al. (2012), [13] Mehrtens et al. (2012), [14] Brodwin et al. (2015), [15] Ford et al. (2014, 2015), [16] Stanford et al. (2014), [17] Gonzalez et al. (2015), [18] Sifón et al. (2016), [19] Hilton et al. (2017), [20] Wen & Han (2018), [21] Decker et al. (2019).

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The current MaDCoWS search attempts to make optimal use of existing surveys, but there are several prospects for upcoming data sets that can yield an improved version of the MaDCoWS search. One notable limitation of the current search is the limited depth of the SuperCOSMOS imaging outside the Pan-STARRS footprint. As described in Section 2.2.3, the shallowness of this imaging yields higher foreground contamination (Figure 3), resulting in a lower fidelity and lower median redshift catalog at δ < −30°. Several surveys are underway that will enable a uniform search comparable in quality to what is currently achieved in the Pan-STARRS region over the full extragalactic sky. Observations for the DES (Dark Energy Survey Collaboration et al. 2016) are expected to provide adequate data over ∼5000 deg², of which over half are at δ < −30°. Of particular note, this area includes the region of the SPT–SZ survey (Bleem et al. 2015), enabling us to compare catalogs and better assess selection biases associated with the MaDCoWS search. Two other surveys that also have the potential to enable a higher fidelity search in the south are the SkyMapper Southern Sky Survey Main Survey (SMSS; Keller et al. 2007) and the Southern Photometric Local Universe Survey (S-PLUS).³⁷ The SMSS is designed to cover the entire southern sky (δ < 0°) to u, g, v, r, i, z = 20.5, 20.5, 21.7, 21.7, 20.7, 19.7 (AB, 5σ).³⁸ These data will significantly improve the rejection of low-redshift galaxies relative to the R_F limit used for SuperCOSMOS, although the i-band depth is still shallow relative to Pan-STARRS. S-PLUS meanwhile plans to cover ∼8000 deg² in ugriz and seven narrowband filters. S-PLUS is designed to have shallower i-band photometry than Pan-STARRS but is expected to be sufficiently deep in z-band to enable an equivalent search.

A more fundamental limitation for the current MaDCoWS search is the depth of the WISE photometric catalog that is used for the initial selection of galaxies. As was shown in Figure 1, the WISE photometry is only currently deep enough to identify at >5σ individual ∼L* galaxies out to z ≃ 1 in W1, and only detects these galaxies at ∼2σ in W2. This depth threshold has multiple implications for the search. First, it necessitates that we use W1 for galaxy selection, reducing the sensitivity of the survey to the highest redshift clusters. Second, because we are only detecting the bright end of the luminosity function with WISE, cluster identification relies upon extracting a cluster signal generated by a small number of bright galaxies. The strength of the signal is therefore highly sensitive to statistical variations in the number counts of cluster galaxies, which can increase due to both blending of individual sources at the resolution of WISE and statistical variations in the luminosity function. Thus, while detections in the current survey catalog result from true overdensities, not all overdensities are detected as significant due to such statistical variance.

There exists the potential for significant improvement on this front. We have used the AllWISE catalog for this paper. This catalog, which was released in 2013, is the deepest currently available all-sky WISE catalog and incorporates all data prior to the end of the post-cryogenic mission in 2011 February. During this period, WISE mapped the full sky twice in the short wavelength bands. In 2013 October, the WISE satellite was reactivated for the NEOWISE mission (Mainzer et al. 2014), resuming survey observations in W1 and W2. The mission is currently scheduled to continue through 2018 December, providing a factor of 5 or more increase in total exposure time in these bands over the full sky, and thus a factor of 5 increase in the total exposure time relative to AllWISE images. Meisner et al. (2017) have demonstrated the potential gain in depth. Stacking three years' worth of data from WISE and NEOWISE, they reach 0.56 (0.46) mag deeper in W1 (W2) than AllWISE data alone. The "CatWISE" effort, funded by NASA's Astrophysics Data Analysis Program, is adapting the AllWISE data processing pipeline to generate a catalog from four years of WISE and NEOWISE data, with planned release in mid-2019. Galaxy catalogs derived from full-depth stacks from the entire WISE and NEOWISE missions will have sufficient depth to detect L* galaxies in W2 out to z ≳ 2 and push much fainter than L* in W1, enabling a higher completeness cluster search at z ∼ 1 and greater sensitivity to high-redshift (z ≃ 1.5–2) clusters.

Finally, from an algorithmic perspective, the increased sensitivity of CatWISE, coupled with the optical surveys, will enable a more sophisticated treatment of foreground rejection and should enable a detection observable that is a significantly lower scatter proxy for cluster mass. The combination of a full-depth CatWISE catalog and the upcoming southern optical surveys together thus hold promise for a uniform, high-fidelity cluster search extending to z > 1.5 and spanning the full extragalactic sky.