© ESO, 2014

1. Introduction

This paper, one of a set associated with the 2013 release of data from the Planck¹ mission (Planck Collaboration I 2014), describes the construction and properties of the Planck catalogue of SZ sources (PSZ).

Clusters of galaxies play several important roles in astrophysics and cosmology. As rare objects, their number density is especially sensitive to properties of the cosmological model such as the amplitude of primordial density perturbations (Peebles 1980), and their development with redshift probes the growth of cosmic structure, hence perhaps helping to distinguish between dark energy and modified gravity explanations for cosmic acceleration (e.g., see reviews by Borgani & Kravtsov 2009; Allen et al. 2011). The galaxies, hot gas and dark matter held in their gravitational potential wells provide a sample of the universal abundance of these components (e.g., Voit 2005), while the thermal state of the gas probes both the cluster formation mechanism and physical processes within the cluster such as cooling and energy-injection feedback (e.g., reviews by Fabian 2012; McNamara & Nulsen 2012). The study of the constituent galaxies, including the brightest cluster galaxies normally found at their centres, allows sensitive tests of galaxy formation models.

Because of these uses, there is considerable interest in developing large galaxy cluster catalogues that can be used for population and cosmological studies (e.g., Schuecker et al. 2003; Böhringer et al. 2004). Clusters are genuinely multi-wavelength objects that can be selected in several ways: optical/infrared (IR) imaging of the galaxy populations; X-ray imaging of bremsstrahlung radiation from the hot cluster gas; and through the Sunyaev-Zeldovich (SZ) effect (Sunyaev & Zeldovich 1972, 1980) whereby scattering of cosmic microwave background (CMB) photons from that hot gas distorts the spectral shape of the CMB along lines of sight through clusters and groups.

Construction of cluster catalogues in the optical/IR and in the X-ray are relatively mature activities. The first large optical cluster survey is now over 50 years old (Abell 1958; Abell et al. 1989), and current catalogues constructed from the Sloan Digital Sky Survey data contain over a hundred thousand clusters (e.g., Koester et al. 2007; Wen et al. 2012). In X-rays, large samples first became available via ROSAT satellite observations (e.g., Vikhlinin et al. 1998; Böhringer et al. 2000, 2004; Gioia et al. 2003; Burenin et al. 2007; Ebeling et al. 2007), but also more recently for instance from dedicated or serendipitous survey with XMM-Newton (Pacaud et al. 2007; Fassbender et al. 2011; Takey et al. 2011; Mehrtens et al. 2012). Currently several thousand X-ray selected clusters are known (see for instance the meta-catalogue MCXC by Piffaretti et al. 2011). By contrast, although proposed about fifteen years ago (e.g., Barbosa et al. 1996; Aghanim et al. 1997), it is only very recently that SZ-selected samples have reached a significant size, with publication of samples containing several hundred clusters from the Early SZ (ESZ) catalogue from the Planck Satellite (Planck Collaboration VIII 2011), the South Pole Telescope (SPT, Reichardt et al. 2013) and the Atacama Cosmology Telescope (ACT, Hasselfield et al. 2013).

The usefulness of the different selection methods, particularly for cosmology, depends not just on the total number of clusters identified but also on how readily the selection function of the survey can be modelled, and on how well the observed cluster properties can be related to quantities such as the total cluster mass that are most readily predicted from theory (e.g., see Voit 2005). It has proven difficult to capitalize on the large size of optical/IR cluster samples because the observable, the number of galaxies in each cluster, exhibits large scatter with respect to the total cluster mass (e.g., Johnston et al. 2007). In this regard the X-ray selected samples are considerably more powerful, due to the tighter correlations of X-ray properties with mass (Arnaud et al. 2005; Vikhlinin et al. 2006; Pratt et al. 2009; Reichert et al. 2011; Maughan et al. 2012). Simulations predict that SZ-selected surveys may do even better, with a very tight relation between SZ signal and mass (e.g., da Silva et al. 2004; Motl et al. 2005; Nagai 2006; Wik et al. 2008; Aghanim et al. 2009; Angulo et al. 2012). Moreover, this relation, except at low redshifts, corresponds to a nearly redshift-independent mass limit, thus allowing such surveys to reach to high redshift and provide a strong lever arm on growth of structure.

We report on the construction and properties of the PSZ catalogue, which is to date the largest SZ-selected cluster catalogue and has value added through compilation of ancillary information. It contains 1227 entries including many multiple systems, e.g., the Shapley super-cluster displayed in Fig. 1 together with a composite image. Of these 861 are confirmed, amongst which 178 are new discoveries, whilst amongst the 366 candidate clusters 54 are of high reliability (class1 in our terminology), 170 are reliable, and the remaining 142 are in the lowest reliability class. In Sect. 2 we start with a description of the Planck data used to provide cluster candidates, and the two different methodologies (one of which has two independent implementations) used to carry out the extraction of the SZ sources. In Sect. 3 we provide a characterization of the PSZ catalogue in terms of completeness, statistical reliability, and accuracy of cluster parameters including size and photometry. Section 4 extensively describes validation of cluster candidates through pre-existing surveys and cluster catalogues in many wavebands, while Sect. 5 describes the follow-up campaigns conducted by the Planck collaboration to confirm new cluster discoveries. This leads to a description of the catalogue properties in Sect. 6. The physical properties of the clusters are exploited in Sect. 7. These include an update of the SZ–X-ray scaling relations from the Planck data, the measure of the X-ray flux for all SZ detections, and the production of homogenized SZ-mass estimates for 813 clusters with measured redshifts that are provided to the community as a value-added element to the Planck SZ catalogue.

Throughout the article, the quantities M₅₀₀ and R₅₀₀ stand for the total mass and radius where the mean enclosed density is 500 times the critical density at the cluster redshift. The SZ flux is denoted Y₅₀₀, where Y₅₀₀${\mathit{D}}_{\mathrm{A}}^{\mathrm{2}}$ is the spherically-integrated Compton parameter within R₅₀₀, and D_A is the angular-diameter distance to the cluster. The physical cluster quantities are computed with a fiducial ΛCDM cosmology with H₀ = 70 km s^-1 Mpc^-1, Ω_m = 0.3 and Ω_Λ = 0.7. Furthermore, all the fits are undertaken in the log-log plane using the BCES orthogonal regression method of Akritas & Bershady (1996), with bootstrap resampling, which allows for intrinsic scatter as well as uncertainties in both variables. All uncertainties are given at 68 per cent confidence level and all dispersions are given in log₁₀.

2. Construction of the Planck SZ Catalogue

2.1. Input Planck data

The Planck catalogue of SZ sources is constructed from the total intensity data taken during the first 15.5 months of Planck survey observations. Raw data were first processed to produce cleaned time-lines (time-ordered information) and associated flags correcting for different systematic effects; channel maps were then produced for all the observing frequencies (see details in Planck Collaboration VI 2014; Planck Collaboration II 2014). These maps, together with the associated beam characteristics, are the main inputs for the SZ-finder algorithms presented in Sect. 2.2. Following Planck Collaboration VIII (2011), we used the six highest-frequency Planck channel maps, from 100 to 857 GHz, to produce the catalogue of SZ detections. This optimizes the signal-to-noise (S/N) of the extracted SZ detections and the usable sky fraction; see Appendix A for the choice of channel maps.

In order to optimize the SZ detection, together with avoiding contamination of the PSZ catalogue by bright point sources (PS), the latter are masked from the channel maps prior to the SZ detection as detailed in the following. To construct the PS mask, we use the Planck Catalogue of Compact Sources (PCCS). The PCCS (Planck Collaboration XXVIII 2014) is a collection of single-frequency source catalogues, one for each of the nine Planck frequency channels. The six single Planck-HFI frequency PS catalogues are used to first produce individual-frequency masks constructed by masking a radius equivalent to 1.28 FWHM (3σ_beam) around every point source detected with (S/N)_PS ≥ 10. Then a single common PS mask (see Fig. 2), which is the union of the six individual HFI-frequency channel masks, is constructed. It is applied to all six highest-frequency Planck channel-maps to mask the point sources prior to running the algorithms to detect SZ signal. The masked regions are filled using a harmonic in-painting method based on that of Bajkova (2005), which has the advantage of eliminating the discontinuities caused by the masking. In order to avoid any possible artificial spurious detections at the edges of the in-painted area, we further reject detections within an expanded common mask, constructed using the same procedure as described above, but using a masking radius equivalent to 2.13 FWHM (5σ_beam) and covering less than 2.9% of the sky.

Bright radio sources are known to exist at the centre of galaxy clusters, but they generally have steep spectra and hence their flux is significantly reduced at the six highest Planck frequencies where the PS mask is constructed and where the clusters are detected. The Perseus cluster (see Fig. 19 later and the associated discussion) is one exception, with a point source that is so bright that the cluster is masked and thus not included in the Planck SZ catalogue.

2.2. Detection methods

The catalogue of SZ sources is the result of a blind multi-frequency search, i.e., no prior positional information on known clusters is used as input to the detection, by three detection algorithms briefly described below. These algorithms were described and tested using simulations (Melin et al. 2012). They were used to construct the Early SZ (ESZ) Planck sample by Planck Collaboration VIII (2011). All three assume priors on the cluster spectral and spatial characteristics, which optimize the SZ detection by enhancing the SZ contrast over a set of observations containing contaminating signals. In the following we present the cluster model used as a template by the SZ-finder algorithms and we briefly describe the three detection methods (for details we refer the reader to Herranz et al. 2002; Melin et al. 2006, 2012; Carvalho et al. 2009, 2012).

2.2.1. Cluster model

The baseline pressure profile model used in the detection methods is the generalized NFW (Navarro et al. 1997) profile of Arnaud et al. (2010). This profile model was constructed by combining the observed, scaled, X-ray pressure profile of 31 clusters from the REXCESS sample (Böhringer et al. 2007) for R<R₅₀₀,² with the mean pressure profile from three sets of numerical simulations (Borgani et al. 2004; Nagai et al. 2007; Piffaretti & Valdarnini 2008) for R₅₀₀<R< 5R₅₀₀. New observational constraints on the pressure distribution at R>R₅₀₀ have become available. Planck Collaboration Int. V (2013) constrained the detection of the thermal pressure distribution out to about 3R₅₀₀ through stacking of the observed SZ profiles of 62 nearby massive clusters detected with high significance in the Planck ESZ sample. The resulting profile is in agreement with that derived for the Coma cluster (Planck Collaboration Int. X 2013). Both show a slightly flatter distribution in the outer parts (i.e., beyond R₅₀₀) with respect to the predictions from the numerical simulations. These results are further confirmed by independent measurements from Bolocam in a smaller radial range (r< 2 R₅₀₀, Sayers et al. 2013). Pressure profiles different from the generalized NFW and consistent with the observations can be devised, e.g., the SuperModel used by Lapi et al. (2012) for SPT stacked clusters or by Fusco-Femiano et al. (2013) for the Coma cluster. Using the profile of Planck Collaboration Int. V (2013) does not affect the detection yield (see Sect. 3) and only slightly modifies the measure of the SZ flux density (see Sect. 7.5) as compared to the generalized NFW (GNFW) profile adopted in the three cluster. The fiducial model parameters for the GNFW profile are given by the parameterization of the pressure profile in Eq. (12) of Arnaud et al. (2010). It states $\mathit{p}\mathrm{\left(}\mathit{x}\mathrm{\right)}\mathrm{=}\frac{{\mathit{P}}_{\mathrm{0}}}{\mathrm{(}{\mathit{c}}_{\mathrm{500}}\mathit{x}{\mathrm{)}}^{\mathit{\gamma }}{\left[\mathrm{1}\mathrm{+}\mathrm{(}{\mathit{c}}_{\mathrm{500}}\mathit{x}{\mathrm{)}}^{\mathit{\alpha }}\right]}^{\mathrm{(}\mathit{\beta }\hspace{0.17em}\mathrm{-}\hspace{0.17em}\mathit{\gamma }\mathrm{)}\mathit{/}\mathit{\alpha }}}\mathit{,}$(1)with the parameters $\mathrm{\left[}{\mathit{P}}_{\mathrm{0}}\mathit{,}{\mathit{c}}_{\mathrm{500}}\mathit{,\gamma ,\alpha ,\beta }\mathrm{\right]}\mathrm{=}\mathrm{[}\mathrm{8.40}\hspace{0.17em}{\mathit{h}}_{\mathrm{70}}^{\mathrm{-}\mathrm{3}\mathit{/}\mathrm{2}}\mathit{,}\mathrm{1.18}\mathit{,}\mathrm{0.308}\mathit{,}\mathrm{1.05}\mathit{,}\mathrm{5.49}\mathrm{]}\mathit{.}$(2)The (weak) mass dependence of the profiles is neglected. Within the SZ-finder algorithms, the size and amplitude of the profile are allowed to vary but all other parameters are fixed. The cluster model is thus equivalent to a shape function characterized by two free parameters, its amplitude and a characteristic scale θ_s = θ₅₀₀/c₅₀₀.

2.2.2. Matched multi-filter (MMF)

Two different implementations of the matched multi-frequency filter algorithm (MMF1 and MMF3) are used to detect SZ clusters. Both are extensions, over the whole sky, of the MMF algorithm (Herranz et al. 2002; Melin et al. 2006). The matched filter optimizes the cluster detection using a linear combination of maps (which requires an estimate of the statistics of the contamination) and uses spatial filtering to suppress both foregrounds and noise (making use of the prior knowledge of the cluster pressure profile and thermal SZ spectrum).

The MMF1 algorithm divides the full-sky Planck frequency maps into 640 patches, each 14.66° × 14.66°, covering 3.33 times the sky. The MMF3 algorithm divides the maps into a smaller set of 504 overlapping square patches of area 10° × 10° with the sky covered 1.22 times. The smaller redundancy of MMF3 with respect to MMF1 implies a potentially lower reliability of the SZ detections. In order to increase the reliability of the detections, the MMF3 algorithm is thus run in two iterations. After a first detection of the SZ candidates, a subsequent run centred on the positions of the candidates refines the estimated S/N and candidate properties. If the S/N of a detection falls below the threshold at the second iteration, it is removed from the catalogue. For both implementations, the matched multi-frequency filter optimally combines the six frequencies of each patch. Auto- and cross-power spectra are directly estimated from the data and are thus adapted to the local instrumental noise and astrophysical contamination, which constitutes the dominant noise contribution. Figure 3 illustrates, for a 6′ filter size, the ensemble noise maps as measured by MMF3 in each of the patches. For both MMF1 and MMF3, the detection of the SZ-candidates is performed on all the patches, and the resultant sub-catalogues are merged together to produce a single SZ-candidate catalogue per method.

The candidate size in both algorithms is estimated by filtering the patches over the range of potential scales, and finding the scale that maximizes the S/N of the detected candidate. When merging the sub-catalogues produced from the analysis of individual patches, it is also the S/N of the detection (the refined S/N estimate for MMF3) which is used when deciding which detection of the candidate is kept. Furthermore, both MMF1 and MMF3 can also be run with fixed cluster size and position to estimate the SZ signal. This version of the algorithms is used to assess the reliability of the association with known clusters and/or to refine the measurement of the integrated Compton parameters of known X-ray clusters, as presented in Sect. 7.2.1.

2.2.3. PowellSnakes

PowellSnakes (PwS) is different from the MMF methods. It is a fast Bayesian multi-frequency detection algorithm designed to identify and characterize compact objects buried in a diffuse background. The detection process is grounded in a statistical model comparison test. The statistical foundations of PwS are described in Carvalho et al. (2009), and more recently in Carvalho et al. (2012) with a greater focus on the Planck setup. PwS may be run either based on a Generalized Likelihood Ratio Test or in full Bayesian mode. This duality allows PwS measured quantities to be consistently compared with those of the MMF algorithms.

PwS also operates in square flat patches of 14.66° × 14.66°. The total number of patches employed, of order 2800, varies with sky area but always guarantees a very large overlap; on average each cluster is detected about 4.7 times. PwS detects putative clusters and at the same time it computes the evidence ratio and samples from the posterior distributions of the cluster parameters. Then, it merges all intermediate sub-catalogues and applies the criterion of acceptance/rejection (Carvalho et al. 2012). PwS computes the cross-channel covariance matrix directly from the pixel data. To reduce the contamination of the background by the SZ signal itself, the estimation of the covariance matrix is performed iteratively. After an initial estimate, all detections in the patch with S/N higher than the current target detection are subtracted from the data using their best-fit values and the cross-channel covariance matrix is re-estimated. This is PwS “native” mode of background estimation that produces, on average, an S/N estimate about 20% higher than MMF. However, in order to produce a homogeneous Planck SZ catalogue from the three algorithms, it is possible to run PwS in “compatibility” mode, skipping the re-estimation step to mimic more closely the evaluation of the background noise cross-power spectrum of the MMF algorithms and thus their evaluation of the S/N. In this mode, PwS is a maximum likelihood estimator like the MMF.

In the following, unless stated otherwise, all quoted or plotted S/N values from PwS are obtained in “compatibility” mode in order to ensure homogeneity across the catalogue entries and in order to ease the comparison with the MMF outputs.

2.3. Outputs of the detection methods

Each of the three detection algorithms outputs a catalogue of SZ detections above S/N = 4.5 outside the highest-emitting Galactic regions (this corresponds to a mask of about 15% of the sky, see masked area in Fig. 2) and the Small and Large Magellanic Clouds and outside the PS mask described in Sect. 2.1. The union PS-Galactic mask covers 16.3% of the sky. The survey area used for the SZ detections in Planck is thus 83.7% of the sky coverage. The three individual lists of SZ candidates are cleaned by removal of obvious false detections. These are spurious sources that pass the MMF and PwS filters despite the pre-processing step applied to the Planck channel maps, see Sect. 2.1. In order to identify them, we cross-match the SZ detections with an intermediate, low S/N cut of 4, catalogue of point sources detected at the highest frequencies of Planck. Galactic sources in dense and cold regions at high latitudes also contaminate the SZ detections outside the Galactic mask. These cold Galactic sources (CGS, see Planck Collaboration XXIII 2011; Planck Collaboration XXII 2011) are detected in the Planck channel maps following an optimized method proposed by Montier et al. (2010). The SZ detections matching with PS at both 545 and 857 GHz, or with CGS sources, all show a rising spectrum at high frequencies, indicating that they are false detections. The SZ detections corresponding to such PCCS or CG sources are removed from the individual lists and from the published Planck catalogue of SZ sources.

The three detection algorithms used in the present study deploy the GNFW cluster profile to detect SZ signal with the two parameters of the shape function, the central value and the characteristic scale θ_s let free, with θ_s = θ₅₀₀/c₅₀₀. Each of the three algorithms therefore assigns, to each detected SZ candidate, a position with estimated uncertainty, a S/N value, and an estimated size, θ_s or equivalently θ₅₀₀, with its uncertainty. The detection likelihood or the posterior probability of the integrated Compton parameter within 5θ₅₀₀, denoted Y_5R500, exhibits a large correlation with the size. Figure 4 illustrates the likelihood plots for two cases: a spatially-resolved cluster detected with a high S/N, Abell 2163; and a non-resolved cluster at high redshift (z ≃ 1), PSZ1 G266.6-27.3 (also known as PLCK G266.6-27.3 in Planck Collaboration XXVI 2011). We also show in Fig. 5 the distribution of maximum likelihood SZ fluxes (Y_5R500) and sizes (θ₅₀₀) for the MMF3 detections.

This “degeneracy” between cluster size and SZ flux propagates the size uncertainty to the SZ flux estimate, increasing and biasing its value dramatically. This effect being so detrimental, both the SZ blind flux and size best-fit estimates, and respective error bars, are not quoted in the catalogue outputs to avoid their misuse. Only the full joint Y_5R500–θ_s, or equivalently Y_5R500–θ₅₀₀, posterior probability contours provide a complete description of the information output by each detection method. They are thus provided for each detection. In order to use the flux measure, one ought to break the size–flux degeneracy. This can be achieved by a joint analysis with a high-resolution observation of the same objects, or by assuming a prior on, or fixing, the cluster size e.g., to the X-ray size. The SZ signal can then be re-extracted with an uncertainty much smaller than the variation of the joint Y–θ probability distribution.

We now perform a systematic comparison of the outputs of the three algorithms and we compare the S/N. In addition and for purposes of illustration, we compare the best-fit blind Y value from maximum-likelihood or posterior probability outputs, namely Y_5R500³. We show the comparison in Fig. 6, considering detections down to S/N = 4.5. We quantify the difference between a given quantity estimated by two different algorithms, Q₂ and Q₁, by fitting a power law to the data in the form Q₂/Q_p = 10^A (Q₁/Q_p)^α with a pivot Q_p = 6 for S/N and Q_p = 4 × 10^-3 arcmin² for Y_5R500. The results are given in Table 1, including the scatter estimates. The raw scatter was estimated using the error-weighted vertical distances to the regression line. The intrinsic scatter on Y₅₀₀ was computed from the quadratic difference between the raw scatter and that expected from the statistical uncertainties. Table 1 also lists the mean difference in logarithm, Δ(log Q) = log (Q₂/Q₁), computed taking into account both statistical errors and intrinsic scatter, estimated iteratively.

2.3.1. Signal-to-noise

A crucial ingredient of the SZ detection algorithms, either the MMFs or PwS, is the background cross-power spectrum used to estimate the noise level. It is evaluated from the data locally on a per-patch basis (see Fig. 3 for an example of the noise per patch across the sky). The algorithms, and implementations, slightly differ with respect to the stabilization assumptions (e.g., smoothing) of the background noise cross-power spectrum and to the treatment of the background SZ signal, now acting as a contaminant. These differences translate into variations in the S/N values per method. In particular, when operated in “compatibility” mode (without background cluster subtraction), PwS estimation of the background cross-power spectrum is more affected than the MMF by SZ signal contamination. The SZ signal adds an extra component to the background noise producing lower S/N estimates. This is particularly noticeable when the SZ signal is very strong compared with background (typically S/N ≥ 15).

Despite the differences in background estimates, the yields from the three algorithms agree. In the left panel of Fig. 7, we show that the detection counts as a function of S/N for each detection method are in good overall agreement. The right panel of Fig. 7 shows the fraction of common detections over the union of detections from all three algorithms as a function of S/N. Sources with S/N> 8.5 are detected by all three methods. However, we note that PwS number counts decrease more rapidly than MMF counts above S/N = 15. This reflects the behaviour of PwS in “compatibility” mode described above, which estimates a higher background than the MMF methods at high S/N. Figure 6 shows the comparison of the S/N estimates from all three methods. The agreement is good on average. The mean ratio (or the normalization at the pivot of the power-law relation) deviates from unity by less than 2% and at less than 3σ significance. Here again at high S/N values, we note the tendency for lower S/N in PwS as compared to MMF (Fig. 6), and indeed the slope of the power-law relation is smaller than unity (α = 0.94 ± 0.01 for MMF3).

2.3.2. Photometry

We now compare the best-fit Y values (from maximum likelihood and posterior probability) for the three detection algorithms. The comparison (Fig. 6, lower panels) shows a systematic bias with PwS, yielding slightly smaller values than MMF, typically by 10%. However, the slope is consistent with unity, showing that this bias is not flux dependent. The MMF values differ from each other by less than 3% on average. The scatter between Y estimates is dominated by the intrinsic scatter (Table 1). It is clearly related to the size-flux degeneracy, the ratio between Y estimates for a given candidate being correlated with the size estimate ratio, as illustrated by Fig. 8. The scatter becomes compatible with the statistical scatter when a prior on the size is used, e.g., size fixed to the X-ray size.

2.4. Definition of the Planck SZ catalogue

As discussed above, the processing details of each algorithm/implementation differ in the computation of the background noise. The significance of the detections in terms of S/N, although in overall agreement, differs from one algorithm to the other and translates into different yields for the candidate lists from the three algorithms. We choose to construct a catalogue of SZ candidates that ensures, through redundant detections, an increased reliability of the low S/N sources, when they are detected by two methods at least, together with maximizing the yield of the catalogue.

The Planck SZ cluster catalogue described in the following is thus constructed from the union of the cleaned SZ-candidate lists produced at S/N ≥ 4.5 by all three algorithms. It contains in total 1227 SZ detections above S/N = 4.5. Note that in order to ensure homogeneity, in terms of detection significance, the S/N values of PwS quoted in the union catalogue are obtained in compatibility mode, whereas the S/N obtained from PwS native mode are quoted in the PwS individual list. The union catalogue is constructed by merging detections from the three methods within an angular separation of at most 5′, in agreement with Planck position accuracy shown later in Fig. 12. As mentioned, no reference photometry is provided. However a reference position for the SZ detection is needed. For compatibility with the ESZ Planck sample, in the case of matching detection between methods we arbitrarily choose to take the coordinates from the MMF3 detection as the fiducial position (MMF3 was the reference method used to construct the ESZ Planck sample). When no detection by MMF3 above S/N = 4.5 is reported, we took the PwS coordinates as fiducial, and the MMF1 coordinates elsewhere. The S/N values in the union catalogue are taken following the same order, which explains why the MMF3 curve in Fig. 6 coincides with the union curve. The cluster candidates in the union catalogue are cross-referenced with the detections in the individual lists. The reference positions and the S/N values are reported in the union catalogue. Given the size-flux degeneracy, the full information on the degeneracy between size and flux is provided with each individual list in the form of the two-dimensional marginal probability distribution for each cluster candidate as discussed above. It is specified on a grid of 256 × 256 values in θ_s and Y_5R500 centred at the best-fit values found by each algorithm for each SZ detection.

An extract of the Planck SZ catalogue is given in Appendix B. The full online table for union Planck catalogue, the individual lists of SZ detections, and the union mask used by the SZ-finder algorithms together with comments assembled in an external file are available at ESA’s Planck Legacy Archive (PLA)⁴.

3. Statistical characterization

The statistical characterization of the PSZ catalogue is achieved through a process of Monte-Carlo quality assessment (MCQA) that can be applied to each individual catalogue and to the merged union catalogues. The statistical quantities produced include completeness, fraction of detections associated with true clusters called, statistical reliability or purity, positional accuracy, and accuracy of parameter estimation. Together, these statistics describe the quality of detections in the catalogue. The quality of the parameter estimation, including astrometry (cluster position and extent), is determined through comparison with the parameters of the input clusters. The statistical characteristics of the different lists are summarized in Table 2.

3.1. MCQA pipeline and simulations

The MCQA pipeline contains a common segment producing simulated input catalogues and processed, source-injected maps, which are then fed into the detection pipeline. In summary, the pipeline steps per Monte-Carlo loop are:

• 1.

  creation of an input cluster catalogue;

• 2.

  injection of clusters into common simulated diffuse frequency maps, including beam convolution;

• 3.

  injection of multi-frequency point sources;

• 4.

  pre-processing of maps, including masking and filling point sources;

• 5.

  detection and construction of individual cluster-candidate catalogues;

• 6.

  construction of a union catalogue given merging criteria;

• 7.

  collation of input and output catalogues, producing detection truth-tables and catalogues of unmatched spurious detections⁵.

To estimate the completeness, clusters are injected into the real data. In this case, steps 3 and 4 are skipped and each detection algorithm estimates noise statistics on the real data prior to injection in order to avoid artificially raising the S/N and biasing the completeness estimates. The pressure profiles of the injected clusters follow that described in Sect. 2.2.1. To account for the profile variation across the cluster population, the profile parameters are drawn from the covariance matrix of the 62 measured pressure profiles from Planck Collaboration Int. V (2013), ensuring that the injected profiles are consistent with measured dispersion and consistent, on average, with the extraction filter. The injected clusters are convolved with effective beams in each pixel including asymmetry computed following Mitra et al. (2011).

The simulated input cluster catalogues differ for statistical reliability and completeness determination. For completeness, clusters injected in real data are drawn from a uniform distribution in (Y₅₀₀,θ₅₀₀) so as to provide equal statistics in each completeness bin. To avoid an over-contamination of the signal, injected clusters are constrained to lie outside an exclusion radius of 5R₅₀₀ around a cluster, either detected in the data or injected.

For the statistical reliability estimation of the input cluster distribution injected in simulations is such that cluster masses and redshifts are drawn from a Tinker et al. (2008) mass function and converted into the observable parameters (Y₅₀₀,θ₅₀₀) using the Planck ESZ Y₅₀₀–M₅₀₀ scaling relation (Planck Collaboration X 2011). The simulated maps consist of CMB realizations, diffuse Galactic components and instrumental noise realizations, including realistic power spectra and inter-detector correlations, from the FFP6 simulations (Planck Collaboration XII 2014; Planck Collaboration 2013). Residual extragalactic point sources are included by injecting, mock-detecting, masking and filling realistic multi-frequency point sources using the same process as for the real data (see Sect. 2.1).

3.2. Completeness

The completeness is the probability that a cluster with given intrinsic parameters (Y₅₀₀,θ₅₀₀) is detected given a selection threshold (here in S/N).

If the Compton-Y estimates are subject to Gaussian errors, the probability of detection per cluster follows the error function and is parameterized by σ_Yi(θ₅₀₀), the standard deviation of pixels in the multi-frequency matched-filtered maps for a given patch i at the scale θ₅₀₀, the intrinsic Compton Y₅₀₀, and the detection threshold q: $\mathit{P}\left(\mathit{d}\mathrm{\left|}{\mathit{Y}}_{\mathrm{500}}\mathit{,}{\mathit{\sigma }}_{\mathit{Yi}}\mathrm{\right(}{\mathit{\theta }}_{\mathrm{500}}\mathrm{)}\mathit{,q}\right)\mathrm{=}\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{1}\mathrm{+}\mathrm{erf}\left(\frac{{\mathit{Y}}_{\mathrm{500}}\mathrm{-}\mathit{q}{\mathit{\sigma }}_{\mathit{Yi}}\mathrm{\left(}{\mathit{\theta }}_{\mathrm{500}}\mathrm{\right)}}{\sqrt{\mathrm{2}}{\mathit{\sigma }}_{\mathit{Yi}}\mathrm{\left(}{\mathit{\theta }}_{\mathrm{500}}\mathrm{\right)}}\right)\right]\mathit{,}$(3)where $\mathrm{erf}\mathrm{\left(}\mathit{x}\mathrm{\right)}\mathrm{=}\mathrm{(}\mathrm{2}\mathit{/}\mathit{\pi }\mathrm{)}{{}^{\mathrm{\int }}}_{\mathrm{0}}^{\mathit{x}}\exp {}^{\mathrm{(}}\mathrm{-}{\mathit{t}}^{\mathrm{2}}{}^{\mathrm{)}}\mathrm{d}\mathit{t}$ and d is the Boolean detection state.

The completeness of the catalogue, thresholded at S/N q, is expected to follow the integrated per-patch error function completeness $\mathit{C}\mathrm{\left(}{\mathit{Y}}_{\mathrm{500}}\mathit{,}{\mathit{\theta }}_{\mathrm{500}}\mathrm{\right)}\mathrm{=}\sum _{\mathit{i}}{\mathit{f}}_{\mathrm{sky}\mathit{,i}}\mathit{P}(\mathit{d}\mathrm{\left|}{\mathit{Y}}_{\mathrm{500}}\mathit{,}{\mathit{\sigma }}_{\mathit{Yi}}\mathrm{\right(}{\mathit{\theta }}_{\mathrm{500}}\mathrm{)}\mathit{,q})\mathit{,}$(4)where f_sky,i is the fraction of the unmasked sky in the patch i. The true completeness departs from this theoretical limit. This is due to the non-Gaussian nature of the noise dominated by the astrophysical, namely Galactic, contamination. This is also the case when the actual cluster pressure profile deviates from the GNFW used in the SZ-finder algorithms, or when the effective beams deviate from constant symmetric Gaussians, and also when the detection algorithm includes extra steps of rejection of spurious sources not formulated in Eq. (3). This is why an MCQA-based assessment of the completeness is essential to characterize the Planck detections.

The Monte-Carlo completeness of each of the individual lists and the union catalogue are shown in Fig. 9. The MMF lists are consistent with one another at θ₅₀₀> 4′, but MMF3 is more complete at lower radii. This is due to an extra step implemented in MMF1 that rejects as spurious the detections estimated to be point-like. The union improves upon the completeness of each of the individual catalogues, because it includes the faint real detections by one method alone. In contrast, the intersection of the lists from the three algorithms, while more robust, is markedly less complete than the union and each of the individual catalogues. The intersection and union catalogues represent the extremes of the trade-off between statistical reliability and completeness. The quantities for each of the catalogues, plus the union and intersection, are summarized in Table 2. Figure 9 shows four constant θ₅₀₀ slices through the completeness contours for MMF3, comparing the MCQA-based completeness with the integrated error function completeness. At radii smaller than 6′, the MCQA-based completeness is systematically less complete, and the drop-off of the completeness function shallower, than the theoretical expectation. This effect is a consequence of the variation of intrinsic cluster profiles from the GNFW profile assumed for extraction.

3.3. Statistical reliability

The fraction of detections above a given S/N that are associated with a real cluster is characterized by injecting clusters into high-fidelity simulations of the Planck channels. Unassociated detections from these simulations define the fraction of spurious detections. We have verified that the simulations produced detection noise σ_Y500 consistent with the real data and that the simulated detection counts match the real data.

The cumulative fraction of true clusters, as characterized by the simulations, is shown for the output of each detection algorithm and for the union catalogue in Fig. 10. The union catalogue is less pure than any of the individual lists because it includes all the lower-reliability, individual-list detections, in addition to the more robust detections made by all three SZ-finder algorithms. The union catalogue constructed over 83.7% of the sky at S/N of 4.5 is 84% pure.

The fraction of false detections is dominated by systematic foreground signals, in particular Galactic dust emission. This is illustrated in Fig. 11 by the effect of dust contamination on the cumulative reliability. We define two sky regions by the level of dust contamination: “region 1” is the low dust-contamination region outside of the Planck Galactic dust, and PS, mask that excludes 35% of the sky. This mask is used in Planck Collaboration XX (2014) for cosmological analysis of SZ counts. “Region 2” is the complementary region included by the smaller 15% dust mask but excluded by the 35% mask. When the larger Galactic dust mask is applied leaving 65% of the Planck sky survey in which to detect SZ signal, the statistical reliability increases from 84% in 83.7% of the sky to 88% in 65% of the sky. As seen in Fig. 11 upper panel, the reliability of the detections deteriorates markedly in “region 2” relative to “region 1”. The noisy behaviour of the curves in Fig. 11 upper panel is due to the reduced size of sky area used in the analysis.

In both regions, the spurious count much higher than is predicted by Gaussian fluctuations. This reflects the non-Gaussian nature of the filtered patches. The bottom panel of Fig. 11 illustrates this for a typical mid-latitude patch from a null-test simulation with no injected clusters. The patches are well approximated as Gaussian at deviations smaller than 3σ (consistent with the assumptions of Eq. (3)), but show enhanced numbers of high significance deviations, which can translate into spurious detections.

3.4. Positional accuracy

Positional accuracy is characterized by the radial offset between estimated and injected positions. The distribution of position error is shown in Fig. 12, for each individual list and the union catalogue. In contrast to the MMFs, which estimate the maximum-likelihood position, the PwS position estimator is the mean of the position posterior, which produces more accurate positional constraints. The union catalogue positions are taken from MMF3 if available, followed by PwS and then MMF1. Its positional estimates are hence consistent with the MMFs. The mode of the union distribution is consistent with a characteristic position error scale of half an HFI map pixel (0.86′).

3.5. Parameter recovery

The Compton Y_5R500 is characterized by comparing detected and input values for matched detections from the injection of clusters into the real data (see Fig. 13). The injection follows the scheme outlined above with one exception: input cluster parameters are drawn using the Tinker mass function and the scaling relations discussed above for reliability simulations. This ensures a realistic distribution of parameters and S/N values.

What we characterize is slightly different for each catalogue. For the MMFs, we characterize the maximum-likelihood point of the 2D degeneracy contours provided in the individual lists. For PwS, we characterize the mean of the marginal distribution for each parameter. In each case, the 2D (Y_5R500,θ_s) are marginalized over position. The contours are scaled for each cluster and are time consuming to compute, so we characterize the parameters from a lower-resolution grid that is better suited to Monte-Carlo analysis⁶.

The scatter between input and detected parameters is shown in Fig. 14 as an example for PwS. Biases are evident at both the low and high end for Y_5R500. The low-flux bias is the Malmquist bias related to the S/N ≥ 4.5 threshold. The high-flux bias is due to a hard prior on the upper limit for cluster radius. Figure 14 also shows the distribution of the ratio of estimated over injected parameters. The median and median absolute deviation of these ratios are shown in Table 3.

The distributions for flux are positively skewed due to Malmquist bias. The median ratios of the flux recoveries are consistent with unity for MMF3 and PwS and are slightly higher for MMF1. The recovery of θ_s is biased high in the median by about 20% for each of the codes. This bias is a consequence of the intrinsic cluster profile variation and disappears when the injected profiles match the detection filter. The Y_5R500 estimate by contrast is relatively unaffected by profile variation. The parameter constraints from PwS are tighter than the MMFs due to the PwS priors and the definition of the estimator as the expected value of the parameters rather than the maximum likelihood.

4. External validation

The cluster-candidate catalogue constructed from the union of all three SZ-finder algorithms undergoes a thorough validation process that permits us to identify previously-known clusters and to assess the reliability of the Planck SZ candidates not associated with known clusters. In order to achieve this, we make use of the existing cluster catalogues and we also search in optical, IR, and X-ray surveys for counter-parts at the position of the Planck SZ sources. In practice, we search within 5′ of the SZ position, in agreement with Planck position errors shown in Fig. 12. In Sect. 5, we present the follow-up programmes that were undertaken by the Planck collaboration in order to confirm and measure the redshifts of the Planck candidate new-clusters.

The first step of the validation of the PSZ catalogue is to identify among the Planck SZ candidates those associated with known clusters. For this purpose, we use existing X-ray, optical or SZ cluster catalogues. A positional matching is not sufficient to decide on the association of a Planck SZ source with a previously-known cluster, and a consolidation of the association is needed. For the X-ray associations, a mass proxy can be built and used to estimate the SZ flux, S/N, etc., that are compared with measured quantities for the Planck cluster candidates. In contrast to the X-ray clusters, optical clusters either have no reliable mass estimates or suffer from large uncertainties in the mass-richness relations. In this case, the consolidation cannot be performed uniquely through the coherence of measured versus predicted properties. It rather relies on extra information from surveys in the X-ray, optical, or IR at the Planck cluster-candidate positions.

In the following, we detail the search for counter-parts in optical, IR, and X-ray surveys; list the cluster catalogues used for the identification; and finally present the identification procedure followed to associate Planck SZ detections with bona fide clusters. In this process, we define quality flags for the association of Planck SZ detections with external data. We set Q = 1 for high-reliability associations, i.e., very clear cluster signatures, Q = 2 for reliable associations, and Q = 3 for low-reliability associations, i.e., unclear cluster signature.

4.1. Search for counter-parts of Planck detections in surveys

We made use of the ROSAT All Sky Survey (RASS, Voges et al. 1999), the all-sky survey with the Wide-field Infrared Survey Explorer (WISE, Wright et al. 2010), and the Sloan Digital Sky Survey (SDSS, York et al. 2000) to search for counter-parts of the Planck SZ detections. This information was used in two ways. When Planck detections were associated with known clusters from catalogues, in particular in the optical, the counter-parts in RASS, WISE, or SDSS helped in consolidating the association, increasing the confidence in the identification of Planck candidates with known clusters. When no association between Planck detections and previously-known clusters was found, the information on the counter-parts, in the surveys, of Planck SZ detections was used to assess the reliability of the Planck cluster candidates, i.e., clear or unclear cluster signatures.

4.1.1. Search in RASS data

As detailed in Planck Collaboration Int. IV (2013), the validation follow-up with XMM-Newton has shown the importance of the RASS data to assess the reliability of the Planck sources. In particular, Planck Collaboration Int. IV (2013) showed that a large fraction of Planck clusters are detectable in RASS maps, but this depends on the region of the sky and on the ratio Y₅₀₀/S_X which exhibits a large scatter (see later in Fig. 31 the case of the PSZ sources). We therefore exploit the RASS data to consolidate the identification with clusters from optical catalogues (see below Sect. 4.3.2) and to assess the reliability of the Planck SZ candidates.

We first perform a cross-match with the RASS bright source catalogue (BSC, Voges et al. 1999) and the faint source catalogue (FSC, Voges et al. 2000) within a 5′ radius of the position of each of the Planck SZ detections. We then perform a reanalysis of the RASS data following the methodology and prescriptions given by Böhringer et al. (2000, 2004) and Reiprich & Böhringer (2002). We compute count-rate growth curves in order to check for the extension of the signal. We estimate the source flux from both the growth curve (when adequate) and from a fixed 5′ aperture radius with respect to the surrounding background (after PS subtraction). We then derive the associated S/N in RASS, (S/N)_RASS. For this, we make use of the RASS hard-band, [0.5–2] keV, data that maximize the S/N of the detections. We furthermore computed the source density map of the BSC and FSC catalogues and the associated probability that a Planck cluster candidate will be associated with a B/FSC source within a radius of 5′. For the BSC, the probability of chance association is relatively low, with a median <1%. As detailed in Planck Collaboration Int. IV (2013), the correspondence of a Planck SZ-candidate with a RASS-BSC source is a semi-certain association with a real cluster, whereas for the FSC catalogue the probability of chance association is larger, 5.2%.

We define a quality flag, Q_RASS, for the association of Planck candidates with RASS counter-parts using both the S/N in RASS and the association with B/FSC sources. This is of particular importance for the Planck candidate new clusters. Based on the results from Planck Collaboration Int. IV (2013), the quality of the association with RASS counter-parts is high, Q_RASS = 1, for Planck cluster candidates matching a RASS-BSC source or with (S/N)_RASS ≥ 2. We find a total of 887 out of 1227 Planck SZ detections in this category, with mean and median S/N of 7.4 and 5.8, respectively. The quality is poor, Q_RASS = 3, for RASS counter-parts with (S/N)_RASS< 0.5 in regions of reasonable depth (quantified by the probability of chance association with FSC sources being larger than 2.5% Planck Collaboration Int. IV 2013).

4.1.2. Search in SDSS data

We performed a systematic search for counter-parts in the SDSS Data Release DR9 (Ahn et al. 2012) at the position of all the Planck SZ detections. This was performed based on a cluster-finder algorithm developed by (Fromenteau et al., in prep.) to search for red galaxy over-densities in the SDSS galaxy catalogues.

For each associated counter-part within a 5′ circle centred at the position of the Planck SZ detection, a quality criterion is defined on the basis of a fit to the luminosity function and the associated mass limit, and on the number of galaxies within 5′, N_gal, such that we have Q_SDSS,dat = 1, i.e., high quality, for cases where N_gal ≥ 40 and for masses M₂₀₀ ≥ 5.7 × 10¹⁴ M_⊙, Q_SDSS,dat = 2, i.e., good quality, for N_gal between 40 and 20 for masses between 1.5 × 10¹⁴ M_⊙ and 5.7 × 10¹⁴ M_⊙, and Q_SDSS,dat = 3 otherwise.

The cluster-finder algorithm outputs the position of the counter-part (Brightest Cluster Galaxy (BCG) and barycentre) and the estimated photometric redshift. When spectroscopic data are available for the brightest selected galaxy a spectroscopic redshift is also reported. The outputs of the cluster-finder algorithm are compared to those obtained by (Li & White, in prep.) from different method based on the analysis of the full photometric-redshift probability distribution function (Cunha et al. 2009). In this approach, the position and redshift in the SDSS data that maximizes the S/N are considered as the best estimates for the counter-parts of the Planck SZ detections.

4.1.3. Search in WISE data

WISE provides an all-sky survey at 3.4, 4.6, 12, and 22 μm (W1, W2, W3, W4) with an angular resolution of 6.1 to 12.0 arcsec in the four bands.

We search for counter-parts of the Planck SZ detections in the WISE source catalogue in two ways. On the one hand, we run an adaptive matched filter cluster finder developed by (Aussel et al., in prep.), similar to the one described by Kepner et al. (1999), using the cluster members’ luminosity function of Lin et al. (2012). The background counts were determined from the neighbouring square degree in the vicinity of the Planck cluster candidate, excluding regions of fifteen arcmin centred on candidate positions. On the other hand, we use a method developed by (Aghanim & Fromenteau, in prep.) based on a search for overdensities of bright (W1 ≤ 17) and red (W1–W2 > 0) sources within a 5′ radius circle centred on the position of Planck detections with respect to a background computed in a 15′ radius area.

Aghanim & Fromenteau (in prep.) find that a good-quality association between a Planck SZ-detection and a counter-part overdensity in WISE data is reached when there are at least ten galaxies above 2σ in the 5′ search region, and when the corresponding fraction of galaxies is at least 30% of the total number of galaxies retained in the 15′ circle. Performing the search for counter-parts of an ensemble of random positions on the sky, we compute the purity of the detections, i.e., the probability of a Planck candidate having a real counter-part in the WISE data as opposed to a chance association. The quality criterion for the association between Planck detection and WISE overdensity is high, Q_WISE = 1, for a purity larger than 90%. When it lies between 90% and 80% the association of Planck SZ-detections and WISE overdensities is assigned a lower quality criterion Q_WISE = 2. We set the quality of the association to Q_WISE = 3, bad, when the purity is below 80%. We find 856 Planck SZ detections with high or good quality counter-parts in WISE data, including 658 Q_WISE = 1 detections.

4.1.4. DSS images

Finally for each Planck cluster candidate, the second Digitized Sky Survey⁷ (DSS) database was queried for a field of 5′ × 5′ centred at the position of the Planck SZ detections in the r and ir bands. The DSS images were used for visual inspection⁸. Clusters and rich groups out to z ≃ 0.3 to 0.4 can easily be identified in these plates as an obvious concentration of galaxies. This qualitative information was thus used: (i) to consolidate some identifications of Planck SZ detections with previously-known clusters; (ii) to optimize our strategy for the follow-up observations of Planck candidates (see Sect. 5); and (iii) to qualitatively assess the reliability or significance of the Planck SZ detections.

4.2. Cluster catalogues

We now present the ensemble of catalogues that were used to identify the Planck SZ detections with previously-known clusters. In the case of the ROSAT- and SDSS-based catalogues, we have used homogenized quantities, see below, that allowed us to perform the identification with comparable association criteria, which ensures homogeneity in the output results.

MCXC meta-catalogue

– For the association of Planck SZ candidates with previously-known X-ray clusters, we use the Meta-Catalogue of X-ray detected Clusters of galaxies (MCXC, Piffaretti et al. 2011, and reference therein) constructed from the publicly availableROSAT All Sky Survey-based and serendipitous cluster catalogues, as well as the Einstein Medium Sensitivity Survey. For each cluster in the MCXC several properties are available, including the X-ray coordinates, redshift, identifiers, and standardized luminosity, L_X,500, measured within R₅₀₀. The MCXC compilation includes only clusters with available redshift information (thus X-ray luminosity) in the original catalogues. We updated the MCXC, considering the first release of the REFLEX-II survey (Chon & Böhringer 2012), the third public release of clusters from the MACS sample (Mann & Ebeling 2012), individual MACS cluster publications and a systematic search in NED and SIMBAD for spectroscopic redshift for clusters without this information in theROSAT catalogues. This yields an ensemble of 1789 clusters with z and L_X,500 values, adding 20 MACS clusters, 21 REFLEX-II clusters and 5 SGP clusters to the MCXC. For these clusters, the expected Compton-parameter, ${\mathit{Y}}_{\mathrm{500}}^{{\mathit{L}}_{\mathrm{X}}}$, and size, ${\mathit{\theta }}_{\mathrm{500}}^{{\mathit{L}}_{\mathrm{X}}}$, are estimated combining the M₅₀₀–L_X,500 relation of Pratt et al. (2009) and the M₅₀₀–Y₅₀₀ relation given by Arnaud et al. (2010). The expected S/N, (S/N)^LX, is computed taking into account the noise within ${\mathit{\theta }}_{\mathrm{500}}^{{\mathit{L}}_{\mathrm{X}}}$ at the cluster location. We furthermore supplement the updated MCXC with 74 clusters fromROSAT catalogues without redshift information and 43 unpublished MACS clusters observed by XMM-Newton or Chandra. For these 117 objects, only centroid positions are available. Finally, we considered the published catalogues from XMM-Newton serendipitous cluster surveys with available redshifts, the XCS catalogue (Mehrtens et al. 2012), the 2XMMi/SDSS catalogue (Takey et al. 2011) and the XDCP catalogue (Fassbender et al. 2011). However, these catalogues mostly extend the MCXC to lower masses and only two Planck candidates were found to be associated with these new clusters.

Optical-cluster catalogues

– The identification of the Planck SZ candidates with clusters known in the optical is based on the Abell (Abell 1958) and the Zwicky (Zwicky et al. 1961) cluster catalogues. Furthermore, we have used four different catalogues of clusters based on the Sloan Digital Sky Survey (SDSS, York et al. 2000) data: (1) the MaxBCG catalogue (13 823 objects, Koester et al. 2007); (2) the GMBCG catalogue (55 424 objects, Hao et al. 2010); (3) the AMF catalogue (69 173 objects, Szabo et al. 2011); and (4) the WHL12 catalogue (132 684 objects, Wen et al. 2012). We refer the reader to Wen et al. (2012) for a comparison of the existing SDSS-based catalogues of clusters and groups. Each of the SDSS-based catalogues provides an estimated richness; we first start by homogenizing the richness estimates to that of WHL12. For each catalogue, we compute the median ratio of WHL12’s richness to that of the considered catalogue over its intersection with WHL12’s. We then renormalize the individual richness by the corresponding ratio. The correcting factors applied to the richness estimators⁹ are respectively 1.52, 1.75, and 0.74 for MaxBCG, GMBCG, and AMF, obtained from 7627, 17 245, and 1358 common clusters¹⁰. The richness is then related to the halo mass, M₅₀₀, by extending the Wen et al. (2012) richness–mass relation provided on about 40 clusters¹¹ to 444 MCXC clusters, with masses estimated from the X-ray luminosities. The data points and the best-fit scaling relation are presented in Fig. 15. The derived M₅₀₀–R_L^⋆ and L_X,200–R_L^⋆ relations are compatible with the findings of Wen et al. (2012). We find log (M₅₀₀/ 10¹⁴ M_⊙) = ( − 2.00 ± 0.17) + (1.37 ± 0.10) × log R_L^⋆. The relation presents a large intrinsic log-scatter, σ_int = 0.27 ± 0.02, hampering any accurate estimation of the cluster mass. This is further illustrated by the richest clusters with R_L^⋆> 110 having MCXC masses systematically below the best-fit M₂₀₀–R_L^⋆ relation (although within the 1σ intrinsic scatter).

SZ catalogues

– At millimetre wavelengths, we cross-check the Planck SZ catalogue with the recent ACT and SPT samples (Menanteau et al. 2010; Vanderlinde et al. 2010; Williamson et al. 2011), including the most recent data that increased the number of SZ detections and updated the redshift estimates for the clusters (Reichardt et al. 2013; Hasselfield et al. 2013). We have furthermore identified the Planck SZ detections associated with previous SZ observations of galaxy clusters from the literature. We used a compilation of SZ observations conducted with the numerous experiments developed during the last 30 years (Ryle, OVRO, BIMA, MITO, Nobeyama, SZA, APEX-SZ, AMI, Diabolo, Suzie, Ryle, AMIBA, ACBAR, etc.).

4.3. Identification with previously-known clusters

4.3.1. Identification with X-ray clusters

The Planck SZ candidates are cross-checked against previously-known X-ray clusters from the updated version of the MCXC. For a given Planck candidate-cluster we identify the closest MCXC cluster¹². The reliability of the association is assessed based on distance, D, compared to the cluster size and on the measured Y₅₀₀ and S/N values compared with the expected values (see Fig. 16). Two clouds of points stand out in the scatter plot of absolute versus relative distance, $\mathit{D}\mathit{/}{\mathit{\theta }}_{\mathrm{500}}^{{\mathit{L}}_{\mathrm{X}}}$ (Fig. 16, left panel). They correspond to two clouds in the scatter plot of the measured over expected S/N versus $\mathit{D}\mathit{/}{\mathit{\theta }}_{\mathrm{500}}^{{\mathit{L}}_{\mathrm{X}}}$ (Fig. 16, middle panel).

The association process follows three main steps. First, we provisionally assign an X-ray identification flag based on distance:

• Q_X = 3 if $\mathit{D}\hspace{0.17em}\mathit{>}\hspace{0.17em}\mathrm{2}{\mathit{\theta }}_{\mathrm{500}}^{{\mathit{L}}_{\mathrm{X}}}$ and D> 10′. Those are considered as definitively not associated with an MCXC cluster in view of Planck positional accuracy and cluster extent.

• Q_X = 1 if $\mathit{D}\hspace{0.17em}\mathit{<}\hspace{0.17em}{\mathit{\theta }}_{\mathrm{500}}^{{\mathit{L}}_{\mathrm{X}}}$ and D< 10′. Those are associated with an MCXC cluster.

• Q_X = 2 otherwise, corresponding to uncertain associations.

We then refine the classification. In the Q_X = 1 category, we identify outliers in terms of the ratio of measured to expected S/N and Y₅₀₀, taking into account the scatter and the size–flux degeneracy. Their flags are changed to Q_X = 2. In some cases, two distinct Q_X> 1 candidates are associated with the same MCXC cluster. The lowest S/N detection is flagged as Q_X = 2.

In the final step, we consolidate the status of Q_X< 3 candidates. We first re-extract the SZ signal at the X-ray position, both leaving the size free and fixing it at the X-ray value. The Y₅₀₀ obtained with the cluster and size fixed to the X-ray values are compared to the expected values, ${\mathit{Y}}_{\mathrm{500}}^{{\mathit{L}}_{\mathrm{X}}}$, in the right panel of Fig. 16. For bona fide association, we expect no major change of Y₅₀₀ and S/N, with, on average, a better agreement with the expected Y₅₀₀ value and some decrease of S/N.

• For Q_X = 1 candidates, the re-extracted Y₅₀₀ and S/N values are compared to both blind and expected values (as a function of distance, S/N, etc.) to identify potential problematic cases, e.g., important decrease of S/N or outliers in terms of measured-over-expected Y₅₀₀ ratio. We found only one such case, whose flag is changed to Q_X = 2. The identification of other candidates is considered as consolidated, with definitive flag Q_X = 1.

• We then examine the Q_X = 2 candidates. We consider the re-extracted Y₅₀₀ and S/N, but also perform a visual inspection of the SZ maps and spectra and ancillary data, including RASS and DSS images. The Q_X = 2 candidates were identified as clearly identified as multiple detections of extended clusters or duplicate detections of the same clusters by different methods that were not merged (the former are flagged as false detections, the latter are merged with the corresponding candidate in the union catalogue) or not associated (e.g., SZ sources clearly distinct from the MCXC clusters with no significant re-extracted signal at the cluster position and size).

Finally, for MCXC clusters without redshift and luminosity information, the association was only based on distance, setting D_X< 5′, and the consolidated based on visual inspection of SZ, RASS and DSS images and other ancillary information. Two cases were found to be a mis-identification. The SZ candidate was closer by chance to a faint XCS cluster, in the vicinity of the real counter-part (another MCXC cluster and an Abell cluster, respectively).

4.3.2. Identification with optical clusters

The Planck SZ candidates are associated with known clusters from optical catalogues (Abell, Zwicky, SDSS-based catalogues) on the basis of distance with a positional matching within a search radius set to 5′. The consolidation of the association was performed using the RASS information as described below, which allows us to mitigate the chance associations with poor optical galaxy groups and clusters.

SDSS-based catalogues

– We have considered the four catalogues listed in Sect. 4.2. We define a quality criterion for the association, Q_SDSS, in terms of cluster richness as a proxy of the cluster mass (see for instance Johnston et al. 2007; Rozo et al. 2009). We set the quality criterion, Q_SDSS, to 3 for low reliability (richness below 70), to 2 for good reliability (richness ranging from 70 to 110) and to 1 for high reliability (richness above 110).

The corresponding estimated masses (given the M₅₀₀–R_L^⋆ relation) are M₅₀₀> 6.5 × 10¹⁴ M_⊙ and M₅₀₀> 3.5 × 10¹⁴ M_⊙. However due to the large scatter and associated uncertainty in the mass estimate from the mass–richness relation, we consolidate the association of the Planck candidates with SDSS clusters by combining the Q_SDSS with the RASS signal at the Planck-candidate position (see Sect. 4.1.1). In practice, only associations with Q_SDSS = 1 or 2 and a S/N, measured at the Planck position in an aperture of 5′ in the RASS survey, (S/N)_RASS ≥ 1 are retained as firm identifications. We stress that our choice of richness thresholds is relatively conservative on average. Indeed, our Q_SDSS = 1 and 2 matched candidates are found with high (S/N)_RASS values as shown in Fig. 17, with mean (S/N)_RASS = 7.1 and 6.6 and median (S/N)_RASS = 5.9 and 5.4 for Q_SDSS = 1 and 2 matches, respectively.

Abell and Zwicky catalogues

– The Planck candidates are associated with Abell and Zwicky clusters on the basis of a positional matching within five arcmin. In the present case, we do not make use of any richness information in order to consolidate the association. We rather use here solely the RASS signal, (S/N)_RASS, at the SZ-candidate position. Planck-candidates associated with Abell or Zwicky clusters and with (S/N)_RASS ≥ 1 are retained as firmly identified. For associations with (S/N)_RASS< 1, we decided on a firm identification only after checking the status of the counter-part in the WISE data and performing a visual inspection of the SZ signal and of the images from ancillary data, including DSS images.

4.3.3. Identification with SZ clusters

The association with known SZ clusters was performed within a 5′ radius. A visual inspection of the ancillary data and an a posteriori check of the RASS signal at the position of the Planck candidates associated with clusters from SZ catalogues is performed. It confirms that the values of (S/N)_RASS, when the coverage is significant, are high with an average value of 5.4.

4.3.4. Identifications from NED and SIMBAD

The information provided from querying NED and SIMBAD databases is mainly redundant with cross-checks with cluster catalogues. However, it lets us avoid missing a few associations. We therefore performed a systematic query in SIMBAD and NED with an adopted search radius set to 5′. Similarly to the association with clusters in optical catalogues, the positional association is consolidated using the results of the search in RASS data. Furthermore, the Planck-candidates solely matching NED or SIMBAD entries were inspected and the identification was confirmed or discarded using the information from WISE counter-parts and the DSS images.

5. Follow-up programme for confirmation of Planck candidates

We have undertaken, since Spring 2010, an extensive follow-up programme in order to perform a cluster-by-cluster confirmation of the Planck cluster candidates and obtain a measurement of their redshifts. A total of 276 Planck candidates, selected down to S/N = 4 from intermediate versions of the Planck SZ catalogue, were observed in pursuit of their redshift measurement. We have constructed our strategy for the selection of the Planck targets primarily on the successful results of the series of follow-up observations in X-rays based on Director’s discretionary time (DDT) on the XMM-Newton observatory (Planck Collaboration IX 2011; Planck Collaboration Int. I 2012; Planck Collaboration Int. IV 2013). Snapshot observations, sufficient to detect extended X-ray emission associated with Planck clusters and to estimate redshifts from the Fe line for the brightest clusters, were conducted sampling the SZ detections down to S/N = 4. These observations allowed us to better understand the SZ signal measured by Planck and hence to refine the criteria to select targets, especially for further optical follow-up.

We have engaged numerous campaigns on optical facilities, which now constitute our main means of confirmation of Planck SZ detections. Planck candidates with low-quality DSS images or without SDSS information, or low (S/N)_RASS, were primarily sent for deeper multi-band imaging observations. They were followed-up to the depth needed for the confirmation, i.e., finding an optical counter-part, and for the determination of a photometric redshift. Candidates with galaxy concentrations in DSS or with counter-parts in SDSS, and/or with high (S/N)_RASS, were preferentially sent for spectroscopic confirmation. The priority being to confirm the clusters and to secure the largest number of robust redshifts, no systematic spectroscopic confirmation of photometric redshifts was performed for low-redshift clusters (z_phot< 0.4). For higher-redshift clusters, spectroscopic confirmation of the photometric redshifts is more crucial. As a result, we have made use of telescopes of different sizes, from 1-m to 10-m class telescopes, optimizing the selection of targets sent to the different observatories (Table 4 gives the list of the main telescopes). Telescopes of 8- and 10-m classes, e.g., GTC, GEMINI and VLT, were used to spectroscopically confirm redshifts above 0.5 for already confirmed clusters.

Our efforts to confirm the Planck cluster candidates, measure redshifts, and characterize cluster physical properties relies on ongoing follow-up of a large number of cluster candidates in the optical (ENO, RTT150, WFI), in the infrared (Spitzer¹³) and at SZ wavelengths (Arcminute Microkelvin Imager, AMI). The output of the confirmation and redshift measurements from the observing campaigns is summarized in Sect. 6.2. Companion publications, in preparation, will detail the observing campaigns and their results.

5.1. XMM-Newton observatory

The X-ray validation follow-up programme of 500 ks observations undertaken in XMM-Newton DDT is detailed in Planck Collaboration IX (2011), Planck Collaboration Int. I (2012), and Planck Collaboration Int. IV (2013). It consisted of observing 51 Planck targets and led to the confirmation of 43 Planck cluster candidates, two triple systems and four double systems. There were eight false candidates. This follow-up programme has constituted the backbone of the Planck cluster confirmation and most importantly has allowed us to better understand the SZ signal measured by Planck and thus to better master the criteria for confirmation (or pre-confirmation) of the Planck cluster candidates. By providing us with the physical properties and redshift estimates of the confirmed clusters, it has furthermore given us a first view on the physical characteristics of the newly discovered Planck clusters. Snapshot observations (around 10 ks) of the Planck candidates took place between May 2010 and October 2011. All the results from the four observing campaigns were published in Planck Collaboration IX (2011), Planck Collaboration Int. I (2012), and Planck Collaboration Int. IV (2013). Calibrated event lists were produced with v11.0 of XMM-Newton-SAS, and used to derive redshifts and global physical parameters for the confirmed clusters (Planck Collaboration IX 2011). The redshifts were estimated by fitting an absorbed redshifted thermal plasma model to the spectrum extracted within a circular region corresponding to the maximum X-ray detection significance. Most of the redshifts were confirmed using optical observations. Additional observations at VLT were conducted to confirm spectroscopically the highest redshifts¹⁴.

5.2. Optical observation in the northern hemisphere

5.2.1. ENO telescopes

In total 64 cluster candidates from Planck were observed at European Northern Observatory (ENO¹⁵) telescopes, both for imaging (at IAC80, INT and WHT) and spectroscopy (at NOT, GTC, INT and TNG), between June 2010 and January 2013¹⁶. The aims of these observations were the confirmation, photometric redshift measurement, and spectroscopic confirmation of redshifts above z = 0.3.

INT, WHT and IAC80

– The optical imaging observations were taken either with the Wide-Field Camera (WFC) on the 2.5-m Isaac Newton Telescope (INT), the auxiliary-port camera (ACAM) at the 4.2-m William-Herschel Telescope (WHT), or with CAMELOT, the optical camera at the 0.82-m telescope (IAC80). The targets were observed in the Sloan gri filters. For the majority of fields, either Sloan z or Gunn Z images are also available. Images were reduced using the publicly-available software IRAF and SExtractor (Bertin & Arnouts 1996). The data reduction included all standard steps, i.e., bias and flat field corrections, astrometric and photometric calibrations. The photometric calibration is based either on standard star observations or, if available, on data from the SDSS. Finally, all magnitudes were corrected for interstellar extinction, based on the dust maps by Schlegel et al. (1998). We obtained photometric redshifts using the BPZ code (Benítez 2000), using a prior based on SDSS data, and fitting a set of galaxy templates. The BPZ code provides the Bayesian posterior probability distribution function for the redshift of each object, which is later used in the process of cluster identification. The identification of the galaxy overdensity located near the Planck positions and the estimate of the photometric redshifts of the associated clusters were performed using a modified version of the cluster-algorithm described in Sect. 4.1.2.

GTC and TNG

– Spectroscopic observations were performed using the 10-m Gran Telescopio Canarias (GTC) telescope and the 3.6-m Telescopio Nazionale Galileo (TNG) telescope. The OSIRIS spectrograph at GTC was used in long-slit mode to observe a total of eight targets with two slit positions per candidate. We used the R500R grism and a binning 2 × 1, which provides a resolution R = 300 with a slit width 1 arcsec, and a wavelength coverage 4800–10 000 Å. We retrieved three exposures of 1200 s each. The final spectra present a S/N of about 20 in galaxies with r′ = 20 mag. We used the DOLORES multi-object spectrograph (MOS) at TNG to observe 9 candidates. The masks were designed to contain more than 30 slitlets, 1.5 arcsec width, placed within an area about 6′ × 8′ in order to cover the target field. We used the LR-B grism, which provides a dispersion of 2.7 Å/pixel, and a wavelength coverage between 4000 and 8000 Å. We carried out three acquisitions of 1800 s each and obtained spectra with S/N ≃ 15 in galaxies with r′ = 20 mag using a total integration time of 5400 s.

Nordic Optical Telescope (NOT)

– Spectroscopic redshift measurements were obtained using the Andalucia Faint Object Spectrograph and Camera (ALFOSC) at the NOT¹⁷. Most targets were observed in MOS mode, targeting typically ten to fifteen galaxies per ALFOSC field (covering 6.4′ × 6.4′, with an image scale of 0.188 arcsec/pixel). One or two unfiltered 300 s pre-imaging exposures were obtained per candidate cluster, in addition to a single 300 s exposure in each of the SDSS g-and i bands. The de-biased and flat field calibrated pre-imaging data were used to select spectroscopy targets. The final mask design¹⁸ was carved out using custom software, generating slits of fixed width 1.5 arcsec and of length typically 15 arcsec. Grism No. 5 of ALFOSC was used, covering a wavelength range 5000–10 250 Å with a resolution of about R = 400 and dispersion 3.1 Å/pixel. Redwards of 7200 Å strong fringing is present in the ALFOSC CCD. It was effectively suppressed using dither pattern alternating the placement of the spectroscopy targets between these sets of slits.

In addition to the MOS observations, spectroscopic observations in single-slit mode were conducted for some Planck candidates. For these observations, a long slit covering the entire 6.4′ length of the ALFOSC field and a width of 1.3 arcsec was employed, with the same grism and wavelength coverage as for the MOS observations. The field angle was rotated to place the long slit over multiple targets, to include the apparent BCG as well as two to three other bright cluster galaxies within the ALFOSC field.

5.2.2. RTT150

A total of 88 Planck cluster candidates were followed up with the Russian Turkish Telescope (RTT150¹⁹) from July 2011 to December 2012 within the Russian quota of observational time. In total, about 50 dark nights, provided by Kazan Federal University and Space Research Institute (IKI, Moscow), were used for these observations. Direct images and spectroscopic redshift measurements were obtained using TÜBİTAK Faint Object Spectrograph and Camera (TFOSC²⁰), similar in layout to ALFOSC at NOT (see above) and to other instruments of this series.

The TFOSC CCD detector cover a 13.3′ × 13.3′ area with 0.39 arcsec per pixel image scale. Direct images of cluster candidates were obtained in Sloan gri filters, in series of 600 s exposures with small (≈10–30 arcsec) shifts of the telescope pointing direction between the exposures. All standard CCD calibrations were applied using IRAF software, individual images in each filter were then aligned and combined. The total of 1800 s exposure time in each filter was typically obtained for each field, longer exposures were used for more distant cluster candidates. Deep multi-filter observations were obtained for all candidates, except those unambiguously detected in SDSS. With these data, galaxy clusters can be efficiently identified at redshifts up to z ≈ 1.

Galaxy clusters were identified as enhancements of surface number density of galaxies with similar colours. Cluster red sequences were then identified in the colour–magnitude diagram of galaxies near the optical centre of the identified cluster. The detected red sequence was used to identify the BCG and cluster member galaxies. Using the measured red-sequence colour photometric redshift estimates were obtained, which were initially calibrated using the data on optical photometry for galaxy clusters from the 400SD X-ray galaxy cluster survey (Burenin et al. 2007).

For spectroscopy we used the long-slit mode of the instrument with grism No. 15, which covers the 3900–9100 Å wavelength range with ≈12 Å resolution when a slit of 1.8 arcsec width is used. Galaxy redshifts were measured through the cross-correlation of obtained spectra with a template spectrum of an elliptical galaxy. Spectroscopic redshifts were typically obtained for the spectra of a few member galaxies, including the BCG, selected from their red sequence in the imaging observations. These data allow us to efficiently measure spectroscopic redshifts for clusters up to z ≈ 0.4. For the highest-redshift clusters, complementary spectroscopic observations were performed with the BTA 6-m telescope of SAO RAS using SCORPIO focal reducer and spectrometer (Afanasiev & Moiseev 2005).

5.3. Optical observation in the southern hemisphere

5.3.1. MPG/ESO 2.2-m Telescope

Optical imaging of 94 Planck cluster candidates in the southern hemisphere was performed under MPG programmes at the MPG/ESO 2.2-m telescope using the Wide-Field Imager (WFI)²¹. The WFI detector is a mosaic of 8 2k × 4k CCDs, covering a total area of 33′ × 34′ on the sky, with an image scale of 0.238 arcsec/pixel. Each field was observed in the V-, R-, and I-bands with a default exposure time of 1800 s (with five dithered sub-exposures) per passband. The basic data calibration, including de-biasing and flat-field frame calibration, followed standard techniques. The individual exposures were re-registered and WCS calibrated using the USNO-B1 catalogue as an astrometric reference before being stacked into a combined frame for each filter, covering the entire WFI field. Photometric redshifts of the observed clusters were then determined from an algorithm that searches for a spatial galaxy overdensity located near the position of the SZ cluster candidate that also corresponds to an overdensity in V − R versus R − I colour–colour space. The median colour of galaxies located in this overdensity was then compared to predicted colours of early-type galaxies at different redshifts by convolving a redshifted elliptical galaxy spectral energy distribution template with the combined filter+telescope+detector response function.

5.3.2. New Technology Telescope (NTT)

Observations²² were conducted at the 3.5-m NTT at the ESO observatory at La Silla to measure spectroscopic redshifts of 33 Planck clusters with the EFOSC2 instrument in the MOS mode. A clear BCG was identified in the clusters in pre-imaging data, and besides the BCG a redshift was measured for at least one other member of the cluster. In the following a brief outline of the observations and the data reduction are given (see Chon & Böhringer 2012, for details).

Each field of the Planck target candidates was optically imaged in Gunn r band for target selection and mask making. The imaging resolution is 0.12′′ × 0.12′′, and the field of view is 4.1′ × 4.1′ for both imaging and spectroscopic observations. When necessary, the field was rotated to optimize target selection. We used the grism that covers the wavelength range between 4085 Å and 7520 Å, with 1.68 Å per pixel at resolution 13.65 Å per arcsec. We typically applied 10 to 15 slitlets per field with a fixed width of 1.5 arcsec for the MOS and of 2.0 arcsec for the long-slit observations. Including at least three bright objects, preferably stars, to orient the field, the slitlets were allocated to the candidate member galaxies. The exposure times for the clusters range from 3600 s to 10 800 s.

The data were reduced with the standard reduction pipeline of IRAF. The redshifts from the emission lines were determined separately after correlation with the passive galaxy templates. We use the rvsao package, which applies the cross-correlation technique to the input templates of galaxy spectra to measure the object redshift. The REFLEX templates were used for this analysis, which include 17 galaxy and stellar templates. We confirmed a spectroscopic cluster detection if at least three galaxies have their R-value greater than 5, and lie within ± 3000 km s^-1 of the mean velocity of the cluster members. We then took the median of those galaxy redshifts as the cluster redshift. For the long-slit observations, the cluster was confirmed with the redshift of the BCG and another galaxy at similar redshift within the aforementioned criteria.

5.4. Observations in the SZ domain with AMI

An ensemble of 60 Planck blind SZ candidates, spanning a range of S/N between 4 and 9 and meeting the Arcminute Microkelvin Imager (AMI) observability criteria, was observed with AMI. The goal of this programme was to confirm Planck cluster candidates through higher-resolution SZ measurements with AMI and to refine the position of confirmed clusters in order to optimize the subsequent optical follow-up observations aiming at redshift measurement. AMI comprises of two arrays: the Small Array (SA); and the Large Array (LA). Further details of the instrument are given in AMI Consortium et al. (2008). Observations carried out with the SA provide information that is well coupled to the angular scales of the SZ effect in clusters, whereas snapshot observations obtained with the LA provide information on the discrete radio-source environment. The latter allowed us to detect the presence of nearby, bright radio sources, helping in further selecting the targets for observation with the SA. Details of the AMI data reduction pipeline and mapping are described in Planck and AMI Collaborations (2013).

6. Results of the validation and follow-up

The external validation allows us to identify Planck SZ detections with previously-known clusters and to assemble crucial information on the identified clusters such as their redshifts. The validation steps corresponding to the association with known clusters were performed following a chosen hierarchy: X-ray clusters from the updated MCXC meta-catalogue; then optical clusters from Abell and Zwicky catalogues; then optical clusters from the SDSS-based catalogues; followed by SZ clusters from SPT and ACT samples; and finally clusters from NED and SIMBAD queries. The first identifiers of the Planck SZ detections given in Table B.1 reflect the validation hierarchy.

In the following, we present the results of the external validation process and of the follow-up campaigns for confirmation of Planck candidates and measurement of their redshifts (see Table 5 and Fig. 18). We also present the confirmation from SDSS galaxy catalogues and from X-ray archival data. We further discuss the unconfirmed candidate new clusters detected by Planck, which we classify into three categories of different reliability.

6.1. Planck clusters associated with known clusters

A total of 683 out of 1227 SZ detections in the Planck catalogue, i.e., 55.7%, are associated with previously-known clusters from X-ray, optical, or SZ catalogues, or with clusters found in the NED or SIMBAD databases. We give the number of clusters identified in each category and we discuss notable cases of known clusters that are not included in the Planck SZ catalogue.

6.1.1. Identification with known X-ray clusters

A total of 472 Planck SZ-candidates are identified with known X-ray clusters from the MCXC meta-catalogue, which represents 38.5% of the Planck SZ detections and 69.1% of the identifications with previously-known clusters. These identifications of course account for many Abell clusters in the RASS-based catalogues of X-ray clusters.

Using the cluster properties reported in the MCXC and the Planck noise maps at the cluster positions, we computed the expected SZ signal and the expected S/N for a measurement with Planck. We have compared the number of detected clusters in the Planck catalogue with S/N ≥ 4.5 to the number MCXC clusters at an expected significance of 4.5. Only 68 clusters expected to be detected at S/N> 4.5 are not included in the Planck catalogue, including 16 with predicted S/N between 4 and 4.5. Of the 52 clusters with expected S/N ≥ 4.5, only 41 are outside the masked regions and could thus be in the PSZ catalogue. Our computation of the expected SZ signal and S/N were based on scaling relations for X-ray-selected clusters, not accounting for the dispersion in the relations. We therefore focus on the non-detected MCXC clusters that significantly depart from the expected S/N value, namely by more than 5σ. A total of 13 clusters are in this category. The two objects RXC J2251.7-3206 and RXC J0117.8-5455 show emission in high-resolution Chandra imaging that is point-like rather than extended and are likely not clusters of galaxies (Mantz et al. 2010; Magliocchetti & Brüggen 2007). Of the other eleven missing MCXC clusters, some present AGN contamination. This is the case for RXC J1326.2+1230 (Magliocchetti & Brüggen 2007), RX J1532.9+3021 (Hlavacek-Larrondo et al. 2012), RXC J1958.2-3011, RXC J2251.7-3206, and RXC J0117.8-5455 (Magliocchetti & Brüggen 2007), Abell 689 (Giles et al. 2012), ZwCl 2089 (Rawle et al. 2012), PKS 0943-76 (Abdo et al. 2010), and Abell 2318 (Crawford et al. 1999). In these cases, the presence of the AGN affects the X-ray luminosity measure leading to an overprediction of the SZ signal. Some exhibit significant radio contamination, e.g., RXC J1253.6-3931 (Plagge et al. 2010) and RXC J1958.2-3011 (Magliocchetti & Brüggen 2007), which hampers the SZ detection. Cool-core clusters for which the X-ray luminosity is boosted due to the central density peak have an over-estimated expected SZ signal. This is the case for RXC J0425.8-0833 (Hudson et al. 2010), ZwCl 2701 (Rawle et al. 2012), Abell 1361 (Rafferty et al. 2008), and RBS 0540 (Eckert et al. 2011; Belsole et al. 2005). Other “missing” clusters are CIZA clusters: RXC J0643.4+4214, RXC J1925.3+3705, RXC J2042.1+2426 and RXC J0640.1-1253, REFLEX cluster RXC J2149.9-1859, APMCC 699, Abell 3995, Abell 2064 and RBS 171.

In addition to the clusters discussed above which are not included in the catalogue due to contamination by AGN or presence of cool-cores etc., we note that some notable nearby extended clusters are also not included in the Planck SZ catalogue. Indeed, the detection methods used to detect the SZ effect are not optimized for the detection of sources with scale radius θ₅₀₀ in excess of 30′. Of the 25 clusters in this category (with z< 0.03) in the MCXC meta-catalogue, six are included in the Planck catalogue. The remaining 19 fall into the masked areas (seven out of 19, among which Perseus and Abell 1060 lie in the PS mask (Fig. 19, first two panels), and Ophiuchus and 3C 129.1 lie in the Galactic mask (Fig. 19, second two panels) and/or have a S/N below the PSZ catalogue threshold S/N = 4.5. This is the case of Virgo cluster (Fig. 19, lowest panel), which is detected in the Planck survey but with a S/N at its position of about 3.9. Virgo’s extension on the sky (θ₅₀₀ = 168 arcmin) further hampers its blind detection.

We show in Fig. 19 the reconstructed SZ signal from the MILCA algorithm (Hurier et al. 2013) for five of the “missing” extended clusters. These clusters, despite not being part of the Planck catalogue of SZ sources, are well detected in the Planck survey. They all are included in the thermal SZ map constructed from the Planck channel maps and presented in Planck Collaboration XXI (2014).

6.1.2. Identification with known optical clusters

A total of 182 Planck SZ detections are identified exclusively with optical clusters from Abell and Zwicky catalogues, and from the SDSS-based published catalogues, i.e., 26.6% of the known clusters in the Planck catalogue.

The Planck SZ candidates at S/N ≥ 4.5 have 111 exclusive associations with Abell or Zwicky clusters, i.e., with clusters not in any of the catalogues compiled in the MCXC meta-catalogue. In addition to these associations, 72 Planck detections are solely identified with clusters from the SDSS-based catalogues. These are either rich and massive systems (R_L^⋆ greater than 110, Q_SDSS = 1 clusters) or moderately low-richness systems (Q_SDSS = 2 clusters, exhibiting hot gas as indicated by their S/N value in the RASS survey). However, not all the rich Q_SDSS = 1 clusters in SDSS-based catalogues are found in the Planck catalogue. A total of 213 Q_SDSS = 1 clusters from all four SDSS-based catalogues (201 outside the Planck union PS and Galactic mask) are not included in the Planck catalogue.

We explore why these rich clusters are not detected blindly by the SZ-finder algorithms. We first compare the richness-based masses against the X-ray luminosity-based masses of 26 of these “missing” clusters found in the MCXC meta-catalogue. We find a median ratio of 2.6 ± 1.2 for the richness-to-X-ray based masses, indicating that the richness-based masses seem to be systematically overestimated. Unlike the X-ray clusters, we thus cannot compute a reliable estimate of the expected S/N value for SZ detection of these optical clusters. We therefore directly search for the SZ signal at the positions of the 201 “missing” SDSS-clusters and found that all of them have S/N values below the Planck threshold, with a mean S/N of 1.6, except for three clusters. Two of these three “missing” SDSS-clusters have their S/N value from the extraction at the cluster position slightly higher than 4.5. The increase in S/N value is due to the difference in estimated background noise when centring the extraction at the cluster position as opposed to the blind detection. The third missing rich cluster is affected by contamination from CMB anisotropy, which results in a bad estimate of its size and consequently of its SZ signal.

6.1.3. Identification with known SZ clusters

The majority of the SZ clusters, from SPT or ACT, used in the validation process are low-mass systems (${\mathit{M}}_{\mathrm{500}}^{\mathrm{median}}$ around 2.3 × 10¹⁴ M_⊙). Planck is particularly sensitive to massive rich clusters and thus only a total of 56 of these clusters match Planck SZ detections, out of which 16 candidates are exclusively associated with SZ clusters²³ from ACT or SPT. Nine more ACT and SPT clusters are associated with Planck SZ detections between S/N = 4 and 4.5. We have searched for the SZ signal in the Planck data at the position of the remaining non-observed ACT/SPT clusters by extracting the SZ signal at their positions. We found that all had S/N values lower than 4.

We have also checked the redundancy of SZ detections within Planck by comparing the ESZ sample, constructed from 10 months of survey with a cut at Galactic latitudes of ±14°, with the present Planck catalogue. Of the 189 high significance ((S/N)_ESZ ≥ 6 ESZ detections, 184 ESZ confirmed clusters are included the present Planck catalogue within a distance of 5′ from their ESZ position. The mean separation between the ESZ and present positions is of order 1.35′, within Planck’s positional accuracy. Their S/N values were increased by a factor 1.17 on average with respect to their (S/N)_ESZ, (Fig. 20) and only four out of six of the ESZ clusters have new S/N values significantly lower than ESZ S/N threshold (S/N)_ESZ = 6. They are displayed as stars in Fig. 20. Four ESZ clusters are not included the present Planck catalogue, they fall in, or nearby, the PS mask used for the pre-processing of the channel maps prior to running the detection algorithms. Such a mask was not utilized for the construction of ESZ sample. We choose not to a posteriori include these four “missing” ESZ clusters in the present Planck SZ catalogue.

6.1.4. Identification with clusters from NED or SIMBAD

As expected only a small number of clusters are identified from querying the databases, supplying identifiers for thirteen SZ Planck detections. This is because the information in NED and SIMBAD is redundant with that in the X-ray, optical, or SZ catalogues used for the external validation. The thirteen clusters found solely from querying the databases are found in the RASS survey but not in dedicated cluster catalogues, and thus not included in the MCXC; they are found in serendipitous Chandra surveys, or they are part of miscellaneous cluster catalogues.

6.2. Newly-discovered Planck clusters and candidates

Among the 544 Planck SZ sources, we distinguish two categories: (1) confirmed clusters, i.e., those that have been confirmed by the follow-up programmes of the Planck collaboration²⁴ or using the SDSS galaxy catalogues, plus also add eight confirmations from X-ray archival data (one of those, PSZ1 G292.00-43.64, coincides with the XCLASS cluster candidate, J023303.4-711630 (Clerc et al. 2012)); (2) Candidate clusters with different levels of reliability, namely, class1 cluster candidates, that fulfil high-quality criteria for the SZ detection and for the associations and/or counterparts in ancillary data, class2 candidate clusters, i.e., those that fulfil, on average, good-quality criteria, and class3, low-reliability cluster candidates.

Confirmation from Planck collaboration follow-up programmes.

At S/N ≥ 4.5, a total of 233 Planck SZ detections were followed up in X-rays, optical, and SZ at the different facilities listed previously, with some observations targeted to the measurement of spectroscopic redshifts for already known clusters. In total 157 Planck SZ detections with S/N ≥ 4.5 were confirmed as new clusters. Some of the Planck-confirmed clusters were also reported in recent cluster catalogues in the optical, e.g., Wen et al. (2012) or in the SZ e.g., Reichardt et al. (2013).

The analysis of the observations of Planck sources by AMI yielded ten sources with strong Bayesian evidences that have clearly visible decrements and were considered as confirmed, including the confirmation of three associations with optical clusters.

For the candidates confirmed by XMM-Newton and by optical telescopes, redshifts from Fe lines and from photometric or spectroscopic data are available. The validation of Planck cluster candidates with XMM-Newton has shown its particular efficiency in confirming SZ candidates due both to the high sensitivity of XMM-Newton, allowing Planck clusters to be detected up to the highest redshifts (Planck Collaboration XXVI 2011), and the tight relation between X-ray and SZ properties. The detection of extended XMM-Newton emission and a comparison between the X-ray and SZ flux permits an unambiguous confirmation of the candidates. By contrast, confirmation in the optical may be hampered by the Planck positional accuracy and by the scatter between the optical observables and the SZ signal, which increase the chance of false associations. The XMM-Newton follow-up programme yielded 51 bona fide newly-discovered clusters, including four double systems and two triple systems. There were eight false candidates. Thirty-two of the 51 individual clusters have high-quality redshift measurements from the Fe line. The relation between the X-ray and SZ properties was used to further constrain the redshift of the other clusters; most of these redshifts were confirmed clusters using optical observations. Out of a total of 37 single clusters confirmed by XMM-Newton, 34 are reported in the Planck catalogue of SZ sources at S/N ≥ 4.5. Additionally four double systems are included in the present PSZ catalogue and were also confirmed by XMM-Newton.

The follow-up observations conducted with optical telescopes lead to the confirmation and to the measurement of spectroscopic or photometric redshifts (companion publications, in preparation, will present the detailed analysis and results from these follow-up). In the northern hemisphere, 26 spectroscopic redshifts for Planck clusters detected at S/N ≥ 4.5 and observed at the RTT150 are reported, to date, in the PSZ catalogue. A dozen additional spectroscopic redshifts were measured for known clusters. Confirmation of 21 Planck SZ clusters detected above 4.5 were obtained with the ENO facilities (at INT, GTC and NOT), and robust redshift measurements were obtained for 19 of them, including 13 spectroscopic redshifts. In the southern hemisphere, WFI observations provided photometric redshifts for 54 clusters included in the Planck catalogue at S/N ≥ 4.5, while 19 spectroscopic redshifts obtained with the NTT-EFOCS2 instrument are reported in the Planck catalogue.

Confirmation from SDSS galaxy catalogues.

The firm confirmation of the candidates was done through the follow-up observations for confirmation and measurement of their redshift as detailed above. However in the case of the Planck candidates falling in the SDSS footprint we also used the SDSS galaxy catalogues to search, as presented in Sect. 4.1.2, for galaxy overdensities associated with Planck SZ detections. This provides us with an estimate of the photometric redshifts, and in some cases we could retrieve spectroscopic redshifts for the BCG as well.

In this process, the major uncertainty in the associations of Planck SZ detections with galaxy overdensities is due to chance associations with low-richness systems or associations with diffuse concentrations of galaxies in the SDSS data. The XMM-Newton confirmation programmes (see Planck Collaboration Int. IV 2013 for discussion) showed that Planck candidates with SDSS counterparts were confirmed including PLCK G193.3−46.1 at z ≃ 0.6. However, the X-ray analysis of the Planck detections with SDSS counterparts illustrated the difficulty in distinguishing between associations of Planck SZ signals with massive clusters and with pre-virialized structures. In particular, in the case of extended filamentary structures or dynamically perturbed sources, an offset between the BCG position and the concentration barycentre is noted.

We considered the Planck SZ candidates with counterparts in the SDSS data taking into account diagnostics such as the richness/mass estimates as well as the offsets between the SZ, the BCG and the barycentre positions. We further used the outputs of the search in WISE and in RASS data, and the associated images, in order to assess the significance of the galaxy overdensity in SDSS at the position of the Planck candidates. For the Planck SZ detections where both ancillary data and SDSS barycentre/BCG positions agreed, we set that they are confirmed. We found a total of 13 such associations for which we report the photometric or the spectroscopic redshifts. It is worth noting that firm confirmation of these associations is needed and needs to be performed using either optical spectroscopic observations or X-ray observations of the Planck SZ detections. In the cases where the offsets between barycentre and BCG position output by the search in SDSS data were too large, and/or when other ancillary information was unable to discriminate between reliable or chance associations, we have chosen to keep the status of candidate for the Planck SZ detection. These cases sometimes also coincide with association of Planck detections with clusters from the SDSS cluster catalogues, with a quality flag Q_SDSS = 0, or with confusion in the association, i.e., with positions not in agreement between counterpart and published SDSS clusters. We provide a note for all these cases in order to indicate that an overdensity in SDSS data was found.

Candidate new clusters.

The remaining 366 Planck SZ sources, not identified with previously known cluster nor confirmed by follow-up observation or ancillary data, are distributed over the whole sky (Fig. 21) and are yet to be firmly confirmed by multi-wavelength follow-up observations. They are characterized by an ensemble of quality flags defined in Sects. 4.1.1, 4.1.2, and 4.1.3 based on the systematic searches for counterparts in the public surveys during the external validation process. We further define an empirical Planck-internal quality flag Q^SZ. It assesses the reliability of the SZ detection itself from three independent visual inspections of the nine Planck frequency maps, of frequency maps cleaned from Galactic emission and CMB, and of reconstructed y-maps or y-maps produced from component separation methods (e.g., Hurier et al. 2013; Remazeilles et al. 2011). Moreover, we visualize the SZ spectra from the SZ-finder algorithms and from aperture photometry measurements at the candidate positions. Finally we correlate, at the position of the Planck SZ candidates and within an area of 10′ radius, the y-map to the 857 GHz channel map, as a tracer of the dust emission, and to the Planck mono-frequency CO map at 217 GHz (Planck Collaboration XIII 2014). The qualitative flag Q^SZ combines all this information into three values 1 to 3 from highest to lowest reliability with the following criteria:

• Q^SZ = 1, i.e., high reliability: (i) Clear compact SZ source in the SZ maps; (ii) significant measurements of the SZ decrement below 217 GHz and good or reasonable detection at 353 GHz; (iii) no correlation with dust nor CO emission and no rise of the 545 and 857 GHz fluxes on the thermal SZ spectrum.

• Q^SZ = 2, i.e., good reliability: (i) visible SZ detection in the SZ map or significant detection of the SZ signal below 217 GHz; (ii) contamination causing rise of the 545 GHz and possibly 857 GHz flux on the SZ spectrum without a strong correlation with dust and CO signals.

• Q^SZ = 3, i.e., low reliability: (i) weak SZ signal in the y-maps and/or noisy SZ maps; (ii) weak or no SZ signal in the cleaned frequency maps (iii) strong correlation (≥80%) with dust and CO emission contamination with rising fluxes on the SZ spectrum at high frequencies, 353 GHz and above.

We combine the qualitative SZ quality flag with the information from the search in the all-sky surveys, RASS and WISE, for counterparts of Planck candidates in order to assess the overall reliability of the cluster candidates. We thus distinguish three classes of candidates:

• class1 candidates. Highly-reliable candidates or pre-confirmedclusters: these are the Planck SZ detections thathave a high probability of being associated with bona fide clustersand need to fulfil high-quality criteria for SZ, RASS, and WISEdetections. We retain in this category Planck SZdetections with high or good SZ quality flags(Q^SZ = 1 or 2) and with a RASS-BSC source (not coinciding with stars) or with (S/N)_RASS ≥ 2, i.e., SZ detections with quality flag Q_RASS = 1. The class1 candidates furthermore have to fulfil a condition of high or good probability (≥80%) of being associated with an overdensity of galaxies in the WISE survey. We find 54 class1 Planck candidates ranging from S/N of 4.5 to 6.3, with a median S/N of 4.8. The majority of them are detected by two methods and 25.9% of them are detected only by one method. They are distributed as 26 and 28 Q^SZ = 1 and 2 candidates, respectively. These candidates show significant X-ray emissions with a median (S/N)_RASS ≃ 3.7 and a mean of 4.2.

• class2 candidates. Reliable cluster candidates: they represent 170 Planck SZ detections that show good or high quality criteria either in SZ or in RASS or in WISE without fulfilling all of them at once. Amongst them 61 have Q^SZ = 1 and 109 have Q^SZ = 2.

• class3 candidates. Low-reliability cluster candidates: these Planck SZ detections are the poor-quality, Q^SZ = 3, detections. They can also be associated with good quality, Q^SZ = 2, detections for which there are no good indications of the presence of an X-ray counterpart ((S/N)_RASS< 0.5 and high probability of false association with FSC sources >2.5%) or a counterpart in the WISE survey (probability of association <70%). This class of candidates contains 142 Planck SZ detections with 27 and 115 SZ detection of quality Q^SZ = 2 and 3, respectively.

It is worth noting that this definition of the class3 Planck candidates is dominated by the assessment of the SZ quality complemented by information from ancillary data. In doing so we assemble in this category of candidates the SZ detections that are either false or very low quality due to contamination. Moreover, according to the statistical characterization from simulations, about 200 false detections are expected. The number of false detections could be smaller since the simulations do not reproduce the entire validation procedure, in particular omitting the cleaning from obvious false detections. Figure 22 suggests that the class3 candidates are likely to be dominated by false detections. Therefore, we would like to warn against dismissing entire class3 of the catalogue as populated with false detections as some class3 candidates may be real clusters. For this reason, we choose not to remove these detections from the PSZ catalogue but rather flag them as low-reliability candidates. Careful follow-up programmes are needed in order to separate real clusters of galaxies from false detections among the class2 and class3 objects.

In order to illustrate our classification defined in terms of reliability, we stack the signal in patches of 2.51° across, centred at the position of the Planck clusters and candidates in the nine channel maps of Planck, removing a mean signal estimated in the outer regions where no SZ signal is expected (see Fig. 22 with the rows arranged from 30 GHz, upper row, to 857 GHz, lower row). The stacked and smoothed images are displayed for the Planck SZ detections identified with known clusters, class1, class2 and class3 candidates, Fig. 22 from left to right column. We clearly see the significant detection of both the decrement and increment of the 683 Planck clusters and of the Planck candidates of class1 and class2. For the Planck SZ detections associated with bona fide clusters the increment is clearly seen at 353 and 545 GHz and is detected at 857 GHz. The smaller sample of the class1 highly reliable candidates shows, in addition to the decrement at low frequency, a good detection of the increment at 353 GHz. The significance of the increment at 545 GHz is marginal and no signal is seen at 857 GHz. The case of the class2 candidates (good reliability) shows that we now have lower-quality SZ detections (62% of the class2 candidates have a good but not high SZ quality flag). This is illustrated by the fact that an excess emission is detected at 217 GHz, most likely due to contamination by IR sources, and both at 545 and 857 GHz where emission from dust is dominating. As for the stacked signal of the class3 sample of low-reliability candidates, it does not show any significant SZ detection across frequencies, as compared to the sample of Planck detections identified with known clusters (Fig. 22, right column). This confirms on statistical grounds the definition of the sample dominated by definition by the low-quality SZ, Q^SZ = 3, detections representing 84% of the detections in this class. Not surprisingly, the stacked signal of the class3 candidates shows a large amount of contamination across all Planck frequencies. The low-frequency signal is dominated by radio contamination, and/or CO emission at 100 GHz, while the high-frequency signal is contaminated by emission from dust or extragalactic point sources. A more quantitative analysis is presented in Sect. 7.1.

6.3. Summary of the external validation and redshift assembly

The Planck catalogue of SZ sources comprises a total of 861 identified or confirmed clusters with only nine percent of them being detected by one SZ-finder algorithm. We summarize in Table 5 and Fig. 18 the results of the cluster identification. Figure 23 illustrates the status of the Planck SZ detections. In particular, 70.2% of the Planck SZ detections with S/N ≥ 4.5 have so far been associated with clusters. The fraction increases to about 73% at S/N = 6.

We have assembled, at the date of submission, a total of 813 redshifts for the 861 identified or confirmed Planck clusters, which we provide together with the published Planck catalogue. Their distribution is shown in Fig. 24. In the process of the redshift assembly that is summarized below, especially for the already known clusters, we have favoured homogeneity for the sources of redshift rather than a cluster-by-cluster assembly of the most accurate z measure. A large fraction of the redshifts, 456 of them, shown as the dashed green histogram in Fig. 24 correspond to the spectroscopic redshifts quoted in the updated MCXC meta-catalogue (Piffaretti et al. 2011). They are associated with the Planck clusters identified with known X-ray clusters and they are denoted Planck-MCXC. For the Planck-MCXC clusters without reported redshifts from the MCXC, we have complemented the information with the available redshifts from NED and SIMBAD. We have further quoted when available, mainly for the MACS clusters, the estimated photometric redshifts from SDSS cluster catalogue of Wen et al. (2012). At the end only two Planck detections identified with MCXC clusters remain without redshifts. The redshift distribution of the Planck clusters identified with MCXC clusters mostly reflects that of the REFLEX/NORAS catalogues at low and moderate redshifts and the MACS clusters at higher redshifts.

For the Planck detections exclusively identified with Abell or Zwicky clusters, we choose to report the redshifts published in the NED and SIMBAD data bases rather than those quoted in the native catalogues. As for the Planck detections identified with clusters from the SDSS-based catalogues, we choose to favour homogeneity by reporting whenever possible the Wen et al. (2012) redshifts. Furthermore, we favour when available spectroscopic redshifts over photometric ones. The Planck detections exclusively associated with ACT or SPT clusters have published redshifts (Sifón et al. 2013; Hasselfield et al. 2013; Reichardt et al. 2013). We select in priority the spectroscopic ones when available. If not, we quote the photometric redshifts.

Finally, the follow-up observations for confirmation of Planck detections started in 2010 and are still ongoing. As mentioned earlier our priority was to assemble the largest possible number of confirmations and redshifts. Therefore, we did not systematically confirm the photometric redshift estimates spectroscopically. We report the obtained redshifts when available. In some cases, the new Planck clusters were confirmed from imaging or pre-imaging observations and the analysis is still ongoing. The spectroscopic redshifts will be updated when available. Spectroscopic redshifts for some known clusters will also be updated. A dozen Planck clusters were confirmed by a search in the SDSS galaxy catalogues. For these clusters, only a photometric redshift estimated by the cluster-finder algorithm of Fromenteau et al. (in prep.) is available and is reported.

We show in Fig. 24 the distribution of redshifts of the Planck clusters. The mean redshift of the sample is 0.25 and its median is 0.22. One third of the Planck clusters with measured redshifts lie above z = 0.3. The new Planck clusters probe higher redshifts and represent 40% of the z ≥ 0.3 clusters. Their mean redshift is 0.38 and the median is z = 0.35. At even higher redshifts, z ≥ 0.5, the Planck catalogue contains 65 clusters including Planck SZ clusters identified with WHL12’s clusters (Wen et al. 2012), or with clusters from ACT and SPT, or with X-ray clusters. The Planck detections in this range of redshifts, 29 Planck new clusters, almost double the number of high redshift clusters.

The Planck SZ catalogue has been followed up by the Planck collaboration using different facilities and only a small fraction of the Planck candidates were observed to date. A systematic follow-up effort for the confirmation of the remaining cluster candidates will likely reveal clusters at redshifts above 0.3. As a matter of fact, very few new clusters were found below z = 0.2 (see Fig. 24). Such an observational programme is challenging and will most likely be undertaken by the Planck collaboration and by the community. It will increase further the value of the Planck SZ catalogue as the first all-sky SZ-selected catalogue.

7. Physical properties of Planck SZ clusters

The first goal of the external validation process based on the ancillary multi-wavelength data is to assess the status of the Planck SZ detections in terms of known clusters, brand new clusters or cluster candidates. The wealth of information assembled and used during this process also allows us to explore the properties of the Planck SZ clusters and candidates. We present in the following some of these properties, namely the contamination levels of the Planck SZ detections, a refined measurement of the Compton Y parameter for the Planck clusters identified with X-ray clusters from the MCXC, an SZ-mass estimate based on a new proxy for all the Planck clusters with measured redshifts, and an estimate of the X-ray flux from the RASS data for the Planck SZ detections not included in the X-ray catalogues. This additional information associated with the Planck clusters and candidates derived from the validation process is summarized in the form of an ensemble of outputs given in Table C.1.

We further present an updated and extended study of the SZ versus X-ray scaling relation, confirming at higher precision the strong agreement between the SZ and X-ray measurements (within R₅₀₀) of the intra-cluster gas properties found by Planck Collaboration XI (2011).

7.1. Point-source contamination

Galactic and extragalactic sources, emitting in the radio or infrared domain, are known to lie in galaxy clusters and hence are a possible source of contamination for the SZ measurement (e.g., Rubiño-Martín & Sunyaev 2003; Aghanim et al. 2005; Lin et al. 2009). We address the possible contamination of the SZ flux by bright radio sources that may affect the measured signal in the direction of some of the Planck SZ detections. In order to do so, we searched for known radio sources in the vicinity of the Planck cluster candidates. In particular, we use the NVSS 1.4 GHz survey (Condon et al. 1998) and SUMMS 0.85 GHz survey (Bock et al. 1999) to identify bright radio sources within 7′ of the Planck cluster or candidate position. This search radius corresponds to the Planck resolution at 143 GHz. We assumed a spectral index α = − 0.5 for these sources to extrapolate their flux to the Planck frequencies. Most bright sources in NVSS and SUMSS have steeper spectral indexes (−0.6 or −0.7), so the value α = − 0.5 provides us with an upper limit in most cases. After convolving the radio sources by Planck’s beam, we estimate the maximum amplitude in units of μK within 5′ of the Planck position. We report only those cases where this amplitude is above 5 μK in the 143 GHz channel and could thus contaminate the SZ signal. Below this value, the emission from radio sources can be considered negligible.

We find that a total of 274 Planck clusters and candidates, i.e., 22% of the SZ detections, are affected by such emission from bright radio sources. These clusters or candidates are identified in the PSZ catalogue and a specific note is provided. We find that the fraction of contaminated Planck SZ clusters identified with known X-ray, optical, or SZ clusters is also 22%. The Planck candidate-clusters of class1 and class2 are less contaminated by bright radio sources; only a fraction of 15% and 17% for class1 and 2, respectively. This is due to the definition of our quality criteria for SZ detection, which results in less contamination for the high and good reliability candidates.

Another approach used to assess the contamination is based on the stacking analysis of the Planck clusters and candidates described in Sect. 6.2. This analysis is performed on the sample of Planck clusters identified with known clusters and on the sample of low-reliability class3 Planck candidates. To do so we fit a GNFW pressure profile to the signal at 100 GHz and 143 GHz and we subtract the associated SZ signal from the stacked maps. The residual signal is then compared with a toy model for point sources (${\mathit{F}}_{\mathit{\nu }}\mathrm{=}{\mathit{S}}_{\mathrm{30}}^{\mathrm{rad}}\mathrm{(}\mathit{\nu }\mathit{/}\mathrm{30}\hspace{0.17em}\mathrm{GHz}{\mathrm{)}}^{{\mathit{\alpha }}_{\mathrm{rad}}}$ for radio sources) and (${\mathit{F}}_{\mathit{\nu }}\mathrm{=}{\mathit{S}}_{\mathrm{857}}^{\mathrm{IR}}\mathrm{(}\mathit{\nu }\mathit{/}\mathrm{857}\hspace{0.17em}\mathrm{GHz}{\mathrm{)}}^{{\mathit{\alpha }}_{\mathrm{IR}}}$ for IR point sources). Note that the residual signal at high frequencies is a combination of possible IR sources and IR emission from Galactic dust; the latter is not explicitly modelled in the present analysis. The PS toy models are convolved by the beam at each frequency and the signal is measured at a fixed aperture set to the FWHM of the 143 GHz channel. The average signal within this aperture is estimated for each channel before (Fig. 25, upper panel) and after (Fig. 25, lower panel) removal of the SZ signal. The black filled circles are for Planck SZ sources associated with known clusters and the red filled triangles stand for class3 candidates. The average signal from the PS models is shown in Fig. 25 as solid (IR sources) and dashed (radio sources) lines. Red and black are for class3 and bona fide clusters, respectively. The error bars correspond to the fluctuation of the background outside the cluster region. For the sample of class3 candidates no SZ-signal removal was applied, since no significant detection is seen at 100 GHz or 143 GHz.

We find that the residual signal (after SZ subtraction) in the sample of known Planck clusters is compatible with the emission from radio sources at low frequencies with $\mathrm{\left(}{\mathit{S}}_{\mathrm{30}}^{\mathrm{rad}}\mathit{,}{\mathit{\alpha }}_{\mathrm{rad}}\mathrm{\right)}\mathrm{=}\mathrm{(}\mathrm{14.6}\hspace{0.17em}\mathrm{mJy}\mathit{,}\mathrm{-}\mathrm{1}\mathrm{)}$ for the known clusters. It is also compatible with IR emission at high frequencies with a spectral index α_IR = 2.5, in agreement with the results of Planck Collaboration Int. VII (2013) and with ${\mathit{S}}_{\mathrm{857}}^{\mathrm{IR}}\mathrm{=}\mathrm{0.117}\hspace{0.17em}$Jy. For class3, where no SZ signal is subtracted, it is the full signal that is compatible with the IR emission at high frequencies, with $\mathrm{\left(}{\mathit{S}}_{\mathrm{857}}^{\mathrm{IR}}\mathit{,}{\mathit{\alpha }}_{\mathrm{IR}}\mathrm{\right)}\mathrm{=}\mathrm{(}\mathrm{43.9}\hspace{0.17em}\mathrm{Jy}\mathit{,}\mathrm{2.5}\mathrm{)}$, and with radio emission from point sources with $\mathrm{\left(}{\mathit{S}}_{\mathrm{30}}^{\mathrm{rad}}\mathit{,}{\mathit{\alpha }}_{\mathrm{rad}}\mathrm{\right)}\mathrm{=}\mathrm{(}\mathrm{117.1}\hspace{0.17em}\mathrm{mJy}\mathit{,}\mathrm{-}\mathrm{0.8}\mathrm{)}$.

7.2. Refined measurement of Y

While the true Y₅₀₀ is expected to be a low-scatter mass proxy, this is not the case for the blind Y₅₀₀. Without a cluster-size estimate, Y₅₀₀ cannot be accurately measured. Moreover, the blind SZ flux is biased high on average, because the size is over-estimated on average. This effect is amplified by the non-linear nature of the size–flux degeneracy, with a larger effect of size over-estimation than size under-estimation. This behaviour, first identified and discussed in Planck Collaboration VIII (2011) and Planck and AMI Collaborations (2013), hampers the direct use of the blind SZ fluxes as a mass proxy. As shown in Planck Collaboration VIII (2011), this degeneracy calls for a refined measurement of the SZ signal. In this section, we present two ways of refining the Y measurement. Both are based on fixing the cluster size in two cases, by setting it equal to the X-ray estimated size or by using the redshift information when available. The outputs of the refined measurement are provided as additional information complementary to the catalogue of Planck SZ detections (see Appendix C and Table C.1).

7.2.1. Y at fixed X-ray size and position

As shown by Planck Collaboration VIII (2011), the size–flux degeneracy can be broken by introducing a higher-quality estimate of the cluster size θ₅₀₀. This prior is directly provided by X-ray observations using an X-ray mass proxy such as Y_X or the luminosity L_X. Resorting to estimates of the cluster size from optical richness is also possible, but suffers from the large scatter in richness-mass relation, as discussed previously.

A detailed investigation of the effects of fixing the cluster size was presented in Planck Collaboration XI (2011, Appendix A). Following this approach, and for the Planck detections identified with clusters from the MCXC meta-catalogue, we have adopted the R₅₀₀ and z values reported in Piffaretti et al. (2011) as priors to re-extract at the X-ray position the SZ signal denoted Y_500,PSX assuming the Arnaud et al. (2010) pressure profile (see Table C.1). The comparison between the blind Y₅₀₀ and refined Y_500,PSX (Fig. 26) shows that both the scatter and the offset are significantly reduced by the refined SZ measure. The SZ re-extraction at X-ray position and fixing the size to the X-ray derived size provides an unbiased estimate of the SZ signal. However, as stressed in Planck Collaboration XI (2011, Appendix A), the MCXC cluster size derivation involves the M₅₀₀–L_X,500 relation, which exhibits a non-negligible scatter. This leads to a remaining systematic discrepancy between the expected Y value from X-ray measurements and the actual SZ flux derived from the Planck data. The use of the Y_X proxy does not suffer from such an effect, but high-quality X-ray data permitting the use of such a quantity are not available for a large number of clusters (see Sect. 7.5 for the presentation of a sample of Planck SZ clusters with high-quality X-ray data).

7.2.2. Y from the Y(θ)–M relation

The size–flux degeneracy can further be broken, as proposed by (Arnaud et al., in prep.), using the M₅₀₀–${\mathit{D}}_{\mathrm{A}}^{\mathrm{2}}{\mathit{Y}}_{\mathrm{500}}$ relation itself that relates θ₅₀₀ and Y₅₀₀, when z is known. Then Y₅₀₀ is derived from the intersection of the M₅₀₀–${\mathit{D}}_{\mathrm{A}}^{\mathrm{2}}{\mathit{Y}}_{\mathrm{500}}$ relation and the size–flux degeneracy curve. A detailed description of the method and the comparison of results in terms of bias and scatter can be found in (Arnaud et al., in prep.).

The derived Y₅₀₀ parameter is denoted Y_z (since it involves a measurement of the Compton Y signal for clusters with measured redshift z). It is the SZ mass proxy Y_z that is equivalent to the X-ray mass proxy Y_X. Y_z is computed for all the 813 Planck clusters with measured redshifts. We use Malmquist-bias-corrected scaling relation between mass and Y given in Planck Collaboration XX (2014)${\mathit{E}}^{\mathrm{-}\mathrm{2}\mathit{/}\mathrm{3}}\mathrm{\left(}\mathit{z}\mathrm{\right)}\left[\frac{{\mathit{D}}_{\mathrm{A}}^{\mathrm{2}}\mathrm{\left(}\mathit{z}\mathrm{\right)}\hspace{0.17em}{\mathit{Y}}_{\mathrm{500}}}{{\mathrm{10}}^{-4}\hspace{0.17em}{\mathrm{Mpc}}^{\mathrm{2}}}\right]\mathrm{=}{\mathrm{10}}^{-0.19}{\left[\frac{{\mathit{M}}_{\mathrm{500}}}{\mathrm{6}\mathrm{\times }{\mathrm{10}}^{\mathrm{14}}\hspace{0.17em}{\mathit{M}}_{\mathrm{\odot }}}\right]}^{\mathrm{1.79}}\mathit{,}$(5)with E²(z) = Ω_m(1 + z)³ + Ω_Λ computed in the fiducial ΛCDM cosmology.

In Fig. 26, the refined Y₅₀₀ value, measured fixing the size and position to the X-ray values Y_500,PSX, is compared to the blind Y as a function of the derived Y_z proxy. We see that the scatter and the offset are significantly reduced.

Under the two hypotheses of cosmology and scaling relation, Y_z provides the best estimate of Y₅₀₀ for the Planck SZ clusters and conversely a homogeneously-defined estimate of an SZ-mass, X-ray calibrated, denoted ${\mathit{M}}_{\mathrm{500}}^{{\mathit{Y}}_{\mathit{z}}}$. For the ensemble of Planck clusters with measured redshifts, the largest such sample of SZ-selected clusters, we show in Fig. 27 the distribution (black solid line) of the masses obtained from the SZ-based mass proxy. The distribution of the SZ masses is compared with those of the RASS clusters (dashed blue line) computed from the X-ray luminosity L_X,500. The mean and median masses of the Planck clusters are 3.3 and 3.5 × 10¹⁴ M_⊙, respectively. The Planck SZ catalogues contains all the massive clusters of the RASS catalogues. Interestingly, the distribution of newly-discovered Planck clusters extends to higher masses with a median mass of 5.7 × 10¹⁴ M_⊙. Besides providing a homogeneous estimate of the masses from an SZ proxy for the largest SZ selected sample of clusters, we show that Planck detections significantly extend the mass range in the high-mass region up to 1.6 × 10¹⁵ M_⊙.

7.3. M–z distribution and comparison with other surveys

Based on the masses derived from the SZ-proxy, we illustrate for MMF3 the M–z distribution of Planck SZ clusters detected over 83.7% of the sky. We show in all panels of Fig. 28 the limiting mass M_lim computed following Planck Collaboration XX (2014) for three values of the completeness: 20% (solid line); 50% (dashed line); and 80% (dotted line). The upper left panel exhibits the Planck clusters, with redshifts, detected by MMF3 at S/N ≥ 4.5. The mass limit corresponds to the average limit computed from the noise over the 83.7% sky fraction used by the SZ-finder algorithm. The resulting M_lim is not representative of the inhomogeneity of the noise across the sky (see Fig. 3). We therefore show the limiting mass in three areas of the sky (Fig. 3): the deep-survey area (upper right panel); the medium-deep survey area (lower left panel); and the shallow-survey area (lower right panel). The lines indicate the limit at which clusters have C% chances to be detected (C being the completeness value). We clearly see that whereas the average M_lim at 20% completeness does not fully represent the SZ detections by MMF3, the limiting masses in different survey depths are more representative of the detection process. We further note that except at low redshifts, z< 0.3 − 0.4, the Planck cluster distribution exhibits a nearly redshift-independent mass limit with a cut that varies according to the survey depth.

It is worth examining the distribution of the Planck SZ clusters in the M–z plane and comparing it to that of other catalogues. For illustration, we compare to an X-ray selected sample, namely REFLEX-I, on the one hand (Fig. 29, right panel green open circles) and to the large-area SZ-selected cluster catalogues by ACT (Hasselfield et al. 2013) and SPT (Reichardt et al. 2013), on the other hand (Fig. 29, red open symbols). In this comparison we report, for the ACT clusters (open squares), the so-called UPP (Universal Pressure Profile) masses given in Hasselfield et al. (2013).

The range of redshifts covered by the Planck SZ sample, from z = 0.01 to about 1 with 67% of the clusters lying below z = 0.3, is quite complementary to the high redshift range explored by ACT and in by SPT. For the comparison of the mass distribution we take advantage of our newly-proposed SZ-mass estimate, derived from Y_z, which provides us with a homogeneous definition of the masses over the whole range of Planck SZ clusters with measured redshifts. The Planck clusters populate the full redshift range and they quite nicely fill a unique space of massive, M ≥ 5 × 10¹⁴ M_⊙, and high redshift z ≥ 0.5 clusters, as shown in Fig. 29. This contrasts with the SZ clusters detected in 720 square degrees of SPT observations and those of ACT observations, which are dominated, as shown in Fig. 29 left panel, by lower-mass higher-redshift clusters (up to z ~ 1.3). The combination of Planck and SPT/ACT catalogues samples the M–z space in a complementary manner. Clearly the all-sky nature of the Planck makes the most massive clusters preferentially accessible to Planck  whereas the highest redshift clusters, z ≥ 1, are accessible to SPT.

Very few massive high-redshift clusters exist in the X-ray catalogues, as seen in Fig. 29 (right panel open blue squares). The all-sky NORAS/REFLEX catalogues (Böhringer et al. 2000, 2004) are limited to z = 0.45, a result of the (1 + z)⁴ surface brightness dependence of the X-ray detection limit (Fig. 29, right panel, solid green line). The smaller-area MACS sample, based on systematic follow-up of ROSAT bright sources (Ebeling et al. 2007), contains a dozen clusters at z ≥ 0.5. The 400SD sample (Burenin et al. 2007), based on serendipitous detections in 400 deg² of ROSAT pointed observations, contains only two clusters with M ≥ 5 × 10¹⁴ M_⊙ and z ≥ 0.5. Finally, only a couple of clusters in the range M ≥ 5 × 10¹⁴ M_⊙ are found in the XMM-Newton based serendipitous cluster samples (XCS, Mehrtens et al. 2012; XMM-LSS, Pacaud et al. 2007; XDCP, Fassbender et al. 2011). By contrast to an X-ray selected cluster catalogue, the Planck detection-limit, illustrated for the medium-deep survey zone and shown in Fig. 29 (right panel, solid black line), has a much shallower dependence on redshift and is quasi-redshift independent above z = 0.4. The difference in cluster selection starts at redshifts z ≥ 0.2. As a result of the quasi-redshift independent mass-selection of SZ surveys, Planck probes deeper than the X-ray selection. This is also seen in the overall distribution of redshifts of the Planck clusters, Fig. 24.

This leaves the Planck SZ catalogue as the deepest all-sky catalogue spanning the broadest cluster mass range from 0.1 to 1.6 × 10¹⁵ M_⊙, and particularly adapted to the detection of rare very massive clusters in the tail of the distribution in the range M ≥ 5 × 10¹⁴ M_⊙ and z ≥ 0.5.

7.4. X-ray flux of the Planck clusters and candidates

For all Planck SZ detections, we estimated the unabsorbed fluxes at Earth in the [0.1–2.4] keV band (as in the MCXC) measured in an aperture of five arcmin. The aperture is centred on the Planck candidate position, except for candidates associated with a BSC source, for which we adopt the X-ray position, since the BSC source is very likely the counterpart (Planck Collaboration Int. IV 2013). The conversion between the RASS count rate in the hard band and flux is performed using an absorbed thermal emission model with the N_H value fixed to the 21 cm value. The conversion depends weakly on temperature and redshift and we assumed typical values of kT = 6 keV and z = 0.5. Planck Collaboration Int. IV (2013) compared such flux estimates with precise XMM-Newton fluxes measured within R₅₀₀, S₅₀₀, for candidates confirmed with the XMM-Newton follow-up programme. These clusters lie in the range 0.1 <z< 0.9 and the 0.3 × 10^-12<S₅₀₀< 6 × 10^-12 erg s^-1 cm^-2 flux range. The RASS aperture fluxes were found to underestimate the “true” flux by about 30%.

Figure 30 extends this comparison further to all the Planck SZ detections identified with MCXC clusters. Piffaretti et al. (2011) published homogenized L₅₀₀ and R₅₀₀ values derived from the flux given in the original catalogues in various apertures, using an iterative procedure based on the REXCESS L₅₀₀–M₅₀₀ relation and gas density profile shape. We simply computed S₅₀₀ from L₅₀₀, taking into account the K-correction at the cluster redshift, but neglecting its variation with temperature.

Although derived fromROSAT survey data as our present flux estimate, S₅₀₀ values from the MCXC are expected to be more accurate due to: (i) optimum choice of the X-ray centre; (ii) higher S/N detection; (iii) more sophisticated flux extraction adapted to data quality and source extent (e.g., growth curve analysis); and (iv) use of R₅₀₀ rather than a fixed aperture. Not surprisingly, the ratio between the present flux estimate and the MCXC value decreases with increasing offset between the Planck position and X-ray position (Fig. 30, left panel). The ratio drops dramatically when the distance is larger than five arcmin, i.e., when the X-ray peak lies outside the integration aperture. Those are rare cases, 18 nearby clusters (z< 0.1 with a median value of z = 0.05), for which a physical offset likely contributes to the overall offset. When these cases are excluded, the median ratio is 0.85 and depends on redshift (Fig. 30, middle panel); it significantly decreases with decreasing redshift below z of 0.1. The median ratio is 0.65 and 0.92, with a standard deviation of 0.10 and 0.15 dex, below and above z = 0.1, respectively. This is mostly due to the choice of a fixed aperture that becomes too small as compared to R₅₀₀ at low z. If we apply the same iterative procedure used by Piffaretti et al. (2011) to estimate S₅₀₀ from the aperture flux, the resulting value is consistent on average with the MCXC value at all redshifts (Fig. 30, right panel). The dispersion is slightly increased. The aperture unabsorbed fluxes are thus reliable estimates of the X-ray fluxes above z> 0.1 on average.

Figure 31 shows the X-ray flux as function of Y₅₀₀ for Planck candidates identified with known clusters, for the confirmed new Planck clusters and for the class1 candidates. For Planck detections identified with MCXC clusters we plot the more precise published S₅₀₀ value. All three categories of sources behave in a similar manner in good agreement with the range of redshifts probed by the sample. In this respect class1 candidates do not exhibit any departure with respect to the known or confirmed clusters. We provide the X-ray fluxes for the Planck clusters and candidates that are not identified with MCXC clusters (see Appendix C and Table C.1). For the Planck cluster with MCXC identifier, we refer the reader to the RASS catalogue outputs or to the homogenized MCXC meta-catalogue. The main limitation of the aperture unabsorbed fluxes is the statistical precision on the RASS estimate (most of the Planck SZ detections not identified with MCXC clusters have low (S/N)_RASS values) and the relatively large scatter (± 30% standard deviation). For z< 0.1 clusters, and if the RASS detection is reasonably good a more precise procedure is recommended, such as an adapted growth curve analysis, on a case-by-case basis.

7.5. Scaling relations between SZ and X-ray quantities

A fundamental scaling relation is that between Y₅₀₀ and its X-ray analogue, Y_X. Introduced by Kravtsov et al. (2006), Y_X is the product of M_g,500, the gas mass within R₅₀₀, and T_X, the spectroscopic temperature outside the core²⁵. From the fact that the gas density profile used to compute M_g,500 is derived from deprojection of the X-ray surface brightness profile, and that the X-ray emission depends on the square of the density, the ratio of these two quantities is

$\begin{array}{ccc}& & \frac{{\mathit{D}}_{\mathrm{A}}^{\mathrm{2}}\hspace{0.17em}{\mathit{Y}}_{\mathrm{500}}}{{\mathit{C}}_{\mathrm{XSZ}}\hspace{0.17em}{\mathit{Y}}_{\mathrm{X}}}\mathrm{=}\frac{\mathrm{1}}{\mathit{Q}}\frac{\mathrm{⟨}{\mathit{n}}_{\mathrm{e}}\mathit{T}{\mathrm{⟩}}_{{\mathit{R}}_{\mathrm{500}}}}{\mathrm{⟨}{\mathit{n}}_{\mathrm{e}}{\mathrm{⟩}}_{{\mathit{R}}_{\mathrm{500}}}{\mathit{T}}_{\mathrm{X}}}\\ & & \end{array}$(6)where the angle brackets denote volume-averaged quantities, and Q is the emissivity-weighted clumpiness factor, which affects the density profile derived from X-ray data radial bins used to derive the density profile (Zhuravleva et al. 2013). Λ_x(T) is the temperature-dependent emissivity in the considered X-ray band. The numerical constant C_XSZ = σ_T/ (m_ec²μ_em_p) = 1.416 × 10^-19 Mpc² (M_⊙ keV)^-1. The ratio thus depends only on the internal structure of the intra-cluster medium.Note that the conversion of Y₅₀₀/Y_x into the amplitude of density/temperature variations depends on the correlation between variations of these thermodynamic properties, which differ between isobaric and adiabatic cases (see Khedekar et al. 2013, for more details).

The properties of the Y_X–Y₅₀₀ relation, in particular its variation with mass and redshift and the dispersion about the mean relation, are important probes of the physics of cluster formation.

7.5.1. Data set

Here we extend the study of a sample of 62 clusters from the Planck–ESZ sample with good quality XMM-Newton archive data presented in Planck Collaboration XI (2011, hereafter PEPXI). This study found ${\mathit{D}}_{\mathrm{A}}^{\mathrm{2}}\hspace{0.17em}{\mathit{Y}}_{\mathrm{500}}\mathit{/}{\mathit{C}}_{\mathrm{XSZ}}\hspace{0.17em}{\mathit{Y}}_{\mathrm{X}}\mathrm{=}\mathrm{0.95}\mathrm{\pm }\mathrm{0.03}$, in a good agreement with REXCESS prediction, 0.924 ± 0.004, of Arnaud et al. (2010).

All 62 objects in the PEPXI sample are included in the present catalogue. We further add 40 clusters from the catalogue, including nine additional objects from the XMM-Newton archival study of Planck-detected LoCuSS systems presented by Planck Collaboration Int. III (2013), and the 31 Planck-discovered clusters with good redshift estimates (Q_z = 2) confirmed with the XMM-Newton (Planck Collaboration IX 2011; Planck Collaboration Int. I 2012; Planck Collaboration Int. IV 2013). The total sample thus consists of 102 clusters.

For each object, Y_X and the corresponding R₅₀₀ value were estimated simultaneously by iteration about the M₅₀₀–Y_X relation of Arnaud et al. (2010), ${\mathit{E}}^{\mathrm{2}\mathit{/}\mathrm{5}}\mathrm{\left(}\mathit{z}\mathrm{\right)}{\mathit{M}}_{\mathrm{500}}\mathrm{=}{\mathrm{10}}^{\mathrm{14.567}}{\left[\frac{{\mathit{Y}}_{\mathrm{X}}}{\mathrm{2}\mathrm{\times }{\mathrm{10}}^{\mathrm{14}}\hspace{0.17em}{\mathit{M}}_{\mathrm{\odot }}\hspace{0.17em}\mathrm{keV}}\right]}^{\mathrm{0.561}}\hspace{0.17em}{\mathit{M}}_{\mathrm{\odot }}\mathit{.}$(7)In the present study, we focus on the physical relation between Y₅₀₀ and Y_X. While these quantities must be estimated within the same radii, the exact value of R₅₀₀ is irrelevant as the radial dependence of the Y₅₀₀/Y_X ratio is negligible. We thus propagated only the measurement uncertainties on the temperature and gas mass profiles, fixing the aperture to R₅₀₀. We ignored the statistical and systematic uncertainties on the M₅₀₀–Y₅₀₀ relation itself²⁶. Similarly Y₅₀₀ was re-extracted at the X-ray position with size fixed to X-ray size. Its uncertainty corresponds to the statistical error on the SZ signal. The results are summarized Table 6, with the best estimate indicated in bold face.

7.5.2. The best-fit Y₅₀₀–Y_X relation

The Y₅₀₀–Y_X scaling relation for the full sample is shown in units of arcmin² in Fig. 32. At high flux the points follow the PEP XI relation. The slope and normalization are determined at slightly higher precision, due to the better quality SZ data. The derived intrinsic scatter (Table 6) is significantly smaller, a consequence of the propagation of gas mass profile errors in the Y_X error budget, which was neglected in our earlier study.

The relation levels off at around Y_X = 5 × 10^-4 arcmin², with a bin average deviation increasing with decreasing Y_X (Fig. 32 left panel). This is an indication of Malmquist bias, as noted by Planck Collaboration Int. I (2012). Full correction of this bias when fitting scaling relations involves drawing mock catalogues according to the cluster mass function, to which the sample selection criteria are then applied. The present sample is a small subset of the full S/N ≥ 4.5Planck catalogue and thus such a procedure cannot be applied. To minimize bias effects we will only consider high S/N detections, S/N> 7. To correct for the residual bias, we adapted the approach proposed by Vikhlinin et al. (2009). Before fitting the Y₅₀₀–Y_X relation, each individual Y value was divided by the mean bias, b, given by $\ln \mathit{b}\mathrm{=}\frac{\exp \mathrm{(}\mathrm{-}{\mathit{x}}^{\mathrm{2}}\mathit{/}\mathrm{2}{\mathit{\sigma }}^{\mathrm{2}}\mathrm{)}}{\sqrt{\mathit{\pi }\mathit{/}\mathrm{2}}\hspace{0.17em}\mathrm{erfc}\mathrm{(}\mathit{x}\mathit{/}\sqrt{\mathrm{2}}{\mathit{\sigma }}^{\mathrm{)}}}\hspace{0.17em}\mathit{\sigma ,}$(8)where x = − log (Y/Y_min), Y_min being the flux threshold corresponding to the S/N cut, (S/N)_cut. At the location of the cluster, Y/Y_min = (S/N)/(S/N)_cut. Here σ is the log-normal dispersion at fixed Y_X. We took into account both the intrinsic dispersion σ_int, estimated iteratively, and the statistical dispersion, given by $\mathit{\sigma }\mathrm{=}\sqrt{\ln {\left[\mathrm{\left(}\mathrm{\right(}\mathit{S}\mathit{/}\mathit{N}\mathrm{)}\mathrm{+}\mathrm{1}\mathrm{)}\mathit{/}\mathrm{\left(}\mathit{S}\mathit{/}\mathit{N}\mathrm{\right)}\right]}^{\mathrm{2}}\mathrm{+}{\left[\ln \mathrm{10}\hspace{0.17em}{\mathit{\sigma }}_{\mathrm{int}}\right]}^{\mathrm{2}}}$. The correction decreases the effective Y₅₀₀ values at a given Y_X, an effect that is larger for clusters closer to the S/N threshold; i.e., low-flux objects. The net effect on the scaling relation is small, giving a 0.7σ decrease of the normalization and a slight steepening of the power-law slope (Table 6).

The slope and normalization of the relation are robust to the inclusion of newly-discovered Planck clusters. The results derived from the extended sample of 78 clusters with S/N> 7 agree with those obtained for the updated ESZ-XMM sample within 0.5σ (Table 6). They are also in agreement with the sub-sample of 71 S/N> 7 clusters included in the cosmological sample discussed by Planck Collaboration XX (2014). We measured a significant intrinsic scatter of σ_int = 0.07 ± 0.01 dex. There is one spectacular outlier with an Y₅₀₀/Y_X ratio nearly twice as big as the mean. This is the Planck ESZ cluster identified with A2813 or RXC J0043.4-2037 in the REFLEX catalogue, located at z = 0.29. Its high ratio is very puzzling. It cannot result from an inaccurate redshift measurement, as this is based on spectroscopic data for several cluster galaxies (Böhringer et al. 2004). There is no evidence of a peculiar dynamical state from the X-ray morphology, and there is no evidence of contamination in the SZ data.

Part of the dispersion could be due to the use of an inappropriate fixed pressure profile in the Y₅₀₀ extraction. When including possible errors on Y₅₀₀ due to dispersion around the mean Arnaud et al. (2010) profile, the scatter is decreased to σ_int = 0.06, a decrease at the 1σ level. To further assess the effect of the choice of the pressure profile, we re-extracted the SZ signal using the Planck+XMM-Newton profile shape measured for ESZ clusters by Planck Collaboration Int. V (2013, hereafter PIPV). Individual profiles are used for Planck ESZ clusters, and the mean profile is used for the other clusters. This should give the most reliable estimate of the Y₅₀₀–Y_X relation, since it is based directly on measured profile shapes. In this case, the slope and scatter remain unchanged but the normalization is slightly decreased (at the 0.5σ level). This is a result of the more inflated nature of the PIPV profile as compared to the Arnaud et al. (2010) REXCESS profile. The relation derived using PIPV pressure profiles is plotted in the right-hand panel of Fig. 32 together with the corresponding data points.

The relation does not exhibit significant evidence of variance of the Y₅₀₀/Y_X ratio with mass, the slope is consistent with unity, as expected from strong self-similarity of pressure profile shape. However, we found an intrinsic scatter about three times larger than the results of Kay et al. (2012). Partly this is due to the presence of outliers in our data set (as discussed above), or it may be due to projection effects in observed data sets (Kay et al. 2012). The mean ratio is very well constrained with a precision of 2.5%, log (Y₅₀₀/Y_X) = − 0.027 ± 0.010. This confirms at higher precision the strong agreement between the SZ and X-ray measurements (within R₅₀₀) of the intra-cluster gas properties found by PEP XI and other studies (Andersson et al. 2011; Sifón et al. 2013; Marrone et al. 2012; Rozo et al. 2012). The ratio is consistent with the X-ray prediction. In the simplest scenario of pure density variations in an isothermal ICM at the scale of the radial bin, this suggests a low clumpiness factor. However there are still large systematics that are discussed in Appendix D. We can translate those into an upper limit of order 30%.

8. Summary

Planck’s all-sky coverage and broad frequency range are designed to detect the SZ signal of galaxy clusters across the sky. We provide, from the first 15.5 months of observations, the largest ensemble of SZ-selected sources detected from an all-sky survey. The Planck catalogue of SZ sources contains 1227 detections. This catalogue, statistically characterized in terms of completeness and statistical reliability, was validated using external X-ray and optical/NIR data, alongside a multi-frequency follow-up programme for confirmation. A total of 861 SZ detections are confirmed associations with bona fide clusters, of which 178 are brand-new clusters. The remaining 366 cluster candidates are divided into three classes according to their reliability, i.e., the quality of evidence that they are likely to be bona fide clusters.

A total of 813 Planck clusters have measured redshifts ranging from z = 0.01 to order one, with one-third of the clusters lying above z = 0.3. The brand-new Planck clusters extend the redshift range above z = 0.3. For all the Planck clusters with measured redshift, a mass can be estimated from the Compton Y measure. We provide a homogeneous mass estimate ranging from (0.1 to 1.6) × 10¹⁵ M_⊙. Except at low redshifts, the Planck cluster distribution exhibits a nearly redshift-independent mass limit and occupies a unique region in the M–z space of massive, M ≥ 5 × 10¹⁴ M_⊙, and high-redshift (z ≥ 0.5) clusters. Owing to its all-sky nature, Planck detects new clusters in a region of the mass–redshift plane that is sparsely populated by the RASS catalogues. It detects the rarest clusters, i.e., the most massive clusters at high redshift in the exponential tail of the cluster mass function that are the most useful clusters for cosmological studies. With the presently confirmed Planck SZ detections, Planck doubles the number of massive clusters above redshift 0.5, as compared to other surveys. The Planck SZ catalogue is, and will be for years to come, the deepest all-sky SZ catalogue spanning the broadest cluster mass range.

The Planck SZ catalogue should motivate multi-wavelength follow-up efforts. The confirmation of the cluster candidates will reveal clusters at higher redshifts than the present distribution. Such follow-up efforts will further enhance the value of the Planck SZ catalogue as the first all-sky SZ selected catalogue. It will serve as a reference for studies of cluster physics (e.g., galaxy properties versus intra-cluster gas physics, dynamical state, evolution, etc.). Using an extended sub-sample of the Planck SZ clusters with high-quality XMM-Newton data, the scaling relations between SZ and X-ray properties were reassessed and updated. With better-quality data and thus higher precision, we show excellent agreement between SZ and X-ray measurements of the intra-cluster gas properties. We have thus derived a new up-to-date reference calibrated local relation between Y and Y_X.

The Planck SZ catalogue will also serve to define samples for cosmological studies. A first step in this direction is already taken in Planck Collaboration XX (2014), where an analysis of the SZ cluster abundance to constrain the cosmological parameters is performed using a sub-sample selected from the PSZ catalogue consisting of 189 clusters detected above a S/N of 7 with measured redshifts. The value-added information derived from the validation of the Planck SZ detections, in particular the SZ-based mass estimate, increases even further the value of the Planck SZ catalogue.

The combination of the Planck all-sky SZ data with near future and planned observations of the large-scale structure by surveys such as PAN-STARRS, LOFAR, Euclid, LSST, and RSG/e-ROSITA will revolutionize our understanding of large-scale structure formation and evolution.

---

Acknowledgments

The development of Planck has been supported by: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MICINN, JA and RES (Spain); Tekes, AoF and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); and PRACE (EU). A description of the Planck Collaboration and a list of its members, including the technical or scientific activities in which they have been involved, can be found at http://www.sciops.esa.int/index.php?project=planck&page=Planck_Collaboration. The authors thank N. Schartel, ESA XMM-Newton project scientist, for granting the Director Discretionary Time used for confirmation of SZ Planck candidates. The authors thank TUBITAK, IKI, KFU and AST for support in using RTT150 (Russian-Turkish 1.5-m telescope, Bakyrlytepe, Turkey); in particular we thank KFU and IKI for providing significant amount of their observing time at RTT150. We also thank BTA 6-m telescope Time Allocation Committee (TAC) for support of optical follow-up project. The authors acknowledge the use of the INT and WHT telescopes operated on the island of La Palma by the Isaac Newton Group of Telescopes at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias (IAC); the Nordic Optical Telescope, operated on La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, at the Spanish Observatorio del Roque de los Muchachos of the IAC; the TNG telescope, operated on La Palma by the Fundacion Galileo Galilei of the INAF at the Spanish Observatorio del Roque de los Muchachos of the IAC; the GTC telescope, operated on La Palma by the IAC at the Spanish Observatorio del Roque de los Muchachos of the IAC; and the IAC80 telescope operated on the island of Tenerife by the IAC at the Spanish Observatorio del Teide of the IAC. Part of this research has been carried out with telescope time awarded by the CCI International Time Programme. The authors thank the TAC of the MPG/ESO-2.2 m telescope for support of optical follow-up with WFI under Max Planck time. Observations were also conducted with ESO NTT at the La Silla Paranal Observatory. This research has made use of SDSS-III data. Funding for SDSS-III http://www.sdss3.org/ has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and DoE. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration. This research has made use of the following databases: the NED and IRSA databases, operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the NASA; SIMBAD, operated at CDS, Strasbourg, France; SZ cluster database operated by Integrated Data and Operation Center (IDOC) operated by IAS under contract with CNES and CNRS. The authors acknowledge the use of software provided by the US National Virtual Observatory.

References

Appendix A: Selection of frequency channel maps

An assessment of which combination of Planck frequency channels to use was performed using the MMF1 implementation of the matched multi-filter described in Sect. 2.2.2. The HFI and LFI channel maps were preprocessed as described in Sect. 2.1, with the only difference being that the point-source mask contained, in addition, detections from the LFI channel maps with S/N ≥ 10. Five different combinations of frequency channels were investigated, all Planck channels (30–857 GHz), all HFI channels plus the 70 GHz channel map from LFI (70–857 GHz), all HFI channels (100–857 GHz), the five lowest frequency HFI channels (100–545 GHz) and the four lowest frequency HFI channels (100–353 GHz). For each combination of frequency channels a catalogue of SZ sources was extracted, resulting in five different catalogues; the only differences between them must be entirely due to the choice of channels in the combination.

The first four of these catalogues are in good agreement in terms of the clusters detected, with all the differences amongst them being due to detections with S/N< 5. The (100–353 GHz) catalogue, however, contains significantly more detections, resulting in a poor agreement between it and the other catalogues that is not limited to low S/N detections. This is interpreted as being due to the lack of a dust-dominated channel in this combination, without which it is more difficult to constrain contamination due to dust emission.

In order to assess any improvement in the S/Ns of detected clusters with the inclusion of extra data, a robust sample of reliable sources is required. To produce this, only clusters outside the 65% dust mask and with S/N ≥ 8 were kept from each combination. The differences in the S/N of the same sources detected using different frequency channel combinations can then be examined. The ratio between the S/N values of the common detections in each combination to those of the (100–857 GHz) combination was then found; the mean of this ratio is shown in Table A.1. This approach clearly shows the (100–353 GHz) combination to be considerably noisier than the other combinations, which is consistent with the observations reported above. Neither the inclusion of the LFI frequency channels or just the 70 GHz channel brings any significant improvement in the S/N of the clusters. Using the six HFI channel combination results in marginally better S/N than the (100–545 GHz) combination. The frequency channel combination chosen therefore is (100–857 GHz) since this gives the highest S/N with the smallest data-set. Reducing the S/N threshold from 8 to 6 and hence doubling the number of SZ sources used to evaluate the mean ratio does not change the conclusions of this analysis.

Appendix B: Extract from the Planck catalogue of SZ sources

We describe here the Planck catalogue of SZ sources delivered by the collaboration and available together with the individual lists from all three detections methods, the union mask used by these methods and the ensemble of notes on individual clusters²⁷.

The union Planck SZ catalogue contains the coordinates and the S/N of the SZ detections and a summary of the validation information, including external identification of the cluster and redshifts if they are available. The external identification quoted in the delivered product corresponds to the first identifier as defined in the external validation hierarchy, namely identification with MCXC clusters followed by Abell and Zwicky, followed by SDSS-based catalogues, followed by SZ catalogues, followed finally by searches in NED and SIMBAD. Due to the size–flux degeneracy discussed in Sect. 2.3, no reference flux quantity is outputted for the union catalogue.

The individual catalogues from the three detection methods, MMF1, MMF3, and PwS, contain the coordinates and the S/N of the detections, and information on the size and flux of the clusters. The size is given in terms of θ_s and the flux is given in terms of the total integrated Comptonization parameter, Y = Y_5R500. The full information on the degeneracy between and Y is provided in the form of the two-dimensional marginal probability distribution for each cluster.

The degeneracy information is provided in this form so that it can be combined with a model or external data to produce tighter constraints on the parameters. For example, combining it with an X-ray determination of the size can be done by taking a slice through the distribution at the appropriate θ_s. This is what is done in Sect. 7.2.1 and the refined measurement using X-ray information can be found in Table C.1.

Table B.1 presents an extract of the PSZ catalogue, in terms of the first rows of the online table and the following selected columns: Name: name of cluster. RA, Dec: right ascension (J2000) and declination (J2000). S/N: signal-to-noise ratio of the SZ detection. Validation: status of the SZ detection from external validation: 20 = previously-known cluster; 10 = new confirmed Planck cluster; 1 = class1 candidate ; 2 = class2 candidate; 3 = class3 candidate. ID_EXT: first external identifier of the known clusters. z: redshift of the cluster as reported from the external validation. Comments: F = no comment; T = comment. Comments are readable in an external file. The complete version of the PSZ catalogue also contains the additional columns: Index: index of the detection, determined by the order of the clusters in the union catalogue and sorted into order of ascending Galactic longitude. GLON, GLAT: Galactic coordinates. POS_ERR: errors on the position. Pipeline: pipeline from which information is taken; namely 1 = MMF1; 2 = MMF3; 3 = PwS. PIPE_DET: pipeline making the detection, with the following order in bits: 1st = MMF1; 2nd = MMF3; 3rd = PwS. PCCS: flag for a match with sources from the PCCS catalogue. COSMO: flag for those clusters that are included in the sample used for the cosmological analysis of Planck Collaboration XX (2014).

Appendix C: Outstanding outputs from the external validation

Based on the ancillary data used for the validation of the Planck SZ catalogue, we provide value-added information to the Planck SZ detections.

Namely, we provide, in addition to the first external identifier, possible other common identifiers, IDs.

We report the redshift information associated with the Planck clusters (z) and specify its source, (scr).

For clusters with measured redshifts, we compute the SZ-proxy Y_z and the mass estimate (${\mathit{M}}_{\mathrm{500}}^{{\mathit{Y}}_{\mathit{z}}}$) and associated errors. For the clusters identified with MCXC clusters we provide the SZ signal, Y_500,PSX, re-extracted fixing the size to the X-ray size provided in the MCXC catalogue at the X-ray position. We also provide the associated S/N in the Planck data. Note that the X-ray positions used in the present study are those quoted in the MCXC meta-catalogue. The positions reported in the ESZ sample were taken from a sampled grid of coordinates with a pixel size of 1.71 arcmin. Due to this sampling, the reported MCXC positions in the ESZ sample exhibit an average offset of 70 arcsec (less than a pixel, which varies depending on the position of the object on the sphere).

For Planck SZ detections not associated with a previously-known X-ray cluster and with (S/N)_RASS ≥ 1σ, we provide the unabsorbed X-ray flux, S_X (and error), measured in an aperture of 5 arcmin in the band [0.1–2.4] keV. We only provide an upper limit in the case of (S/N)_RASS< 1σ, except for three SZ detections for which RASS exposure is very low and (S/N)_RASS< − 5σ. The aperture is centred on the Planck position, except for candidates associated with a BSC source for which we adopt the X-ray position. These clusters are flagged.

Appendix D: Systematic effects on the X-ray versus SZ scaling relation

Both X-ray and SZ measurements are likely affected by systematic effects linked to e.g., background estimation and subtraction methods, calibration issues, etc. One sign of the impact of these effects is the fact that the slope of the relation between Y₅₀₀ flux and ${\mathit{Y}}_{\mathrm{X}}\mathit{/}{\mathit{D}}_{\mathrm{A}}^{\mathrm{2}}$ in units of arcmin² is α = 0.91±0.02, which is significantly smaller than unity even after Malmquist bias correction. As this is not the case for the relation in physical units (Mpc²), the observed slope cannot be due to a true physical variation in the ratio (e.g., with mass).

SZ fluxes are subject to uncertainties due to systematic differences between measurement methods. From the comparison between PwS and MMF photometry (Sect. 2.3), we estimate that the net effect is typically 0.03 dex. The effect is independent of SZ flux, thus cannot explain the shallower than expected slope.

Uncertainties in the X-ray measurements are dominated by temperature uncertainties due to calibration systematics. We can investigate the magnitude of these effects by examining the relation between the Y_X values obtained with XMM-Newton by Planck Collaboration XI (2011, hereafter the PEP XI ESZ-XMM sample) to those obtained with Chandra in a study of 28 clusters from the same sample by Rozo et al. (2012; hereafter the ESZ–Chandra sample). The Chandra values are larger, with a mean offset of 0.02 dex. However, there is no significant evidence of variation with Y_X, thus X-ray calibration issues again cannot explain the observed slope.

A further source of uncertainty in X-ray measurements concerns the X-ray analysis method (e.g., due to background estimation and subtraction of point sources and substructure). Rozo et al. (2012) noted the difference between the ratio obtained with ESZ-Chandra and ESZ-XMM samples and suggested that it might be due to XMM-Newton data analysis issues. The PEP XI ESZ-XMM sample was analysed by two independent methods depending on the cluster extension in the field-of-view. Sub-sample A consisted of 19 nearby clusters that extend beyond the XMM-Newton field–of–view, and for which direct background estimates are not possible, while the background for the remaining 43 objects was estimated using a region external to the cluster. The ESZ–Chandra sample studied by Rozo et al. (2012) consists mostly sub-sample A objects. While systematic effects due to background estimation are certainly more important for sub-sample A than for sub-sample B, these effects cannot fully explain the observed behaviour of the Y₅₀₀/Y_X ratio. Indeed, excluding sub-sample A clusters, the slope of the Y₅₀₀–${\mathit{Y}}_{\mathrm{X}}\mathit{/}{\mathit{D}}_{\mathrm{A}}^{\mathrm{2}}$ relation is α = 0.89 ± 0.04, still significantly smaller than unity. The origin of the systematic differences between sub-sample A and B objects is unclear.

The variation of the Y₅₀₀/Y_X ratio with flux remains largely unexplained. It may be due to residual Malmquist bias, in addition to a complex combination of systematic effects in SZ and X–ray measurements. For instance, we note that higher flux clusters correspond to nearby objects that have larger angular sizes. The background estimate in both X-ray and SZ signals is subject to larger uncertainty in this case.

The lack of a complete explanation for the observed slope of the Y₅₀₀–Y_X relation, and its ultimate correction, has several implications. Firstly, the shallower slope in units of arcmin² translates into an over-estimate of the dispersion about the relation when measured in Mpc². From the difference in intrinsic scatter about the relation in both physical and arcmin units, we estimate that this effect contributes at the level of about 0.01 dex to the scatter seen in the physical Y₅₀₀–Y_X relation.

Secondly, the Y₅₀₀/Y_X ratio will depend on the exact sample definition, via the range of fluxes probed. The observed slope of α = 0.91 ± 0.02 translates into a variation of about ± 0.06 dex of the Y₅₀₀/Y_X ratio over the range of SZ fluxes studied here. The ESZ–Chandra objects studied by Rozo et al. (2012) lie preferentially at high fluxes, with a median flux two times higher than the PEP XI-XMM sample. For α = 0.91, this will translate into a roughly 0.03 dex difference in the Y₅₀₀/Y_X ratio. The Y₅₀₀/Y_X ratio found by Rozo et al. (2012), log (Y₅₀₀/Y_X) = − 0.088 ± 0.012, is significantly lower than our value of −0.027 ± 0.010. However, it can be explained by a combination of their sample definition, a neglect of Malmquist bias, and the aforementioned calibration issues between XMM-Newton and Chandra.

In summary, uncertainties on the Y₅₀₀/Y_X ratio are dominated by systematic effects in both X–ray and SZ measurements. This unfortunately precludes any definitive statement on the magnitude of the gas clumpiness within R₅₀₀. Follow-up of well-defined sub-samples (e.g., above a given S/N) should help to disentangle biases due to sample selection and measurement of the different quantities.

All Tables

All Figures