The XMM-LSS survey: the Class 1 cluster sample over the extended 11 deg² and its spatial distribution

Abstract

This paper presents 52 X-ray bright galaxy clusters selected within the 11 deg²XMM-LSS survey. 51 of them have spectroscopic redshifts (0.05 < z < 1.06), one is identified at z_phot = 1.9, and all together make the high-purity ‘Class 1’ (C1) cluster sample of the XMM-LSS, the highest density sample of X-ray-selected clusters with a monitored selection function. Their X-ray fluxes, averaged gas temperatures (median T_X = 2 keV), luminosities (median L_{X, 500} = 5 × 10⁴³ erg s⁻¹) and total mass estimates (median 5 × 10¹³ h⁻¹ M_⊙) are measured, adapting to the specific signal-to-noise regime of XMM-LSS observations. Particular care is taken in deriving the sample selection function by means of realistic simulations reproducing the main characteristics of XMM observations. The redshift distribution of clusters shows a deficit of sources when compared to the cosmological expectations, regardless of whether Wilkinson Microwave Anisotropy Probe-9 or Planck-2013 cosmic microwave background parameters are assumed. This lack of sources is particularly noticeable at 0.4 ≲ z ≲ 0.9. However, after quantifying uncertainties due to small number statistics and sample variance, we are not able to put firm (i.e. >3σ) constraints on the presence of a large void in the cluster distribution. We work out alternative hypotheses and demonstrate that a negative redshift evolution in the normalization of the L_X-T_X relation (with respect to a self-similar evolution) is a plausible explanation for the observed deficit. We confirm this evolutionary trend by directly studying how C1 clusters populate the L_X-T_X-z space, properly accounting for selection biases. We also point out that a systematically evolving, unresolved, central component in clusters and groups (AGN contamination or cool core) can impact the classification as extended sources and be partly responsible for the observed redshift distribution. We provide in a table the catalogue of 52 clusters together with their measured properties.

INTRODUCTION

Studying the spatial distribution of galaxy clusters in a volume of cosmological size enables the cartography of large-scale structure in the Universe through its most massive building blocks. The number counts distribution of clusters is therefore an excellent test for cosmological models and the growth of structure (e.g. Borgani et al. 2001; Henry et al. 2009; Vikhlinin et al. 2009; Mantz et al. 2010; Rozo et al. 2010; Pierre et al. 2011; Benson et al. 2013).

From an observational point of view, galaxy clusters are advantageously high-signal astrophysical sources: as expected from simple scaling arguments (e.g. Kaiser 1986), the most massive virialized objects are also the largest in size and their observable properties scale up with mass. This is especially true in X-ray wavelengths because of the large amount of X-ray photons emitted by the hot (T ∼ 10⁷ K) intracluster baryonic gas trapped in their deep potential wells. With typical X-ray luminosities of 10^43-45 erg s⁻¹, clusters can be detected up to large cosmological distances in a systematic and controlled way. On the other hand, galaxy clusters are rare objects and robust analyses of their spatial distribution (e.g. redshift distribution, two-point correlation function, etc.) and their ensemble properties (e.g. scaling relations, mass distribution, etc.) require medium- to large-area surveys in order to accumulate statistical power. These characteristics motivated the assembly of large samples of galaxy clusters detected in X-rays. In particular, studies based on the ROSAT All-Sky Survey (Truemper 1993) such as REFLEX (Böhringer et al. 2001), NORAS (Böhringer et al. 2000), the ROSAT North Ecliptic Pole Survey (Henry et al. 2001) and the 400d (Burenin et al. 2007) delivered solid cosmological results based on galaxy clusters (e.g. Schuecker et al. 2003; Vikhlinin et al. 2009; Mantz et al. 2010). During the last decade, the very sensitive XMM–Newton (Fassbender et al. 2011; Willis et al. 2013) and Chandra (e.g. Tozzi et al. 2013) observatories revealed the presence of their characteristic emission beyond redshifts of 1, and even up to z ∼ 2 (Gobat et al. 2011), demonstrating the ability to construct deep samples of cosmological interest.

The XMM-LSS survey (Pierre et al. 2004) is unique in this respect: it covers a contiguous sky area of 11 deg² with XMM pointed observations, reaching a sensitivity of 10⁻¹⁴ erg s⁻¹ cm⁻² for extended sources in the [0.5–2] keV band. Thanks to the wide and complementary multiwavelength coverage (from radio to γ-rays) and dedicated follow-up effort, it constitutes a relevant field for studies of galaxy clusters and groups. The complete X-ray source catalogue is published in Chiappetti et al. (2013) along with the optical associations. The XMM-XXL survey is currently extending its area to 50 deg² following a similar strategy as for the detection and characterization of galaxy clusters, with international support and expertise (Pierre et al., in preparation) The sample used in this work is unique in terms of X-ray and spectroscopic redshifts’ completenesses – (i) spectroscopic redshifts (from observations of cluster galaxy members) enable us to position clusters in 3D space and accurate derivation of their physical properties: gas temperature, luminosity, physical size; (ii) a trade-off between completeness, purity and assessment of selection effects has been carefully designed: Pacaud et al. (2006) indeed demonstrated the existence of an uncontaminated sample of extended sources detected in XMM-LSS images called ‘C1’; 29 of them were detected in the first 5 deg² of the XMM-LSS survey (Pacaud et al. 2007).

In this study, we focus on the redshift distribution of the complete set of 52 XMM-LSS C1 clusters and its cosmological modelling. Results from the catalogue of sources detected in the Planck survey by the Sunyaev–Zel'dovich (S–Z) effect indicated a deficit of clusters at all redshifts when compared to expectations from the Planck cosmic microwave background (CMB) cosmological model (Planck Collaboration XX 2013). Tension could be alleviated by modifying the mass-observable relation. Studies based on galaxy clusters indeed appeal for a simultaneous modelling of the cosmological halo mass function, the mass-observable relations (scaling laws and their evolutions with redshift) and modelling of selection effects (e.g. Pacaud et al. 2007; Pratt et al. 2009; Vikhlinin et al. 2009; Mantz et al. 2010; Allen, Evrard & Mantz 2011; Clerc et al. 2012b; Planck Collaboration XX 2013). Therefore, part of our results concerns the L_X-T relation of C1 clusters and its evolution. This latter point is particularly debated in current studies of clusters detected in XMM data. Pacaud et al. (2007) pointed out the importance of selection biases in such studies. Reichert et al. (2011) found a negative trend (relative to self-similar expectations) by analysing a heterogeneous sample of objects. Both the XMM Cluster Survey (XCS; Hilton et al. 2012) and the XMM CLuster Archive Super Survey (X-CLASS; Clerc et al. 2012b) indicated a negative evolution in the normalization of the relation. However, differences in the selection and analyses methods make such comparisons difficult.

This paper is organized as follows. In Section 2, we describe the data set and our choice of sample for this study. An in-depth characterization of the survey selection function is presented in Section 3. Derivation of cluster properties is detailed in Section 4. The spatial distribution and the luminosity–temperature relation of clusters in the sample are shown in Section 5, and we discuss further the modelling of the redshift distribution in Section 6. Section 7 summarizes our findings.

Throughout this paper, we assume Ω_m = 0.3, Ω_Λ = 0.7 and h = 0.7 with H₀ = 100 h km s⁻¹, except otherwise stated. In particular, our discussion of the redshift distribution (Sections 5 and 6) alternates between Wilkinson Microwave Anisotropy Probe-9-9 (WMAP-9; Hinshaw et al. 2013) and Planck CMB (Planck Collaboration XVI 2013) cosmologies. In all that follows, M_δ( = M_δc) is the mass within a sphere of radius R_δ( = R_δc), inside which the mass density is δ times the critical density of the Universe at the considered redshift. Transformations between different values of δ will assume an NFW profile (Navarro, Frenk & White 1997).

CONSTRUCTION OF THE SAMPLE

The complete XMM-LSS 11 deg² source catalogue is presented in full extent by Chiappetti et al. (2013). In this section, we briefly recall the main characteristics of the 11 deg²XMM-LSS survey and our procedure for detecting sources, with particular emphasis on the confirmation of C1 galaxy clusters.

The XMM data set

The XMM-LSS survey is located at |${\rm {\rm RA} = 02^h22^m}$| and δ = −04°30^′ and consists of 98 XMM pointings on an ∼3| $_{.}^{\circ}$|5 × 3| $_{.}^{\circ}$|5 contiguous footprint (Fig. 1). It represents a sub-area of the larger XMM-XXL survey (Pierre et al. 2011) for which a full description of the observation strategy and quality is given in Pierre et al. (in preparation). Each of those pointings corresponds to a single observation with the EPIC detectors (MOS1, MOS2 and PN) in full frame imaging mode, spanning a field of view of roughly 30 arcmin diameter each.

The centre of each observation is defined by the exposure-weighted location of the optical axes of all three XMM telescopes. The work presented in this study relies on X-ray data collected by each pointing up to an off-axis radius of 13 arcmin. The total geometrical area of the survey amounts to 11.1 deg²; 3.0 deg² (27 per cent) of that area consists in overlaps between adjacent pointings (Fig. 1). The remaining area (8.1 deg²) is covered by one unique pointing. For each individual observation, an event list is created and filtered from solar proton flares by automatic inspection of the high-energy light curves. High count rate periods associated with particle flares are flagged and removed for each of the three detectors separately. Cleaned exposure times after flares removal amount to ∼10 ks for the majority of the pointings (Fig. 1), although spatial fluctuations in the survey depth do exist and will be modelled in the selection function (Section 3).

Source detection

Our source detection procedure builds upon the algorithm described in Pacaud et al. (2006, 2007) with several revisions as detailed in Chiappetti et al. (2013). These revisions mainly consist in a transcription of the algorithm code from idl to python and a correction in the relative astrometry.

Individual detector images are created in the [0.5–2] keV band from cleaned event lists and binned in pixels of 2.5 arcsec width. Sources are detected on each pointing image separately: in the first step, all three EPIC images are co-added, then filtered using the mr_filter multiresolution algorithm (Starck, Murtagh & Bijaoui 1998). Such a filtering adequately accounts for the Poisson nature of the noise in the background and source areas. An sextractor (Bertin & Arnouts 1996) pass over this image provides an initial detection list and a first guess for their positions. In the second step, each source from this list is characterized thanks to a maximum likelihood fitting algorithm (xamin, Pacaud et al. 2006) specifically developed to assess the extension of sources in XMM-LSS data. Among the output parameters of interest are the detection likelihood quantifying the significance of the detection relative to a case without source and the extension likelihood, comparing the case of an extended source and a point-like source. These likelihood values are defined (and corrected) so as to match a two-parameter χ² statistics, hence convertible into equivalent probabilities following P = exp (−L/2).

The C1 selection

Following the methodology presented in Pacaud et al. (2006), we define a C1 (Class 1) sample of sources by filtering on xamin output parameters, namely the extension ( > 5 arcsec), the extension likelihood (>33) and the detection likelihood (>32). This set of parameters defines a sub-sample of extended sources. This sub-sample is almost unoccupied by point-like and spurious sources (1–3 per cent contamination, see Section 3). It was originally defined by analysing extensive simulations of typical XMM-LSS pointings showing an exposure time of 10 ks and a nominal background level from Read & Ponman (2003). In order to provide a more accurate description of sensitivity fluctuations across the survey area, we extended this set of simulations to a wider range of exposures and background levels (see Section 3). Importantly, they show that C1 criteria remain stable against these variations, in the sense that contamination by point-like and spurious sources remains at a low level, ensuring high purity. However, it is worth noting that the same physical extended object would be detected with different output parameters depending on its spatial location in the survey. In other terms, the sample completeness slightly varies across the survey.

A total of 58 sources fulfilling C1 criteria were detected in the XMM-LSS survey thanks to the newest processing of each individual pointing. Of them, five are duplicates detected on a neighbouring pointing, three are actually nearby galaxies emitting X-rays as revealed by the inspection of optical/X-ray overlays and one is identified as a sub-structure in the X-ray emission of XLSSC 50, hence not considered as a distinct source.

All 32 sources presented in Adami et al. (2011; C1 sample, their table 2) were detected by our new processing. However, six of them were downgraded and no longer classified as C1: three were classified as C2¹ and three were deblended as two distinct, non-C1 sources (XLSSC 12, 28 and 74; see images in Appendix C of this paper and fig. C1 of Pacaud et al. 2007). In all three cases, such deblending arose because of point sources present close to the cluster centre. It is a direct consequence of the multiscale approach implemented in our detection algorithm. On the other hand, five sources within the 6 deg² area explored by Adami et al. (2011) were promoted as C1 sources with this new processing, four of them previously classified as C2. We attribute these differences to changes in the xamin pipeline version, the event list processing and/or the xmm-sas version and calibration data. Such changes can be viewed as additional ‘noise’ in the images on top of the usual Poisson and background noise. However, they are not handled by the noise model of our pipeline and thus induce variations in the final source list near the selection thresholds. The maximal list of C1-classified sources (either by one or the other processing runs) contains 54 entries. We manually discarded one detection whose characterization as an extended source is doubtful, since it suffers from severe projection effects due to a bright X-ray emitting star and a large X-ray cluster (XLSSC 061 in Table 1 and Fig. C1) in the foreground.

Cluster validation and redshifts

Our procedure for confirming and validating C1 sources as galaxy clusters involves optical spectroscopic observations and is fully described in Adami et al. (2011). Spectroscopic follow-up campaigns were dedicated to the confirmation of C1 clusters, making use of different observing facilities in order to cover the range of redshifts encountered in the sample. Selection of spectroscopic targets was based on ugriz optical imaging from the CFHT-LS survey, choosing in priority bright red-sequence galaxies in the vicinity of the cluster X-ray emission. Each spectrum was reduced and its corresponding redshift measured by several independent persons. A final redshift value and associated quality flag was assigned by a moderator. We refer to Adami et al. (2011) for the meaning of these flags in terms of redshift reliability. Additional galaxy redshifts from the VVDS Deep and Ultradeep Surveys (Le Fèvre et al. 2005) and the Subaru Deep Survey (Ueda et al. 2008) as well as redshifts collected from the NED² were added to the sample. Spectroscopic data is stored in cesam³ and will be publicly released in the end of the XMM-XXL survey.

Cluster redshift validation was first based on identification of groups of galaxies sharing similar radial velocities along a line of sight by using the gapper method (e.g. Biviano et al. 1997). We assigned membership in each putative group using a physical radius of 500 kpc around the X-ray position, computed using a cosmological angular distance at the mean group redshift. We used catalogues of galaxies with photometric redshifts derived from the CFHT-LS Wide Imaging Survey and inspected galaxy density maps in photometric redshifts slices centred around each group. A clear overlap between the X-ray isophotes and the density map at the (true) redshift of the source is expected. In this case, the nature of the X-ray source is confirmed as a galaxy cluster and its redshift validated (‘C1 confirmed’ clusters). 1 source out of the 53 selected C1 candidates could not have any related spectroscopic observation and falls outside of the CFHT-LS footprint, preventing the derivation of a photometric redshift. Noting that it was classified as a C2 source by our former pipeline, it is discarded from this analysis.

Table 1 lists the C1 cluster catalogue including all 52 sources validated as bona fide C1 clusters for this work. It represents a superset of Pacaud et al. (2007) and Adami et al. (2011) C1 samples and a sub-set of the full XMM-LSS source catalogue (Chiappetti et al. 2013). All but one (98 per cent) have spectroscopically validated redshifts. We note that XLSSC 035 and XLSSC 048 are not ‘C1 confirmed clusters’ according to the definition above, because of their current low number of securely identified spectroscopic members (see Adami et al. 2011, for a discussion). The remaining cluster (XLSSU J021744.1-034536) is located at z_phot = 1.9 on the basis of a photometric redshift analysis involving deep, near-infrared, imaging data (Willis et al. 2013) and included in the present sample since it clearly is detected as a C1 source in X-rays. A discussion of the errors on cluster spectroscopic redshifts can be found in Adami et al. (2011) and we choose to be conservative in quoting values up to the second decimal in Table 1. Three-colour images and X-ray overlays not already published in Pacaud et al. (2007) are presented in Appendix C.

CHARACTERIZATION OF THE SURVEY

In order to obtain statistically relevant results from the present cluster sample, we derive a survey selection function. It is straightforwardly associated with the detection process described in previous section and our procedure follows closely Pacaud et al. (2006), Elyiv et al. (2012) and Clerc et al. (2012b).

Simulations and observational selection function

We first compute a selection function for each individual pointing. To this purpose, we designed simulations of realistic XMM observations containing point sources representative of the observed AGN logN–logS (Moretti et al. 2003) and extended sources. The latter are represented as β-models with β = 2/3, with varying core radii and fluxes, placed at random positions on the detectors. Our simulations span a variety of detector exposure times (T_exp = 3, 7, 10, 20, 40 ks) and particle background levels (b = 0.25, 0.5, 1, 2, 4 times the nominal value of Read & Ponman 2003). For each value of the exposure time (T_exp), of the background value (b), cluster extent (input core-radius ext) and input count rate (cr), 2500–3500 fake XMM pointings were produced, each of them containing four–eight extended sources. All simulated observations went through the same detection and characterization pipeline as used for real data. As discussed earlier, our simulations show that contamination of a C1 selected sample by point-like and spurious sources is very low, ranging from 1 to 3 per cent depending on exposure time and background level. This contamination rate results from simulations where the point-source population is spatially uncorrelated from the extended sources. We will discuss in Section 6 an extreme case, in which point sources systematically populate the centre of clusters in simulations. The observational selection function is the probability of detecting and characterizing an extended source as a C1. Output detection lists were correlated in position with input source lists, and the selection function |$P_{{\rm C}1,{[\theta _1,\theta _2]}}(T_{{\rm exp}},b,{\rm cr},{\rm ext})$| was derived by selecting only sources satisfying the C1 criteria (see Section 2) and detected within a given a range of off-axis values [θ₁, θ₂].

Selection function of the actual data set

The next step in characterizing the survey selection function consists of linking simulations to real observations. Each actual XMM pointing is assigned its proper selection function by interpolating along the (T_exp, b) grid used for simulations. We estimated background levels (b) in real observations by matching the average local background level around each detected point-like source to the value seen in simulated pointings, similarly to Elyiv et al. (2012) and Clerc et al. (2012b).

Such a formulation of the survey selection function only depends on observational quantities (apparent size and flux). Assuming a cosmological model and a set of mass-observable relations, it can be rewritten in terms of a limiting mass as a function of redshift. We provide an example in Fig. 3, assuming Planck 2013 cosmology and illustrate the changes due to the choice of model, specifically the luminosity–temperature relation.

CHARACTERIZATION OF INDIVIDUAL CLUSTER PROPERTIES

X-ray spectral properties

An X-ray spectrum was extracted around each cluster position in a circular aperture. Similarly to Pacaud et al. (2007), a background annulus is chosen so that it does not contain emission from the cluster. The spectral extraction radius (R_spec) is optimized on the basis of the signal to noise estimated from the cluster surface brightness profile. Background-subtracted spectra are fitted with xspec v.12.8.0 (Arnaud 1996) using a single-temperature apec plasma model (v.2.0.1) and assuming a galactic hydrogen density column given by Kalberla et al. (2005). Metallicity abundances were fixed at 0.3 times the solar value, except for XLSSC 60⁴. The median temperature measured in the sample is 2.1 keV, with a typical uncertainty of ∼15 per cent.

A comparison with previously measured values for the 29 clusters in common with Pacaud et al. (2007) is presented in Appendix A, with an attempt to disentangle between the different causes of discrepancies. We reach the conclusion that a change in apec models slightly impacts the temperatures for the coolest systems, while other results agree well within the error bars: changes in the X-ray processing, xspec version and plasma models only create scatter around the one-to-one relation.

Flux and luminosity measurements

Net count rates and physical fluxes

X-ray cluster fluxes were measured in the [0.5–2] keV band directly on images created from cleaned event lists. Two methods were tested and compared: (i) modelling the surface brightness radial profile, and (ii) integrating the source flux in growing circular apertures (‘growth curve analysis’; Böhringer et al. 2004; Šuhada et al. 2012), as applied in Adami et al. (2011) and Clerc et al. (2012b). We detail here our procedures.

• The first method follows Pacaud et al. (2007) by assuming a one-dimensional β-model (Cavaliere & Fusco-Femiano 1976) and three free parameters: angular core-radius, β and normalization. A local background level is estimated by means of a double-component model (vignetted and unvignetted) adjusted in a source-free area over each of the three XMM EPIC detectors. A local, one-dimensional, analytic PSF (point spread function) model (as in Arnaud et al. 2002) is convolved to the model β-profile and accounts for the telescopes spatial resolution. Model and data profiles are binned to ensure a minimal 3σ signal-to-noise ratio in each bin. χ² statistics provide a best-fitting value and confidence levels on a β-core radius grid. The normalization is derived from the number of counts collected in the fit area. Given the generally low signal-to-noise ratios of C1 clusters and the high background levels in XMM images, χ² contours are degenerate in the two-dimensional β-core radius parameter space (e.g. Alshino et al. 2010). We ranked χ² contours and surface brightness profiles according to their level of degeneracy and found that objects with more than 300 net counts in the [0.5–2] keV band provide well-behaved χ² surfaces. For those 30 clusters, the three-parameter model is then considered as a good description of its surface brightness profile. For the remaining 22 objects, we instead forced β = 2/3 and only derived a best-fitting core-radius associated with this particular choice of prior. The surface brightness model corresponding to the set of best-fitting parameters can then be integrated up to any given radius and provides the cluster flux within the corresponding aperture (e.g. R_spec in Fig. 4).

• The second method does not assume any model as for the cluster surface brightness profile. Cluster emissivity is integrated in circular annuli of growing sizes around the cluster centroid. Background subtraction is controlled via an annulus whose size is adjusted by hand, and a double-component model (vignetted+unvignetted) is fitted over the pixels inside the annulus. This background model is then transported at the source location. Surrounding sources detected by the detection pipeline are masked out and any removed area is accounted for by assuming circular symmetry of the count rate profile. Since this method involves manual intervention, we checked for its robustness by comparing the results of two independent measurers (T. Sadibekova, N. Clerc). In all 22 cases that underwent this comparison, we found results in agreement within 1σ error bars.

Finally, conversion factors from count rates to physical, galactic-absorbed, fluxes were computed using xspec and the best-fitting apec model derived from X-ray spectral analysis (Section 4.1). Fig. 4 displays a comparison of fluxes measured by methods (i) and (ii). It shows that both agree within their 1σ error bars. This comparison is shown within the radius R_spec, specifically chosen for maximizing the signal-to-noise ratio of each cluster emissivity (see Section 4.1 and numerical values in Table 1). Hence, discrepancies due to β-model extrapolation or background removal uncertainties are kept at their lowest level. Finally, we show the good agreement between these calculations and previously published values (Pacaud et al. 2007) in Appendix A.

Bolometric and rest-frame band luminosities

We derived X-ray bolometric and [0.5–2] keV (rest-frame) luminosities by combining physical fluxes measured in the [0.5–2] keV (observer frame) band with the best-fitting spectral model found in Section 4.1. We quote in Table 1 luminosities measured within R₅₀₀ as estimated for each cluster (equation 2). The median bolometric (resp. soft-band) luminosity of our sample is 4.9 × 10⁴³ erg s⁻¹ (resp. 2.0 × 10⁴³ erg s⁻¹) within R₅₀₀. Individual uncertainties are dominated by count rate measurement uncertainties (including background removal) and their median level is 11 per cent.

Mass estimates

The ultimate quantity of interest describing galaxy clusters is their individual, total, mass as derived from X-ray data. Given the low signal-to-noise ratios associated with each cluster, we choose to only provide rough estimates and no error bars. However, we illustrate results obtained by two different methods, each one depending on different observables.

Method 1: isothermal, hydrostatic equilibrium

Similarly to Pacaud et al. (2007), we can estimate the mass within R₅₀₀ by using

• a mass–temperature relation (Sun et al. 2009, see equation 2) in order to obtain a value of R₅₀₀,

• the best-fitting β-model profile injected into the equation of hydrostatic equilibrium under the assumption of isothermality of the intracluster medium (e.g. Ettori 2000), which reads

Mass estimates obtained by this method are listed in Table 1 under column label ‘M1’. In principle, we note that assuming an R₅₀₀-T relation is unnecessary and redundant since the equation linking R₅₀₀ to M₅₀₀ is univocal. We discuss our choice further in Appendix B.

Method 2: luminosity–mass relation

The second method starts from growth-curve flux measurements. They provide luminosities integrated within a cylindrical aperture of any given size. We make use of an L_X-M₅₀₀ relation from Sun (2012) and iteratively find the value of R₅₀₀ that leads to a converged set of L_{X, 500} and M₅₀₀ values. This approach is similar to the one presented by Šuhada et al. (2012) for the XMM-SPT (South Pole Telescope) cluster sample. However, in contrast to the XMM-SPT clusters, temperature measurements are available in this work. They are used to model the cluster X-ray spectrum (using apec v.2.0.2) and convert from instrumental count rates to physical quantities. We checked that this iterative analysis returns values of L_{X, 500} consistent with the computation described in Section 4.2.2 within their respective error bars, although the underlying scaling relations used in deriving the radius R₅₀₀ differ. Values obtained with this method are quoted in Table 1 under column label ‘M2’.

Comparison of values

Fig. 5 compares mass estimates obtained from these two methods. Although the scatter is high and differences up to a factor of ∼5 are clearly apparent, the broad agreement is encouraging and confirms the validity of our X-ray analysis. Indeed, both methods rely on distinct X-ray observables. Method 1 does not require knowledge of the total luminosity (or flux) of the cluster, while this is a key ingredient of Method 2. Conversely, Method 2 requires knowledge of the gas temperature only for converting from count rates to luminosities (which includes a k-correction), while it directly enters Method 1 (see equation 3). The correlation between these values thus reflects the intrinsic correlation between mass, luminosity and temperature in the intracluster medium. Based on these results, we find that the median mass (M_500c) of clusters in the present sample is ∼5 × 10¹³h⁻¹ M_⊙.

RESULTS

Redshift distribution

Fig. 6 shows the redshift distribution of all 52 sources entering this analysis (plain blue histogram). Typical uncertainties on cluster redshift are much smaller than the bin size of Δz = 0.1 used for this plot (of the order few ×10⁻³; Adami et al. 2011). A model distribution is superimposed, whose derivation follows the steps presented in Pacaud et al. (2007) and Pierre et al. (2011; see also Clerc et al. 2012a). In brief, a model halo distribution (Tinker et al. 2008) is projected on to the X-ray observable space (+redshift) using standard scaling relations (Arnaud et al. 2005; Maughan et al. 2012) and XMM detector responses. Evolution of these scaling relations follows a self-similar model. Our observational selection (shown on Fig. 2) filters out undetectable clusters. To this purpose, it assumes a fixed physical core-radius of 180 kpc for all clusters. The resulting distribution is further integrated over all quantities but redshift and provides the expected dn/dz distribution. This quantity is summed in finite redshift bins and uncertainties on the histogram are computed following the formalism described in Valageas et al. (2011). They account for both shot-noise (i.e. |$\sqrt{n_i}$|⁠) and sample variance in each bin. These uncertainties are almost uncorrelated (e.g. |${\rm C}_{ij,i \ne j} \ll \sqrt{{\rm C}_{ii} {\rm C}_{jj}}$|⁠). Given the number of assumptions involved here, Section 6 will discuss further the hypotheses entering the derivation of this model histogram.

L_X-T scaling relation and evolution

The luminosity–temperature relation (L_X-T) is one of the main studied scaling laws of X-ray clusters (see e.g. Arnaud & Evrard 1999; Pratt et al. 2009; Mittal et al. 2011; Maughan et al. 2012; Takey, Schwope & Lamer 2013). It reflects the history of heating and cooling of the intracluster gas (see e.g. Voit 2005) and relates two major cluster properties ultimately linked to the total cluster mass (Kaiser 1986). Taking advantage of the wide redshift range spanned by our sample, we address the evolution in the normalization of this scaling law assuming various local relations selected in the literature. We pay particular attention to the role of selection effects in this analysis.

L_X-T relation in the sample

Fig. 7 shows the relationship between the bolometric luminosity and the temperature measured for the 52 clusters in this sample. The X-ray luminosity correlates well with gas temperature in all three redshift slices displayed in Fig. 7 as expected from basic scaling arguments (Kaiser 1986). We plot in the same figure a selection of recent scaling relations (Arnaud & Evrard 1999; Pratt et al. 2009; Maughan et al. 2012; Sun 2012). Although these scaling relations were derived with samples of clusters spanning relatively wide redshift ranges, the numerical values corresponding to these relations were published for the local Universe (z = 0). Hence, in the following, we will refer to them as ‘local’ scaling relations. Each of them is evolved self-similarly to the median redshift in each panel of Fig. 7 (z = 0.20, 0.43, 0.96), i.e. L_X(T, z) = L(T, 0) × E(z). The slope of these extrapolated relations appears compatible with our data points, as is the normalization. However, this visually good agreement has to be checked against selection effects and we describe our findings in the next paragraph.

Evolution of the L_X-T normalization and impact of selection biases

Since many objects in the sample are close to the detection threshold, it is necessary to correctly account for selection effects before any attempt to interpret the data point distribution in Fig. 7 (e.g. Pacaud et al. 2007; Mantz et al. 2010; Allen et al. 2011; Reichert et al. 2011). A typical misinterpretation can arise from Malmquist bias: intrinsically brighter objects are favourably present in the sample, which translates into an average luminosity at a given temperature and redshift higher than the true expected luminosity. Such a bias is increasingly important as the intrinsic scatter in the studied scaling law is high. This is the case for the L_X-T relation (of the order of σ_ln L|T ∼ 0.6, e.g. Pratt et al. 2009). We follow the same approach as in Pacaud et al. (2007) for studying the evolution in the normalization of the relation from our sample. Namely, we model at each redshift the L_X-T relation assuming a local (z = 0) relation and a normalization following E(z) (1 + z)^α. The exponent α is a free parameter in the analysis. The scatter σ_ln L|T is kept at its z = 0 value. The resulting distribution is folded with the survey selection function (Fig. 2) after passing it through the XMM instrumental response. The likelihood of each cluster being drawn from this particular model is computed taking into account uncertainties on the temperature⁵ and neglecting uncertainties on luminosities.

Repeating this procedure for a range of values in α enables the derivation of 68 per cent confidence intervals for α, as quoted in Table 2 (under column ‘corrected’). The resulting value depends on the assumed local (z = 0) scaling relation because of the differences in their slopes, normalizations and scatters. Fig. 8 visually illustrates our results. The disagreement between data points and best-fitting scaling relations is only apparent and due to the impact of selection effects. This is reflected in the numbers shown in Table 2 (column ‘uncorrected’) where the same procedure is applied, but the selection function is artificially neglected (i.e. we assume that P_C1 = 1). In the latter case, the normalization is found to be positive or mildly negative (with respect to self-similar evolution, α = 0), while a proper account for selection effects clearly hints towards a negative evolution. This result is in agreement with the findings of Reichert et al. (2011), Hilton et al. (2012) and Clerc et al. (2012b), although these studies differ in their treatment of selection effects and modelling.

We note here that self-similar evolution does not necessarily imply a ∝ E(z) scaling of the L_X-T normalization (Maughan 2014). This actually depends on the assumed slope of the M_gas-M scaling relation and Maughan (2014) find a E(z)^0.4 behaviour instead. The present significance of the negative evolution is thus reduced when expressed relative to this particular scaling.

Tridimensional distribution of clusters

The sample presented in this work is unique in several respects: it is drawn from a homogeneous, contiguous, X-ray survey, it is 98 per cent complete in terms of spectroscopic redshift availability, spans a wide range of redshifts and masses and the sample selection function is well understood. This is summarized in Fig. 9, where each C1 cluster from Table 1 is drawn at its location in a comoving coordinates frame (the observer is located at the origin and the line of sight is the z-axis). We note that the number of objects (52) presented in this study is too low to enable robust, quantitative, interpretations of the three-dimensional distribution of clusters in the volume (e.g. correlation function analysis). However, this is an open window for the ongoing XMM-XXL survey (Pierre et al. 2011, Pierre et al. in preparation), which multiplies the surveyed area by a factor of 5 (in two separate areas).

Fig. 10 shows the location of galaxies detected in two large spectroscopic samples: BOSS-DR10 (Ahn et al. 2014) and VIPERS-PDR1 (Garilli et al. 2014; Guzzo et al. 2014). The declination range was shrunk to only display objects in the common sky area. Moreover, radial selection effects differ from one survey to the other, in particular, VIPERS galaxies are preferentially selected in the 0.5 ≲ z ≲ 1 redshift range. As we will describe in the next section, the most striking visual result in this figure is the absence of C1 X-ray clusters in this redshift domain, while clustering seems apparent in the VIPERS data set.

DISCUSSION

We focus now on modelling the redshift distribution of clusters as presented in Section 5.1 and Fig. 6. The first redshift bin (0 < z < 0.1) contains six groups (XLSSC 035, 062, 021, 054, 011, 052) of low mass and small size. It is thus likely that our assumption of a fixed core-radius value (180 kpc) fails in this redshift range. For example, assuming a core-radius size of half this value roughly doubles the number of predicted clusters in this bin. However, given the small volume of Universe involved, we refrain from deriving quantitative results from this bin. Hence, the following results rely on the 46 clusters with z > 0.1.

A gap in the redshift distribution?

The redshift distribution model of Fig. 6 presents a rough agreement with the observed redshift histogram of the sample. Rebinning the histograms such that each model bin contains at least five objects, we compute a χ² value of 18.0 using 10 bins. Given that P(χ² ≤ 18.0) = 96 per cent, we conclude on a marginal agreement between data and this model.

Updating the cosmological model to the best-fitting model derived from Planck CMB results (Planck Collaboration XVI 2013), we obtain a new curve, as shown in Fig. 11. Because of higher values of σ₈ (0.834 instead of 0.821) and Ω_m (0.316 instead of 0.279), the total number of predicted clusters is higher in each Δz bin. Taking into account uncertainties in each bin, we find a χ² of 28.0 (in 12 bins). Since P(χ² ≤ 28.0) = 99.7 per cent, we reject the hypothesis that the observed redshift distribution derives from this model, with a false-alarm error probability of ∼0.3 per cent (equivalent to a 3σ rejection).

Fig. 11 suggests that the strongest disagreement between data and model occurs in the 0.4 ≲ z ≲ 0.9 range, in which too many clusters are expected. The data histogram alone suggests the presence of a ‘gap’ in this range, reinforced by the fact that four C1 clusters are clearly detected at z ∼ 1, ruling out a severe sensitivity effect. Limiting to this ‘ad hoc’ redshift range provides a χ² of 15.4 in five bins, also leading to model rejection with false-alarm error probability of 0.4 per cent. Taking these results at face value let us postulate the existence of a substantial lack of massive structures around z ∼ 0.7. This deficit would be rare enough to be marginally accounted for in our sample variance calculations. However, in what follows, we discuss several physical effects that can be held responsible for this observation and argue for a combination of observational and physical effects.

L_X-T evolution and redshift histogram

Model redshift distributions shown in Figs 6 and 11 depend on the exact scaling relations used for converting cluster masses into observed properties. This is particularly true for the luminosity–temperature relation, which is involved in the computation of a cluster mass from its apparent flux. As shown in Section 5.2, our data set prefers a negative evolution of the L_X-T, namely a normalization evolving as E(z)(1 + z)^{−1.6 ± 0.4} instead of E(z). Fig. 12 demonstrates the impact of such an evolution on the modelled redshift distribution, still under the assumption of a Planck 2013 CMB cosmology (i.e. equivalent to Fig. 11). With this evolution, clusters of a given mass become fainter with increasing redshift, thus we expect less detections at higher redshifts, simply due to a dimming of these objects. In this case, the χ² value is 6.1 (in eight bins), sufficiently low to prevent the model rejection. Hence, the additional assumption of a non-self-similar L_X-T reconciles the observed redshift histogram with our model and reduces the significance of the central gap.

We note that a complete analysis should simultaneously fit a cosmological model and a scaling relation model in order to properly account for Eddington bias (e.g. Mantz et al. 2010). This kind of self-consistent analysis in the signal-to-noise regime of ‘XMMLSS-like’ clusters is particularly well handled by the z-CR-HR method presented in Clerc et al. (2012a) and will be applied to the much larger sample of XMM-XXL clusters.

Finally, we stress that previous results were derived assuming a local L_X-T from Maughan et al. (2012). The other three local scaling laws considered earlier (Table 2) lead to even higher cluster densities, hence in stronger disagreement with this data set (see also Clerc et al. 2012b for a discussion).

Central AGN contamination and redshift distribution

Simplifying hypotheses entering the derivation of our selection function do not account for the true physical nature of galaxy clusters and possibly impact the model redshift distribution shown on Figs 6 and 11. We explore in this section the impact of an evolving AGN contamination fraction in the centre of galaxy clusters by means of simple simulations and a demonstrative toy-model.

Simulations with point-source contamination

The presence of a central AGN in galaxy cluster is a common source of concern for extended source detection algorithms. A central, blended, point-like source increases the total flux of a cluster in X-rays, thus increasing its detection probability. However, beyond a certain flux the detected source can no longer be classified as a ‘secure’ extended source on morphological grounds only, given the sharply peaked profile of the blend. We modified our set of XMM cluster simulations by adding a point source with varying flux at the centre of each β-model. We processed these simulations with the exact same methodology as for real data and derived the C1 detection probability of a cluster as a function of its count rate, extent and central contamination.

Our raw results are displayed on Fig. 13. As expected, a very bright central AGN (e.g. 80 per cent contamination) causes a misclassification of the detected source and a decrease in the C1 detection probability. On the other hand, a 10–20 per cent contamination in relatively bright and extended clusters (e.g. 0.02–0.05 cts s⁻¹ and 40–60 arcsec core-radius) slightly enhances the detection probability (‘flux boosting’), while bright, compact clusters are less affected at this level of contamination. The increase in detection with AGN contamination is conspicuous for faint (e.g. 0.005–0.01 cts s⁻¹) clusters, provided their morphology is not too compact and the AGN flux remains reasonable (below ∼50 per cent).

Obviously, characterization of extended sources contaminated by a point is heavily dependent upon the surrounding background level in the X-ray images. We repeated this exercise for a higher background level and a different exposure time (20 ks). The general statements above remain unchanged, but they impact the selection function at slightly different locations in the extent-flux-contamination parameter space.

Impact of point-source contamination on dn/dz

We fold the modified selection functions of Fig. 13 into the model predicting C1 cluster redshift distribution. Results are shown in Fig. 14. Each separate histogram shows the expected density of clusters assuming that all of them are contaminated by a central AGN at a given level (from 0 to 80 per cent)⁶ From this analysis, we conclude that high contamination rates dramatically reduce the number of C1 detections because of misclassifications of the sources. On the other hand, a slight increase in number of C1 is barely perceptible for light AGN contamination (5–10 per cent), lowering the impact of ‘flux boosting’ on C1 detection. Relying on this simple model, we conclude that mild (>20 per cent) contamination is a valid explanation for the lack of observed C1 in the 0.5 < z < 1 redshift range, but we rule out the possibility that central point-source flux excess is the cause for the apparent increase at z ∼ 1 in the observed redshift distribution of C1 clusters (Fig. 6). We illustrate this finding more clearly on Fig. 15. This shows a toy-model in which clusters around z ∼ 0.7 are contaminated by a central AGN with flux ratios 0.5 ± 0.25 and almost uncontaminated in the remaining redshift intervals. This simple model creates a ‘gap’ in the redshift distribution, simply because of selection effects.

Towards a more realistic AGN population model in clusters

The toy-model depicted in the previous section is an ‘ad hoc’ illustration of the impact of selection effects on the redshift histogram of objects we classify as galaxy clusters. Recent findings in the field of X-ray surveys show that (i) X-ray AGN preferentially live in 10^13.5 M_⊙ haloes (see e.g. Cappelluti, Allevato & Finoguenov 2012, for a review) and (ii) the density of low-luminosity AGN (L_X ≲ 10⁴⁴ erg s⁻¹) peaks at redshifts ∼ 0.5-1 (e.g. Hasinger, Miyaji & Schmidt 2005; Ueda et al. 2014). This suggests a likely enhancement of AGN flux in low-mass clusters at redshifts around ∼0.7. Such an enhancement should depend both on the number density and emissivity of clusters and the AGN luminosity function across cosmic times. We propose here a simple model in order to estimate the typical flux contamination of clusters by AGN. A more detailed investigation is deferred to future work (Ramos Ceja et al., in preparation).

In the first step, we calculate the [0.5–2] keV emissivity of AGN per unit volume at different redshifts. This is done by linking the AGN X-ray luminosity function computed by Ueda et al. (2014) to a bank of AGN spectral models (adapted from Gilli, Comastri & Hasinger 2007). Such spectra depend on the source redshift, the intrinsic power-law index Γ, the absorbing column density of obscuring material N_H and the source luminosity in the [2–10] keV band. Assuming Γ = 1.9 (Gilli et al. 2007), we integrate the distribution of AGN over values of N_H (10²⁰–10²⁶ cm⁻²) and L_X (10⁴¹–10⁴⁷ erg s⁻¹) and we obtain the total [0.5–2] keV flux emitted by AGN as a function of redshift. As already shown in Ueda et al. (2014), it peaks at z ∼ 0.7. In the second step, we derive the distribution of group/cluster fluxes using the cluster model described in Section 5.1, restricted to haloes of mass 10¹³ ≤ M_200b/(h⁻¹ M_⊙) ≤ 10¹⁴. We finally derive the typical AGN-to-cluster flux ratio in the [0.5–2] keV band. We assume a typical cluster radius of 0.5 Mpc (hence a volume ∼0.5 Mpc³) and a linear scaling of AGN number density with matter density (i.e. the number of AGN per unit volume is x times higher in clusters than in the field, x being of the order of a few hundreds). Integrating this ratio weighted by the number of clusters at a given redshift provides the series of curves shown in Fig. 16.

This model suggests an enhancement of the flux ratio between AGN and cluster around z ∼ 0.4, and a slight decrease at higher redshifts. The order of magnitude of the contamination level must reach ∼ 40-50 per cent in order to account for the gap in the C1 redshift histogram (Fig. 15): this is in rough agreement with the level calculated in our simple model (e.g. for x = 500 and L_X > 10⁴³ erg s⁻¹). Although instructive, this model presents two main caveats, as it neglects interactions between AGNs and clusters. First, physical mechanisms activating cluster central AGN differ from those in the field (e.g. Fabian 2012). Moreover, AGN in clusters may not be centrally concentrated and more likely to spread within the cluster volume (e.g. Branchesi et al. 2007; Haines et al. 2012).

Surface brightness profiles and redshift distribution

The predicted redshift distribution of XMM-LSS clusters discussed so far relies on the assumption of a particular surface brightness profile for the clusters. Indeed, the selection function as shown in Fig. 2 is a function of the cluster angular core-radius. This core radius is relative to a β = 2/3 model, since the extended sources in simulations follow this surface brightness profile. It enters our cosmological model by assuming a physical value of R_c = 180 kpc. Similarly to Section 6.3, we investigate the impact of such a hypothesis on the predicted redshift histogram.

In the first step, we relaxed the assumption on β and created a new set of simulations with different values: β = 0.55, 0.60, 0.75 and 0.90. We analysed these images with our pipeline and derived the C1 detection probability as a function of core radius, input count rate and β. Unsurprisingly, changing the value of β at fixed core-radius and flux changes the C1 detection probability. Higher values lead to sharply peaked profiles, hence increased detection rates. Very concentrated clusters (R_c = 10 arcsec) with high β values (≳0.75) are misclassified as point sources. Folding the modified selection functions into the model predicting the C1 redshift distribution leads to results shown in Fig. 17. Each histogram represents the predicted density of C1 clusters assuming all of them follow a β-profile with R_c = 180 kpc and different β. As precedently in the case of AGN contamination, these results can be interpreted in two complementary ways. First, a possible explanation for the lack of clusters in the current sample can be attributed to selection biases due to a (evolving) variation of surface brightness profiles in the cluster population. Secondly and conversely, statistical surface brightness analyses of an (X-ray-selected) cluster sample must correctly take into account selection biases, since such a sample may be biased towards sharply peaked profiles (e.g. high values of β or small core-radius values).

In order to estimate the impact of a centrally luminous, cool-core, cluster on our selection function, we followed Eckert, Molendi, & Paltani (2011) and modelled such objects with a ‘double-β’ model. Namely, a broad β = 2/3 component with a physical core-radius of size 170 kpc hosts a smaller β = 2/3 component with a size 40 kpc and a relative peak intensity 15 times higher than the larger one. These sources were inputs of our realistic XMM simulations. Running our detection algorithm provides a new selection function, which is subsequently folded into our cosmological model and provides an expected redshift distribution assuming that all galaxy clusters follow this particular profile. The result is also shown in Fig. 17 and can be interpreted in a similar fashion as in the case of central point-source contamination: a cool core slightly enhances the detection probability at lower redshifts (z ≲ 0.3), thus increasing the number density of C1 clusters. At higher redshifts, such clusters appear more concentrated and are less likely to be classified as ‘secure extended source’ (C1) by the detection algorithm.

Recently, McDonald et al. (2013) investigated the X-ray surface brightness evolution of 83 clusters detected by the SPT through their S–Z signature. Based on high-resolution Chandra data, they found no change in the cooling properties of those clusters (central entropy and cooling time). However, they found an evolution in the distribution of surface brightness profiles, namely a deficit of cuspy, cool-core clusters at high redshifts (z > 0.75) as compared to lower redshifts. Our observed redshift distribution is compatible with such an evolution, as is visible in Fig. 17 by comparing the plain black and plain thick blue lines. A large presence of cool cores at lower redshifts would decrease the observed density of clusters in the 0.4 ≲ z ≲ 0.7 range, while a lack of cool cores at higher redshifts would enhance the number density above z > 0.8, hence leading to a ‘gap’ in the observed redshift distribution of C1 clusters. Proper assessment of such important evolution trends will ideally be addressed by comparing multiwavelength cluster selection, by targeted Chandra follow-up observations of the sample and by investigation of numerical simulations.

CONCLUSIONS

This work presents a detailed study of a complete sample of 52 galaxy clusters. All are detected in an X-ray contiguous survey with XMM–Newton and covering 11 deg² in sky. We used an improved version of the well-qualified xamin algorithm (Pacaud et al. 2006) to reduce event lists, produce images in the [0.5–2]��keV band and detect sources in the X-ray data. Relying on a set of extensive, realistic simulations, we defined a clean and uncontaminated ‘C1’ sample of extended sources. A series of follow-up optical observations confirmed the nature of these galaxy clusters. All but one are spectroscopically confirmed and their redshift is determined with high accuracy (Δz < 0.01).

We measured X-ray properties of each of these clusters in a homogeneous way. We demonstrated the good agreement between fluxes measured assuming a model surface brightness profile and fluxes measured by aperture photometry. X-ray spectra provided temperature measurements of the intracluster gas, which displays a typical 15 per cent relative uncertainty, as well as X-ray luminosities within R₅₀₀, radius estimated from scaling relations. We finally computed cluster total mass estimates with two different methods, one relying on the assumption of intracluster medium isothermality and hydrostatic equilibrium, the other on a scaling relation between luminosity and mass. We interpret their rough agreement as a reflection of the underlying X-ray scaling relations between mass, temperature and luminosity, and as a consequence of the consistency in our measurements.

We modelled the C1 cluster selection function across the wide survey area using a set of synthetic simulations and found a theoretical limiting mass (M_200c) of 1-2 × 10¹⁴ h^{− 1} M_⊙ (80 per cent detection probability), depending on redshift and detailed assumptions of the mass-to-observable conversion. Folding this selection function into a cosmological model allowed us to compare the observed redshift distribution of clusters in the sample to theoretical expectations. Accounting for uncertainties due to small number statistics and cosmological sample variance, we find a marginal agreement between the predicted model and the observed distribution, and we note that results depend on the choice of model. In particular, assuming the Planck CMB cosmological model leads to predict too high a density of objects at 0.4 < z < 0.9, as compared to the current sample.

We compared several bolometric luminosity–temperature relations extrapolated from the recent literature to our data points. Taking advantage of our knowledge of sample selection effects, we suggest a simple parametrization for the evolution of the normalization of the L_X-T and confirm a negative trend with respect to a pure self-similar evolution. This result is observed in numerical simulations (e.g. Short et al. 2010), when pre-heating of the intracluster medium occurs at the early stage of cluster formation. Interestingly, different assumptions for local (z = 0) scaling relations lead to different results for their evolution (see numbers quoted in Table 2). This is due to their different slopes and normalizations and the fact that our sample spans different loci of the L_X-T plane as redshift increases. Indeed, selection effects move the high-redshift sample to higher temperatures and luminosities. Importantly, we confirm that mistakenly neglecting selection effects substantially changes these conclusions and leads to a quasi-self-similar evolution.

We concluded this study by investigating the reality of the apparent ‘gap’ in the redshift distribution of clusters between 0.4 ≲ z ≲ 0.9.

• Considering the negative evolution of the L_X-T relation found earlier, we find a milder disagreement between the Planck 2013 cosmology model and our data set. We note however that a complete analysis should self-consistently address the cosmological model and the evolution of scaling relations.

• We explored to what extent the observed redshift distribution can be explained in terms of a selection bias due to central point-source contamination of clusters. Based on our simulations, we cannot attribute the increase of cluster density at z = 1 to a detection enhancement (‘flux boosting’). We propose instead an ad hoc scenario in which the AGN contamination evolves with redshift, both in its occurrence and its strength and peaks at 0.5 ≲ z ≲ 1. Interestingly, combining our cluster population model to the luminosity function of AGN in the Universe points towards a similar trend, although a more thorough modelling is needed (in particular using numerical simulations).

• We finally described the impact of various surface brightness profiles on the C1 selection function. Our results show that the enhanced presence of cuspy, cool-core clusters at low redshifts (e.g. at z < 0.75, as observed by McDonald et al. 2013) could also lead to an apparent gap in the observed C1 redshift distribution, since cool-core clusters in 0.4 ≲ z < 0.75 would be considered as less likely extended sources by detection algorithms.

Comparison of cluster catalogues selected in X-ray and other wavelengths (e.g. optical and S–Z) will confirm these possible scenarios. So will do detailed studies with the Chandra observatory by assessing the point-source content and surface brightness shape evolution of these galaxy clusters. Future results will therefore rely on the larger XMM-XXL survey (50 deg² at a similar depth), separated in two independent fields in order to beat sample variance. Echoing our discussion on selection effects and their impact on cosmological observables (here dn/dz), a large effort has been undertaken within the XMM-XXL team in order to develop and compare multiwavelength cluster selections, to perform detailed follow-up of selected samples and analyses of clusters from numerical simulations. The full-sky survey of eRosita (Predehl et al. 2010; Merloni et al. 2012) starting early 2016 will bring the statistical power (∼10⁵ X-ray galaxy clusters up to z ≳ 1) needed to break degeneracies between the multiple assumptions entering the cosmological analysis of X-ray cluster surveys and will offer an unprecedented tridimensional view on the large-scale structure as traced by its most massive constituents.

We are thankful to the anonymous referee for his careful reading and his help in improving the quality of this manuscript.

We thank P. Giles, T. Ponman and J. B. Melin for useful discussions on the X-ray properties of the clusters, J. P. Le Fèvre for the cluster data base management, C. Libbrecht and A. Gueguen for their contribution in the X-ray pipeline development. We also thank Ian McCarthy for assistance with the calculation of cluster masses.

ML acknowledges a post-graduate studentship from the UK Science and Technology Facilities Council (STFC). GPS acknowledges support from the Royal Society and STFC.

FP acknowledges support from the DLR Verbunforschung grant 50 OR 1117.

This research is based on observations obtained with XMM–Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.

This research is also based on observations collected at TNG (La Palma, Spain), Magellan (Chile), and at ESO Telescopes at the La Silla and Paranal Observatories under programmes ID 072.A-0312, 074.A-0476, 076.A-0509, 070.A-0283, 072.A-0104, 074.A-0360, 089.A-0666 and 191.A-0268.

This research has made use of the XMM-LSS data base, operated at CeSAM/LAM, Marseille, France.

This research is based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/IRFU, at the Canada–France–Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Science de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at Terapix available at the Canadian Astronomy Data Centre as part of the Canada–France–Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS.

This paper uses data from the VIMOS Public Extragalactic Redshift Survey (VIPERS). VIPERS has been performed using the ESO Very Large Telescope, under the ‘Large Programme’ 182.A-0886. The participating institutions and funding agencies are listed at http://vipers.inaf.it.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation and the US Department of Energy Office of Science. The SDSS-III website is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington and Yale University.

REFERENCES

APPENDIX A: COMPARISON WITH PACAUD ET AL. (2007) MEASUREMENTS

As described in Section 2, 29 of the 52 clusters presented in Table 1 pertain to the sample published by Pacaud et al. (2007, hereafter P07). They are issued from similar data sets and were analysed through similar methodologies. However, several changes have occurred between these two analyses:

• the xamin software used to extract sources, leading to slight changes in the masking of sources and definition of the optimal extraction radius R_spec;

• the event list processing and spectral extraction algorithms, in particular the xmm-sas⁷ version;

• the version of xspec (from v.11.3.2 to v.12.8.0);

• the apec model, specifically the ATOMDB⁸ data base models (from v.1.3.1 to v.2.0.1).

Updated cluster redshift

XLSSC 35 has been updated to a new redshift value of z = 0.07 instead of z = 0.17 as quoted in P07. The presence of a giant elliptical at z = 0.069 coincident with the X-ray peak argues in favour of this cluster redshift, although a superposition of two layers cannot be ruled out (see discussion in Adami et al. 2011).

Temperature measurements

We first compare the X-ray spectral measurements, through the values of temperatures T_X. Fig. A1 compares values listed in P07 to those published in this work. Taking into account measurement uncertainties, we conclude to good agreement between these two series. In order to address the discrepancies, we defined a series of additional temperature measurements for all clusters by applying changes as listed in Table A1. We summarize our findings as follows, the numbers referring to this table.

• (5) provided identical results as P07 (2), proving that there is no other source of bias than the one listed in the table.

• (4) and (5) provided identical results, as did (3) and (7). Since only the xspec version was changed in these comparisons, we cannot attribute the discrepancies to the spectral fitting routines in xspec.

• (6) and (7) led to the identification of a bias in the temperatures of cool systems (T ≲ 2 keV), attributed to a change in the apec plasma models. The newest apec version (v.2.0.1) delivers higher temperatures as the v.1.3.1, the effect being more pronounced for the coolest systems (from 1σ differences above 1 keV to 2σ–3σ differences below 1 keV). As a straightforward consequence, this bias is also found in the (1) and (3) comparison.

• (1) and (6) provided almost identical results, except for the presence of two outliers with large error bars. We attribute these differences to the changes in spectral extraction regions and the low signal to noise of the spectra involved.

• (3) and (5), and (3) and (2) provided similar results, although with some scatter around the one-to-one relation. This is attributed to the change in event lists creation and spectral extraction routines.

In brief, we attribute the scatter around the equality line in Fig. A1 to changes in the event lists processing and our definition of source extraction regions, while the small bias at low temperatures is attributed to a recent change in apec models.

Note that the updated redshift value for XLSSC 35 leads to an updated value of the temperature that is consistent with the previously published value (T_X = 1.2 ± 0.1 keV in P07, T_X = 1.1 ± 0.1 in this work).

Flux measurements

We compare in Fig. A2 our flux measurements with those obtained in P07. The methodology adopted in P07 is very similar to our ‘method (i)’ in Section 4.2. Namely, it relies on fitting a surface brightness profile by means of β-models. For this reason, we do not compare fluxes measured with method (ii) with those of P07. As this comparison is shown in a radius of 0.5 Mpc at the cluster redshift, we corrected our angular apertures from the change of cosmological model. Note that XLSSC 35 was quoted with a redshift of 0.17 in P07, implying a smaller angular aperture than the one used for this work. Overall, both flux measurements are in excellent agreement.

APPENDIX B: DERIVATION OF MASSES AND ASSUMPTION ON R₅₀₀

APPENDIX C: NOTES ON INDIVIDUAL CLUSTERS

Fig. C1 shows X-ray/optical overlays for 23 C1 clusters in this sample (the other 29 are shown in P07, their appendix B).

• XLSSC 060: Abell cluster A0329. Our pipeline wrongly deblended multiple components, due to the exceptional extent and brightness of this source and the presence of gaps on XMM detectors. They were manually merged together for the purpose of measuring its X-ray properties. Cruddace et al. (2002) measured an unabsorbed, [0.1–2.4] keV flux of 2.12 ± 0.42 × 10⁻¹² erg s⁻¹ cm⁻² from ROSAT data. This translates into a [0.5–2] keV, galactic-absorbed, flux of 1.2 ± 0.2 × 10⁻¹² erg s⁻¹ cm⁻², hence entirely consistent with our XMM value.

• XLSSC 079: this cluster is detected on the deepest pointing of the survey (80 ks on-axis) at an off-axis radius of 8 arcmin. The X-ray analysis is therefore severely limited by confusion: its extended emission is contaminated by a number of point sources. Despite our efforts to correctly mask all point sources, we recommend to consider its temperature and luminosity measurements with caution. This is reinforced by the fact that this cluster appears as a clear outlier in the L_X-T diagram (lower-right point in the first panel of Fig. 7).

• XLSSC 053: this cluster is probably a group of clusters at z ∼ 0.5, as hinted by the projected distribution of galaxies and the faint, large, X-ray surface brightness. An assessment of its multiple-component nature will be possible thanks to the analysis of spectroscopic redshifts in the vicinity of this object.

• XLSSU J021744.1-034536: this cluster was first presented and discussed in Willis et al. (2013). We note that recent data obtained with the Combined Array for Research in Millimeter-wave Astronomy (CARMA) interferometer confirmed the presence of hot gas at the location of this object via S–Z effect (Mantz et al. 2014). To date, its spectroscopic confirmation is awaited. A 3 × 9 min exposure spectrum was obtained using the FORS2 instrument at ESO-VLT. A long slit was centred on the bright, blue object close to the X-ray centroid and on the bright, blue, object located 21 arcsec southwards. Both their spectra indicate these objects are probably stars. The red cD galaxy (visible in the image of Willis et al. 2013) partly falls on to the slit but is too faint to provide a spectrum. A very faint object located within the X-ray contours at |$\mathrm{{\rm RA}}=34.434$|⁠, δ = −3.753 (J2000, 2 arcsec positional uncertainty) shows one emission line in all three exposures at λ = 5437.5 Å. We postulate this line is Lyα emitted by an active emitter at z = 3.47. With this data in hand, we cannot exclude that the two stars and the active object also emit X-rays contaminating the galaxy cluster emission.