redMaPPer – III. A detailed comparison of the Planck 2013 and SDSS DR8 redMaPPer cluster catalogues

Abstract

INTRODUCTION

The abundance of galaxy clusters as a function of mass is a well-known cosmological probe (Oukbir & Blanchard 1992; Bartlett & Silk 1993; Eke, Cole & Frenk 1996; Viana & Liddle 1996; Henry et al. 2009; Vikhlinin et al. 2009; Mantz et al. 2010; Rozo et al. 2010, and many others). As such, it is of critical importance for galaxy cluster surveys to control the level of systematic failures in the cluster selection and redshift assignment, lest the corresponding cosmological inferences be biased.

One way to test a particular cluster selection algorithm is to utilize multiwavelength data to establish the scaling relations of galaxy clusters: gross deviations from the mean behaviour can be used to flag systems that may be subject to otherwise unsuspected systematic effects. In Rozo & Rykoff (2014, hereafter Paper II), we performed an extended analysis of this type in order to characterize the failure rate in the recently published Sloan Digital Sky Survey (SDSS) redMaPPer cluster catalogue (Rykoff et al. 2014, hereafter Paper I). In this context, ‘failure’ refers to either false cluster identifications or incorrect cluster property assignments, e.g. redshifts and/or richness. In that work, we estimated the redMaPPer failure rate at ∼1 per cent.

Paper II was limited partly by the availability of X-ray data at higher redshifts, partly by the large statistical noise in how X-ray luminosity traces cluster mass, and mostly by the lack of high-resolution X-ray data for complete optical samples. Consequently, Planck data on a large number of galaxy clusters provides additional critical consistency tests to help better characterize failures in the redMaPPer cluster finding algorithm. We note that while in Paper II we did in fact consider Planck Sunyaev–Zeldovich (SZ) data in our analysis, at the time only the early Planck SZ results had been published, which did not allow for the significantly more detailed analysis performed in this work. Here, we extend the analysis of Paper II to include the newly released Planck SZ cluster sample (PSZ1; Planck Collaboration XXIX 2014, hereafter PXXIX).

Our analysis also tests the robustness of the PSZ1 cluster selection algorithm, complementing the validation presented in PXXIX with the well-characterized redMaPPer optical catalogue. While PXXIX encountered difficulty in using their selected optical samples to uniquely identify PSZ1 sources, we demonstrate that this difficulty is not endemic to photometric cluster catalogues. Specifically, the redMaPPer galaxy cluster richness produces a well defined, tight scaling relation with SZ mass proxies, and outliers of this relation always signal a systematic error in either the redMaPPer or the PSZ1 cluster catalogues. Our results firmly establish optical data as a critical component of multiwavelength efforts aimed at defining well controlled, fully characterized galaxy cluster samples.

Our paper is laid out as follows. Section 2 introduces the various data sets employed in our study. Section 3 describes our analysis and presents our results, and Section 4 presents our conclusions. Throughout, we adopt a fiducial flat Λ cold dark matter cosmology with Ω_m = 0.3 and h = 0.7, consistent with the choice in PXXIX.

DATA

The Planck XXIX cluster catalogue

The Planck satellite (Tauber et al. 2010) was launched on 2009 May 14, as the third-generation space mission dedicated to cosmic microwave background observations. The Planck payload consists of two instruments, the Low Frequency Instrument covering 30, 44, and 70 GHz (Bersanelli et al. 2010; Mennella et al. 2011), and the High Frequency Instrument with bands centred at 100, 143, 217, 353, 545, and 857 GHz (Lamarre et al. 2010; Planck HFI Core Team 2011), with angular resolution varying from 33 arcmin to 5 arcmin. A series of early results were published in 2011 (Planck Collaboration I 2011), and the first cosmology results were published in 2013 along with 15.5 months of science data (Planck Collaboration I 2013).

The PSZ1 is based on the first 15.5 months of Planck observations (Planck Collaboration XXIX 2014). The SZ detection uses the six highest Planck frequency channels, spanning 100 GHz to 857 GHz. Prior to detecting SZ sources, a Galactic mask and a point source mask based on the Planck Catalogue of Compact Sources (Planck Collaboration XXVIII 2013) are applied. The resulting holes in the maps are filled in prior to searching for SZ sources, and the catalogue is trimmed around the mask. The resulting survey area is |${\approx } 34\,500\ \deg ^2$|⁠. SZ sources are detected using three different types of algorithms: two matched filter algorithms (MMF1, MMF3; Melin, Bartlett & Delabrouille 2006) and a Bayesian finder called Powell–Snakes (PwS; Carvalho et al. 2012). All three algorithms place priors on the cluster spectral and spatial characteristics, which are in turn employed to distinguish SZ sources from random noise fluctuations. A comparison of various SZ cluster selection algorithms is presented in Melin et al. (2012).

After running each of the three cluster finders, all S/N > 4.5 sources are collated into a master catalogue, which is cleaned for obvious contamination based on the Planck high-frequency spectral information. The SZ signal strength, measured by the integrated Compton-y parameter Y_SZ, of the remaining sources is typically strongly degenerate with the cluster size, a problem that is resolved by the use of informative priors on the relation between Y_SZ and cluster size. Since cluster radii are typically defined in terms of matter overdensity criteria, such a prior takes the form of a fiducial M–Y_SZ relation, so that a by-product of the measurement is a cluster mass estimate for each system. PXXIX utilizes the M–Y_SZ relation of Arnaud et al. (2010) for these purposes, and a full description of the algorithm will appear in a future publication (Arnaud et al., in preparation, see also Gruen et al. 2014) .

In a detailed study, Rozo et al. (2014a,b,c) noted significant differences in published cluster X-ray mass calibrations and argued that the mass calibration adopted in Arnaud et al. (2010) would lead to tension between observed cluster abundance and the cosmological constraints from the cosmic microwave background (Rozo et al. 2013). This was borne out in the first results from Planck. Consequently, we do not take the ‘SZ-mass’ (M_SZ) reported in PXXIX as an accurate determination of cluster total mass. However, the reported SZ mass is a well-defined SZ observable – indeed, it is mathematically equivalent to Y_SZ – and thus it can be used to define scaling relations and to study the regularity of the Planck and redMaPPer cluster samples. Of course, any SZ observable would suffice. We rely on SZ-mass because it is convenient and easily available.

Finally, we note that in order to estimate Y_SZ and the corresponding SZ mass M_SZ, a cluster redshift is needed for each detection. In the PSZ1, these redshifts are obtained either by cross-matching with various catalogues, or through extensive photometric and spectroscopic follow-up of Planck SZ sources. When matching to external catalogues, PXXIX follows a rank-ordered priority list. The top priority is the Meta-Catalogue of X-ray Clusters (MCXC) catalogue (Piffaretti et al. 2011), followed by Nasa/IPAC Extragalactic Database (NED) and SIMBAD, followed by redshifts from the Wen, Han & Liu (2012) SDSS photometric cluster catalogue. A few remaining clusters get their redshifts either from additional external photometric catalogues, or from an internal analysis of SDSS data within the Planck team. Many clusters (more than 200) were also subjects of both photometric and spectroscopic follow-up. The final PXXIX SZ cluster catalogue is a compilation of all this data.

Throughout, we only consider the list of galaxy clusters labelled in PXXIX as confirmed systems (861 clusters). We restrict ourselves to systems with reported redshifts in the ranges z ∈ [0.08, 0.6] since z = 0.6 is the maximum redshift at which redMaPPer can detect massive clusters in the SDSS with reliable redshift estimates. When considering scaling relations, we exclude clusters with z > 0.5 since clusters above this redshift have very large measurement errors in their richness.

The SDSS DR8 redMaPPer cluster catalogue

redMaPPer is a new red-sequence photometric cluster finding algorithm which was recently applied to the SDSS Data Release 8 (Aihara et al. 2011). The algorithm and SDSS DR8 catalogue is described in detail in Paper I. A detailed comparison of redMaPPer to other photometric cluster finding algorithms is presented in Paper II, which also includes a multiwavelength study of the performance of redMaPPer in the SDSS.

Briefly, redMaPPer iteratively self-trains a model of red-sequence galaxies calibrated by exploiting an initial seed spectroscopic galaxy sample. The associated spectroscopic requirements are minimal, and easily satisfied by existing SDSS spectroscopy. Once the red-sequence model has been trained, the algorithm attempts to grow a galaxy cluster centred about every SDSS photometric galaxy. The galaxies are first rank-ordered according to their likelihood of being a central galaxy. Once a rich galaxy cluster has been identified (λ ≥ 5, where λ is the number of red-sequence galaxies hosted by the cluster), the algorithm iteratively determines a photometric redshift based on the calibrated red-sequence model, and recentres the clusters about the best cluster centre, as gauged from the photometric data. The final published cluster catalogue is then further trimmed to a richness limit of λ ≥ 20 for z ≤ 0.35. Above this redshift, the catalogue becomes ‘flux’ limited due to the SDSS survey depth, and the richness limit increases rapidly with redshift. Roughly speaking, richness measurements are reliable out to z = 0.5. For z ∈ [0.5, 0.6], clusters can be detected, but their richness measurements become very noisy. When run on SDSS data, automated cluster finding is not really feasible with the redMaPPer algorithm above redshift z = 0.6. The total area covered by the redMaPPer catalog is |${\approx } 10\,000\ \deg ^2$|⁠, and the catalogue comprises ≈25 000 systems.

In what follows, we will match the Planck cluster catalogue to the redMaPPer cluster catalogue. One obvious concern of this type of exercise is that a Planck cluster may go unmatched if the system falls below the redMaPPer detection threshold. In order to minimize this possibility, we always match the Planck catalogue to our own private redMaPPer catalogue, which lowers the detection threshold from λ = 20 to 5. Doing so increases the redMaPPer cluster sample by almost a factor of 16, from ≈26 000 clusters to ≈412 000 systems. As it turns out, however, all good Planck–redMaPPer cluster matches result in pairs of richness λ ≥ 20.

The MCXC cluster catalogue

The MCXC (Piffaretti et al. 2011) is a compilation of galaxy clusters based on publicly available X-ray data from both the ROSAT All Sky Survey (RASS; Voges et al. 1999) and serendipitous searches in ROSAT pointed observations. The RASS contributing catalogues are NORAS (Böhringer et al. 2000), REFLEX (Böhringer et al. 2004), BCS (Ebeling et al. 1998), SGP (Cruddace et al. 2002), NEP (Henry et al. 2006), MACS (Ebeling et al. 2001), and CIZA (Ebeling et al. 2002; Kocevski et al. 2007), while the contributing serendipitous catalogues are 160D (Mullis et al. 2003), 400D (Burenin et al. 2007), SHARC (Romer et al. 2000), WARPS (Horner et al. 2008), and EMSS (Gioia et al. 1990). The data from each of the individual galaxy catalogues was collected and homogenized, deleting duplicate entries, and enforcing a consistent X-ray luminosity definition. In the catalogue, L_X is defined to be the X-ray luminosity in the 0.1–2.4 keV band within an R_500c aperture. We will use this catalogue as a baseline for understanding the centring offset distribution between the Planck and redMaPPer cluster centres.

ANALYSIS OF PSZ1 CLUSTERS

Cluster matching

We match the PSZ1 to the SDSS DR8 redMaPPer catalogue using a simple angular matching algorithm. To match the two catalogues, we rank-order the PSZ1 clusters by signal-to-noise (S/N). Starting from the top (largest S/N) cluster, we define its match as the richest redMaPPer system within 10 arcmin of the reported Planck detection. If a match is found, the corresponding redMaPPer system is removed from the list of candidate redMaPPer matches, and we move on to the next PSZ1 cluster. We emphasize that our matching criteria does not impose any restrictions on the redshifts of matched cluster pairs. This is purposely so, as we wish to compare the redshifts reported in the two cluster catalogues. Of course, this also implies that all Planck–redMaPPer cluster pairs should only be considered tentative associations, pending the results of our full analysis, summarized in Section 3.5.

Fig. 1 compares the PSZ1 cluster redshifts to those of the matched redMaPPer clusters. We restrict ourselves to the redshift range z ∈ [0.08, 0.6], where the redMaPPer redshifts are expected to be accurate. There are 245 PSZ1 systems in this redshift range within our angular mask, 35 of which show up as redshift outliers. These outliers will be discussed in Section 3.4. For now, we will focus on the sub-sample of galaxy clusters where the two redshift estimates agree. This way, by characterizing the relation between optical and SZ data first using our well-matched clusters, we can later on use this information to resolve the redshift conflicts shown in Fig. 1.

Figure 1.

Comparison of PSZ1 redshift to the redshift of its tentative redMaPPer match. The matches will be revised based on the results of our subsequent analysis. Blue points are systems included in the PXX cosmology analysis (Planck Collaboration XX 2014). Black points are clusters for which the redMaPPer and PSZ1 redshifts are consistent with each other. There are 33 3σ outliers, shown in red, and two additional obvious outliers in blue that form part of the PXX cosmology sample. We discuss the outliers in Section 3.4.

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The λ-M_SZ scaling relation

We consider the λ–M_SZ relation of the galaxy clusters for which the PSZ1 and redMaPPer redshifts agree. Since the richness errors become very large at z > 0.5, we further restrict our analysis to systems with redMaPPer redshift z_λ ≤ 0.5 (this is the redshift assigned by redMaPPer photometry). This results in a sample of 191 galaxy clusters, shown in Fig. 2. We see that there is a tight relation between the redMaPPer cluster richness λ and the SZ-mass M_SZ, though the existence of a small outlier population with low richness and high SZ mass is immediately apparent.

Figure 2.

Relation between cluster richness λ and SZ-mass M_SZ. The cluster richness is evaluated at the optical centre, and is taken directly from the redMaPPer cluster catalog. The SZ-mass is taken directly from PXXIX. Only clusters with consistent redshift matches are included (i.e. black points in Fig. 1). To avoid clusters with large richness errors, we restrict our analysis to systems with z_λ ≤ 0.5; this leaves a total of 191 objects. The red solid line is the best-fitting scaling relation, while the dashed lines mark the 1σ intrinsic scatter. Blue points are 3σ outliers. Planck 299 is shown as a purple point with error bars. Only a small random fraction of clusters is shown with error bars to avoid overcrowding the plot.

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Our algorithm identifies five outliers (Planck 617, 1093, 719, 729, and 441), which are discussed individually in Appendix A. Briefly, one outlier is due to problematic photometry associated with a bright star, while the remaining outliers appear to be incorrect cluster associations. These outliers also appear to have high-redshift (z ≳ 0.6) counterparts apparent from the SDSS and WISE images of these fields. There is an additional ‘by-eye’ outlier, Planck 299 (see Fig. 3), which is not considered an outlier by our algorithm because of the large richness error bar, but also appears to be an incorrect association, and also has a possible high-redshift counterpart. The RA and DEC of the corresponding candidate galaxy overdensities are reported in Table 3, which includes DR8 photometric or spectroscopic redshifts where available.

Figure 3.

Proposed high-redshift cluster match to Planck SZ source 299. The cluster candidate (red circle) shown above is at a distance of 3 arcmin from the reported Planck location for the SZ source 299. The purple circle segment has a radius of 3 arcmin, and is centred at the reported Planck location. The entire box is 2 arcmin × 2 arcmin, centred on the optical high-z cluster candidate. The central galaxy of the proposed cluster candidate has a spectroscopic redshift z_spec = 0.748. The red circle has a radius of 0.3 arcmin or ≈130 kpc.

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While we believe the above outliers are explained as either incorrect associations or bad photometry, it is in principle possible that SZ-selected clusters can rarely (≈5/191 ≈ 3 per cent of the time) have very unusual optical properties, thereby population a long tail of low-richness outliers. However, we believe this is highly unlikely, both because all five of the SZ detections above appear to have high-redshift optical counterparts, and because it is difficulty to imagine a star formation quenching mechanism that can reduce the number of bright galaxies in a cluster by a factor of 3 to 4 in ≲3 per cent of clusters.

Before we move on, we emphasize that this analysis does not properly account for selection effects, so we caution against relying on the above scaling relation for precision work. Our only goals in this work are to demonstrate the existence of a tight scaling relation, to highlight the regularity of optical richnesses as a mass tracer, and to demonstrate the utility of optical data in understanding and improving the Planck SZ cluster catalogue.

In short, of the 210 non-redshift outliers in Section 3.1, only 191 have z ≤ 0.5. These define a tight scaling relation, from which we estimate a scatter in mass at fixed richness of ≈21 per cent. There are, however, six outliers. One outlier is due to bad photometry in SDSS, while the remaining five systems were incorrectly associated by our matching algorithm and thus have incorrect redshifts in PSZ1. Visual inspection reveals possible high-redshift (z ≥ 0.6) counterparts for all five of these systems. Interestingly, all six of these systems were SZ sources matched to low richness clusters in the Wen et al. (2012), Hao et al. (2010) or Szabo et al. (2011) catalogues.

Cluster centering

Fig. 4 shows the distribution of angular offsets of the PSZ1 clusters relative to the redMaPPer centres. As in the previous section, we restrict our analysis to galaxy clusters where the redMaPPer and PSZ1 redshifts agree. Moreover, we remove from the sample the six galaxy clusters identified as erroneous cluster matches in Section 3.2. For comparison, we also show the corresponding distribution for Planck–MCXC cluster matches (red histogram). The two offset distributions (Planck–redMaPPer and Planck–MCXC) are not consistent with each other, as determined via a KS test. We attribute this difference to miscentering in the optical. To test this hypothesis, we first use a Kernel Density Estimator (red dashed line) to obtain a smooth model of the Planck–MCXC centring distribution. This model is then convolved with a simple miscentering model for redMaPPer systems, in which 85 per cent of the clusters are correctly centred, and the remaining 15 per cent have a centring offset that is uniformly distributed out to 1 Mpc. The resulting distribution of angular offsets is the black dashed line. A KS test reveals that the model is consistent with the observed distribution for Planck–redMaPPer matches. We note that the difference between the black and red dashed curves in Fig. 4 is relatively minor: optical miscentering acts to transfer a small but non-negligible amount of probability from the peak at 1 arcmin separation to a tail at ≈5 arcmin separation.

Figure 4.

Distribution of angular offset between Planck location and the corresponding redMaPPer or MCXC cluster centre, as labelled. Both sets of clusters are restricted to the same redshift range. The red and black dashed curves are smooth models for each of the distributions (see text).

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We have visually inspected all galaxy clusters where the offset relative to redMaPPer is larger than 5 arcmin. There are 10 such clusters. Of these, two clusters (Planck 278 and 445) appear to be simple statistical fluctuations, four (Planck 728, 249, 472, and 587) are systems with two obvious galaxy clumps, one (Planck 113) is an obvious redMaPPer centring, one (Planck 280) appears to be a false association, and one (Planck 77) appears to be a candidate false detection. These clusters are all discussed individually in Appendix A.

The remaining large centring offset cluster is Planck 52, which PXXIX notes forms a complicated triple system with Planck 51 and Planck 53. With redMaPPer we are able to shed considerable light on the region. The entire field containing clusters Planck 51 through 53 is shown in Fig. 5. The southernmost rich redMaPPer cluster is RM 1195 (λ = 85.4, z_spec = 0.338, member galaxies in red), which is matched to Planck 51. Note, however, that Planck 51 sits directly on top of RM 11143 (λ = 23.5, z_spec = 0.443, member galaxies in cyan). This suggests that Planck 51 is picking up the SZ signal of the richer redMaPPer cluster RM 1195, but that the Planck detection is miscentered due to a projection effect in the SZ between RM 1195 and RM 11143, pulling the SZ detection towards the latter system.

Figure 5.

SDSS image of the sky around Planck SZ sources 51, 52, and 53. Each Planck cluster is marked with a 3 arcmin circle, as labelled. There are three rich redMaPPer clusters in the region, for which we have circled galaxies brighter than 0.5L_* with a membership probability p ≥ 0.5. Each redMaPPer cluster is assigned a different colour: RM 1995 is red (z_spec = 0.338), RM11143 is cyan(z_spec = 0.443), and RM 689 is blue (z_spec = 0.382).

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The northernmost Planck cluster is Planck 53, which is a good match to RM 689 (λ = 97.0, z_spec = 0.382, member galaxies in blue). Note that the spectroscopic redshifts of Planck 51 and Planck 53 are significantly different (z_spec = 0.338 versus z_spec = 0.382), corresponding to a line of sight distance of ≈180 Mpc, or nearly 10⁴ km s⁻¹, suggesting these structures are not correlated.

This leaves us with Planck 52, which sits on an essentially empty piece of sky, roughly halfway between Planck 51 and Planck 53. It has three candidate matches with richness λ ≥ 20, two of which are better associated with Planck 51 (RM 1995 and RM 11143 discussed above), and one of which is clearly associated with Planck 53. We have inspected both the SDSS and WISE images for a possible high-redshift cluster counter part, but were unable to find one.

To explain the origin of Planck 52, we recall that the PSZ1 is the union of three distinct cluster finding algorithms, two matched filter methods (MMF1 and MMF3) and a Baysian source detector called PwS. Clusters Planck 51 and 53 were only detected by the PwS method, while Planck 52 was only detected by the MMF3 method (Planck Collaboration XXIX 2014). This strongly suggests that the MMF3 detection is a blend of the Planck 51 and Planck 53 clusters, explaining why it sits in between the two systems and has no good redMaPPer association. This is consistent with the large positional error assigned by MMF3 to this detection. In short, we consider Planck 51 as affected by projection effects in the SZ, Planck 52 we flag as a false detection (really, a blend of Planck 51 and 52), and Planck 53 is robustly associated with RM 689.

In short, of the 10 clusters with large angular separations, two we consider good matches, four are double clusters, one is an obvious case of optical miscentering, one is a high-redshift cluster candidate, and two are labelled as false detections.

Redshift outliers

We now turn our attention to the 35 redshift outliers in Fig. 1. These outliers could arise in one of three ways. If the Planck and redMaPPer clusters have been properly matched, then either the PXXIX redshift is incorrect, or the redMaPPer redshift is incorrect. Alternatively, the matching algorithm may have failed. We now determine the origin of each of the redshift conflicts identified in Fig. 1.

Visual inspection

To begin with, we check our cluster matching by visually inspecting the SDSS and WISE images for each of the PSZ1 clusters that resulted in a redshift conflict in Section 3.1. Our goal is to ensure that every PSZ1 cluster is matched to the best possible redMaPPer match. We emphasize that ‘best possible’ does not mean correct; we sometimes find Planck sources that have no convincing redMaPPer match. In such cases, we let the original match stand, with the expectation that subsequent analysis will confirm those clusters as poor matches. It should also be noted that ‘unconvincing’ is a qualitative decision made by us based on the visual inspection. Quantitative tests will be presented in subsequent sections. Our visual inspection also revealed several Planck detections where the SZ signal is likely to be affected by projection effects, i.e. there are multiple rich galaxy clusters along the line of sight of the Planck detection. These clusters are flagged as such .

Our results are summarized in Table 1. The table includes both the PSZ1 redshift, and the redMaPPer photometric redshift of the best redMaPPer match as determined from visual inspection. When a match is ambiguous, we do not report a redMaPPer redshift. In the cases where a correct cluster redshift can be unambiguously identified, the corresponding redshift is written in bold. In brief, we find

• three clusters where we confirm that the PSZ1 redshift is correct (Planck 1216, 500, and 216). The original redshift conflicts were due to two incorrect cluster associations (including one incorrect match due to redMaPPer incompleteness), and one incorrect redMaPPer redshift due to bad SDSS photometry.

• 19 clusters where we confirm that the original association with redMaPPer clusters is correct, and the redMaPPer redshift is correct.

• Eight unconvincing cluster matches. For these clusters, we expect the PSZ1 redshift to be incorrect, and for our best redMaPPer match to prove unsatisfactory as well. In seven out of eight cases, our visual inspection reveals a candidate high-redshift match for the Planck detection, with varying degrees of confidence.

• Five clusters where the SZ signal appears to be sourced by an SZ-projection effect. These are Planck 732, 1128, 73, 510, and 376.

Comments on individual systems can be found in Appendix A. Here, we showcase only two systems. The first is cluster Planck 513, which is the only PSZ1 cluster in the SDSS region that belongs to the Planck cosmology sample in Planck Collaboration XX (2014) and has been assigned an incorrect redshift. The SDSS image of this SZ source is shown in Fig. 6. There is an obvious cluster in the image (RM 87), which itself has an obvious central galaxy. The central galaxy has a spectroscopic redshift available, from which we see z_spec = 0.350. There are also multiple spectroscopic members that confirm this redshift. By contrast, the assigned redshift in PXXIX is z = 0.211. This redshift was matched to Abell 1430, and the association is correct, but the cluster redshift taken from SIMBAD is clearly erroneous. We have chosen to highlight this cluster because it formed part of the cosmology sample in Planck Collaboration XX (2014), not because it is a particularly egregious example of an incorrect redshift: there were multiple cluster for which the correct cluster redshift was equally obvious in the SDSS data.

Figure 6.

SDSS image for Planck 513. The large purple circle shown is 3 arcmin (≈0.9 Mpc) in radius, centred on the Planck location. There is an obvious cluster of galaxies at this location, with spectroscopic redshift z_spec = 0.350 (RM 87). However, this cluster was assigned a redshift of z = 0.211 in the PSZ1. The red circles are galaxies with redMaPPer membership probability p ≥ 0.8 brighter than 0.8L_*.

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Figure 7.

SDSS image for Planck 510. The large purple circle shown is 3 arcmin in radius, centred on the Planck location. There are two redMaPPer clusters at this location, RM 128 and RM 141, each with at five spectroscopic members that confirm the redMaPPer cluster redshift for their parent cluster. Cluster members with membership probability p ≥ p_0.8 (see text) and luminosity L ≥ 0.8L_* are shown with red (RM 128) and cyan (RM 141) circles. Evidently, Planck 510 is a spectacular example of an SZ projection effect.

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We see from Fig. 7 that the two redMaPPer clusters are obviously collocated in the sky, and both coincide with the Planck SZ detection. Both systems have five members with spectroscopic redshifts, from which we derive cluster redshifts z_spec = 0.2566 and 0.3715. These compare well with the redMaPPer photometric redshift estimates z_λ = 0.267 ± 0.008 and z_λ = 0.372 ± 0.014. In short, there is no doubt that these clusters are two separate systems projected along the line of sight, and that the deprojection by redMaPPer via photometric data was successful. The richnesses of the two clusters are λ = 87.8 and λ = 84.0, respectively, which demonstrates that neither system is obviously dominant. It is difficult to imagine a more spectacular example of an SZ projection effect.

Validation tests for the PSZ1 redshifts

We use the λ–M_SZ relation from Section 3.2 as a validation test of the PSZ1 cluster redshifts. Specifically, let us assume that for each of our redshift conflicts, the PSZ1 redshifts are correct. Papers I and II demonstrated that the failure rate of the redMaPPer photometric redshifts is below 1 per cent. Consequently, if the PSZ1 redshifts are correct, we ought to be able to find good redMaPPer matches to the PSZ1 systems by redoing our rank-ordered circular matching while adding the additional constraint that the redMaPPer matches must be consistent (3σ) with the PSZ1 cluster redshifts. In addition, based on our results in Section 3.3, we only look for cluster matches within 6 arcmin of the Planck sources.

Our visual inspection indicates that for the majority of the 35 redshift outliers identified in Section 3.1, the PSZ1 redshifts are incorrect. To test this, we perform the above matching – including the redshift consistency requirement – and compare how these 35 galaxy clusters populate the λ–M_SZ plane relative to the 185 galaxy clusters that defined λ–M_SZ relation in Section 3.2. Any PSZ1 clusters that go unmatched are arbitrarily assigned a richness λ = 5, the minimum richness of the galaxy clusters in our full redMaPPer catalogue.

Our results are shown in Fig. 8. The solid blue line is the mean λ–M_SZ relation (see Fig. 2), while the dashed lines mark the 3σ band. Of our 35 original outliers, only five clusters can plausibly be matched assuming the PSZ1 redshift. In decreasing order of S/N, these are Planck 732, 1128, 73, 510, and 216. Turning to the results from our visual inspection (Section 3.4.1 and Table 1), we see that the first four systems were identified as SZ-projections of multiple clusters, while the last system is one for which our original matching was incorrect. The IDs of the projection clusters are given in Table 3. The remaining 30 outliers break into 28 incorrect redshifts in PSZ1 and two redMaPPer failures (one incompleteness, one bad photometry, Planck 1216 and 500, respectively).

Figure 8.

Comparison of the location in the λ–M_SZ plane for the 35 3σ redshift outliers in Fig. 1 (red points) and the points from Fig. 2 defining the λ–M_SZ relation. The solid blue line is the mean scaling relation, and the dashed lines delineate the 3σ scatter band. The points at richness λ = 5 are unmatched clusters. To assign a richness to the PSZ1 clusters, we have re-matched the redshift outliers from Fig. 1 while demanding that the redMaPPer and PSZ1 redshifts agree. In so doing, 30 clusters remain as outliers in the λ–M_SZ plane, two of which are due to bad SDSS photometry. The rest are PSZ1 redshift failures (see text).

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We note that despite the fact that four of the five clusters we flagged as SZ projection are non-outliers in the λ–M_SZ plane, we should not consider this as evidence that the PSZ1 redshift is appropriate. Indeed, in the following section, we find that these systems do not appear as outliers when we remeasure M_SZ using the assigned redMaPPer redshift either. In other words, the fundamental problem for these systems is that these projection effects cannot be assigned a single, unambiguous redshift: the SZ detection is fundamentally a combination of more than one structure along the line of sight.

Validation tests for the redMaPPer redshifts

We now perform the converse analysis to that of Section 3.4.2, that is, we take the 35 redshift conflicts from Fig. 1 and assume that the automatically assigned redMaPPer match is correct. We then remeasure M_SZ for each of these 35 systems, holding the Planck location fixed, but adopting the redshift of the assigned redMaPPer cluster as the correct redshift.

Our visual inspection of the redshift outliers suggests that we will be able to confirm 19 cluster redshifts as correct. In addition, it is possible for the five systems labelled as SZ-projections to appear to be acceptable cluster matches, for a total of 24 expected non-outliers. The remaining 11 systems (eight unconvincing clusters, three clusters where the PSZ1 redshift is correct) we expect will be outliers in the λ–M_SZ plane.

As shown in Fig. 9, this is almost exactly what we find. The solid blue line in the figure is the mean λ–M_SZ relation, while the dashed lines mark the 3σ band. Of the original 35 redshift outliers, nine fall below the 3σ intrinsic scatter line. These are the three clusters with correct PSZ1 redshifts, and six of the eight unconvincing cluster matches. However, two of the unconvincing matches are not obvious outliers in the M_SZ–λ plane, and therefore remain as plausible cluster matches. These are cluster Planck 376 and 768. Note that Planck 376 is an unconvincing match in part because it may be an SZ projection.

Figure 9.

Comparison of the location in the λ–M_SZ plane for the redshift outliers in Fig. 1 (red points) and the points from Fig. 2 defining the λ–M_SZ relation. The clusters are assigned the richness of the best redMaPPer match, and we have remeasured M_SZ at the assigned redMaPPer redshift for each of the clusters. Note a significant fraction of the clusters that were outliers in Fig. 8 are not outliers in this figure. This analysis confirms the results of our visual inspection with regards to the incidence of redshift failures in the PSZ1 and the existence of SZ projections (see text for details).

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Turning to the remaining clusters labelled as projection effects, we see that these systems do not show up as outliers in the M_SZ–λ plane, so the scaling relation test is not able to rule out either the PSZ1 or the redMaPPer redshifts. Thus, the redshift association for these systems is ambiguous. Importantly, the fact that these clusters are not outliers is not due to covariance of the type studied, e.g. in Cohn & White (2009), Noh & Cohn (2012), Angulo et al. (2012), or Rozo et al. (2014b). These clusters are clear projections in the SZ, but they are not optical blends; the clusters are very well separated along the line of sight in the optical.

Table 2 below includes the 21 PSZ1 clusters with revised redshifts that result in λ and M_SZ values consistent with the cluster scaling relations. These are the 35−9 = 26 objects, minus the latter five labelled as projection effects. In conjunction with the 185 galaxy clusters that originally defined the λ–M_SZ scaling relation, these redshift-corrected systems brings the total number of galaxy clusters establishing the λ–M_SZ relation to over 200 clusters.

Summary of results

There are 245 Planck SZ-detections in PSZ1 labelled as confirmed that fall within the SDSS redMaPPer footprint with an assigned redshift z in the range z ∈ [0.08, 0.6]. These have allowed us to identify three failures in the redMaPPer cluster catalogue. One (Planck 1216) is a low (z ≤ 0.6) redshift cluster missing from the redMaPPer catalogue because of a combination of miscentering and angular masking, reflecting ≈0.5 per cent incompleteness in redMaPPer. One (Planck 500) is a redshift failure because of bad photometry in the SDSS, and one (Planck 617, Section 3.2) has an unusually low richness because of bad SDSS photometry. Our estimate of the catastrophic failure rate for the SDSS redMaPPer catalogue from this analysis is therefore 3/245 ≈ 1.2 per cent. In addition, we identified four redMaPPer clusters as having two obvious galaxy concentrations, which can lead to large centring uncertainties (Planck 728, 249, 472, and 587, Section 3.3), and one obvious centring failure in redMaPPer (Planck 113, Section 3.3). Note that the centring failure rate of redMaPPer is, in fact, higher, as evidenced by utilizing high-resolution X-ray data (Rozo & Rykoff 2014). The low rate of miscentering identifications from this analysis reflects the fact that Planck cluster centring is noisy.

Our analysis has also allowed us to flag 36 clusters that were assigned an incorrect redshift in PSZ1: five in Section 3.2, three in Section 3.3, and 28 in Sections 3.4.2. For each of the clusters with incorrectly assigned redshifts in the PSZ1, we have assigned the correct cluster redshift where possible, and remeasured M_SZ at the newly assigned redshift. This is larger than the number of outliers in Fig. 1 because some of the clusters that do not show up as outliers in that figure have incorrect redshifts, as found in Sections 3.2 and 3.3. The corresponding redshift failure rate in the PSZ1 over the SDSS region is 36/245 = 14.7 per cent. These results are collected in Table 2.

We caution that the PSZ1 failure rate is not easily extrapolated outside the SDSS region, since some of the PSZ1 failures occur because of the reliance on existing optical catalogues in the SDSS region. For instance, the five failures from Section 3.2 were matched to existing SDSS catalogues, and would have remained as cluster candidates (rather than confirmed clusters) had they fallen outside the SDSS footprint. We have investigated each of the failures identified in this work, and have found that roughly a third of them tracked back to errors in either NED, SIMBAD, or the REFLEX cluster catalogue. Another third of the failures are systems in which the association made in the construction of the PSZ1 cluster catalogue was incorrect. The remaining third are systems where the origin of the failure is unusual and/or not easily understood. We collect notes on each of the failures we identified in Appendix A.

It is important to note, however, that some clusters remain with uncertain redshifts, as we were neither able to confirm the PSZ1 redshift as correct, nor to assign a new redshift to the Planck SZ source. In some cases, this is because the Planck SZ detection is associated with two comparably rich clusters that are projected along the line of sight, making a unique association impossible. In other cases, the Planck sources have no acceptable redMaPPer counterpart. In the latter case, we have classified these systems as either high-redshift cluster candidates or false detections based on visual inspection of SDSS and WISE data. The set of clusters for which we do not assign a robust redshift is collected in Table 3.²

DISCUSSION

We have performed a detailed comparison of the SDSS DR8 redMaPPer and PSZ1 cluster catalogues that has enabled us to characterize systematic failures in both. The resulting failure rates are 1.2 per cent for redMaPPer and 14.7 per cent for the PSZ1 over the SDSS area. A summary of the various failure modes is presented in Section 3.5.

These results firmly demonstrated that robust photometric cluster finding is possible, and that state-of-the-art photometric cluster finding algorithms like redMaPPer can deliver the necessary cluster samples to exploit near future photometric surveys. Moreover, we have confirmed optical cluster richness as a relatively low-scatter mass proxy (σ_ln M|λ ≈ 0.21), a result that has now been independently established with three different mass proxies: M_gas, T_X, and M_SZ. We note that this scatter in mass at fixed observable for cluster richness is comparable to that which can be attained using X-ray or SZ survey-quality data. Of course, pointed follow-up X-ray observations with high-resolution instruments such as Chandra and XMM remains valuable, and the corresponding mass proxies exhibit lower scatter.

Our findings do not affect the Planck cluster cosmology analysis presented in Planck Collaboration XX (2014). We found only one object over the SDSS area from the cosmology cluster sample with an incorrect redshift; the vast majority of the redshift failures in the PSZ1 are lower S/N systems that have not yet been included as part of the cosmological analysis. In addition, it is not clear to what extent the PSZ1 failure rate can be extended outside the SDSS region. The northern extragalactic sky, and in particular the SDSS area, has been extensively studied, and many of the PSZ1 redshift failures originate in identifications with catalogues not available elsewhere on the sky. In short, the failure rate in the PSZ1 calculated in this work is at least in part due to failures in existing data bases and/or optical cluster catalogues, or failures due to the difficulty of performing unambiguous associations between the Planck SZ detections and other optical catalogues.

Indeed, this is one of more significant aspects of our results. PXXIX found it difficult to capitalize on available optical/IR cluster samples for validation of the PSZ1 because of the large scatter in the richness–M_SZ relation. Our results unambiguously demonstrate that the difficulties encountered by PXXIX are not due to a generic feature of photometric cluster catalogues; one can construct high-quality photometric catalogues for which scaling relations may be used to unambiguously pair optical and SZ cluster samples. Our success with redMaPPer is of particular importance given that we are about to usher in a new era of large photometric surveys, which include the Dark Energy Survey (DES; The DES Collaboration 2005), the Hyper-Suprime Camera (HSC) survey, the Large Synoptic Survey Telescope (LSST; LSST Science Collaboration. 2009), the Euclid mission and WFIRST.

Our results also highlight the importance of multiwavelength data for cluster cosmology. As in PXXIX and Paper II, we have found that comparing clusters catalogues selected in different wavelengths can help identify previously unaccounted for systematics. Just as importantly, we find that optical survey data can inform X-ray/SZ cluster catalogues just as much as X-ray/SZ data can help inform optical cluster catalogues. Thus, our success with redMaPPer is important not only from the point of view of utilizing future photometric surveys for cluster cosmology, it also highlights the important role that these surveys will have on future SZ and X-ray clusters samples. In short, our results clearly demonstrate that there is good reason to believe that surveys like DES, HSC, LSST, Euclid, and WFIRST will play an important role in the development of cluster science together with X-ray and SZ surveys such as eRosita, Planck, the Atacama Cosmology Telescope (ACT), and the South Pole Telescope (SPT).

Our results also highlight the importance of multiwavelength data for cluster cosmology. As in PXXIX and Paper II, we have found that comparing clusters catalogues selected in different wavelengths can help identify previously unaccounted for systematics. The improved understanding of cluster selection and characterization gained by combining redMaPPer and Planck analyses demonstrates the intrinsic value to cluster science in combining next generation optical-IR (DES, HSC, LSST, Euclid, and WFIRST) surveys with X-ray (XCS, XMM-XXL, eRosita) and SZ (Planck, ACT, SPT) surveys.

The authors wish to thank the anonymous referee for comments that helped improved the presentation of this work. We thank August Evrard for comments on an early draft of this manuscript. We also thank Nabila Aghanim for help with accessing the full Planck cluster catalogue and validation table. This work was supported in part by the US Department of Energy contract to SLAC no. DE-AC02-76SF00515. JGB gratefully acknowledges support from the Institut Universitaire de France. A portion of the research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

REFERENCES

APPENDIX A: COMMENTS ON INDIVIDUAL CLUSTERS

Planck 13: This is a redshift outlier. The SZ source is associated with ZwCl 1454.5+0656 at 2 arcmin from the Planck position. The redshift is associated with NSC J145659+064610 at 2.3 arcmin, and these two clusters appear to be one and the same. Thus, the association in the PSZ1 is correct, but the NED photometric redshift is incorrect, as can be confirmed with SDSS spectroscopy (z_spec = 0.312). There is a Wen et al. (2012) object close to the redMaPPer object, at 2.3 arcmin, with the same redshift.

Planck 73: The Planck location is roughly half way between two modestly rich redMaPPer clusters, RM 1130 (λ = 42.1, z_spec = 0.091, Δθ = 3.4 arcmin) and RM 4408 (λ = 56.9, z_spec = 0.386, Δθ = 2.0 arcmin). As such, it appears to be a clear case of an SZ projection. The cluster is not an outlier in the M_SZ–λ plane when adopting either redshift, demonstrating that there is no unique redshift that can be associated with this detection.

Planck 77:PXXIX associated this cluster with RXC J1453.1+2153 and A1986 in the PSZ1, at z = 0.1186 and 7.8 arcmin from the Planck position (Section 3.3). There is no good redMaPPer counterpart. The Planck detection is made by a single algorithm at an S/N = 4.58. The positional shift between Planck and A1986 corresponds to a separation of ∼θ₅₀₀, a significant shift, but one that has been seen before for low-redshift clusters with large images on the sky. We tentatively consider this a false detection, though this classification is insecure.

Planck 97: This is a redshift outlier. The Planck location is roughly half way between two rich redMaPPer clusters, RM 19525 (λ = 28.0, z_λ = 0.357 ± 0.016, Δθ = 3.5 arcmin) and RM 4470 (λ = 48.2, z_spec = 0.310, Δθ = 4.3 arcmin). PXXIX assigned this SZ source the redshift of the closer, less massive clusters, which results in an outlier in the λ–M_SZ plane. The source is not an outlier when adopting RM 4470 as the correct cluster match, so we adopt this match as correct.

Planck 113: This is a cluster with a large centring offset between the Planck and redMaPPer centres. Visual inspection reveals the cluster is obviously miscentered by redMaPPer.

Planck 216: Our automated matching algorithm matched this Planck cluster to RM 96829 (λ = 50.9, z_λ = 0.600, Δθ = 6.0 arcmin). A second, obviously correct candidate is RM 5279 (λ = 48.5, z_spec = 0.336, Δθ = 1.5 arcmin). This latter choice corresponds to the redshift assigned by PXXIX, so this cluster is one of the redshift outliers introduced by a failure of the matching algorithm.

Planck 222: This is a redshift outlier. The SZ source is associated with RXC J1421.6+3717 in the PSZ1 and the redshift taken from the MCXC. The position also matches A1902 and an object from the Wen et al. (2012) catalogue. The latter two objects have redshifts compatible with the redMaPPer value of z = 0.162 ± 0.005. The Planck association is correct, but the redshift from the MCXC is incorrect.

Planck 234: The Planck source sits almost directly in between two redMaPPer clusters, RM 24517 (λ = 92.4, z_λ = 0.584, Δθ = 2.5 arcmin) and RM 24933 (λ = 28.6, z_λ = 0.594, Δθ = 3.3 arcmin). Note the richness values are highly uncertain because of the high redshift. Given that the SZ detection is nearly in the middle of the two systems, and that the redshift values are unreliable, we consider this an SZ-projection effect. It is notable that a third system with λ = 20.0 at z_λ = 0.470 and Δθ = 2.0 arcmin is also present in the field.

Planck 249: This cluster exhibits a large (≥5 arcmin) angular offset between the Planck and redMaPPer centres. Visual inspection reveals two obvious galaxy clumps and it is unclear which component is dominant. We do not rely on the Planck centring to determine the dominant component since Planck centres are themselves highly uncertain, and in some cases our visual inspection suggests that the main cluster component is the one that is further from the Planck position (Planck Collaboration XXIX 2014). A more definitive statement about these clusters will require modest resolution X-ray data.

Planck 278: This cluster is offset from its redMaPPer match by more than 5 arcmin. Visual inspection suggests the Planck–redMaPPer association is correct, and we do not find other clusters within the field. This cluster appears to a simple statistical fluctuation of the Planck centring distribution.

Planck 280: This cluster was associated with RXC J2241.8+1732 and A2472 in the PSZ1, at z = 0.3137 and 7.2 arcmin from the Planck position (Section 3.3). This is also the closest candidate redMaPPer match. This corresponds to a rather large shift of ∼2θ₅₀₀. There is a possible match to an overdensity in SDSS and WISE at RA = 340.6030 and DEC = 17.5214 (2.2 arcmin separation) and z = 0.86. May be a projection of two SZ sources.

Planck 292: This is a redshift outlier. The SZ source is associated with ZwCl 1341.2+4022 in the PSZ1 at 2.9 arcmin from the Planck position, which has no redshift in NED. The redshift given in the PSZ1 is z = 0.186 is that of GMBCG J205.85324+40.09379 at 1.5 arcmin.

Planck 299: Outlier in the λ–M_SZ relation (Section 3.2). The SZ source is associated with AMF J231.538+54.1303 in the PSZ1, at z = 0.4735 and 2.9 arcmin from the Planck position. It is also identified with the low-richness clusters WHL (N₂₀₀ = 15) and GMBCG |$N_{\rm scaled{\rm -}gals}=13$|⁠. It has a redMaPPer counterpart at the same redshift, but of too low richness to be an acceptable match. There is an SDSS overdensity at 3 arcmin from the Planck position, at RA = 231.6383 and DEC = 54.1520, with a spectroscopic redshift z_spec = 0.748 (Fig. 3, and Table 3). This is a candidate high-z cluster that appears to have been incorrectly associated with a low-mass system in the foreground.

Planck 303: This is a redshift outlier. The SZ source is associated with ZwCl 2341.1+0000 in the PSZ1 at 2.5 arcmin from the Planck position. This object is also known as SDSS CE J355.930756+00.303606 and NSCS J234339+001747 with redshift compatible with the redMaPPer value of z = 0.274 ± 009. The redshift given in the PSZ1 comes from SIMBAD. The Planck association appears correct, but the SIMBAD redshift inaccurate.

Planck 308: This is a redshift outlier. The SZ source is associated with ACO 2623 in the PSZ1 at 2.2 arcmin from the Planck position. The ACO cluster lies between the Planck SZ source and the redMaPPer cluster at 2.6 arcmin from the Planck position. The redshift given in NED for ACO 2623 is based on a single galaxy redshift.

Planck 316: This is a redshift outlier. The SZ source is associated with ZwCl 2341.8+0251 at 4.1 arcmin separation, but the redshift reported in the PSZ1 (z = 0.43) corresponds to NSCS J234433+030506 at a separation of 1.5 arcmin from the Planck position. The redMaPPer counterpart lies at 1.2 arcmin from the Planck position and also from the NSCS object, which is also clearly the same system as the redMaPPer object. The redshift from NED is photometric, and incorrect, as confirmed with SDSS spectroscopy (z_spec = 0.350).

Planck 376: The Planck source sits almost directly in between two redMaPPer clusters, RM 4427 (λ = 37.6, z_spec = 0.159, Δθ = 5.8 arcmin) and RM 27136 (λ = 14.6, z_spec = 0.178, Δθ = 5.3 arcmin). The second system is the one that PXXIX associated with Planck 376, and is an outlier in the λ–M_SZ relation. Given the modest richness of the two clusters, and the relatively large angular offsets, neither cluster match is particularly convincing. This appears to be either a false detection, or an SZ-projection effect.

Planck 391: This is a redshift outlier. The SZ source is associated with ZwCl 0017.0+0320 in the PSZ1, at 0.2 arcmin separation, which also corresponds to the correct redMaPPer match. The quoted photometric redshift in NED utilized by PXXIX is incorrect.

Planck 400: This cluster has no acceptable redMaPPer match. Visual inspection of SDSS and WISE reveals a rich high-redshift cluster candidate at RA = 3.080 68, DEC = 16.462 09, z = 0.64 ± 0.08.

Planck 416: This is a redshift outlier. The SZ source is associated with RXC J0019.6+2517 with z = 0.1353 taken from the NED data base. The RXC and redMaPPer counterpart, at z = 0.373 ± 0.014, are separated by only 0.8 arcmin. There is another redMaPPer system close to the RXC with the redshift given by NED, but it has a low richness, λ = 7.1, which is to be compared with λ = 156.5 for the higher redshift system. It is possible that the association between the X-ray source and the Planck SZ detection is correct, and that the X-ray source was incorrectly associated with the foreground group rather than the background cluster that we identify as the proper counterpart to the Planck SZ source.

Planck 441: Outlier in the λ–M_SZ relation (Section 3.2). The SZ source is associated with the low-richness cluster WHL J10.6526+18.4259 (N₂₀₀ = 14) in the PSZ1, at z = 0.2668 and 6.5 arcmin from the Planck position. It has a redMaPPer counterpart at the same redshift, but of too low richness. There is a WISE overdensity with faint optical counterpart located 1.4 arcmin from the Planck position, at RA = 10.7735 and DEC = 18.3686, with estimated z = 0.63 (Table 3). This is a candidate high-z cluster that has been incorrectly associated with a low-mass system in the foreground.

Planck 443: Our automated matching algorithm matched this cluster to RM 319 (λ = 90.6, z_spec = 0.221, Δθ = 5.2 arcmin). A second candidate is RM 49592 (λ = 28.1, z_λ = 0.438, Δθ = 0.4 arcmin). This is the association made by PXXIX. Neither candidate is obviously correct based on our visual inspection. The cluster is an outlier in λ–M_SZ when paired with RM 49592, but is not an outlier when paired with RM 319. We make this association, noting the cluster likely suffers from SZ projection.

Planck 445: This cluster is offset from its redMaPPer match by more than 5 arcmin. Visual inspection suggests the Planck–redMaPPer association is correct, and we do not find other clusters within the field. This cluster appears to a simple statistical fluctuation of the Planck centring distribution.

Planck 472: This cluster exhibits a large (≥5 arcmin) angular offset between the Planck and redMaPPer centres. Visual inspection reveals two obvious galaxy clumps and it is unclear which component is dominant. We do not rely on the Planck centring to determine the dominant component since Planck centres are themselves highly uncertain, and in some cases our visual inspection suggests that the main cluster component is the one that is further from the Planck position (Planck Collaboration XXIX 2014). A more definitive statement about these clusters will modest resolution X-ray data.

Planck 484: This is a redshift outlier. The SZ source is associated with WHL J178.058+61.33, with z = 0.3169 at 1.8 arcmin. This is a low-richness system (N₂₀₀ = 11) that is unlikely to be the Planck counterpart. There is no good redMaPPer counterpart, but we were able to identify a possible high-z match at RA = 178.1366 and DEC = 61.3629 with z = 0.86 ± 0.11 (see Table 1).

Planck 505: This is a redshift outlier. The SZ source is detected by only one (MMF3) of the three Planck methods, at S/N = 4.53. The redshift comes from dedicated follow-up observations. The cluster has no good redMaPPer counterpart, but we were able to identify a candidate high-redshift galaxy overdensity.

Planck 510: This cluster sits directly on top of two rich (λ = 87.8 and 84.0) galaxy clusters at redshifts z_spec = 0.256 and z_spec = 0.373, respectively. The corresponding angular separations relative to the Planck location are 2.0 arcmin and 0.6 arcmin. This is a spectacular example of an SZ-projection effect.

Planck 513: This is a redshift outlier. The SZ source is associated with RXC J1159.2+4947, also A1430, in the PSZ1. The redshift for the counterpart was taken from NED and SIMBAD, both of which incorrectly give z = 0.211. The PSZ1 association is correct, but the redshift incorrect. This cluster is part of the Planck cluster cosmology sample.

Planck 527: This is a redshift outlier. The SZ source is detected by only one (MMF1) of the three Planck detection methods, at S/N = 4.52. Its redshift comes from dedicated follow-up observations. The cluster has no good redMaPPer counterpart, but we were able to identify a candidate high-redshift galaxy overdensity.

Planck 537: This is a redshift outlier. The SZ source is associated with RXC J1017.5+5934, also A0959. The redshift assigned in the PSZ1 (z = 0.353) is given by SIMBAD. The redshift for the same object in NED is z = 0.2883, in agreement with the redMaPPer match. The Planck association appears correct, but with an incorrect redshift from SIMBAD.

Planck 574: The Planck cluster was originally matched to RM 97769 (λ = 36.9, z_λ = 0.530, Δθ = 7.1 arcmin). The cluster is clearly properly centred in the optical, so the large angular separation suggests this is not a good match. A second candidate is RM 4112 (λ = 19.5, z_λ = 0.192, Δθ = 3.0 arcmin). This is the association made by PXXIX, but we note this cluster is less rich than all 185 good cluster matches shown in Fig. 2, and that this association results in an outlier in the λ–M_SZ plane. This suggests the cluster is not rich enough to lead to a Planck detection. SDSS and WISE images both reveal a candidate high-redshift system at z ≈ 0.7 within 2.9 arcmin, making this a good high-redshift cluster candidate.

Planck 587: This cluster exhibits a large (≥5 arcmin) angular offset between the Planck and redMaPPer centres. Visual inspection reveals two obvious galaxy clumps and it is unclear which component is dominant. We do not rely on the Planck centring to determine the dominant component since Planck centres are themselves highly uncertain, and in some cases our visual inspection suggests that the main cluster component is the one that is further from the Planck position (Planck Collaboration XXIX 2014). A more definitive statement about these clusters will require modest resolution X-ray data.

Planck 617: This cluster (aka Abell 963) is one of the outliers identified in Section 3.2. In Paper II, this cluster was identified as having a systematically low richness because of a small region of bad photometry around a bright star in the cluster core.

Planck 622: This is a redshift outlier. The redshift assigned by Planck was obtained in dedicated follow-up imaging with the Russian Turkish Telescope. The cluster has no good redMaPPer counterpart, but we were able to identify a candidate high-redshift galaxy overdensity, albeit with low confidence.

Planck 660: This is a redshift outlier. The SZ source is correctly associated with ZwCl 0928.0+2904, which NED reports has a photometric redshift z = 0.3185 (SDSS gives a spectroscopic redshift z_spec = 0.2959), and is at 1.8 arcmin from the Planck position. However, the redshift assigned in the PSZ1 is z = 0.222, corresponding to the cluster GMBCG J142.68564+28.82848, which is incorrect.

Planck 668: This is a redshift outlier. The SZ source is associated with ZwCl 0824.5+2244 in the PSZ1 at 0.66 arcmin from the Planck position with z = 0.3175, compatible with the redMaPPer value of z = 0.329 ± 0.013. SDSS spectroscopy confirms z_spec = 0.335. The PSZ1 redshift of z = 0.287 corresponds to that of NSC J082722+223244 at 2.9 arcmin from the Planck position. This last incorrect redshift comes rom NED, where it is reported as a photometric redshift. The Planck association is correct, but the redshift is incorrectly assigned.

Planck 678: There are no good matching candidates for this system in redMaPPer. Visual inspection reveals a very bright WISE source at (RA = 147.0918, DEC = 24.7901), also detected in SDSS, with a photometric redshift z = 0.59 ± 0.04. Several other candidate cluster galaxies can be discerned in the WISE image, making this a high-redshift cluster candidate. The SZ source is only detected by one (MMF1) of the three Planck methods.

Planck 719: Outlier in the λ–M_SZ relation (Section 3.2). The SZ source is associated with the low-richness cluster WHL J158.665+20.5346 (N₂₀₀ = 11) in the PSZ1, at z = 0.4674 and 1.2 arcmin from the Planck position. It has a redMaPPer counterpart at the same redshift, but of too low richness to be an acceptable match. There is a WISE overdensity with faint optical counterpart located 1.5 arcmin from the Planck position, at RA = 158.6913 and DEC = 20.5628, of unknown redshift (Table 3). This is a candidate high-z cluster that appears to have been incorrectly associated with a low-mass system in the foreground.

Planck 728: This cluster exhibits a large (≥5 arcmin) angular offset between the Planck and redMaPPer centres. Visual inspection reveals two obvious galaxy clumps and it is unclear which component is dominant. We do not rely on the Planck centring to determine the dominant component since Planck centres are themselves highly uncertain, and in some cases our visual inspection suggests that the main cluster component is the one that is further from the Planck position (Planck Collaboration XXIX 2014). A more definitive statement about these clusters will require modest resolution X-ray data.

Planck 729: This cluster is an outlier in the λ–M_SZ relation (Section 3.2). The SZ source was associated with the low-richness cluster WHL J140.630+11.6581 (N₂₀₀ = 21) in the PSZ1, at z = 0.2609 and 2.3 arcmin from the Planck position; also listed in the maxBCG and GMBCG catalogues. It has a redMaPPer counterpart at the same redshift, but of too low richness. There is a WISE overdensity with faint optical counterpart located 0.8 arcmin from the Planck position, at RA = 140.6389 and DEC = 11.6842, of unknown redshift (Table 3). This is a candidate high-z cluster that has been incorrectly associated with a low-mass system in the foreground.

Planck 732: The Planck location is roughly half way between two rich redMaPPer clusters, RM 1057 (λ = 62.1, z_λ = 0.234, Δθ = 3.3 arcmin) and RM 373 (λ = 212.4, z_λ = 0.477, Δθ = 3.0 arcmin). As such, it appears to be a clear case of an SZ-projection. If we were to choose a single match, the better match is RM 373, which is both richer and closer to the Planck detection, whereas PXXIX assigned this detection the redshift of the smaller, slightly more distant cluster RM 1057. That said, we consider this cluster an SZ projection with no unambiguous redshift. Neither of the two matchings noted above results in the cluster being an outlier in the λ–M_SZ plane.

Planck 764: This is a redshift outlier. The PSZ1 associated this SZ source with ZwCl 0924.4+0511 at 2.7 arcmin from the Planck position (with z = 0.27), but the given redshift of z = 0.2845 is that of NSC J092656+045928, at 1.6 arcmin. The two clusters should be identified. There is also a low-richness redMaPPer cluster at this redshift (λ = 29.6, z_λ = 0.263 ± 0.009), consistent with SDSS spectroscopy for the group (z_spec = 0.264). However, the correct redMaPPer match is a higher redshift system (λ = 130.8, z_λ = 0.466 ± 0.011). SDSS spectra confirms the cluster's redshift as z_spec = 0.462.

Planck 768: The Planck cluster was originally matched to RM 399 (λ = 94.3, z_spec = 0.315, Δθ = 5.8 arcmin). There are no other plausible redMaPPer matches. This association does not make the cluster an outlier in the λ–M_SZ plane, but nevertheless, the angular offset is uncommonly large. Inspection of the SDSS and WISE images reveal a possible high-redshift cluster match.

Planck 779: This is a redshift outlier. The SZ source is associated with ACO 1127 in the PSZ1 at 4 arcmin from the Planck position (with z_photo = 0.3294), but the given redshift z_photo = 0.2564 of NSC J105417+143835 at 1.8 arcmin. The two clusters are one and the same, and they are the correct cluster match to the SZ source, but neither redshift is correct. SDSS spectroscopy confirms z_spec = 0.299, in agreement with the redMaPPer redshift z_λ = 0.296 ± 0.010. Planck 795: This SZ source is not a good match to any redMaPPer clusters. Visual inspection reveals a rich high-redshift cluster at RA = 170.463 58, DEC = 15.803 01, z = 0.77 ± 0.07. The galaxy overdensity is confirmed with WISE.

Planck 865: This is a redshift outlier. The SZ source is associated with A1208 in the PSZ1. There is no redshift given in SIMBAD. The redshift given in NED is compatible with the redMaPPer z = 0.234 ± 0.007, as is the redshift of a nearby Wen et al. (2012) object. The Planck association appears correct, but the redshift is incorrect.

Planck 888: This is a redshift outlier. The SZ source is associated with ZwCl 1232.1+2319 at 2.7 arcmin from the Planck position, but the redshift assigned in the PSZ1 is z_photo = 0.4125, corresponding to the cluster NSC J123444+230059 at 0.451 arcmin. The two clusters appear to be one and the same, and they correspond to the correct cluster match, but the redshift is incorrect. The redMaPPer object lies at 0.67 arcmin, and appears to be properly centred. SDSS spectra gives z_spec = 0.323, confirming the redMaPPer redshift z_λ = 0.327 ± 0.013.

Planck 1093: Outlier in the λ–M_SZ relation (Section 3.2). The SZ source is associated with the low-richness cluster GMBCG J193.82512+21.04201 (N_{scaled–gals} = 8) in the PSZ1, at z = 0.4457 and 4.8 arcmin from the Planck position. It has a redMaPPer counterpart at the same redshift, but of too low richness. There is a WISE overdensity with faint optical counterpart located 0.2 arcmin from the Planck position, at RA = 193.8617 and DEC = 21.1175, of unknown redshift (Table 3). This is a candidate high-z cluster that appears to have been incorrectly associated with a low-mass system in the foreground.

Planck 1123: Our automated algorithm matched this cluster to RM 897 (λ = 69.3, z_spec = 0.233, Δθ = 5.1 arcmin). This tentative association is not an outlier in the λ–M_SZ plane. PXXIX assigned a redshift z = 0.114, and an inspection of the SDSS field reveals the presence of a group at this redshift. There is a nearby redMaPPer candidate match, RM 11263. The redshift of RM 11263 is just over 3σ away over the PXXIX redshift, and it appears to have been affected by a blend with slightly lower redshift structures, which also led to the cluster being miscentered. We have evaluated λ at the obvious optical centre of the cluster, setting z = 0.114. The change to the richness relative to RM 11293 was insignificant, and the cluster remained an outlier in the λ–M_SZ plane, with too low a richness given M_SZ. Consequently, the fact that the new richness may be somewhat affected by blending is irrelevant: no blending would only exacerbate the problem. We conclude that RM 897 is the correct cluster match, and that the redshift assigned by PXXIX is incorrect. Alternatively, the cluster could be considered an SZ projection effect.

Planck 1128: The Planck location is roughly half way between two rich redMaPPer clusters, RM 683 (Abell 1750, λ = 65.3, z_spec = 0.088, Δθ = 4.2 arcmin) and RM 18367 (λ = 86.0, z_spec = 0.559, Δθ = 3.2 arcmin). As such, it appears to be a clear case of an SZ projection. If we were to choose a single match, the better match is RM 18367, which is both richer and closer to the Planck detection, whereas PXXIX assigned this detection the redshift of the smaller, slightly more distant cluster RM 683. However, either association is acceptable as probed by the λ–M_SZ scaling relation. We note that there exist deep XMM images of this field which easily detect the background cluster RM 18367.

Planck 1216: This cluster is next to a bright star. At the reported Planck location, the masked fraction of the cluster is 0.17. redMaPPer finds the cluster, but the assigned centre (which is incorrect) is such that the masked fraction is above our mask cut of 0.2. Consequently, the cluster matching procedure failed. This cluster has an obvious starburst central galaxy, which led to the incorrect centre in redMaPPer, which in turn led to the cluster missing from the catalogue. This is a clear form of incompleteness in the redMaPPer catalogue due centring.