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DES 2015-0146 SLAC PUB-16454 Fermilab PUB-16-012-E-PPD Draft version May 27, 2016 DOI 10.3847/0067-0049/224/1/1 PreprinttypesetusingLATEXstyleemulateapjv.5/2/11 THE REDMAPPER GALAXY CLUSTER CATALOG FROM DES SCIENCE VERIFICATION DATA E. S. Rykoff1,2,(cid:63), E. Rozo3, D. Hollowood4, A. Bermeo-Hernandez5, T. Jeltema4, J. Mayers5, A. K. Romer5, P. Rooney5, A. Saro6, C. Vergara Cervantes5, R. H. Wechsler7,1,2, H. Wilcox8, T. M. C. Abbott9, F. B. Abdalla10,11, S. Allam12, J. Annis12, A. Benoit-Le´vy13,10,14, G. M. Bernstein15, E. Bertin13,14, D. Brooks10, D. L. Burke1,2, D. Capozzi8, A. Carnero Rosell16,17, M. Carrasco Kind18,19, F. J. Castander20, M. Childress21,22, C. A. Collins23, C. E. Cunha1, C. B. D’Andrea8,24, L. N. da Costa16,17, T. M. Davis25, S. Desai26,6, H. T. Diehl12, J. P. Dietrich26,6, P. Doel10, A. E. Evrard27,28, D. A. Finley12, B. Flaugher12, P. Fosalba20, J. Frieman12,29, K. Glazebrook30, D. A. Goldstein31,32, D. Gruen1,33,2,34, R. A. Gruendl18,19, G. Gutierrez12, M. Hilton35, 6 K. Honscheid36,37, B. Hoyle34, D. J. James9, S. T. Kay38, K. Kuehn39, N. Kuropatkin12, O. Lahav10, G. F. Lewis40, C. Lidman39, M. Lima41,16, M. A. G. Maia16,17, R. G. Mann42, J. L. Marshall43, P. Martini36,44, P. Melchior45, 1 C. J. Miller27,28, R. Miquel46,47, J. J. Mohr26,6,33, R. C. Nichol8, B. Nord12, R. Ogando16,17, A. A. Plazas48, 0 K. Reil2, M. Sahle´n49, E. Sanchez50, B. Santiago51,16, V. Scarpine12, M. Schubnell28, I. Sevilla-Noarbe50,18, 2 R. C. Smith9, M. Soares-Santos12, F. Sobreira12,16, J. P. Stott49, E. Suchyta15, M. E. C. Swanson19, G. Tarle28, y D. Thomas8, D. Tucker12, S. Uddin30, P. T. P. Viana52,53, V. Vikram54, A. R. Walker9, Y. Zhang28 a (The DES Collaboration) M Draft version May 27, 2016 5 ABSTRACT 2 WedescribeupdatestotheredMaPPeralgorithm, aphotometricred-sequenceclusterfinderspecif- ] icallydesignedforlargephotometricsurveys. Theupdatedalgorithmisappliedto150deg2 ofScience O Verification (SV) data from the Dark Energy Survey (DES), and to the Sloan Digital Sky Survey C (SDSS) DR8 photometric data set. The DES SV catalog is locally volume limited, and contains 786 . clusters with richness λ > 20 (roughly equivalent to M (cid:38) 1014h−1M ) and 0.2 < z < 0.9. The h 500c 70 (cid:12) DR8 catalog consists of 26311 clusters with 0.08<z <0.6, with a sharply increasing richness thresh- p old as a function of redshift for z (cid:38) 0.35. The photometric redshift performance of both catalogs is - o shown to be excellent, with photometric redshift uncertainties controlled at the σ /(1+z) ∼ 0.01 z r level for z (cid:46) 0.7, rising to ∼ 0.02 at z ∼ 0.9 in DES SV. We make use of Chandra and XMM X-ray t s and South Pole Telescope Sunyaev-Zeldovich data to show that the centering performance and mass– a richnessscatterareconsistentwithexpectationsbasedonpriorrunsofredMaPPeronSDSSdata. We [ also show how the redMaPPer photo-z and richness estimates are relatively insensitive to imperfect 2 star/galaxy separation and small-scale star masks. v Subject headings: galaxies: clusters 1 2 6 1. INTRODUCTION troduced the red-sequence matched-filter Probabalistic 0 Percolation cluster finder (redMaPPer; Rykoff et al. Clusters of galaxies are the largest bound objects in 0 2014, henceforth RM1). RedMaPPer identified galaxy the Universe, and are uniquely powerful cosmological . clusters by making use of the fact that the bulk of the 1 probes (e.g., Henry et al. 2009; Vikhlinin et al. 2009; cluster population is made up of old, red galaxies with 0 Mantz et al. 2010; Rozo et al. 2010; Clerc et al. 2012; 6 Benson et al. 2013; Hasselfield et al. 2013; Planck Col- a prominent 4000˚A break. Focusing on this specific 1 laboration et al. 2014) (see also reviews in Allen et al. galaxy population increases the contrast between clus- : (2011); Weinberg et al. (2013)). In particular, galaxy ter and background galaxies in color space, and enables v clusters are one of the key probes of growth of struc- accurate and precise photometric redshift (photo-z) es- i X ture and dark energy measurements from ongoing and timates. The associated cluster richness estimator, λ, is r upcoming photometric surveys such as the Dark En- thesumofofthemembershipprobabilityofeverygalaxy a ergy Survey (DES; The DES Collaboration 2005), the intheclusterfield,andhasbeenoptimizedtoreducethe Kilo-Degree Survey (KiDS; de Jong et al. 2015), the scatter in the richness–mass relation (Rozo et al. 2009, Hyper-SuprimeCamera(HSC)1,theLargeSynopticSur- 2011; Rykoff et al. 2012a). The initial application of redMaPPer in RM1 was on vey Telescope (LSST; LSST Science Collaboration et al. theSloanDigitalSkySurveyDataRelease8photometric 2009), Euclid (Laureijs et al. 2011), and WFIRST2. data (SDSS DR8; York et al. 2000; Aihara et al. 2011). There are already a wide range of photometric clus- As such, the catalog was limited to relatively low red- ter finders (e.g. Goto et al. 2002; Gladders et al. 2007; shifts (z (cid:46) 0.5). The SDSS redMaPPer catalog has Koester et al. 2007a; Hao et al. 2010; Soares-Santos been extensively validated using X-ray (Rozo & Rykoff et al. 2011; Szabo et al. 2011; Wen et al. 2012; Murphy 2014, henceforth RM2); (Sadibekova et al. 2014) and et al. 2012; Ascaso et al. 2012, 2014; Oguri 2014), each Sunyaev-Zeldovich (SZ) data (Rozo et al. 2015a, hence- with various strengths and weaknesses. In 2014, we in- forth RM3), and with spectroscopic data (Rozo et al. (cid:63)erykoff@slac.stanford.edu 2015b, henceforth RM4), demonstrating that the cata- 1 http://www.naoj.org/Projects/HSC/HSCProject.html log has low scatter in the mass–richness relation; well- 2 http://wfirst.gsfc.nasa.gov/ quantified centering performance; and accurate and pre- 2 Rykoff et al. cise cluster photo-zs. The low scatter has also made it of which covers a single DECam 2.2-degree-wide field of possible to use the redMaPPer SDSS catalog to verify view, for a total of ∼32deg2 of deeper imaging (includ- Planckclusters(Rozoetal.2015a;PlanckCollaboration ing extra offset pointings of SN fields taken during SV). et al. 2015). In a comparison of numerous spectroscopic Finally, there are smaller discontinguous regions target- cluster finders on mock catalogs, redMaPPer achieved ing massive clusters (Melchior et al. 2015) and the COS- one of the smallest variances in estimated cluster mass MOS field (Scoville et al. 2007). We utilize this DES SV at fixed halo mass, despite being the only cluster finder data set to construct the first DES redMaPPer cluster relying solely on two-band photometric data (all other catalog. The redMaPPer footprint used in this paper cluster finders were spectroscopic) (Old et al. 2015). is the same as that used for the associated redMaGiC RedMaPPer was designed to easily handle a broad (red-sequence matched-filter Galaxies Catalog) of red range in redshift, as well as to run efficiently over a wide galaxies with well-behaved photo-z performance (Rozo and deep galaxy catalog. As such, it is ideally suited et al. 2015c, henceforth RM15). to DES data, which can be used to detect faint red- The DES SV data was processed by the DES Data sequence galaxies to much higher redshifts than SDSS Management(DESDM)infrastructure(Gruendletal, in (z (cid:46)0.9). Inthispaper,wedescribethefirstapplication prep),whichincludesimagedetrending,astrometricreg- ofredMaPPertoDESScienceVerification(SV)data. In istration, global calibration, image coaddition, and ob- addition, we describe updates to the redMaPPer algo- ject catalog creation. Details of the DES single-epoch rithm since versions 5.2 (RM1) and 5.10 (RM4) to the andcoaddprocessingcanbefoundinSevillaetal.(2011) present version 6.3, and apply the updated algorithm to and Desai et al. (2012). We use SExtractor to create the SDSS DR8 photometric data. We characterize the object catalogs from the single-epoch and coadded im- photo-z performanceofredMaPPerusingavailablespec- ages (Bertin & Arnouts 1996; Bertin 2011). troscopy, and use available SZ data from the South Pole After the initial production of these early data prod- TelescopeSZclustersurvey(SPT;Bleemetal.2015), as ucts, we detected several issues that were mitigated in well as X-ray observations from Chandra and XMM, to post-processing, leading to the creation of the “SVA1 measurethecenteringpropertiesoftheDESSVredMaP- Gold”photometrycatalog3. First,wemaskedpreviously Per catalog, and to test the validity of the redMaPPer unmasked satellite trails. Second, we use a modified clusterrichnessasaphotometricmasstracer. Adetailed version of the big-macs stellar-locus regression (SLR) analysis of the richness and SZ scaling relations is pre- fitting code (Kelly et al. 2014)4 to recompute coadd sented in Saro et al. (2015, henceforth S15). A similar zero-points over the full SVA1 footprint. Third, regions analyisofX-rayobservationsincludingSDSSoverlapwill around bright stars (J < 13) from the Two Micron All be presented in Bermeo Hernendez et al. (in prep) and SkySurvey(2MASS;Skrutskieetal.2006)weremasked. Hollowood et al. (in prep). Finally, we removed 4% of the area with a large con- The layout of this paper is as follows. In Section 2 centration of centroid shifts between bandpasses in indi- wedescribetheDESScienceVerificationandSDSSDR8 vidual objects, indicating scattered light, ghosts, satel- data used in this work. Section 3 describes the updates lite trails, and other artifacts (Jarvis et al. 2015, Sec- totheredMaPPeralgorithmsincetheRM1andRM4pa- tion 2.1). We utilize the SExtractor MAG AUTO quantity pers. Section 4 describes the cluster catalogs, as well as derivedfromthecoaddedimagesforgalaxytotalmagni- thephotometricredshiftperformanceonDESandSDSS tudesandcolors. Thischoicesreflectsthefactthatmeth- data. In Section 5 we detail the effects of star/galaxy ods to compute multi-epoch fitting photometric quan- separation and small-scale masking on the cluster prop- tities are still under development. The added noise in erties, and in Section 6 we compare the redMaPPer cat- thecolorresultsinalargerobservedred-sequencewidth, alog with X-ray and SZ clusters in the DES SVA1 foot- which results in slightly poorer photometric redshifts, as print. Finally, in Section 7 we summarize our results. shown in Section 4.1.2. For the present work, we have When necessary, distances are estimated assuming a flat not made use of the DES Y-band imaging because of ΛCDM model with Ωm = 0.30. For consistency with uncertain calibration, and the minimal lever-arm gained previous redMaPPer work, we use h=1.0 when quoting at the redshifts probed in this paper. Finally, our fidu- distances (h−1Mpc) and h = 0.7 when quoting masses cial star/galaxy separation is done using the multi-band (h−701M(cid:12)). multi-epochimageprocessingcodengmixusedforgalaxy shape measurement in DES data (Jarvis et al. 2015), as 2. DATA detailed in Appendix A of RM15. 2.1. DES Science Verification Data The footprint is initially defined by MANGLE (Swanson The DES is an ongoing 5-band (grizY) photometric et al. 2008) maps generated by DESDM which describe survey performed with the Dark Energy Camera (DE- the geometry of the coadded data in polygons of arbi- Cam, Flaugher et al. 2015) on the 4-meter Blanco trary resolution. For ease of use, these are then av- Telescope at Cerro Tololo Inter-American Observatory eraged over HEALPIX NSIDE=4096 pixels (G´orski et al. (CTIO). Prior to the beginning of the DES survey, 2005), where each pixel is approximately 0.7(cid:48) on a side. from November 2012 to March 2013, DES conducted The pixelized MANGLE maps are combined with maps of a ∼ 250deg2 “Science Verification” (SV) survey. The thesurveyobservingproperties(e.g.,airmass,full-width- half-maximum, etc.) compiled by Leistedt et al. (2015) largestcontiguousregioncovers∼160deg2oftheeastern using the method of Rykoff et al. (2015) to generate 10σ edge of the SPT survey (“SPT-E” hereafter). A smaller MAG AUTO limiting magnitude maps. We first restrict the ∼ 35deg2 region is in the western edge of the footprint (“SPT-W” hereafter). In addition, DES surveys 10 Su- 3 http://des.ncsa.illinois.edu/releases/sva1 pernovafields(“SNfields”hereafter)every5-7days,each 4 https://code.google.com/p/big-macs-calibrate/ redMaPPer on DES SVA1 3 SVA1 (SPT-E) (z-band) usedinthecalibrationoftheredsequenceinSection3.3. 2.2. SDSS DR8 -45.0° 22.6 In addition to our new catalog on DES SVA1 data, we have updated the redMaPPer catalog for SDSS DR8 22.4 photometricdata(Aiharaetal.2011),whichremainsthe -50.0° most recent photometric data release from SDSS. The σ) Dec 22.2m (10lim wDhRi8chgwaleacxuytctaottahloeg10c4o0n1tadiengs2∼ofc1o4n0t0i0gudoegu2shoifghimqaugailnitgy, -55.0° observations using the mask from the Baryon Acoustic 22.0 Oscillation Survey (BOSS, Dawson et al. 2013). The mask is further extended to exclude all stars in the Yale Bright Star Catalog (Hoffleit & Jaschek 1991), as well -60.0° 21.8 as the area around objects in the New General Catalog (NGC Sinnott 1988). The resulting mask is that used 90.0° 80.0° 70.0° 60.0° R A by RM1 to generate the SDSS DR8 redMaPPer catalog. We refer the reader to that work for further discussion Figure 1. Map of 10σ depth (in magnitudes) in ∼ 125deg2 in on the mask, as well as object and flag selection. the SVA1 SPT-E footprint, for SLR-corrected zauto magnitudes. Small scale variations are caused by variations in the number of Total magnitudes are determined from i-band SDSS exposures,chipgaps,andobservingconditions. CMODEL MAG, which we denote m , and colors from ugriz i SDSS MODEL MAG. All spectroscopy is drawn from SDSS footprint to regions with deep MAG AUTO on the z band DR10 (Ahn et al. 2014). Finally, we make use of the (m ) such that m >22, as shown in Figure 1 for 10σ limiting magnitude maps from Rykoff et al. (2015, z,lim z,lim ∼125deg2 intheSPT-Eregion.5 Onlygalaxiesbrighter see, e.g., Figure 4). As with SVA1 data, only galaxies than the local 10σ limiting magnitude are used in the brighter than the local 10σ limiting magnitude are used input catalog. in the input catalog. Thengmixrunsusedforstar/galaxyseparationinthis paper and RM15 were primarily used for galaxy shape 3. UPDATES TO THE redMaPPer ALGORITHM estimationforDEScosmicshear(Beckeretal.2015)and RedMaPPer is a matched-filter red-sequence photo- cosmological constraints (The Dark Energy Survey Col- metric cluster finding algorithm with three filters based laboration et al. 2015). Therefore, the runs were per- on galaxy color, position, and luminosity. The most formed on regions with very tight tolerance for image important filter characterizes the color of red-sequence quality, and were restricted to the largest contiguous re- galaxies as a function of redshift. This filter is a linear gion (SPT-E) as well as supplementary runs on the SN red-sequencemodelincolor-magnitudespace(withslope fields. These regions comprise our fiducial footprint for andintercept)inn dimensions,wheren isthenum- col col the input galaxy catalog of 148deg2 (of which 125deg2 berofindependentcolorsintheinputdataset. Thefilter is in SPT-E). However, mask boundaries and holes re- also incorporates the intrinsic scatter, C , which is the int duce the effective area for extended cluster sources to n ×n covariance matrix assuming Gaussian errors col col ∼ 100deg2 (see Section 3.6 for details). In Section 5 in photometric magnitudes. This filter is self-calibrated we describe an expanded footprint where we relax some by making use of clusters with known spectroscopic red- of these constraints, and include SPT-W and COSMOS, shifts. The additional two filters are the radial filter, with less robust star/galaxy separation. comprised of a projected NFW profile (Navarro et al. Spectroscopic data used in this paper comes from the 1994), and a luminosity filter based on a Schechter func- GalaxyandMassAssemblysurvey(GAMADriveretal. tion. Once the parameters of the red-sequence filter is 2011),theVIMOSVLTDeepSurvey(VVDSGarillietal. known, we use this information to compute a probabil- 2008), the 2dF Galaxy Redshift Survey (2dFGRS Col- ity p that each galaxy in the vicinity of the cluster mem less et al. 2001), the Sloan Digital Sky Survey (SDSS is a red-sequence member. The richness λ is defined as Ahn et al. 2014), the VIMOS Public Extragalactic Sur- thesumofthemembershipprobabilitiesoverallgalaxies vey (VIMOS Garilli et al. 2014), and the Arizona CDFS within a scale-radius R : λ Environment Survey (ACES Cooper et al. 2012). In (cid:88) addition, we have a small sample of cluster redshifts λ= p θ θ , (1) mem L R from SPT used in the cluster validation of Bleem et al. (2015). These data sets have been further supplemented where θL and θR are luminosity- and radius-dependent bygalaxyspectraacquiredaspartoftheOzDESspectro- weights defined in Appendix B of RM4. The radius scopic survey, which is performing spectroscopic follow- scales with the size of the cluster such that Rλ = upontheAAOmegainstrumentattheAnglo-Australian 1.0(λ/100)0.2h−1Mpc, which we have shown minimizes Telescope(AAT)intheDESsupernovafields(Yuanetal. the scatter in the mass–richness relation (Rykoff et al. 2015). In all, there are 36,607 photometric galaxies with 2012b). Allgalaxieswithmagnitudesconsistentwithbe- spectroscopic redshifts in our input catalog, although ingbrighterthan0.2L∗ areconsideredforcomputingthe only ∼ 2000 are red cluster members, and ∼ 1400 are richness,asdescribedbelowinSection3.2. Wenotethat the weights θ and θ are “soft cuts” to ensure cluster L R 5 Thisisequivalenttoa0.2L∗galaxyatz=0.65,asdescribed richnessmeasurementsarerobusttosmallperturbations inSection3.2 in galaxy magnitudes. The cluster photometric redshift, 4 Rykoff et al. z ,isconstrainedatthesametimeastheclusterrichness account for this missing galaxy, as per the above formal- λ byfittingallpossiblemembergalaxiessimultaneouslyto ism. To do so, however, one needs to know the survey the red-sequence color function. depth over the full area coverage of the galaxy cluster. The above equation describes the richness computa- The original redMaPPer application to SDSS DR8 in tionintheabsenceofanymasking(starholesandsurvey RM1 (redMaPPer v5.2) assumed the survey had a uni- boundaries), and in the regime where the local limiting form depth with m < 21.0. In the update described in i magnitude is deeper than 0.2L at the cluster redshift. RM4 (redMaPPer v5.10), we empirically computed the ∗ As described in Section 5 of RM1, we additionally com- local survey depth averaged over the location of each pute a scale factor S to correct for these missing cluster cluster. This was superior to assuming a constant-depth members, such that survey, but ignored small-scale depth variations, as well as being somewhat noisy. In this updated version ver- λ (cid:88) = p (2) sion (redMaPPer v6.3), we have extended redMaPPer S mem to incorporate variable survey limiting magnitude maps gals as detailed in (Rykoff et al. 2015) and described in Sec- so that each cluster with richness λ has λ/S galaxies tion 2. Specifically, we utilize the local survey depth brighterthanthelimitingmagnitudeofthesurveywithin from these depth maps to estimate the fraction of clus- the geometric survey mask. At the same time, we esti- ter galaxies that are masked, as defined in Section 3 and mate the variance S which is used in the computation of detailedinAppendixBofRM4. Inthepresentversionof theuncertaintyonrichnessλ, asdetailedinAppendixB thealgorithm,weassumethattheredgalaxydetectionis of RM4. In this way, the total uncertainty on λ includes complete(modulomasking)atmagnitudesbrighterthan the uncertainty from correcting for mask and depth ef- the local 10σ limiting magnitude used to select the in- fects. put catalog. In future versions, we intend to track the Inaddition,asdescribedinSection5.1ofRM1(specifi- full completeness function, as described in Section 5 of callyEqn. 24),itisusefultocomputethefractionofthe Rykoff et al. (2015). effective cluster area that is masked solely by geomet- ric factors such as stars, bad regions, and survey edges. 3.2. Generalization of the Characteristic Magnitude This mask fraction, denoted f , is complementary to m (z) to Arbitrary Survey Filters mask ∗ S above in that it contains all the local masking except As with the previous versions of the redMaPPer algo- the depth limit. rithm our luminosity filter is based on a Schechter func- As well as estimating membership probabilities, the tion (e.g., Hansen et al. 2009) of the form: redMaPPer centering algorithm is also probabilistic (see Section 8 of RM1). The centering probability Pcen is a φ(m )∝10−0.4(mi−m∗)(α+1)exp(cid:16)−10−0.4(mi−m∗)(cid:17), likelihood-basedestimateoftheprobabilitythatagalaxy i underconsiderationisacentralgalaxy(CG).Thislikeli- (3) hood includes the fact that the photo-z of the CG must where we set the faint-end slope α=1.0 independent of beconsistentwiththeclusterredshift;thattheCGlumi- redshift. Previously,wesetthecharacteristicmagnitude, nosity must be consistent (using a Gaussian filter) with m∗(z),usingak-correctedpassivelyevolvingstellarpop- the expected luminosity of the CG of a cluster of the ulation which we had derived from a PEGASE.2 stel- observed richness; and that the local red galaxy density lar population/galaxy formation model (Fioc & Rocca- (on the scale of ∼ 200h−1kpc) is consistent with that Volmerange 1997; Koester et al. 2007b; Eisenstein et al. of CGs. We additionally assume that each cluster can 2001). As this was derived specifically for the SDSS fil- have at most one CG, and store the top 5 most likely ters at relatively low redshift, we have updated our ref- central candidates. Our fiducial cluster position is given erencem∗(z)tomoresimplyallowfordifferentfiltersets by the highest likelihood central galaxy. Because of the and a broader redshift range. luminosity filter, the CG candidate with the largest Pcen The new value of m∗(z) is computed using a Bruzual tendstobeverybright,butisnotnecessarilythebright- &Charlot(2003,BC03)modeltopredictthemagnitude est member. Thus, we do not refer to it as the brightest evolutionofagalaxywithasinglestarformationburstat cluster galaxy (BCG), only as the central galaxy. Typ- z =3(withsolarmetallicityandSalpeterIMF)asimple- ically, for ∼ 15−20% of the clusters the CG chosen by mented in the EzGal Python package (Mancone & Gon- redMaPPer is not the brightest member. zalez2012). Wenormalizem∗ sothatmi,SDSS =17.85at TheredMaPPeralgorithmhaspreviouslybeenapplied z =0.2 for an L∗ galaxy. This was chosen to match the toSDSSDR8photometricdata. Formoredetailsonthe m∗(z) relation from RM1 and Rykoff et al. (2012a). We redMaPPer algorithm, we refer the reader to RM1 and have additionally confirmed that the evolution of m∗(z) the updates in the appendix of RM4. In this section, we is within 8% of that used in RM1 over the RM1 redshift detail the various modifications that have been imple- domain (0.1 < z < 0.5), with the largest deviations at mentedontheredMaPPeralgorithmsinceitslastpublic z ∼ 0.5. The normalization condition for mz for DES data release (RM4). is then derived from the BC03 model using the DECam passbands (Flaugher et al. 2015). 3.1. Incorporating Small Scale Structure in the Local Survey Depth 3.3. Initial Selection of Red Spectroscopic Galaxies Variable survey depth can lead to galaxies being As described in RM1, the initial calibration of the red “masked out” from galaxy clusters. Specifically, if a sequence relies on spectroscopic “seed” galaxies. This membergalaxy(withL≥0.2L )hasamagnitudebelow may be comprised of a set of training clusters with spec- ∗ our brightness threshold, then one needs to statistically troscopic redshifts (as in DES SVA1) or a large spectro- redMaPPer on DES SVA1 5 scopic catalog with a sufficient number of red galaxies in and redshift reach of the DES SV catalog, as the impact clusters(asinSDSSDR8). InRM1(seeSection6.2),we on the uncertainty estimate of λ (see Eqn. 2) is mod- selected red galaxies by splitting the spectroscopic cata- est for clusters that only require a small extrapolation. log into narrow redshift bins, and using a Gaussian mix- For SVA1, we have chosen the luminosity threshold to turemodel(Haoetal.2009)toseparategalaxiesineach be L =0.4L for the construction of the z map. thresh ∗ max redshift bin into blue and red components. However, we For DR8, we have chosen L = 1.0L , such that thresh ∗ havefoundthatthismethodisonlyrobustwhenwehave z ∼ 0.6 over > 99% of the DR8 footprint. Although max a plethora of spectra, as is the case with SDSS. this requires a large richness extrapolation at high red- In this paper, the initial red galaxy selection is per- shift(andhencelargerichnesserrors),thiscutmaintains formed by computing color residuals of galaxies in a consistency with previous redMaPPer catalogs (versions broad range of redshifts relative to the BC03-derived 5.2 and 5.10) where we did not use a z map. How- max colormodelsfromSection3.2. Asweareonlyconcerned ever, if users wish to utilize a volume-limited subset of withmakinganinitialselectionofredandbluegalaxies, the DR8 redMaPPer catalog, restricting to z < 0.33 λ any color calibration offsets between the data and the will ensure that the local depth at every cluster is deep BC03 model are irrelevant; we just need to get an ini- enough to detect 0.2L galaxies. ∗ tial sample of red galaxies. We again employ a Gaussian mixture model to obtain a first estimate for the mean 3.5. Differences Between the SVA1 and DR8 Analyses colorandintrinsicscatteroftheredspectroscopicgalax- AlthoughthecodeusedtorunonSVA1andDR8isthe ies. To ensure a clean selection, we use the g−r color same, there are a few key differences that we highlight for z < 0.35; r−i for 0.35 < z < 0.7; and i−z spec spec here. forz >0.7. Atthispoint, weproceedasdescribedin spec Step 3 of RM1 Section 6.2. 1. For DR8, we use i-band for the detection mag- nitude; for SVA1 we use z-band, which is better 3.4. Redshift Reach of the Cluster Catalog suited to the broad redshift range and the excel- Ideally, a photometric survey would be deep enough lent z-band performance of DECam. to detect the faintest 0.2L galaxies that contribute to ∗ our richness estimator λ over the full redshift range and 2. For DR8, we use ugriz for galaxy colors, while for footprint of the catalog. In a roughly uniform survey SVA1 we only use griz. The lack of u band has such as the SDSS, this limitation translates into a max- negligibleeffectontheclusterdetectionandcluster imum redshift, zmax, below which the cluster catalog is photo-zs at z >0.2 (see Section 8.1 of RM15). volume limited; for SDSS, z <0.33. By contrast, the max observing strategy of a multi-epoch survey such as the 3. For DR8, reddening corrections are applied to cat- DES may yield much greater depth variations, as shown alogmagnitudes. ForSVA1,theseareincorporated in Figure 1. Furthermore, the depth variations can be into the SLR zero-point calibration. different in different bands. Consequently, the redshift 4. For DR8, we train the red sequence model over range which can be successfully probed with redMaP- 2000deg2 (∼20%ofthefullfootprint),asinRM1, Per will depend on the local survey depth, with deeper toensuresufficientstatisticsofspectroscopictrain- regions allowing us to detect galaxy clusters to higher ing while avoiding any possibility of over-training. redshifts. ForthemuchsmallerSVA1catalog,weusethefull We define a maximum redshift z at each position max footprint and all available spectra. The impact of in the sky as follows. Given a point in the survey, our this is detailed in Section 4.1.2. initialdepthmapforthemaindetectionband(m inthe z case of SVA1), and a luminosity threshold (L ), we thresh 3.6. Generation of Random Points calculate the maximum redshift to which a typical red galaxy (defined by our red-sequence model) of L is: In RM1, we describe a method of estimating purity thresh detectable at >10σ in the main detection band (z-band and completeness of the cluster catalog using the data for DES); and at > 5σ in the remaining bands. Only itself, by placing fake clusters into the data and recover- clusters with z ≤z are accepted into our cluster cat- ingtherichness. Whilethismethod(describedinSection max alog, with z defining the redshift component of our 11ofRM1)isusefulforestimatingtheselectionfunction max survey mask. In this way, we can simply (and conserva- andprojectioneffects,itisnotappropriateforgenerating tively)accountfortheregionsthatareextremelyshallow a cluster random catalog for cross-correlation measure- in one or more bands. This happens in SVA1 primarily ments, such as the cluster–shear cross-correlation used at the boundaries, and other regions that were observed for stacked weak-lensing mass estimates (e.g., Johnston in non-photometric conditions. The result is a map of et al. 2007; Reyes et al. 2008), as existing large-scale z in HEALPIX format with NSIDE=4096, where each structure is imprinted on the random catalog. max pixel is approximately 0.7(cid:48) on a side, that is matched to In this section, we describe a new way of generating the resolution of the input depth maps. cluster random points by making use of the z map max Given this procedure, we still have an arbitrary deci- from Section 3.4. A particular challenge is the fact that sion as to where to set our luminosity threshold L . galaxy clusters are extended objects, and thus the de- thresh The most conservative option would be to demand that tectabilitydependsnotjustontheredshift,buttheclus- every cluster in the final catalog be at a redshift such ter size and the survey boundaries. We generate a ran- thatwecandetectredgalaxiestoL =0.2L . How- dom cluster catalog that has the same richness and red- thresh ∗ ever, we have chosen to be somewhat more aggressive in shift distribution of the data catalog by randomly sam- the interest of increasing the number of galaxy clusters pling {λ,z } pairs from the data catalog. To ensure that λ 6 Rykoff et al. therandomcatalogcorrectlysamplesthesurveyvolume, we utilize the redshift mask. Specifically, after sampling Table 1 redMaPPerClusterSamples aclusterfromtheclustercatalog,werandomlysamplea position({α,δ})fortherandompoint. Iftheclusterred- Sample Area(deg2) a RedshiftRange No. ofClustersb shiftz islargerthanthemaximumredshiftatwhichthe λ cluster can be detected, we draw a new {α,δ}, repeat- DR8 10134 0.08<z <0.6 26111 λ ing the procedure until the cluster is assigned a position SVA1 116 0.2<zλ<0.9 787 SVA1expanded 208 0.2<z <0.9 1382 consistent with the cluster properties. In all, we sample λ each cluster n ∼ 1000 times to ensure that any cor- samp a Area including effect of f <0.2 cut for extended cluster sources relationmeasurementswemakearenotaffectedbynoise mask (seeSection3.6). in the random catalog. b Richnessthreshold,λ/S>20 Having assigned a position, we use the depth map and the footprint mask to estimate the local mask fraction that λ/S >20. f and scale factor S, as defined in Section 3. This is mask thepointatwhichthefiniteextentoftheclustersistaken 2. The volume limited mask for SVA1 is as described into account. Only random points that have fmask <0.2 above. ThevolumelimitedcatalogforDR8issim- and λ/S > 20 are properly within the cluster detection ply z <0.33. λ footprint. These cuts will locally modify the richness andredshiftdistributionoftherandompointsrelativeto 3. Forthe DR8catalog, the richness scalefactor S(z) the data. In particular, the random points will tend to isillustratedbyFigure19inRM1. Forthevolume- undersample the regions from which we discard clusters, limitedSVA1catalog,S(z)(cid:46)1.3atallredshiftsby particularly for low richness and high redshift clusters. construction. We address this difficulty by using weighted randoms. 4. Verylowredshiftclustershavebiasedredshiftsand Specifically, given all n random points generated samp richnesses due to boundary effects, so we have set from a given {λ,z } pair, we calculate the number of λ the lower redshift limit z >0.08 and z >0.2 for random points that pass our mask and threshold cuts, λ λ the DR8 and SVA1 catalogs, respectively. denoted n . Each random point is then upweighted keep by a factor w = n /n . This ensures that the samp keep 5. Only clusters with f <0.2 are included. That weighteddistributionofrandompointsmatchestheclus- mask is,clustersneartheboundaryandontopofmasked ter catalog as a function of both λ and z , while taking λ regionswillberemoved. Theclusterrandompoints into account all boundaries and depth variations. As we properlysamplethefootprint,reflectingthesecuts. typically sample each cluster ∼ 1000 times, the weight w is sufficiently well measured that we neglect noise in Asummaryofthenumberofclusters,effectivearea,and w when making use of the weighted random points. We redshift range of the catalogs (including the SVA1 ex- note that in this procedure we neglect sample variance panded catalog described in Section 5.2) is given in Ta- from large-scale structure that may be imprinted in the ble 1. clustercatalog;whilethismaybeasmallissueforSVA1, Figure 2 shows the angular density contrast of our this will be averaged out over large surveys such as DES redMaPPer sample for SDSS DR8 (0.1<z <0.3), and and SDSS. λ Figure3showsthesameforDESSVA1(0.2<z <0.8). Finally, we compute the effective area of the survey λ We restrict ourselves to z <0.8 because only the deep- for cluster detection. For any given redshift z, we com- λ estregions(andSNfields)haveredMaPPerselectedclus- pute the total area (A ) covered where we might have tot ters at z > 0.8. Due to the relatively small density of a chance of detecting a cluster, such that z < z . λ max clustersonthesky,thedensitycontrastissmoothedona Taking into account boundaries and the finite size of 30(cid:48) scaletosuppressnoise. Largescalestructureisread- clusters, the effective area is simply A ×n /n , tot samp keep ily apparent in the cluster density. Previous DES work where n /n is computed for all random points samp keep hasshownthatthedensityfieldofredMaPPerclustersis with z <z . We then use a cubic spline to perform a max well correlated with the underlying matter density field smoothinterpolationasafunctionofredshift. Duetothe as determined from weak lensing measurements (Chang finitesizeoftheclustersandthesmallfootprintofSVA1 et al. 2015b; Vikram et al. 2015). with a lot of boundaries, the effective area for λ > 20 cluster detection is reduced from 148deg2 to ∼100deg2 4.1. Photo-z Performance at z <0.6. 4.1.1. SDSS DR8 4. THE FIDUCIAL CLUSTER CATALOGS In Figure4 we comparethe photometric redshift z to λ We have run the updated redMaPPer v6.3 algorithm the spectroscopic redshift of the CG (where available) on SDSS DR8 and DES SVA1 data as described in Sec- for all clusters in DR8 with λ > 20. The top panel tion 2. Following RM1, the full cluster finder run con- shows a density map of the zspec–zλ relation, with 4σ tains all clusters with λ ≥ 5S, over the redshift range outliers (such that |(zspec −zλ)/σzλ| > 4), which make z ∈[0.05,0.6] (for DR8) and z ∈[0.15,0.9] (for SVA1). up 1.1% of the population, marked as red points. The λ λ However,wehavechosentoapplyrelativelyconservative outlier clump at zλ ∼ 0.4 is due to cluster miscentering cuts to our catalogs. The cuts we apply are as follows. rather than photometric redshift failures. In RM1, we demonstrated that this clump of outliers is due to errors 1. There must be at least 20 unmasked galaxies in cluster centering rather than photometric redshift es- brighter than the local limiting magnitude, such timation. Specifically,theseoutliersrepresentclustersin redMaPPer on DES SVA1 7 DR8 70.0° 1.0 55.0° 40.0° y 0.5 sit n e Dec 25.0° e D v ti 0.0 a 10.0° Rel -5.0° -0.5 -20.0 ° 240.0° 200.0° 160.0° 120.0° 80.0° 40.0° 0.0° 320. 0 ° R A Figure 2. Angularclusterdensitycontrastδ=(ρ−ρ¯)/ρ¯fortheSDSSDR8redMaPPercatalogintheredshiftrange[0.1,0.3],averaged ona30(cid:48) scale. which the photometrically assigned central galaxy has a and reserving the second half for a validation test. This spectroscopic redshift that is inconsistent not only with is not ideal, as we then fall below the required number thephotometricredshiftofthecluster,butalsothespec- of spectra for a good fit to the red-sequence model (see troscopic redshift of the remaining cluster members (see Appendix B of RM1). Nevertheless, the z statistics of λ Figure10inRM1). Thisfailuremodeisparticularlypro- the validation catalog are equivalent to those of the full nounced near filter transitions. The bottom panel shows fiducial run6. the bias (magenta dot-dashed line) and scatter (cyan dot-dot-dashed line) about the 1–1 line (blue dashes). 4.2. Density of Clusters The performance is equivalent to that from RM1, with In Figure 6 we show the comoving density of redMaP- σ /(1+z)<0.01 over most of the redshift range. z Per clusters for DR8 (red) and SVA1 (blue). Densities are computed using our fiducial cosmology for clusters 4.1.2. DES SVA1 withλ/S >20bysummingindividualclusterP(z)func- Figure 5 is the analogue to Figure 4 for DES SVA1. tions. Thewidthofthelinesaresmoothedoveraredshift Because of the significantly smaller number of spectra, range δz = 0.02, and assume Poisson errors (which are weshowallclusterswithλ>5,despitethefactthatthis consistent with jackknife errors). The black dashed line will increase the rate of 4σ outliers due to miscentering. shows the predicted abundance of halos with M500c > Nevertheless,theperformanceisstillverygoodwithonly 1×1014h−1M , with the dash-dotted lines showing the 70 (cid:12) 5% outliers. All of these outliers have λ < 20; thus same with a mass threshold of 0.7 × 1014h−1M and 70 (cid:12) there are no 4σ outliers in the set of 52 clusters with 1.3×1014h−1M (Tinker et al. 2008). spectra in the fiducial λ/S > 20 catalog. The bias and 70 (cid:12) WenotethattheredMaPPer clusterisvolumelimited scatter are all very good at z (cid:46) 0.7, with an increase only out to z ≤ 0.33. Above this redshift, the cluster of σ /(1 + z) from ∼ 0.01 to ∼ 0.02 at high redshift. z density as a function of redshift reflects two competing This increase is caused by both the variations in survey trends: an increasing Eddington (1913) bias in the esti- depth, as well as noise in the high-z red-sequence model mated cluster richness, which tends to increase the clus- that will be reduced as we obtain more cluster spectra ter density as a function of richness, and an increasing andincreaseourfootprintinfullDESsurveyoperations. detection threshold due to the shallow survey depth of Atlowredshift,wenotethatthescatterinz islargerin λ the SDSS. For z ≈ 0.4, the number of galaxies lost due DES SVA1 than in SDSS DR8. This is primarily caused to the shallow survey depth is relatively small, and Ed- by the relatively noisy MAG AUTO galaxy colors employed dington bias dominates, leading to an apparent increase for our SVA1 catalog which increase the red-sequence intheclusterdensity. Asonemovestowardsevenhigher width and hence the noise in z . λ redshifts,theincreasingdetectionthresholdquicklydom- Becauseouranalysisutilizedallavailablespectroscopy inates, and the density of clusters falls as an increasing for training redMaPPer, it is possible that our photo-z performance is artificially good due to over-training. To 6Thoughthez statisticsarethesame,therichnessestimations λ test for this, we have done a second full training of the are not as stable, and thus our primary catalog utilizes all the red-sequencemodelusingonly50%oftheclusterspectra, spectrafortraining. 8 Rykoff et al. SVA1 (SPT-E) 0.6 -45.0° 0.4 0.2 y -50.0° sit n e c D De 0.0 e v ti a el R -55.0° -0.2 -0.4 -60.0° -0.6 90.0° 80.0° 70.0° 60.0° R A Figure 3. Angularclusterdensitycontrastδ=(ρ−ρ¯)/ρ¯fortheDESSVA1redMaPPercatalogintheredshiftrange[0.2,0.8],averaged ona30(cid:48) scale. function of redshift. RM15),itsignificantlyreducedthefootprintoftheSVA1 The SVA1 density is roughly consistent with DR8 redMaPPercatalog. Thisisespeciallydetrimentalforthe at low redshift, although the volume probed is much purposes of comparing the redMaPPer catalog against smaller; the peak at z ∼ 0.6 is caused by the same Ed- external X-ray cluster catalogs (see Section 6.2). Simi- dington bias effects as in DR8 at lower redshift. The larly, while the bad region mask is clearly beneficial for number density slowly declines with redshift in SVA1, shape measurements, it creates a footprint with many which is consistent with a constant mass threshold at holes, which negatively impacts cluster centering. In fixed richness. However, we caution that the possibil- thissection,weinvestigatetheimpactofthesechoiceson ity of a varying mass threshold (due to the build-up of therichnessandredshiftrecoveryofredMaPPerclusters. thered-sequence, forexample)aswellasEddingtonbias We also describe an expanded redMaPPer catalog with and projection effects must both be taken into account a larger footprint that can be used for multi-wavelength to compute a proper cluster abundance function n(z,M) cross-correlation measurements, increasing the number for cosmological studies. of clusters available in Section 6.2 by ∼50%. 5. EFFECTS OF STAR/GALAXY SEPARATION 5.1. Star/Galaxy Separation AND MASKING IN SVA1 The initial star/galaxy classifier in SVA1 data AsdiscussedinSection2.1,thefiducialSVA1redMaP- is the modest classifier, based on the SExtractor Per footprint was based on the area used for the ngmix SPREAD MODELquantity(Changetal.2015a;Jarvisetal. galaxy shape catalog, in order to utilize the improved 2015,Section2.2)whichcomparesthefitofaPSFmodel morphological star/galaxy separation in this region. In tothatofaPSFconvolvedwithasmallcircularexponen- addition, we removed 4% of the area with a relatively tialmodelformorphologicalclassification. Whilemodest large concentration of centroid shifts between band- works reasonably well at bright magnitudes, at z ∼ 0.7 passes in individual objects. However, these two choices the stellar locus (in the DES optical bands griz) comes come with some trade-offs. While the improvement in closetothegalaxyredsequence. Foraccurateselectionof star/galaxy separation is clearly necessary in the se- individual red galaxies as in the redMaGiC catalog, this lection of redMaGiC red galaxies (see Appendix A of requiredourimprovedstar/galaxyclassificationbasedon redMaPPer on DES SVA1 9 0.7 0.6 DR8, λ > 20 0.25 0.5 fout = 0.011 n(M>1×1014) zspec 00..34 3c)0.20 DSVRA81 p 0.2 M 0.1 3−0.15 0.0 /h s 0.02 r e t 0.01 us0.10 zλ cl z - spec -00..0001 Bias 4n(10−0.05 σ/(1+z) -0.02 z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.000.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 zλ zλ Figure 4. Top: Central galaxy spectroscopic redshift zspec vs. Figure 6. Comovingdensityofclusters(λ/S>20)forDR8(red clusterphotometricredshiftzλforSDSSDR8clusterswithλ>20. curve) and SVA1 (blue curve), assuming our fiducial cosmology. Grey shaded regions show 1, 2, and 3σ density contours. Red WidthofthelinescorrespondtotheassumptionofPoissonerrors points, comprising 1.1% of the total sample, show > 4σ outliers. (which are consistent with jackknife errors). The black dashed The outlier clump at zλ ∼0.4 is not due to photometric redshift line shows the predicted abundance of halos with M500c > 1× fwsaigiitlnuherdaescc,eobnrurtertactrlagptahhloeartxoycmeinsettneroirctinrignedffsaahcilituftar,ecsbl:uuttshtweerhsemosaeermepbhpeorrti.moBmaoreittltryoicmcal:lulysBteaiarsss- 1m0a1s4sht−7h0r1eMsh(cid:12)ol,dwoift0h.7th×e10d1a4shh-−7d01otMte(cid:12)dalinndes1.s3h×ow10in1g4hth−70e1sMam(cid:12)e(Twiinthkear inzspec−zλ(magenta)andzλscatterσz/(1+z)(cyan)forclusters etal.2008). with central galaxy spectra. Over most of the redshift range the biasis<0.005andthescatterσz/(1+z)<0.01. tion from ngmix). We also notice that the global back- groundisslightlyincreasedathighredshift,thusslightly depressing the richness estimates. The richness bias is 1.0 ∼ 3% at z = 0.8, with the bias decreasing linearly with SVA1, λ > 5 redshiftsuchthattheclusterrichnessesatz =0.2areun- 0.8 fout = 0.050 biased. Wecalibratethisbiaswithasimplelinearmodel, zspec 00..46 asoncdiactoerdrescytstfeomr aittiicnuonucrerfitnaainlteyxipnanridcehdnecsastdaluoeg.toTthheeains-- efficientstar/galaxyseparationis∼2%,smallerthanthe 0.2 statistical uncertainty on λ. Thus, aside from mild mis- 0.0 centering problems, redMaPPer richness estimates are 0.03 quite insensitive to stellar contamination in the galaxy 0.02 catalog, as expected. zλ 0.01 z - spec -00..0001 Bias In addition to the ov5e.2r.allMgaeoskminegtric mask, our fiducial -0.02 σz/(1+z) footprint includes masking for bright (J < 13) 2MASS -0.03 stars and 4% of the area with a larger-than-typical con- 0.0 0.2 0.4 0.6 0.8 1.0 centration of object centroid shifts. However, we have z λ found that several good cluster centers are masked in Figure 5. Same as Figure 4, for SVA1 clusters with λ>5. The these regions causing significant offsets from the X-ray lowerrichnessthresholdwasusedfortheplotbecauseofthesmall and SZ centers (e.g., Section 2.3 of S15). number of cluster spectra for λ > 20 clusters. At z (cid:38) 0.7 the Inordertoestimatetheimpactofmasking(inaddition scatter increases to σz/(1+z) ∼ 0.02 as our red-sequence model tostar/galaxyseparation),wehavererunredMaPPeron is noisy due to the relative lack of training spectra. As discussed in the text, the increased z scatter over all redshifts (relative to the expanded footprint using the modest classifier (as λ DR8)iscausedbyrelativelynoisyMAG AUTOcolors. above), andincludinggalaxiesthathadbeenrejectedby both the 2MASS mask and the “4%” mask. We then ngmix(Rozoetal.2015c),whichreducedstellarcontam- match clusters from this expanded catalog to the fidu- ination from (cid:38)15% at z ∼0.7 to less than 5%. cial catalog. Aside from the clusters that are now badly In order to estimate the impact of star/galaxy separa- miscentered due to stellar contamination, two SPT clus- tion, we have rerun the redMaPPer cluster finder on a ters (SPT-CLJ0417−4748 and SPT-CL0456−5116; see slightlyexpandedfootprintusingthemodeststar/galaxy S15) are now properly centered as the central galaxies classifier,whileleavingeverythingelse(includingthered- are no longer masked. sequence calibration) the same. We then match clusters Figure 7 shows the comparison in cluster redshift z λ from this catalog to our fiducial catalog. The first thing between the expanded (z ) and fiducial (z ) catalogs. λ(cid:48) λ we find is that a small number of clusters (∼ 1.4%) are Theclusterredshiftsareveryconsistent, withafewout- now badly miscentered on bright, red, misclassified stars liers at ∆z > 0.01. The red curve in the right panel λ (as determined from our improved star/galaxy separa- shows a Gaussian fit to the ∆z histogram, with mean λ 10 Rykoff et al. photo-z bias richness bias 0.02 1.3 1.2 0.01 1.1 z - zλλ’ 0.00 λλ’/ 1.0 0.9 -0.01 0.8 -0.02 0.7 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 zλ zλ Figure 7. Plot of ∆zλ = zλ(cid:48) −zλ for the expanded (zλ(cid:48)) and Figure 8. Plotofrichnessbias, λ(cid:48)/λ, fortheexpanded(λ(cid:48))and fiducial (zλ) catalogs. The cluster redshifts are very consistent, fiducial (λ) catalogs. All values of λ(cid:48) have been corrected for the with few outliers at ∆zλ > 0.01, which is already < 1σ on the star/galaxy separation bias model in Section 5.1. The richness redshifterror. ThereddashedcurveintherightpanelisaGaussian estimates are consistent, with a Gaussian fit (red dashed curve) fittothe∆zλ histogram,withmean5×10−5 andRMS7×10−4. showingλ(cid:48)/λ=0.99±0.04. 5×10−5 andRMS7×10−4. Thus,theworsestar/galaxy 0.25 separationandlessconservativemaskhavenosignificant SPT-E, fiducial catalog impact on the cluster redshift estimation. SPT-E, expanded catalog Figure 8 shows the richness bias as the ratio of λ(cid:48) )0.20 3c (expanded catalog) to λ (fiducial catalog) in the SPT- p M E region. All values of λ(cid:48) have been corrected for the 3−0.15 h star/galaxyseparationbiasmodelinSection5.1. Again, / tshheowriicnhgneλs(cid:48)s/λest=im0a.t9e9s±are0.c0o4n.siWsteennt,owteitthhaatGtahuisssi∼an4fi%t clusters0.10 richness scatter is fully consistent with the expectations 4− 0 based on the richness extrapolations in the fiducial cat- n(10.05 alog which made use of a more aggressive mask. How- ever, we also find that for ∼ 7% of clusters λ(cid:48)/λ differs 0.00 from unity by more than 3σ. These apparent outliers 0.2 0.3 0.4 0.5 0.6 0.7 0.8 z are caused by clusters seen in projection. Changes in λ masking can change the way these projected clusters are Figure 9. Numberdensityofclustersfortheexpanded(magenta) and fiducial (blue) catalogs, limited to the SPT-E region. The deblendedormergedbytheredMaPPeralgorithm,lead- number density is consistent within 1σ at all redshifts in spite of ing to these outliers. This result suggests a lower limit thechangesinstar/galaxyseparationandmasking. of ≈7% for the redMaPPer projection rate, and demon- strates the need for a full model of projection effects in- A detailed comparison of the DES SVA1 redMaPPer corporated into a cluster abundance function. and SPT SZ cluster catalogs has been published in S15. InFigure9weshowthecomovingdensityofclustersin We briefly summarize their most important results. Us- the SPT-E region for our fiducial (blue) and expanded ing 129deg2 of overlapping data, they find 25 clusters (magenta) catalogs. The number densities are clearly between 0.1<z <0.8, including 3 new clusters that did consistent at all redshifts. Therefore, in future versions not have identified optical counterparts in Bleem et al. ofredMaPPeronDESdataourfiducialrunswillbeper- (2015). Every SZ cluster within the redMaPPer foot- formedwithalessaggressivemask(withmorearea)asit print and at z < z was detected in the redMaPPer has no impact in the richness estimation, yet it does im- max catalog. Due to the high mass threshold of the Bleem proveclustercenteringinasmallnumberofcases. While et al. (2015) sample, these are all high-mass and high- improvedstar/galaxyseparationishelpfulformanypur- richness clusters, with a typical richness λ ∼ 70. Using poses,itishearteningtoknowthatourrichnessestimates the method of Bocquet et al. (2015), they implement a are not strongly biased by a less-than-ideal separator. full likelihood formalism to constrain the λ–mass rela- For this version of the catalog, however, we recommend tion of SPT-selected clusters. By inverting the scaling that the fiducial catalog should be used for all purposes relation from S15 using the methods of Evrard et al. except where the greater area can be made use of in (2014), they compute that the mass of a λ ∼ 20 cluster cross-checks with X-ray catalogs, as in Section 6. is M ∼ 1014h−1M , consistent with the density of 500c 70 (cid:12) 6. THE CORRELATION OF redMaPPer CLUSTER clusters from Section 4.2. In addition, they find a mass RICHNESS WITH X-RAY AND SZ GALAXY scatteratfixedrichness,σ =0.18+0.08,atarichness lnM|λ −0.05 CLUSTER PROPERTIES of λ=70. Thus, they confirm that the redMaPPer rich- nessλisalow-scattermassproxyforDESdata,acrossa 6.1. Correlation with the SPT SZ Cluster Catalog muchbroaderrangeofredshiftthanwasprobedinRozo

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Preview The redMaPPer Galaxy Cluster Catalog From DES Science Verification Data

DES 2015-0146 SLAC PUB-16454 Fermilab PUB-16-012-E-PPD Draft version May 27, 2016 DOI 10.3847/0067-0049/224/1/1 PreprinttypesetusingLATEXstyleemulateapjv.5/2/11 THE REDMAPPER GALAXY CLUSTER CATALOG FROM DES SCIENCE VERIFICATION DATA E. S. Rykoff1,2,(cid:63), E. Rozo3, D. Hollowood4, A. Bermeo-Hernandez5, T. Jeltema4, J. Mayers5, A. K. Romer5, P. Rooney5, A. Saro6, C. Vergara Cervantes5, R. H. Wechsler7,1,2, H. Wilcox8, T. M. C. Abbott9, F. B. Abdalla10,11, S. Allam12, J. Annis12, A. Benoit-Le´vy13,10,14, G. M. Bernstein15, E. Bertin13,14, D. Brooks10, D. L. Burke1,2, D. Capozzi8, A. Carnero Rosell16,17, M. Carrasco Kind18,19, F. J. Castander20, M. Childress21,22, C. A. Collins23, C. E. Cunha1, C. B. D’Andrea8,24, L. N. da Costa16,17, T. M. Davis25, S. Desai26,6, H. T. Diehl12, J. P. Dietrich26,6, P. Doel10, A. E. Evrard27,28, D. A. Finley12, B. Flaugher12, P. Fosalba20, J. Frieman12,29, K. Glazebrook30, D. A. Goldstein31,32, D. Gruen1,33,2,34, R. A. Gruendl18,19, G. Gutierrez12, M. Hilton35, 6 K. Honscheid36,37, B. Hoyle34, D. J. James9, S. T. Kay38, K. Kuehn39, N. Kuropatkin12, O. Lahav10, G. F. Lewis40, C. Lidman39, M. Lima41,16, M. A. G. Maia16,17, R. G. Mann42, J. L. Marshall43, P. Martini36,44, P. Melchior45, 1 C. J. Miller27,28, R. Miquel46,47, J. J. Mohr26,6,33, R. C. Nichol8, B. Nord12, R. Ogando16,17, A. A. Plazas48, 0 K. Reil2, M. Sahle´n49, E. Sanchez50, B. Santiago51,16, V. Scarpine12, M. Schubnell28, I. Sevilla-Noarbe50,18, 2 R. C. Smith9, M. Soares-Santos12, F. Sobreira12,16, J. P. Stott49, E. Suchyta15, M. E. C. Swanson19, G. Tarle28, y D. Thomas8, D. Tucker12, S. Uddin30, P. T. P. Viana52,53, V. Vikram54, A. R. Walker9, Y. Zhang28 a (The DES Collaboration) M Draft version May 27, 2016 5 ABSTRACT 2 WedescribeupdatestotheredMaPPeralgorithm, aphotometricred-sequenceclusterfinderspecif- ] icallydesignedforlargephotometricsurveys. Theupdatedalgorithmisappliedto150deg2 ofScience O Verification (SV) data from the Dark Energy Survey (DES), and to the Sloan Digital Sky Survey C (SDSS) DR8 photometric data set. The DES SV catalog is locally volume limited, and contains 786 . clusters with richness λ > 20 (roughly equivalent to M (cid:38) 1014h−1M ) and 0.2 < z < 0.9. The h 500c 70 (cid:12) DR8 catalog consists of 26311 clusters with 0.08<z <0.6, with a sharply increasing richness thresh- p old as a function of redshift for z (cid:38) 0.35. The photometric redshift performance of both catalogs is - o shown to be excellent, with photometric redshift uncertainties controlled at the σ /(1+z) ∼ 0.01 z r level for z (cid:46) 0.7, rising to ∼ 0.02 at z ∼ 0.9 in DES SV. We make use of Chandra and XMM X-ray t s and South Pole Telescope Sunyaev-Zeldovich data to show that the centering performance and mass– a richnessscatterareconsistentwithexpectationsbasedonpriorrunsofredMaPPeronSDSSdata. We [ also show how the redMaPPer photo-z and richness estimates are relatively insensitive to imperfect 2 star/galaxy separation and small-scale star masks. v Subject headings: galaxies: clusters 1 2 6 1. INTRODUCTION troduced the red-sequence matched-filter Probabalistic 0 Percolation cluster finder (redMaPPer; Rykoff et al. Clusters of galaxies are the largest bound objects in 0 2014, henceforth RM1). RedMaPPer identified galaxy the Universe, and are uniquely powerful cosmological . clusters by making use of the fact that the bulk of the 1 probes (e.g., Henry et al. 2009; Vikhlinin et al. 2009; cluster population is made up of old, red galaxies with 0 Mantz et al. 2010; Rozo et al. 2010; Clerc et al. 2012; 6 Benson et al. 2013; Hasselfield et al. 2013; Planck Col- a prominent 4000˚A break. Focusing on this specific 1 laboration et al. 2014) (see also reviews in Allen et al. galaxy population increases the contrast between clus- : (2011); Weinberg et al. (2013)). In particular, galaxy ter and background galaxies in color space, and enables v clusters are one of the key probes of growth of struc- accurate and precise photometric redshift (photo-z) es- i X ture and dark energy measurements from ongoing and timates. The associated cluster richness estimator, λ, is r upcoming photometric surveys such as the Dark En- thesumofofthemembershipprobabilityofeverygalaxy a ergy Survey (DES; The DES Collaboration 2005), the intheclusterfield,andhasbeenoptimizedtoreducethe Kilo-Degree Survey (KiDS; de Jong et al. 2015), the scatter in the richness–mass relation (Rozo et al. 2009, Hyper-SuprimeCamera(HSC)1,theLargeSynopticSur- 2011; Rykoff et al. 2012a). The initial application of redMaPPer in RM1 was on vey Telescope (LSST; LSST Science Collaboration et al. theSloanDigitalSkySurveyDataRelease8photometric 2009), Euclid (Laureijs et al. 2011), and WFIRST2. data (SDSS DR8; York et al. 2000; Aihara et al. 2011). There are already a wide range of photometric clus- As such, the catalog was limited to relatively low red- ter finders (e.g. Goto et al. 2002; Gladders et al. 2007; shifts (z (cid:46) 0.5). The SDSS redMaPPer catalog has Koester et al. 2007a; Hao et al. 2010; Soares-Santos been extensively validated using X-ray (Rozo & Rykoff et al. 2011; Szabo et al. 2011; Wen et al. 2012; Murphy 2014, henceforth RM2); (Sadibekova et al. 2014) and et al. 2012; Ascaso et al. 2012, 2014; Oguri 2014), each Sunyaev-Zeldovich (SZ) data (Rozo et al. 2015a, hence- with various strengths and weaknesses. In 2014, we in- forth RM3), and with spectroscopic data (Rozo et al. (cid:63)erykoff@slac.stanford.edu 2015b, henceforth RM4), demonstrating that the cata- 1 http://www.naoj.org/Projects/HSC/HSCProject.html log has low scatter in the mass–richness relation; well- 2 http://wfirst.gsfc.nasa.gov/ quantified centering performance; and accurate and pre- 2 Rykoff et al. cise cluster photo-zs. The low scatter has also made it of which covers a single DECam 2.2-degree-wide field of possible to use the redMaPPer SDSS catalog to verify view, for a total of ∼32deg2 of deeper imaging (includ- Planckclusters(Rozoetal.2015a;PlanckCollaboration ing extra offset pointings of SN fields taken during SV). et al. 2015). In a comparison of numerous spectroscopic Finally, there are smaller discontinguous regions target- cluster finders on mock catalogs, redMaPPer achieved ing massive clusters (Melchior et al. 2015) and the COS- one of the smallest variances in estimated cluster mass MOS field (Scoville et al. 2007). We utilize this DES SV at fixed halo mass, despite being the only cluster finder data set to construct the first DES redMaPPer cluster relying solely on two-band photometric data (all other catalog. The redMaPPer footprint used in this paper cluster finders were spectroscopic) (Old et al. 2015). is the same as that used for the associated redMaGiC RedMaPPer was designed to easily handle a broad (red-sequence matched-filter Galaxies Catalog) of red range in redshift, as well as to run efficiently over a wide galaxies with well-behaved photo-z performance (Rozo and deep galaxy catalog. As such, it is ideally suited et al. 2015c, henceforth RM15). to DES data, which can be used to detect faint red- The DES SV data was processed by the DES Data sequence galaxies to much higher redshifts than SDSS Management(DESDM)infrastructure(Gruendletal, in (z (cid:46)0.9). Inthispaper,wedescribethefirstapplication prep),whichincludesimagedetrending,astrometricreg- ofredMaPPertoDESScienceVerification(SV)data. In istration, global calibration, image coaddition, and ob- addition, we describe updates to the redMaPPer algo- ject catalog creation. Details of the DES single-epoch rithm since versions 5.2 (RM1) and 5.10 (RM4) to the andcoaddprocessingcanbefoundinSevillaetal.(2011) present version 6.3, and apply the updated algorithm to and Desai et al. (2012). We use SExtractor to create the SDSS DR8 photometric data. We characterize the object catalogs from the single-epoch and coadded im- photo-z performanceofredMaPPerusingavailablespec- ages (Bertin & Arnouts 1996; Bertin 2011). troscopy, and use available SZ data from the South Pole After the initial production of these early data prod- TelescopeSZclustersurvey(SPT;Bleemetal.2015), as ucts, we detected several issues that were mitigated in well as X-ray observations from Chandra and XMM, to post-processing, leading to the creation of the “SVA1 measurethecenteringpropertiesoftheDESSVredMaP- Gold”photometrycatalog3. First,wemaskedpreviously Per catalog, and to test the validity of the redMaPPer unmasked satellite trails. Second, we use a modified clusterrichnessasaphotometricmasstracer. Adetailed version of the big-macs stellar-locus regression (SLR) analysis of the richness and SZ scaling relations is pre- fitting code (Kelly et al. 2014)4 to recompute coadd sented in Saro et al. (2015, henceforth S15). A similar zero-points over the full SVA1 footprint. Third, regions analyisofX-rayobservationsincludingSDSSoverlapwill around bright stars (J < 13) from the Two Micron All be presented in Bermeo Hernendez et al. (in prep) and SkySurvey(2MASS;Skrutskieetal.2006)weremasked. Hollowood et al. (in prep). Finally, we removed 4% of the area with a large con- The layout of this paper is as follows. In Section 2 centration of centroid shifts between bandpasses in indi- wedescribetheDESScienceVerificationandSDSSDR8 vidual objects, indicating scattered light, ghosts, satel- data used in this work. Section 3 describes the updates lite trails, and other artifacts (Jarvis et al. 2015, Sec- totheredMaPPeralgorithmsincetheRM1andRM4pa- tion 2.1). We utilize the SExtractor MAG AUTO quantity pers. Section 4 describes the cluster catalogs, as well as derivedfromthecoaddedimagesforgalaxytotalmagni- thephotometricredshiftperformanceonDESandSDSS tudesandcolors. Thischoicesreflectsthefactthatmeth- data. In Section 5 we detail the effects of star/galaxy ods to compute multi-epoch fitting photometric quan- separation and small-scale masking on the cluster prop- tities are still under development. The added noise in erties, and in Section 6 we compare the redMaPPer cat- thecolorresultsinalargerobservedred-sequencewidth, alog with X-ray and SZ clusters in the DES SVA1 foot- which results in slightly poorer photometric redshifts, as print. Finally, in Section 7 we summarize our results. shown in Section 4.1.2. For the present work, we have When necessary, distances are estimated assuming a flat not made use of the DES Y-band imaging because of ΛCDM model with Ωm = 0.30. For consistency with uncertain calibration, and the minimal lever-arm gained previous redMaPPer work, we use h=1.0 when quoting at the redshifts probed in this paper. Finally, our fidu- distances (h−1Mpc) and h = 0.7 when quoting masses cial star/galaxy separation is done using the multi-band (h−701M(cid:12)). multi-epochimageprocessingcodengmixusedforgalaxy shape measurement in DES data (Jarvis et al. 2015), as 2. DATA detailed in Appendix A of RM15. 2.1. DES Science Verification Data The footprint is initially defined by MANGLE (Swanson The DES is an ongoing 5-band (grizY) photometric et al. 2008) maps generated by DESDM which describe survey performed with the Dark Energy Camera (DE- the geometry of the coadded data in polygons of arbi- Cam, Flaugher et al. 2015) on the 4-meter Blanco trary resolution. For ease of use, these are then av- Telescope at Cerro Tololo Inter-American Observatory eraged over HEALPIX NSIDE=4096 pixels (G´orski et al. (CTIO). Prior to the beginning of the DES survey, 2005), where each pixel is approximately 0.7(cid:48) on a side. from November 2012 to March 2013, DES conducted The pixelized MANGLE maps are combined with maps of a ∼ 250deg2 “Science Verification” (SV) survey. The thesurveyobservingproperties(e.g.,airmass,full-width- half-maximum, etc.) compiled by Leistedt et al. (2015) largestcontiguousregioncovers∼160deg2oftheeastern using the method of Rykoff et al. (2015) to generate 10σ edge of the SPT survey (“SPT-E” hereafter). A smaller MAG AUTO limiting magnitude maps. We first restrict the ∼ 35deg2 region is in the western edge of the footprint (“SPT-W” hereafter). In addition, DES surveys 10 Su- 3 http://des.ncsa.illinois.edu/releases/sva1 pernovafields(“SNfields”hereafter)every5-7days,each 4 https://code.google.com/p/big-macs-calibrate/ redMaPPer on DES SVA1 3 SVA1 (SPT-E) (z-band) usedinthecalibrationoftheredsequenceinSection3.3. 2.2. SDSS DR8 -45.0° 22.6 In addition to our new catalog on DES SVA1 data, we have updated the redMaPPer catalog for SDSS DR8 22.4 photometricdata(Aiharaetal.2011),whichremainsthe -50.0° most recent photometric data release from SDSS. The σ) Dec 22.2m (10lim wDhRi8chgwaleacxuytctaottahloeg10c4o0n1tadiengs2∼ofc1o4n0t0i0gudoegu2shoifghimqaugailnitgy, -55.0° observations using the mask from the Baryon Acoustic 22.0 Oscillation Survey (BOSS, Dawson et al. 2013). The mask is further extended to exclude all stars in the Yale Bright Star Catalog (Hoffleit & Jaschek 1991), as well -60.0° 21.8 as the area around objects in the New General Catalog (NGC Sinnott 1988). The resulting mask is that used 90.0° 80.0° 70.0° 60.0° R A by RM1 to generate the SDSS DR8 redMaPPer catalog. We refer the reader to that work for further discussion Figure 1. Map of 10σ depth (in magnitudes) in ∼ 125deg2 in on the mask, as well as object and flag selection. the SVA1 SPT-E footprint, for SLR-corrected zauto magnitudes. Small scale variations are caused by variations in the number of Total magnitudes are determined from i-band SDSS exposures,chipgaps,andobservingconditions. CMODEL MAG, which we denote m , and colors from ugriz i SDSS MODEL MAG. All spectroscopy is drawn from SDSS footprint to regions with deep MAG AUTO on the z band DR10 (Ahn et al. 2014). Finally, we make use of the (m ) such that m >22, as shown in Figure 1 for 10σ limiting magnitude maps from Rykoff et al. (2015, z,lim z,lim ∼125deg2 intheSPT-Eregion.5 Onlygalaxiesbrighter see, e.g., Figure 4). As with SVA1 data, only galaxies than the local 10σ limiting magnitude are used in the brighter than the local 10σ limiting magnitude are used input catalog. in the input catalog. Thengmixrunsusedforstar/galaxyseparationinthis paper and RM15 were primarily used for galaxy shape 3. UPDATES TO THE redMaPPer ALGORITHM estimationforDEScosmicshear(Beckeretal.2015)and RedMaPPer is a matched-filter red-sequence photo- cosmological constraints (The Dark Energy Survey Col- metric cluster finding algorithm with three filters based laboration et al. 2015). Therefore, the runs were per- on galaxy color, position, and luminosity. The most formed on regions with very tight tolerance for image important filter characterizes the color of red-sequence quality, and were restricted to the largest contiguous re- galaxies as a function of redshift. This filter is a linear gion (SPT-E) as well as supplementary runs on the SN red-sequencemodelincolor-magnitudespace(withslope fields. These regions comprise our fiducial footprint for andintercept)inn dimensions,wheren isthenum- col col the input galaxy catalog of 148deg2 (of which 125deg2 berofindependentcolorsintheinputdataset. Thefilter is in SPT-E). However, mask boundaries and holes re- also incorporates the intrinsic scatter, C , which is the int duce the effective area for extended cluster sources to n ×n covariance matrix assuming Gaussian errors col col ∼ 100deg2 (see Section 3.6 for details). In Section 5 in photometric magnitudes. This filter is self-calibrated we describe an expanded footprint where we relax some by making use of clusters with known spectroscopic red- of these constraints, and include SPT-W and COSMOS, shifts. The additional two filters are the radial filter, with less robust star/galaxy separation. comprised of a projected NFW profile (Navarro et al. Spectroscopic data used in this paper comes from the 1994), and a luminosity filter based on a Schechter func- GalaxyandMassAssemblysurvey(GAMADriveretal. tion. Once the parameters of the red-sequence filter is 2011),theVIMOSVLTDeepSurvey(VVDSGarillietal. known, we use this information to compute a probabil- 2008), the 2dF Galaxy Redshift Survey (2dFGRS Col- ity p that each galaxy in the vicinity of the cluster mem less et al. 2001), the Sloan Digital Sky Survey (SDSS is a red-sequence member. The richness λ is defined as Ahn et al. 2014), the VIMOS Public Extragalactic Sur- thesumofthemembershipprobabilitiesoverallgalaxies vey (VIMOS Garilli et al. 2014), and the Arizona CDFS within a scale-radius R : λ Environment Survey (ACES Cooper et al. 2012). In (cid:88) addition, we have a small sample of cluster redshifts λ= p θ θ , (1) mem L R from SPT used in the cluster validation of Bleem et al. (2015). These data sets have been further supplemented where θL and θR are luminosity- and radius-dependent bygalaxyspectraacquiredaspartoftheOzDESspectro- weights defined in Appendix B of RM4. The radius scopic survey, which is performing spectroscopic follow- scales with the size of the cluster such that Rλ = upontheAAOmegainstrumentattheAnglo-Australian 1.0(λ/100)0.2h−1Mpc, which we have shown minimizes Telescope(AAT)intheDESsupernovafields(Yuanetal. the scatter in the mass–richness relation (Rykoff et al. 2015). In all, there are 36,607 photometric galaxies with 2012b). Allgalaxieswithmagnitudesconsistentwithbe- spectroscopic redshifts in our input catalog, although ingbrighterthan0.2L∗ areconsideredforcomputingthe only ∼ 2000 are red cluster members, and ∼ 1400 are richness,asdescribedbelowinSection3.2. Wenotethat the weights θ and θ are “soft cuts” to ensure cluster L R 5 Thisisequivalenttoa0.2L∗galaxyatz=0.65,asdescribed richnessmeasurementsarerobusttosmallperturbations inSection3.2 in galaxy magnitudes. The cluster photometric redshift, 4 Rykoff et al. z ,isconstrainedatthesametimeastheclusterrichness account for this missing galaxy, as per the above formal- λ byfittingallpossiblemembergalaxiessimultaneouslyto ism. To do so, however, one needs to know the survey the red-sequence color function. depth over the full area coverage of the galaxy cluster. The above equation describes the richness computa- The original redMaPPer application to SDSS DR8 in tionintheabsenceofanymasking(starholesandsurvey RM1 (redMaPPer v5.2) assumed the survey had a uni- boundaries), and in the regime where the local limiting form depth with m < 21.0. In the update described in i magnitude is deeper than 0.2L at the cluster redshift. RM4 (redMaPPer v5.10), we empirically computed the ∗ As described in Section 5 of RM1, we additionally com- local survey depth averaged over the location of each pute a scale factor S to correct for these missing cluster cluster. This was superior to assuming a constant-depth members, such that survey, but ignored small-scale depth variations, as well as being somewhat noisy. In this updated version ver- λ (cid:88) = p (2) sion (redMaPPer v6.3), we have extended redMaPPer S mem to incorporate variable survey limiting magnitude maps gals as detailed in (Rykoff et al. 2015) and described in Sec- so that each cluster with richness λ has λ/S galaxies tion 2. Specifically, we utilize the local survey depth brighterthanthelimitingmagnitudeofthesurveywithin from these depth maps to estimate the fraction of clus- the geometric survey mask. At the same time, we esti- ter galaxies that are masked, as defined in Section 3 and mate the variance S which is used in the computation of detailedinAppendixBofRM4. Inthepresentversionof theuncertaintyonrichnessλ, asdetailedinAppendixB thealgorithm,weassumethattheredgalaxydetectionis of RM4. In this way, the total uncertainty on λ includes complete(modulomasking)atmagnitudesbrighterthan the uncertainty from correcting for mask and depth ef- the local 10σ limiting magnitude used to select the in- fects. put catalog. In future versions, we intend to track the Inaddition,asdescribedinSection5.1ofRM1(specifi- full completeness function, as described in Section 5 of callyEqn. 24),itisusefultocomputethefractionofthe Rykoff et al. (2015). effective cluster area that is masked solely by geomet- ric factors such as stars, bad regions, and survey edges. 3.2. Generalization of the Characteristic Magnitude This mask fraction, denoted f , is complementary to m (z) to Arbitrary Survey Filters mask ∗ S above in that it contains all the local masking except As with the previous versions of the redMaPPer algo- the depth limit. rithm our luminosity filter is based on a Schechter func- As well as estimating membership probabilities, the tion (e.g., Hansen et al. 2009) of the form: redMaPPer centering algorithm is also probabilistic (see Section 8 of RM1). The centering probability Pcen is a φ(m )∝10−0.4(mi−m∗)(α+1)exp(cid:16)−10−0.4(mi−m∗)(cid:17), likelihood-basedestimateoftheprobabilitythatagalaxy i underconsiderationisacentralgalaxy(CG).Thislikeli- (3) hood includes the fact that the photo-z of the CG must where we set the faint-end slope α=1.0 independent of beconsistentwiththeclusterredshift;thattheCGlumi- redshift. Previously,wesetthecharacteristicmagnitude, nosity must be consistent (using a Gaussian filter) with m∗(z),usingak-correctedpassivelyevolvingstellarpop- the expected luminosity of the CG of a cluster of the ulation which we had derived from a PEGASE.2 stel- observed richness; and that the local red galaxy density lar population/galaxy formation model (Fioc & Rocca- (on the scale of ∼ 200h−1kpc) is consistent with that Volmerange 1997; Koester et al. 2007b; Eisenstein et al. of CGs. We additionally assume that each cluster can 2001). As this was derived specifically for the SDSS fil- have at most one CG, and store the top 5 most likely ters at relatively low redshift, we have updated our ref- central candidates. Our fiducial cluster position is given erencem∗(z)tomoresimplyallowfordifferentfiltersets by the highest likelihood central galaxy. Because of the and a broader redshift range. luminosity filter, the CG candidate with the largest Pcen The new value of m∗(z) is computed using a Bruzual tendstobeverybright,butisnotnecessarilythebright- &Charlot(2003,BC03)modeltopredictthemagnitude est member. Thus, we do not refer to it as the brightest evolutionofagalaxywithasinglestarformationburstat cluster galaxy (BCG), only as the central galaxy. Typ- z =3(withsolarmetallicityandSalpeterIMF)asimple- ically, for ∼ 15−20% of the clusters the CG chosen by mented in the EzGal Python package (Mancone & Gon- redMaPPer is not the brightest member. zalez2012). Wenormalizem∗ sothatmi,SDSS =17.85at TheredMaPPeralgorithmhaspreviouslybeenapplied z =0.2 for an L∗ galaxy. This was chosen to match the toSDSSDR8photometricdata. Formoredetailsonthe m∗(z) relation from RM1 and Rykoff et al. (2012a). We redMaPPer algorithm, we refer the reader to RM1 and have additionally confirmed that the evolution of m∗(z) the updates in the appendix of RM4. In this section, we is within 8% of that used in RM1 over the RM1 redshift detail the various modifications that have been imple- domain (0.1 < z < 0.5), with the largest deviations at mentedontheredMaPPeralgorithmsinceitslastpublic z ∼ 0.5. The normalization condition for mz for DES data release (RM4). is then derived from the BC03 model using the DECam passbands (Flaugher et al. 2015). 3.1. Incorporating Small Scale Structure in the Local Survey Depth 3.3. Initial Selection of Red Spectroscopic Galaxies Variable survey depth can lead to galaxies being As described in RM1, the initial calibration of the red “masked out” from galaxy clusters. Specifically, if a sequence relies on spectroscopic “seed” galaxies. This membergalaxy(withL≥0.2L )hasamagnitudebelow may be comprised of a set of training clusters with spec- ∗ our brightness threshold, then one needs to statistically troscopic redshifts (as in DES SVA1) or a large spectro- redMaPPer on DES SVA1 5 scopic catalog with a sufficient number of red galaxies in and redshift reach of the DES SV catalog, as the impact clusters(asinSDSSDR8). InRM1(seeSection6.2),we on the uncertainty estimate of λ (see Eqn. 2) is mod- selected red galaxies by splitting the spectroscopic cata- est for clusters that only require a small extrapolation. log into narrow redshift bins, and using a Gaussian mix- For SVA1, we have chosen the luminosity threshold to turemodel(Haoetal.2009)toseparategalaxiesineach be L =0.4L for the construction of the z map. thresh ∗ max redshift bin into blue and red components. However, we For DR8, we have chosen L = 1.0L , such that thresh ∗ havefoundthatthismethodisonlyrobustwhenwehave z ∼ 0.6 over > 99% of the DR8 footprint. Although max a plethora of spectra, as is the case with SDSS. this requires a large richness extrapolation at high red- In this paper, the initial red galaxy selection is per- shift(andhencelargerichnesserrors),thiscutmaintains formed by computing color residuals of galaxies in a consistency with previous redMaPPer catalogs (versions broad range of redshifts relative to the BC03-derived 5.2 and 5.10) where we did not use a z map. How- max colormodelsfromSection3.2. Asweareonlyconcerned ever, if users wish to utilize a volume-limited subset of withmakinganinitialselectionofredandbluegalaxies, the DR8 redMaPPer catalog, restricting to z < 0.33 λ any color calibration offsets between the data and the will ensure that the local depth at every cluster is deep BC03 model are irrelevant; we just need to get an ini- enough to detect 0.2L galaxies. ∗ tial sample of red galaxies. We again employ a Gaussian mixture model to obtain a first estimate for the mean 3.5. Differences Between the SVA1 and DR8 Analyses colorandintrinsicscatteroftheredspectroscopicgalax- AlthoughthecodeusedtorunonSVA1andDR8isthe ies. To ensure a clean selection, we use the g−r color same, there are a few key differences that we highlight for z < 0.35; r−i for 0.35 < z < 0.7; and i−z spec spec here. forz >0.7. Atthispoint, weproceedasdescribedin spec Step 3 of RM1 Section 6.2. 1. For DR8, we use i-band for the detection mag- nitude; for SVA1 we use z-band, which is better 3.4. Redshift Reach of the Cluster Catalog suited to the broad redshift range and the excel- Ideally, a photometric survey would be deep enough lent z-band performance of DECam. to detect the faintest 0.2L galaxies that contribute to ∗ our richness estimator λ over the full redshift range and 2. For DR8, we use ugriz for galaxy colors, while for footprint of the catalog. In a roughly uniform survey SVA1 we only use griz. The lack of u band has such as the SDSS, this limitation translates into a max- negligibleeffectontheclusterdetectionandcluster imum redshift, zmax, below which the cluster catalog is photo-zs at z >0.2 (see Section 8.1 of RM15). volume limited; for SDSS, z <0.33. By contrast, the max observing strategy of a multi-epoch survey such as the 3. For DR8, reddening corrections are applied to cat- DES may yield much greater depth variations, as shown alogmagnitudes. ForSVA1,theseareincorporated in Figure 1. Furthermore, the depth variations can be into the SLR zero-point calibration. different in different bands. Consequently, the redshift 4. For DR8, we train the red sequence model over range which can be successfully probed with redMaP- 2000deg2 (∼20%ofthefullfootprint),asinRM1, Per will depend on the local survey depth, with deeper toensuresufficientstatisticsofspectroscopictrain- regions allowing us to detect galaxy clusters to higher ing while avoiding any possibility of over-training. redshifts. ForthemuchsmallerSVA1catalog,weusethefull We define a maximum redshift z at each position max footprint and all available spectra. The impact of in the sky as follows. Given a point in the survey, our this is detailed in Section 4.1.2. initialdepthmapforthemaindetectionband(m inthe z case of SVA1), and a luminosity threshold (L ), we thresh 3.6. Generation of Random Points calculate the maximum redshift to which a typical red galaxy (defined by our red-sequence model) of L is: In RM1, we describe a method of estimating purity thresh detectable at >10σ in the main detection band (z-band and completeness of the cluster catalog using the data for DES); and at > 5σ in the remaining bands. Only itself, by placing fake clusters into the data and recover- clusters with z ≤z are accepted into our cluster cat- ingtherichness. Whilethismethod(describedinSection max alog, with z defining the redshift component of our 11ofRM1)isusefulforestimatingtheselectionfunction max survey mask. In this way, we can simply (and conserva- andprojectioneffects,itisnotappropriateforgenerating tively)accountfortheregionsthatareextremelyshallow a cluster random catalog for cross-correlation measure- in one or more bands. This happens in SVA1 primarily ments, such as the cluster–shear cross-correlation used at the boundaries, and other regions that were observed for stacked weak-lensing mass estimates (e.g., Johnston in non-photometric conditions. The result is a map of et al. 2007; Reyes et al. 2008), as existing large-scale z in HEALPIX format with NSIDE=4096, where each structure is imprinted on the random catalog. max pixel is approximately 0.7(cid:48) on a side, that is matched to In this section, we describe a new way of generating the resolution of the input depth maps. cluster random points by making use of the z map max Given this procedure, we still have an arbitrary deci- from Section 3.4. A particular challenge is the fact that sion as to where to set our luminosity threshold L . galaxy clusters are extended objects, and thus the de- thresh The most conservative option would be to demand that tectabilitydependsnotjustontheredshift,buttheclus- every cluster in the final catalog be at a redshift such ter size and the survey boundaries. We generate a ran- thatwecandetectredgalaxiestoL =0.2L . How- dom cluster catalog that has the same richness and red- thresh ∗ ever, we have chosen to be somewhat more aggressive in shift distribution of the data catalog by randomly sam- the interest of increasing the number of galaxy clusters pling {λ,z } pairs from the data catalog. To ensure that λ 6 Rykoff et al. therandomcatalogcorrectlysamplesthesurveyvolume, we utilize the redshift mask. Specifically, after sampling Table 1 redMaPPerClusterSamples aclusterfromtheclustercatalog,werandomlysamplea position({α,δ})fortherandompoint. Iftheclusterred- Sample Area(deg2) a RedshiftRange No. ofClustersb shiftz islargerthanthemaximumredshiftatwhichthe λ cluster can be detected, we draw a new {α,δ}, repeat- DR8 10134 0.08<z <0.6 26111 λ ing the procedure until the cluster is assigned a position SVA1 116 0.2<zλ<0.9 787 SVA1expanded 208 0.2<z <0.9 1382 consistent with the cluster properties. In all, we sample λ each cluster n ∼ 1000 times to ensure that any cor- samp a Area including effect of f <0.2 cut for extended cluster sources relationmeasurementswemakearenotaffectedbynoise mask (seeSection3.6). in the random catalog. b Richnessthreshold,λ/S>20 Having assigned a position, we use the depth map and the footprint mask to estimate the local mask fraction that λ/S >20. f and scale factor S, as defined in Section 3. This is mask thepointatwhichthefiniteextentoftheclustersistaken 2. The volume limited mask for SVA1 is as described into account. Only random points that have fmask <0.2 above. ThevolumelimitedcatalogforDR8issim- and λ/S > 20 are properly within the cluster detection ply z <0.33. λ footprint. These cuts will locally modify the richness andredshiftdistributionoftherandompointsrelativeto 3. Forthe DR8catalog, the richness scalefactor S(z) the data. In particular, the random points will tend to isillustratedbyFigure19inRM1. Forthevolume- undersample the regions from which we discard clusters, limitedSVA1catalog,S(z)(cid:46)1.3atallredshiftsby particularly for low richness and high redshift clusters. construction. We address this difficulty by using weighted randoms. 4. Verylowredshiftclustershavebiasedredshiftsand Specifically, given all n random points generated samp richnesses due to boundary effects, so we have set from a given {λ,z } pair, we calculate the number of λ the lower redshift limit z >0.08 and z >0.2 for random points that pass our mask and threshold cuts, λ λ the DR8 and SVA1 catalogs, respectively. denoted n . Each random point is then upweighted keep by a factor w = n /n . This ensures that the samp keep 5. Only clusters with f <0.2 are included. That weighteddistributionofrandompointsmatchestheclus- mask is,clustersneartheboundaryandontopofmasked ter catalog as a function of both λ and z , while taking λ regionswillberemoved. Theclusterrandompoints into account all boundaries and depth variations. As we properlysamplethefootprint,reflectingthesecuts. typically sample each cluster ∼ 1000 times, the weight w is sufficiently well measured that we neglect noise in Asummaryofthenumberofclusters,effectivearea,and w when making use of the weighted random points. We redshift range of the catalogs (including the SVA1 ex- note that in this procedure we neglect sample variance panded catalog described in Section 5.2) is given in Ta- from large-scale structure that may be imprinted in the ble 1. clustercatalog;whilethismaybeasmallissueforSVA1, Figure 2 shows the angular density contrast of our this will be averaged out over large surveys such as DES redMaPPer sample for SDSS DR8 (0.1<z <0.3), and and SDSS. λ Figure3showsthesameforDESSVA1(0.2<z <0.8). Finally, we compute the effective area of the survey λ We restrict ourselves to z <0.8 because only the deep- for cluster detection. For any given redshift z, we com- λ estregions(andSNfields)haveredMaPPerselectedclus- pute the total area (A ) covered where we might have tot ters at z > 0.8. Due to the relatively small density of a chance of detecting a cluster, such that z < z . λ max clustersonthesky,thedensitycontrastissmoothedona Taking into account boundaries and the finite size of 30(cid:48) scaletosuppressnoise. Largescalestructureisread- clusters, the effective area is simply A ×n /n , tot samp keep ily apparent in the cluster density. Previous DES work where n /n is computed for all random points samp keep hasshownthatthedensityfieldofredMaPPerclustersis with z <z . We then use a cubic spline to perform a max well correlated with the underlying matter density field smoothinterpolationasafunctionofredshift. Duetothe as determined from weak lensing measurements (Chang finitesizeoftheclustersandthesmallfootprintofSVA1 et al. 2015b; Vikram et al. 2015). with a lot of boundaries, the effective area for λ > 20 cluster detection is reduced from 148deg2 to ∼100deg2 4.1. Photo-z Performance at z <0.6. 4.1.1. SDSS DR8 4. THE FIDUCIAL CLUSTER CATALOGS In Figure4 we comparethe photometric redshift z to λ We have run the updated redMaPPer v6.3 algorithm the spectroscopic redshift of the CG (where available) on SDSS DR8 and DES SVA1 data as described in Sec- for all clusters in DR8 with λ > 20. The top panel tion 2. Following RM1, the full cluster finder run con- shows a density map of the zspec–zλ relation, with 4σ tains all clusters with λ ≥ 5S, over the redshift range outliers (such that |(zspec −zλ)/σzλ| > 4), which make z ∈[0.05,0.6] (for DR8) and z ∈[0.15,0.9] (for SVA1). up 1.1% of the population, marked as red points. The λ λ However,wehavechosentoapplyrelativelyconservative outlier clump at zλ ∼ 0.4 is due to cluster miscentering cuts to our catalogs. The cuts we apply are as follows. rather than photometric redshift failures. In RM1, we demonstrated that this clump of outliers is due to errors 1. There must be at least 20 unmasked galaxies in cluster centering rather than photometric redshift es- brighter than the local limiting magnitude, such timation. Specifically,theseoutliersrepresentclustersin redMaPPer on DES SVA1 7 DR8 70.0° 1.0 55.0° 40.0° y 0.5 sit n e Dec 25.0° e D v ti 0.0 a 10.0° Rel -5.0° -0.5 -20.0 ° 240.0° 200.0° 160.0° 120.0° 80.0° 40.0° 0.0° 320. 0 ° R A Figure 2. Angularclusterdensitycontrastδ=(ρ−ρ¯)/ρ¯fortheSDSSDR8redMaPPercatalogintheredshiftrange[0.1,0.3],averaged ona30(cid:48) scale. which the photometrically assigned central galaxy has a and reserving the second half for a validation test. This spectroscopic redshift that is inconsistent not only with is not ideal, as we then fall below the required number thephotometricredshiftofthecluster,butalsothespec- of spectra for a good fit to the red-sequence model (see troscopic redshift of the remaining cluster members (see Appendix B of RM1). Nevertheless, the z statistics of λ Figure10inRM1). Thisfailuremodeisparticularlypro- the validation catalog are equivalent to those of the full nounced near filter transitions. The bottom panel shows fiducial run6. the bias (magenta dot-dashed line) and scatter (cyan dot-dot-dashed line) about the 1–1 line (blue dashes). 4.2. Density of Clusters The performance is equivalent to that from RM1, with In Figure 6 we show the comoving density of redMaP- σ /(1+z)<0.01 over most of the redshift range. z Per clusters for DR8 (red) and SVA1 (blue). Densities are computed using our fiducial cosmology for clusters 4.1.2. DES SVA1 withλ/S >20bysummingindividualclusterP(z)func- Figure 5 is the analogue to Figure 4 for DES SVA1. tions. Thewidthofthelinesaresmoothedoveraredshift Because of the significantly smaller number of spectra, range δz = 0.02, and assume Poisson errors (which are weshowallclusterswithλ>5,despitethefactthatthis consistent with jackknife errors). The black dashed line will increase the rate of 4σ outliers due to miscentering. shows the predicted abundance of halos with M500c > Nevertheless,theperformanceisstillverygoodwithonly 1×1014h−1M , with the dash-dotted lines showing the 70 (cid:12) 5% outliers. All of these outliers have λ < 20; thus same with a mass threshold of 0.7 × 1014h−1M and 70 (cid:12) there are no 4σ outliers in the set of 52 clusters with 1.3×1014h−1M (Tinker et al. 2008). spectra in the fiducial λ/S > 20 catalog. The bias and 70 (cid:12) WenotethattheredMaPPer clusterisvolumelimited scatter are all very good at z (cid:46) 0.7, with an increase only out to z ≤ 0.33. Above this redshift, the cluster of σ /(1 + z) from ∼ 0.01 to ∼ 0.02 at high redshift. z density as a function of redshift reflects two competing This increase is caused by both the variations in survey trends: an increasing Eddington (1913) bias in the esti- depth, as well as noise in the high-z red-sequence model mated cluster richness, which tends to increase the clus- that will be reduced as we obtain more cluster spectra ter density as a function of richness, and an increasing andincreaseourfootprintinfullDESsurveyoperations. detection threshold due to the shallow survey depth of Atlowredshift,wenotethatthescatterinz islargerin λ the SDSS. For z ≈ 0.4, the number of galaxies lost due DES SVA1 than in SDSS DR8. This is primarily caused to the shallow survey depth is relatively small, and Ed- by the relatively noisy MAG AUTO galaxy colors employed dington bias dominates, leading to an apparent increase for our SVA1 catalog which increase the red-sequence intheclusterdensity. Asonemovestowardsevenhigher width and hence the noise in z . λ redshifts,theincreasingdetectionthresholdquicklydom- Becauseouranalysisutilizedallavailablespectroscopy inates, and the density of clusters falls as an increasing for training redMaPPer, it is possible that our photo-z performance is artificially good due to over-training. To 6Thoughthez statisticsarethesame,therichnessestimations λ test for this, we have done a second full training of the are not as stable, and thus our primary catalog utilizes all the red-sequencemodelusingonly50%oftheclusterspectra, spectrafortraining. 8 Rykoff et al. SVA1 (SPT-E) 0.6 -45.0° 0.4 0.2 y -50.0° sit n e c D De 0.0 e v ti a el R -55.0° -0.2 -0.4 -60.0° -0.6 90.0° 80.0° 70.0° 60.0° R A Figure 3. Angularclusterdensitycontrastδ=(ρ−ρ¯)/ρ¯fortheDESSVA1redMaPPercatalogintheredshiftrange[0.2,0.8],averaged ona30(cid:48) scale. function of redshift. RM15),itsignificantlyreducedthefootprintoftheSVA1 The SVA1 density is roughly consistent with DR8 redMaPPercatalog. Thisisespeciallydetrimentalforthe at low redshift, although the volume probed is much purposes of comparing the redMaPPer catalog against smaller; the peak at z ∼ 0.6 is caused by the same Ed- external X-ray cluster catalogs (see Section 6.2). Simi- dington bias effects as in DR8 at lower redshift. The larly, while the bad region mask is clearly beneficial for number density slowly declines with redshift in SVA1, shape measurements, it creates a footprint with many which is consistent with a constant mass threshold at holes, which negatively impacts cluster centering. In fixed richness. However, we caution that the possibil- thissection,weinvestigatetheimpactofthesechoiceson ity of a varying mass threshold (due to the build-up of therichnessandredshiftrecoveryofredMaPPerclusters. thered-sequence, forexample)aswellasEddingtonbias We also describe an expanded redMaPPer catalog with and projection effects must both be taken into account a larger footprint that can be used for multi-wavelength to compute a proper cluster abundance function n(z,M) cross-correlation measurements, increasing the number for cosmological studies. of clusters available in Section 6.2 by ∼50%. 5. EFFECTS OF STAR/GALAXY SEPARATION 5.1. Star/Galaxy Separation AND MASKING IN SVA1 The initial star/galaxy classifier in SVA1 data AsdiscussedinSection2.1,thefiducialSVA1redMaP- is the modest classifier, based on the SExtractor Per footprint was based on the area used for the ngmix SPREAD MODELquantity(Changetal.2015a;Jarvisetal. galaxy shape catalog, in order to utilize the improved 2015,Section2.2)whichcomparesthefitofaPSFmodel morphological star/galaxy separation in this region. In tothatofaPSFconvolvedwithasmallcircularexponen- addition, we removed 4% of the area with a relatively tialmodelformorphologicalclassification. Whilemodest large concentration of centroid shifts between band- works reasonably well at bright magnitudes, at z ∼ 0.7 passes in individual objects. However, these two choices the stellar locus (in the DES optical bands griz) comes come with some trade-offs. While the improvement in closetothegalaxyredsequence. Foraccurateselectionof star/galaxy separation is clearly necessary in the se- individual red galaxies as in the redMaGiC catalog, this lection of redMaGiC red galaxies (see Appendix A of requiredourimprovedstar/galaxyclassificationbasedon redMaPPer on DES SVA1 9 0.7 0.6 DR8, λ > 20 0.25 0.5 fout = 0.011 n(M>1×1014) zspec 00..34 3c)0.20 DSVRA81 p 0.2 M 0.1 3−0.15 0.0 /h s 0.02 r e t 0.01 us0.10 zλ cl z - spec -00..0001 Bias 4n(10−0.05 σ/(1+z) -0.02 z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.000.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 zλ zλ Figure 4. Top: Central galaxy spectroscopic redshift zspec vs. Figure 6. Comovingdensityofclusters(λ/S>20)forDR8(red clusterphotometricredshiftzλforSDSSDR8clusterswithλ>20. curve) and SVA1 (blue curve), assuming our fiducial cosmology. Grey shaded regions show 1, 2, and 3σ density contours. Red WidthofthelinescorrespondtotheassumptionofPoissonerrors points, comprising 1.1% of the total sample, show > 4σ outliers. (which are consistent with jackknife errors). The black dashed The outlier clump at zλ ∼0.4 is not due to photometric redshift line shows the predicted abundance of halos with M500c > 1× fwsaigiitlnuherdaescc,eobnrurtertactrlagptahhloeartxoycmeinsettneroirctinrignedffsaahcilituftar,ecsbl:uuttshtweerhsemosaeermepbhpeorrti.moBmaoreittltryoicmcal:lulysBteaiarsss- 1m0a1s4sht−7h0r1eMsh(cid:12)ol,dwoift0h.7th×e10d1a4shh-−7d01otMte(cid:12)dalinndes1.s3h×ow10in1g4hth−70e1sMam(cid:12)e(Twiinthkear inzspec−zλ(magenta)andzλscatterσz/(1+z)(cyan)forclusters etal.2008). with central galaxy spectra. Over most of the redshift range the biasis<0.005andthescatterσz/(1+z)<0.01. tion from ngmix). We also notice that the global back- groundisslightlyincreasedathighredshift,thusslightly depressing the richness estimates. The richness bias is 1.0 ∼ 3% at z = 0.8, with the bias decreasing linearly with SVA1, λ > 5 redshiftsuchthattheclusterrichnessesatz =0.2areun- 0.8 fout = 0.050 biased. Wecalibratethisbiaswithasimplelinearmodel, zspec 00..46 asoncdiactoerdrescytstfeomr aittiicnuonucrerfitnaainlteyxipnanridcehdnecsastdaluoeg.toTthheeains-- efficientstar/galaxyseparationis∼2%,smallerthanthe 0.2 statistical uncertainty on λ. Thus, aside from mild mis- 0.0 centering problems, redMaPPer richness estimates are 0.03 quite insensitive to stellar contamination in the galaxy 0.02 catalog, as expected. zλ 0.01 z - spec -00..0001 Bias In addition to the ov5e.2r.allMgaeoskminegtric mask, our fiducial -0.02 σz/(1+z) footprint includes masking for bright (J < 13) 2MASS -0.03 stars and 4% of the area with a larger-than-typical con- 0.0 0.2 0.4 0.6 0.8 1.0 centration of object centroid shifts. However, we have z λ found that several good cluster centers are masked in Figure 5. Same as Figure 4, for SVA1 clusters with λ>5. The these regions causing significant offsets from the X-ray lowerrichnessthresholdwasusedfortheplotbecauseofthesmall and SZ centers (e.g., Section 2.3 of S15). number of cluster spectra for λ > 20 clusters. At z (cid:38) 0.7 the Inordertoestimatetheimpactofmasking(inaddition scatter increases to σz/(1+z) ∼ 0.02 as our red-sequence model tostar/galaxyseparation),wehavererunredMaPPeron is noisy due to the relative lack of training spectra. As discussed in the text, the increased z scatter over all redshifts (relative to the expanded footprint using the modest classifier (as λ DR8)iscausedbyrelativelynoisyMAG AUTOcolors. above), andincludinggalaxiesthathadbeenrejectedby both the 2MASS mask and the “4%” mask. We then ngmix(Rozoetal.2015c),whichreducedstellarcontam- match clusters from this expanded catalog to the fidu- ination from (cid:38)15% at z ∼0.7 to less than 5%. cial catalog. Aside from the clusters that are now badly In order to estimate the impact of star/galaxy separa- miscentered due to stellar contamination, two SPT clus- tion, we have rerun the redMaPPer cluster finder on a ters (SPT-CLJ0417−4748 and SPT-CL0456−5116; see slightlyexpandedfootprintusingthemodeststar/galaxy S15) are now properly centered as the central galaxies classifier,whileleavingeverythingelse(includingthered- are no longer masked. sequence calibration) the same. We then match clusters Figure 7 shows the comparison in cluster redshift z λ from this catalog to our fiducial catalog. The first thing between the expanded (z ) and fiducial (z ) catalogs. λ(cid:48) λ we find is that a small number of clusters (∼ 1.4%) are Theclusterredshiftsareveryconsistent, withafewout- now badly miscentered on bright, red, misclassified stars liers at ∆z > 0.01. The red curve in the right panel λ (as determined from our improved star/galaxy separa- shows a Gaussian fit to the ∆z histogram, with mean λ 10 Rykoff et al. photo-z bias richness bias 0.02 1.3 1.2 0.01 1.1 z - zλλ’ 0.00 λλ’/ 1.0 0.9 -0.01 0.8 -0.02 0.7 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 zλ zλ Figure 7. Plot of ∆zλ = zλ(cid:48) −zλ for the expanded (zλ(cid:48)) and Figure 8. Plotofrichnessbias, λ(cid:48)/λ, fortheexpanded(λ(cid:48))and fiducial (zλ) catalogs. The cluster redshifts are very consistent, fiducial (λ) catalogs. All values of λ(cid:48) have been corrected for the with few outliers at ∆zλ > 0.01, which is already < 1σ on the star/galaxy separation bias model in Section 5.1. The richness redshifterror. ThereddashedcurveintherightpanelisaGaussian estimates are consistent, with a Gaussian fit (red dashed curve) fittothe∆zλ histogram,withmean5×10−5 andRMS7×10−4. showingλ(cid:48)/λ=0.99±0.04. 5×10−5 andRMS7×10−4. Thus,theworsestar/galaxy 0.25 separationandlessconservativemaskhavenosignificant SPT-E, fiducial catalog impact on the cluster redshift estimation. SPT-E, expanded catalog Figure 8 shows the richness bias as the ratio of λ(cid:48) )0.20 3c (expanded catalog) to λ (fiducial catalog) in the SPT- p M E region. All values of λ(cid:48) have been corrected for the 3−0.15 h star/galaxyseparationbiasmodelinSection5.1. Again, / tshheowriicnhgneλs(cid:48)s/λest=im0a.t9e9s±are0.c0o4n.siWsteennt,owteitthhaatGtahuisssi∼an4fi%t clusters0.10 richness scatter is fully consistent with the expectations 4− 0 based on the richness extrapolations in the fiducial cat- n(10.05 alog which made use of a more aggressive mask. How- ever, we also find that for ∼ 7% of clusters λ(cid:48)/λ differs 0.00 from unity by more than 3σ. These apparent outliers 0.2 0.3 0.4 0.5 0.6 0.7 0.8 z are caused by clusters seen in projection. Changes in λ masking can change the way these projected clusters are Figure 9. Numberdensityofclustersfortheexpanded(magenta) and fiducial (blue) catalogs, limited to the SPT-E region. The deblendedormergedbytheredMaPPeralgorithm,lead- number density is consistent within 1σ at all redshifts in spite of ing to these outliers. This result suggests a lower limit thechangesinstar/galaxyseparationandmasking. of ≈7% for the redMaPPer projection rate, and demon- strates the need for a full model of projection effects in- A detailed comparison of the DES SVA1 redMaPPer corporated into a cluster abundance function. and SPT SZ cluster catalogs has been published in S15. InFigure9weshowthecomovingdensityofclustersin We briefly summarize their most important results. Us- the SPT-E region for our fiducial (blue) and expanded ing 129deg2 of overlapping data, they find 25 clusters (magenta) catalogs. The number densities are clearly between 0.1<z <0.8, including 3 new clusters that did consistent at all redshifts. Therefore, in future versions not have identified optical counterparts in Bleem et al. ofredMaPPeronDESdataourfiducialrunswillbeper- (2015). Every SZ cluster within the redMaPPer foot- formedwithalessaggressivemask(withmorearea)asit print and at z < z was detected in the redMaPPer has no impact in the richness estimation, yet it does im- max catalog. Due to the high mass threshold of the Bleem proveclustercenteringinasmallnumberofcases. While et al. (2015) sample, these are all high-mass and high- improvedstar/galaxyseparationishelpfulformanypur- richness clusters, with a typical richness λ ∼ 70. Using poses,itishearteningtoknowthatourrichnessestimates the method of Bocquet et al. (2015), they implement a are not strongly biased by a less-than-ideal separator. full likelihood formalism to constrain the λ–mass rela- For this version of the catalog, however, we recommend tion of SPT-selected clusters. By inverting the scaling that the fiducial catalog should be used for all purposes relation from S15 using the methods of Evrard et al. except where the greater area can be made use of in (2014), they compute that the mass of a λ ∼ 20 cluster cross-checks with X-ray catalogs, as in Section 6. is M ∼ 1014h−1M , consistent with the density of 500c 70 (cid:12) 6. THE CORRELATION OF redMaPPer CLUSTER clusters from Section 4.2. In addition, they find a mass RICHNESS WITH X-RAY AND SZ GALAXY scatteratfixedrichness,σ =0.18+0.08,atarichness lnM|λ −0.05 CLUSTER PROPERTIES of λ=70. Thus, they confirm that the redMaPPer rich- nessλisalow-scattermassproxyforDESdata,acrossa 6.1. Correlation with the SPT SZ Cluster Catalog muchbroaderrangeofredshiftthanwasprobedinRozo

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