The WaZP galaxy cluster sample of the Dark Energy Survey Year 1

The abundance and clustering properties of galaxy clusters have been shown to be powerful probes to constrain cosmological models, provided that their astrophysical properties are well characterized and linked to theoretical predictions (e.g., Lima & Hu, 2005; Vikhlinin et al., 2009; Mantz et al., 2010; Benson et al., 2013; Weinberg et al., 2013; Planck Collaboration et al., 2016; DES Collaboration et al., 2020).

Galaxy clusters can be detected from X-ray observations (Kim et al. 2007; Lloyd-Davies et al. 2011; Adami et al. 2018) and from the Sunyaev-Zel’dovich (SZ) effect (Bleem et al., 2015), but on-going and future large photometric surveys constitute a very promising approach to build large controlled galaxy cluster samples for both cosmological and astrophysical studies. These include the Kilo Degree Survey (KIDS, de Jong et al. 2013), the Dark Energy Survey (DES, The Dark Energy Survey Collaboration Flaugher 2005), Pan-STARRS (Kaiser et al., 2002), the Legacy Survey of Space and Time (LSST, LSST Science Collaboration et al. 2009) and the European Space Agency Cosmic Vision mission (Euclid, Laureijs et al. 2011).

However, detecting and characterizing clusters through their galaxy component remains a nontrivial task, especially when considering lower mass or higher redshift clusters. One has to distinguish between gravitationally bound groups of galaxies and projection effects due to the underlying large scale distribution of galaxies. Projection effects not only impact detection, but also several fundamental properties of detected clusters, such as centering, redshift, and mass proxy (e.g., cluster richness).

Many automated algorithms were developed in the last three decades to overcome these difficulties. Automatic optical cluster finders can generally be described as algorithms searching for cluster scale galaxy overdensities. Galaxies are first filtered (or weighted) following prescriptions to increase the detection contrast relative to background galaxies. The main techniques used for searching galaxy overdensities include kernel smoothing (e.g., Shectman, 1985; Lumsden et al., 1992; Adami et al., 2010; Gladders & Yee, 2000), Friends-of-Friends (e.g., Botzler et al., 2004; Trevese et al., 2007; Wen et al., 2012) or Voronoi tesselation (e.g., Ramella et al., 1999; Soares-Santos et al., 2011). These techniques have been applied to galaxy catalogs that are usually previously filtered in one or several dimensions (e.g., magnitudes, colors, or photometric redshifts). More sophisticated approaches assume an underlying cluster model (e.g., density profile, luminosity function, color content) and identify clusters in likelihood maps based on matched filter techniques (e.g., Postman et al., 1996; Olsen et al., 1999; Koester et al., 2007; Olsen et al., 2008; Rykoff et al., 2014, 2016; Bellagamba et al., 2018).

A typical assumption of optical cluster finders is to consider the presence of a red sequence of galaxies (Gladders & Yee, 2000; Koester et al., 2007; Hao et al., 2010; Murphy et al., 2012). In low redshift clusters, the most luminous galaxies define a tight sequence in the color-magnitude diagram, the so-called "E/S0 ridge line", or "red sequence". Red sequence galaxies have very uniform colors and are among the reddest galaxies at a given redshift. Because of the strong 4000 Åbreak in their rest-frame spectra, their color is tightly correlated with redshift and can be used to estimate cluster redshifts. This feature has been observed in rich clusters up to $z\sim 1.7$ (e.g., Mei et al., 2009; George et al., 2011; Wetzel et al., 2013; Strazzullo et al., 2019). However, some galaxy clusters observed at high redshifts can display appreciable star formation, even in cluster cores (e.g., Brodwin et al., 2013), weakening the red sequence.

Cluster finders such as maxBCG (Koester et al., 2007), redMaPPer (Rykoff et al., 2014, 2016) or RedGOLD (Licitra et al., 2016) rely on the red sequence for cluster detection and redshift estimate. In the context of recent surveys, cluster finders not based on the red sequence usually rely on photometric redshifts. An alternative based on the knee of the cluster luminosity function was also used in the context of surveys with a limited number of passbands (e.g., Postman et al., 1996; Olsen et al., 1999).

Even if current automated optical cluster finders are all able to identify rich clusters, evaluating their performances over broad ranges of masses and redshifts and deriving the selection function of the resulting cluster samples remain highly complex tasks. On the theoretical side, this requires the development of ever more realistic simulated galaxy catalogs. On the observational side, we need multiple surveys covering the same area at different frequency domains to detect clusters through a variety of signatures.

There is not a unique methodological framework to evaluate and compare the performances of optical cluster finders. A variety of approaches have been proposed, based either on mock galaxy catalogs (e.g., Euclid Collaboration et al. (2019) and references therein), or on real data, or even on a mix of the two approaches (e.g., Goto et al., 2002; Kim et al., 2002; Rykoff et al., 2014; Costanzi, M. & Rozo, E. et al., 2019).

Within simulations assumptions, simulation-driven methods provide a truth table useful for comparison, with clusters embedded in realistic large scale structures. These methods also offer a direct link between galaxy clusters and dark matter halos. However, they rely on sophisticated modeling that so far does not fully reproduce all observed galaxy properties, specially at high redshift (e.g., DeRose et al., 2019). In addition to this fundamental problem, mock catalogs do not usually reproduce the variety and complexity of defects occurring in observed images and introduced at the stage of source extraction and classification. DES has recently started to deal with this using the Balrog algorithm (Suchyta et al., 2016), which embeds simulations into real data and should accompany future releases.

Addressing the cluster selection function based on real data is necessarily limited by the absence of an absolute reference to confront the results of any cluster finder. Nonetheless, useful information can be extracted from the cross-match of a given optical cluster sample with detections based on different tracers that do not suffer from the same projection effects (e.g., Saro et al., 2015) A better understanding of the galaxy cluster selection function can also be improved from cross-matching samples from different optical cluster finders. The resulting samples may differ not only due the different adopted physical assumptions but also due to the details of cluster finder implementation (Ascaso et al., 2017; Aguena & Lima, 2018), or even the way the algorithms deal with specific features of real data (e.g. noise, missing data, star/galaxy separation, etc.).

DES has produced galaxy cluster samples with the redMaPPer algorithm which were published in Rykoff et al. (2016) and McClintock, T. & Varga, T. N. et al. (2019), based on DES Science Verification and DES-Y1 data releases, respectively. These samples led to several studies focusing on the mass-richness relation (Melchior et al. 2015; Saro et al. 2015; Zhang et al. 2016; Palmese et al. 2016; Saro et al. 2017; Melchior, P. & Gruen, D. et al. 2017; Pereira et al. 2018; McClintock, T. & Varga, T. N. et al. 2019; Bleem et al. 2020; Pereira et al. 2020). Complementary analyses were also performed on cluster luminosity function (Zhang et al., 2019b), baryon content (Chiu et al., 2018), and cluster miscentering relative to X-ray detections (Zhang et al., 2019a). These clusters were also used for the detection of voids (Pollina et al., 2019). Most of these studies contribute to the work on cosmological constraints using DES first year release redMaPPer clusters (DES Collaboration et al., 2020).

In this paper, we present the Wavelet Z Photometric (WaZP) cluster finder and apply it to DES-Y1 data. WaZP is an optical cluster finder designed to detect clusters based mainly on the spatial clustering of galaxies using photometric redshift information. The primary motivation for developing WaZP is to limit assumptions on the properties of cluster galaxies such as the presence of a red sequence, the shape of their luminosity function or radial profile, assumptions that may impact cluster detection, in particular at high redshift or at lower mass regime.

Here, the WaZP DES-Y1 sample is compared to cluster samples obtained from the SPT survey based on the SZ effect and those obtained by the redMaPPer cluster finder on the same DES-Y1 data set. The first comparison allows to test how well the WaZP algorithm recovers the massive clusters detected by the SPT. The second comparison, for which the two samples have similar cluster densities, gives insights on the relative completnesses of the two optical cluster samples, and on the derived properties of the common detections. Variations may occur in the samples due to the different assumptions made in terms of cluster modelling. They may also occur due to different uses of the underlying galaxy dataset as the WaZP algorithm uses magnitude information from all bands through photometric redshifts and $i$-band as a reference band, whereas redMaPPer uses combinations of band pairs (colors) to select likely red sequence galaxies and $z$-band as a reference. Considered survey coverage can therefore be slightly different with one approach or the other. Depth variability in all bands will also impact differently cluster detection with each algorithm. While the comparisons performed here provide a valuable heuristic approach to partly qualify the cluster samples, a complete evaluation of the WaZP sample requires to address a quantitative assessment of its purity, a work that will be presented in a companion paper based on mock galaxy catalogs.

The present paper is organized as follows. In Section 2, we describe the DES Y1 data used in our analysis. In Section 3, we describe the main properties of the WaZP cluster finder. In Section 4, we present our main results on DES-Y1 data. In Section 5 we matched the derived WaZP cluster samples to the SZ sample and to the redMaPPer sample obtained from DES-Y1 data. Finally, in Section 6 we analyze the properties of the catalog, and discuss the differences between our catalog and the others compared in Section 5.

Throughout this work, we fix cosmological parameters from the Planck results (Planck Collaboration et al., 2016) for a flat $\Lambda$CDM model with $\Omega_{m}=0.308$ and $H_{0}=67.8$ km s^-1 Mpc^-1.

The DES is an imaging survey covering 5,000 deg² in 5 bands ($g,r,i,z,Y$ ) (e.g., Flaugher, 2005; Diehl et al., 2016; Dark Energy Survey Collaboration et al., 2016). In this paper, we use the DES Year 1 data release, which has been extensively studied by the DES collaboration (e.g., Troxel et al., 2018; Shipp et al., 2018). The DES built the Dark Energy Camera (DECam, Flaugher et al., 2015) with a field of view diameter of 2.2 deg covered by 520 Megapixels distributed on a mosaic of 62 CCDs that are extra sensitive on the red part of the electromagnetic spectrum, enhancing its capability of observing high redshift galaxies. DECam is installed on CTIO 4-meter Blanco telescope prime focus, and its observations follow a strategy that optimizes pointings based on properties like weather and moon phase (Neilsen et al., 2019). The images are reduced and calibrated by the DES Data Management (DESDM) team at the National Center for Supercomputing Applications (NCSA). The DESDM pipeline includes the reduction of single-exposure images, their co-addition into deeper images, source extraction and calibration, all resulting in the creation of the main scientific catalog (Morganson et al., 2018).

The DES Year 1 Annual Release (Y1A1, Abbott et al., 2018) co-added catalog used in this analysis covers a total area of $\sim$1,520 deg², split into two main wide regions. One of them has an area of $\sim$140 deg² overlapping the SDSS Stripe 82 area (Aihara et al., 2011). The other part has an area of $\sim$1,380 deg² overlapping the South Pole Telescope footprint (SPT, Carlstrom et al., 2011). In the following, we will refer to these two regions as Y1-S82 and Y1-SPT, respectively. They were observed with three to four exposures in each filter (Drlica-Wagner et al., 2018).

In addition to catalogs, we also use ancillary maps to track defects and foreground objects (e.g., bright stars, very bright galaxies, and globular clusters) all over DES footprint. The resulting coverage map is represented by a detection fraction map, where pixels have values of area fraction from 0 to 1. We also use systematic maps to track observing conditions across the footprint, such as number of exposures, seeing, and airmass (Leistedt et al., 2016). These maps are combined to produce depth maps based on galaxy magnitude limits, as described in Rykoff et al. (2015). All maps are recorded in Healpix format (nside = 4096) (Górski et al., 2005).

The Y1A1 coadd catalog and maps produced by DES DM were transferred to the Laboratório Interinstitucional de e-Astronomia (LIneA)¹¹1http://www.linea.gov.br and ingested into the database associated to the DES Science Portal (henceforth, the Portal) as described in Fausti Neto et al. (2018). We used the Portal infrastructure to create a galaxy Value Added Catalog (VAC) tailored for galaxy cluster search based on photometric redshift. The creation of the galaxy VAC includes: computation of photometric redshifts, star-galaxy classification, and pruning regions and objects to produce a clean galaxy catalog with well controlled levels of completeness and homogeneity. Along with the VAC, a final footprint map in Healpix format is created, reflecting the selection and pruning applied to this VAC.

The computation of photometric redshifts relies on the machine-learning algorithm DNF (Directional Neightbourhood Fitting, De Vicente et al. 2016), operated in Euclidean Neighborhood Fitting (ENF) mode since tests using DES Y1 data have shown that ENF mode is considerably faster, while providing similar results as in DNF mode. DNF uses as input observables SExtractor MAG_AUTO magnitudes (Bertin & Arnouts, 1996). DNF was trained with a large sample of spectroscopic redshifts extracted from a compilation of 29 public surveys intercepting the DES footprint. Quality flags of all surveys are brought to a common standard following OzDES approach (Yuan et al., 2015). As described in Gschwend et al. (2018), sources with flags 0 and 1 have unknown redshift, flag 2 redshifts are not reliable, flag 3 redshift reliability is above 90% confidence, and flag 4 is attributed to a trusted redshift (over 99% confidence). The DES photometric catalog is matched to this spectroscopic redshift sample with a 1.0 arcsec search radius and down to $m_{i}=23$ mag, producing a catalog of 101,971 galaxies with a mean redshift of 0.63, and covering the redshift range $z=0-1.1$. Although color and magnitude distributions of this spectroscopic sample differ from the global photometric set under study, we stress that it does cover the same color-magnitude ranges with the exception of faint low redshift galaxies (typically magnitudes fainter than 19 and redshifts below 0.15). The spectro-photometric catalog is then randomly split into a training and a validation sets. Details about all the steps carried out to compute photometric redshifts in the DES Science Portal for Y1A1 data are described in Gschwend et al. (2018).

Star-galaxy classification follows a morphological prescription developed within the DES consortium called MODEST, described by equations (3) and (4) of Sevilla-Noarbe et al. (2018). It mainly depends on the SExtractor SPREAD_MODEL (Desai et al., 2012; Bouy et al., 2013) and its error, assessing how extended is the source to the local PSF. Note that this classification is based on the DES $i$-band and extends to the faintest sources.

Based on bad regions maps (Drlica-Wagner et al., 2018), areas around bright stars, bleed trails, bright foreground galaxies, or globular clusters (from Harris, 2010) are removed from the footprint. Pixels with an effective coverage $\leq$ 0.1 are discarded from our analysis. We also exclude regions not covered simultaneously by $g,r,i,z$ bands with a minimum of 90s total exposure time. Besides region-based filtering, we also discard individual sources based on SExtractor FLAGS (only sources with FLAGS $\leq$ 3 are kept), apply a magnitude cut ($m_{i}\geq 15$), and color cuts ($-2.0\leq m_{g}-m_{r}\leq 10.0$; $-2.0\leq m_{r}-m_{i}\leq 4.0$; $-2.0\leq m_{i}-m_{z}\leq 4.0$).

Depth maps, defined here as 10$\sigma$ limiting magnitude maps, were built following the method described in Rykoff et al. 2015. These maps correspond to the limit where the flux is at least 10 times its variance $\sigma$, computed from the magnitude errors. This definition assures a galaxy completeness larger than 90%. Figure 1 shows what survey area fraction is covered at a given 10$\sigma$ $i$-band limiting magnitude (the $i$-band being the reference band in this work). The whole survey is at least as deep as $m_{i}=22.27$ and shallower than $m_{i}=23.25$ with half of the survey area reaching $m_{i}=22.7$. In Figure 2 we compare galaxy number counts for Y1-S82 and Y1-SPT with number counts from Arnouts et al. (2001) and Capak et al. (2007) as compiled by Nigel Metcalfe²²2http://astro.dur.ac.uk/ nm/pubhtml/counts/counts.html. The surveys used for comparison are deeper than our own, and number counts are comparable through a wide range of magnitudes up to $m_{i}\sim 22.5$ mag, beyond which we observe an increasing deficit of galaxies, consistent with the median depth of the survey.

Based on the survey depth shown above, the present analysis considers galaxies down to a limiting magnitude $m_{i}=23$ (98% of the survey area). The resulting galaxy VACs for Y1-S82 and Y1-SPT contain, respectively, 4,721,380 and 45,206,403 galaxies, in a total of 49,927,783 galaxies covering 1,511.13 deg². Both regions have similar galaxy number densities and mean photometric redshift (Table 1).

Figure 3 presents the projected galaxy distribution of Y1-S82 (top) and Y1-SPT (bottom)³³3These were produced with skymapper by Peter Melchior. The distributions are fairly uniform and galaxy densities comparable. Holes caused by masking and dents on the footprint caused by unobserved regions can be seen in both regions.

Normalized photometric redshift distributions are shown in Figure 4 for both regioggns. Our magnitude cut leads to a mean $z_{phot}\sim 0.63$ in both cases and very similar distributions. They both suffer from a counts drop around $z\sim$0.4 due to the lack of the $u$-band. This can also be seen in the left panel of Figure 5 where photometric redshifts are compared to spectroscopic redshifts for a validation sample of 50,476 galaxies built during DNF processing. There is an excellent correlation between spectroscopic and photometric redshifts; however, galaxies around $z_{spec}\sim$0.3 show a very large scatter, especially towards higher values of $z_{phot}$. This can also be seen in the right panel of Figure 5, where we assessed the global quality of the photometric redshifts by characterizing the average bias and standard deviation of $(z_{ph}-z_{sp})/(1+z_{sp})$. These points will be examined in detail in sections 4 and 6.

The Wavelet Z-Photometric (WaZP) cluster finder is designed to detect galaxy clusters from multi-wavelength optical imaging galaxy surveys. It searches for projected galaxy overdensities in photometric redshift space without any assumption on the red sequence. In a nutshell, WaZP first slices the galaxy catalog in photometric redshift space, and then generates smooth wavelet-based density maps for each slice where peaks are extracted (see Figure 6). These overdensity peaks are then merged to create a unique list of clusters and associated galaxy members. Hereafter, these various steps are described in detail.

1. 1.

   Slicing in photometric redshifts. By photometric redshift slices, we mean here the photometric redshift support over which individual galaxy redshift PDF’s are integrated around a given redshift of interest. Therefore, at a given considered redshift, galaxies are weighted by that quantity. These weights are used to build density maps at different redshifts or estimate richnesses as described in the next steps.

   The adopted strategy to define photometric redshift slices is based on the statistical comparison of the "best-estimate" discrete photometric redshifts (taken here as the mean of the galaxy redshift PDF) and corresponding spectroscopic redshifts if available. Based on available spectroscopic samples, the mean bias and scatter of photometric redshifts ($z_{ph}$) relative to spectroscopic redshifts ($z_{sp}$) were derived. Following the standard way to evaluate the performance of photometric redshifts (e.g., Ilbert et al., 2006), we computed statistics of $(z_{ph}-z_{sp})/(1+z_{sp})$ as a function of both $z_{sp}$ and $z_{ph}$. The location and width of a slice is then built in such a way that it includes 95% of the galaxies of a given spectroscopic redshift. The separation between two slices corresponds to a fourth of their width assuring a sufficient overlap to avoid missing clusters being between two consecutive slices.

2. 2.

   Generation of galaxy number density maps. WaZP does not consider photometric redshifts as discrete values. Instead, it operates with redshift PDF’s when provided, or generates them from the errors provided by the chosen photometric redshift algorithm. In each one of the slices defined above, galaxies are weighted by the integral of their redshift PDF over that slice. The resulting weighted RA-Dec distribution is then pixelized on a grid with a step of physical size 1/16^th of a Mpc. This image is finally filtered using the wavelet task MR_FILTER from the multi-resolution package MR/1 (Starck et al., 1998). This task incorporates a statistically rigorous treatment of the Poisson noise, which allows us to keep significant structures in the desired scale range. Here we select structures with scales in the range $0.5-2$ Mpc, typical of cluster scales, and apply a 3$\sigma$ iterative multi-resolution thresholding with a B-spline wavelet transform.

3. 3.

   Extraction of peaks. The smooth density maps obtained in the previous step are segmented, and in each object domain, one or more peaks are extracted. In the case of several peaks in one domain, depending on the distance between a peak and the closest saddle point, the peak can be merged or preserve its identity. Pixels of a domain are then distributed to peaks by proximity.

4. 4.

   Assessing peak significance The peak significance is chosen to be computed in a radius of $R_{S}=300$ kpc, a radius that encloses typical cluster cores (Adami et al., 1998). To perform background statistics, the survey is pixelized with pixel areas equal to $\pi R_{S}^{2}$. Any pixel intersecting a bad region or an edge is removed. Standard counts in cells are then applied to estimate the mean density ($N_{bkg-global}$) and standard deviation ($\sigma_{bkg}$). The significance, defined as $SNR=(N-N_{bkg-global})/\sigma_{bkg}$, where $N$ is the total density of galaxies in a cylinder centered at the peak position, with a length that is the width of the redshift slice and an angular radius $R_{S}$.

5. 5.

   Peak merging along the redshift direction. As $z_{ph}$ slices overlap, one can expect clusters to be detected in several consecutive slices. To build the final list of clusters, peaks of consecutive slices are associated, and only the slice in which the system has maximum significance is kept. Note that two clusters can be deblended along the line of sight if their distance in redshift is larger than 2$\times 3\sigma_{dz/(1+z)}$ where $\sigma_{dz/(1+z)}$ denotes here the 68^th percentile of the $dz/(1+z)=(z_{ph}-z_{sp})/(1+z_{sp})$ distribution.

6. 6.

   Centering and cluster redshift. The cluster center is defined as the location of the density map peak. However, if the brightest cluster member is found within the first neighbouring pixels, then this galaxy marks the center. This leads to a maximum shift of  100 kpc from the peak location. Concerning the redshift, an initial value is derived as the mode of the sum of the galaxy redshift PDF’s within a 0.5 Mpc radius around the cluster center. This value is refined iteratively based on the membership probabilities described below.

7. 7.

   Assignment of membership probabilities. Membership probabilities ($P_{mem}$) are computed following the prescription given in Castignani & Benoist (2016). In a nutshell, galaxies of the cluster field are piled up in a 3-dimensional grid (cluster-centric distance, magnitude, photometric redshift) where magnitudes and redshifts are included as probability distribution functions. The same is done for local background galaxies in (magnitude, photometric redshift) space. The local background galaxies are selected in a ring from 3 to 6 Mpc to the cluster center, whereas cluster field galaxies are selected within a 3 Mpc disk. The membership probability is the combination of the probability to be at the cluster redshift and the probability not to be a background galaxy. The final membership probability at a given cluster-centric distance, magnitude, and redshift is derived from the density ratio between the cluster field and the background field. Note that, as in Castignani & Benoist (2016), no parametric modelling is used for the radial density, nor for the luminosity function.

8. 8.

   Richness and radius The cluster richness and radius are estimated jointly. The richness is the sum of the membership probabilities within a radius that corresponds to an overdensity of 200 times the mean galaxy background number density (similar to Hansen et al. 2005). This is done considering galaxies, both in the field and in the cluster, down to a given fraction of $L^{*}$ luminosity. Practically, galaxies brighter than ${\rm m}^{\star}(z_{cluster})+\delta{\rm mag}$ are counted, where ${\rm m}^{\star}$ is the characteristic magnitude marking the knee of the luminosity function and $\delta{\rm mag}$ is a fixed quantity, chosen here to be 1.5. The adopted definition allows to produce "redshift independent richnesses", in the sense that the same cluster seen at two different redshifts would have the same richness. The evolution of the characteristic luminosity of the Luminosity Function can be described by a passively evolving population formed in a single burst (e.g., Lin et al., 2006). In this study, we derive ${\rm m}^{\star}(z)$ from the passive evolution of a burst galaxy with a formation redshift $z_{form}=3$ taken from the PEGASE2 library (burst_sc86_zo.sed, Fioc & Rocca-Volmerange, 1997). It is calibrated using the value of ${\rm K}^{\star}$($z=0.25$) derived by Lin et al. (2006) from an observed cluster sample. The choice of $\delta{\rm mag}$ is critical as it sets the redshift limit (${z}_{lim}$) of the final cluster sample through the relation ${\rm m}^{\star}({z}_{cluster})+\delta{\rm mag}={\rm mag}_{lim}$, where ${\rm mag}_{lim}$ is the survey apparent magnitude limit.

In this section, we compare the WaZP Y1A1 clusters identified in the previous section to those derived by other methods covering the same region. A first comparison is made with clusters detected by the South Pole Telescope (SPT) survey via the Sunyaev-Zel’dovich (SZ) effect (Bleem et al., 2015). A second comparison is done with clusters detected by the redMaPPer optical cluster finder, based on the same photometric data but using an algorithm searching for overdensities of red sequence galaxies (Rykoff et al., 2014). These comparisons are based on matching clusters from two different catalogs. This is a complex operation that has led to a variety of proposed algorithms (e.g., Gerke et al., 2005; Knobel et al., 2009; Cucciati et al., 2010; Gerke et al., 2012; Euclid Collaboration et al., 2019). We point out that adopting one algorithm or another or using different configurations of the same may result in different cluster associations. In particular, when a given cluster can potentially be connected to several counterparts. As detailed below, we have experimented with several of these approaches and finally adopted a hybrid iterative procedure to optimally solve multiple matches. This appeared to be the only way to avoid having systems left unmatched due to a wrong matching of their obvious counterpart. Several such cases appeared in particular with interacting clusters for which richness rankings were reversed. The resulting pairing seems, from intensive visual inspection, optimal for addressing statistically the different properties of the commonly detected clusters (centering, redshift), and evaluating systems without any counterparts. In particular, our matching procedure allowed us to decrease the number of incorrect matches of rich clusters on each side significantly.

In this paper, we use a cylindrical matching where we require the angular distance of cluster centers to be smaller than some defined length (be it their respective radii or a fixed physical distance), and their redshift separation to be constrained by the typical redshift errors from both samples. In carrying out this comparison, some issues have to be considered. First, the cluster radius definition for each cluster sample may be different. Second, we must define the redshift window to be used. It should be large enough to take into consideration the errors in photometric redshift assigned to clusters in both samples. However, a large window may lead to an increased number of multiple matches that need to be resolved as discussed in more detail below. Finally, it is crucial to ensure that the projected area of overlap of the samples is properly taken into account. To do that, footprints of the samples are used to flag clusters falling outside the overlapping regions or near their edges. This flag is useful when unmatched clusters are near the edges, in which case they can be removed from the matching statistics.

As mentioned above, we compare the combined Y1-S82 and Y1-SPT clusters identified by WaZP with those in the SZ and redMaPPer samples. In the first case, we take the SZ sample as reference, treating the SZ clusters as true representatives of the underlying mass distribution and test how well these systems are recovered. In the redMaPPer case, we investigate the unmatched cases in both directions to understand the specificities or the possible limitations of each algorithm.

We have shown that all SZ clusters with redshifts $\leq$ 0.76 intersecting our footprint are recovered by WaZP cluster finder applied on DES-Y1 data. We have also shown that more than 90% of clusters with richnesses above $\sim$20 detected by redMaPPer (or 25 by WaZP) are matched to those detected by WaZP (or by redMaPPer). In this section we compare some properties of the the two optical cluster samples. In particular, we explore differences such as redshift discrepancies, overmerging / fragmentation, and the reasons for unmatched systems on both sides.

In this paper we present WaZP  a new (2+1)D cluster finder based on photometric redshifts. It is applied to DES-Y1A1 data and resulting samples are compared to those derived from the SPT survey based on the SZ effect, and from the redMaPPer cluster finder applied to the same photometric data.

Our conclusions can be listed as follows.

• •

  A galaxy Value Added Catalog was derived from the DES Y1A1 survey. It is controlled by the $i$-band that is used for star-galaxy separation and for determining the local depth. Depending on the location, complete galaxy samples can be built down to $m_{i}=22.25-23$, with a median (corresponding to half of the survey area) completeness magnitude limit of $m_{i}=22.7$.

• •

  The WaZP cluster finder was applied to DES Y1A1 survey led to the detection of 60,547 clusters over 1,511.13 deg², with redshifts ranging from 0.05 to 0.9 and richness greater than $5$. Due to the $i$-band limiting magnitude of the survey and the adopted limiting magnitude for estimating richnesses, complete richnesses are derived for clusters in the redshift range 0.05-0.60. Clusters detected at larger redshifts get increasingly incomplete richnesses depending on the local depth.

• •

  Considering the SPT cluster sample intersecting the DES Y1A1 footprint in the redshift range 0.05 - 0.76, WaZP was shown to recover all 293 SZ clusters. Comparing redshifts of both cluster finders, we found a bias of $0.012$ and a scatter of the same order of redshift uncertainties ($\sim 0.025$). When we restrict to SZ clusters with an assigned spectroscopic redshift, all these quantities are lowered by 40%.

• •

  Cross-matching WaZP and redMaPPer catalog led to the development of an iterative matching algorithm to minimize incorrect associations. Special care was taken to deal with edge effects and depth variations. It resulted in matching 28,621 clusters in the two-way criteria with richnesses $N_{gals}$ (and $\lambda$) down to 5. Considering one-way matching for clusters richer than $N_{gals}=25$ ($\lambda=20$) with $0.1<z<0.6$, we showed that WaZP recovered 96% redMaPPer clusters, and, symmetrically, redMaPPer recovered 94% WaZP clusters.

• •

  The centering offset between WaZP and redMaPPer is less than 200 kpc in most cases (97%), which is much less than the matching criteria used.

• •

  Comparison of the estimated redshifts from redMaPPer and WaZP shows an overall good agreement. However, a fraction of WaZP clusters suffer from a redshift bias, reflecting the underlying galaxy photometric redshift bias. Note that this effect does not seem to prevent detection in general.

• •

  Despite different definitions, the comparison of WaZP and redMaPPer richnesses shows a strong correlation. The scatter of this relation will be analyzed in details on a separate paper in a future work. We also computed a richness relation based on thresholds that provided the same densities of clusters. This relation is remarkably close to the fit from matched clusters, supporting the idea that, on average, the ranking of the two cluster samples by their richness is similar.

• •

  The study of the relative fragmentation of WaZP and redMaPPer clusters showed that WaZP tends to find pairs of relatively rich clusters more frequently than redMaPPer.

• •

  The visual inspection of 60 unmatched clusters richer than $N_{gals}\geq 25$ (for WaZP) and $\lambda\geq 20$ (for redMaPPer), showed that (for both samples)  1/3 of these are clear concentrations of red galaxies, which, in itself could help to improve the completeness of both samples. A second category representing more than half of the inspected unmatched systems is composed of much looser systems or more filamentary structures. This dominant category of unmatched clusters has been shown statistically to be characterized by lower SNRs (for WaZP) and lower likelihoods (for redMaPPer) than for the matched clusters.

One of the main aspects of this work is to address the relative completenesses of two optical cluster finders based on different methods and applied to the same survey. As shown in this paper, the comparison of the resulting samples in itself is not a trivial task free of assumptions. However, it is a useful guide to detect features of cluster finding algorithms when applied to large surveys with all their complexity (missing data, mis-classified sources, depth variation, etc.). In that sense, such comparisons are complementary to those performed with mock catalogs, that can be used, for instance, to address the sample purity in addition to completeness.

A limitation of the present study is the quality of the photometric redshifts partly hampered by the poor representation of faint red galaxies in our spectroscopic training set, in particular at low redshifts ($z\leq 0.35$). In a companion paper we are exploring the impact of using a much larger spectroscopic training set, and the use of several photometric redshift codes. We will also study the impact of the star-galaxy classification algorithm. Finally, we will compare WaZP cluster samples based on $i$-band and $z$-band reference magnitudes with a special focus on high redshift cluster detection.

M.A. was supported by FAPESP (2013/26612-2) and CNPq (380101/2017-3, 165049/2017-0, 381135/2018-7). C.B. acknowledges the support obtained from the Bonus-Qualité-Recherche 2013 & 2017 Programs of the J.-L. Lagrange Laboratory (UMR 7293).

C.B. thanks J.-L. Starck for his help in using and configuring the MR/1 multi-resolution to optimally build galaxy density maps. C.B. also thanks S. Maurogordato, A. Cappi and E. Slezak for many stimulating discussions during the development of the WaZP cluster finder algorithm.

Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey.

The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, NFS’s NOIRLab, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas A&M University, and the OzDES Membership Consortium.

Based in part on observations at Cerro Tololo Inter-American Observatory at NSF’s NOIRLab (NOIRLab Prop. ID 2012B-0001; PI: J. Frieman), which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

The DES data management system is supported by the National Science Foundation under Grant Numbers AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MICINN under grants ESP2017-89838, PGC2018-094773, PGC2018-102021, SEV-2016-0588, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013) including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Brazilian Instituto Nacional de Ciência e Tecnologia (INCT) do e-Universo (CNPq grant 465376/2014-2).

This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics.

The WaZP DES-Y1A1 cluster products with a full description of the catalogs and columns can be found are available in its online supplementary material ⁵⁵5https://www.linea.gov.br/catalogs/wazp/.

1. Laboratório Interinstitucional de e-Astronomia - LIneA, Rua Gal. José Cristino 77, Rio de Janeiro, RJ - 20921-400, Brazil
2. Laboratoire d’Annecy De Physique Des Particules (LAPP), 9 Chemin de Bellevue, 74940 Annecy, France
3. Université Côte d’Azur, OCA, CNRS, Lagrange, UMR 7293, CS 34229, 06304, Nice Cedex 4, France
4. Observatório Nacional, Rua Gal. José Cristino 77, Rio de Janeiro, RJ - 20921-400, Brazil
5. Departamento de Física Matemática, Instituto de Física, Universidade de São Paulo, CP 66318, São Paulo, SP, 05314-970, Brazil
6. Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USA
7. Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain
8. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK
9. CNRS, UMR 7095, Institut d’Astrophysique de Paris, F-75014, Paris, France
0. Sorbonne Universités, UPMC Univ Paris 06, UMR 7095, Institut d’Astrophysique de Paris, F-75014, Paris, France
11. Department of Physics and Astronomy, Pevensey Building, University of Sussex, Brighton, BN1 9QH, UK
12. Department of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
13. Instituto de Astrofisica de Canarias, E-38205 La Laguna, Tenerife, Spain
14. Universidad de La Laguna, Dpto. Astrofísica, E-38206 La Laguna, Tenerife, Spain
15. Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, IL 61801, USA
16. National Center for Supercomputing Applications, 1205 West Clark St., Urbana, IL 61801, USA
17. Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona) Spain
18. INAF-Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, I-34143 Trieste, Italy
19. Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
20. Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
21. Department of Physics, IIT Hyderabad, Kandi, Telangana 502285, India
22. Santa Cruz Institute for Particle Physics, Santa Cruz, CA 95064, USA
23. Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA
24. Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
25. Institute of Theoretical Astrophysics, University of Oslo. P.O. Box 1029 Blindern, NO-0315 Oslo, Norway
26. Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109, USA
27. Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain
28. Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
29. Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
30. School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
31. Center for Cosmology and Astro-Particle Physics, The Ohio State University, Columbus, OH 43210, USA
32. Department of Physics, The Ohio State University, Columbus, OH 43210, USA
33. Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
34. Australian Astronomical Optics, Macquarie University, North Ryde, NSW 2113, Australia
35. Lowell Observatory, 1400 Mars Hill Rd, Flagstaff, AZ 86001, USA
36. Department of Astrophysical Sciences, Princeton University, Peyton Hall, Princeton, NJ 08544, USA
37. Institució Catalana de Recerca i Estudis Avançats, E-08010 Barcelona, Spain
38. Physics Department, 2320 Chamberlin Hall, University of Wisconsin-Madison, 1150 University Avenue Madison, WI 53706-1390
39. Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
40. Instituto de Física, UFRGS, Caixa Postal 15051, Porto Alegre, RS - 91501-970, Brazil
41. School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK
42. Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
43. Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA