4. MASS DISTRIBUTION OF CLUSTER SAMPLES

Although the careful modeling of individual cluster cores and extended regions offers a unique way to characterize the mass distribution and understand cluster physics in detail, analysis of cluster samples provides important insights into cluster assembly and evolution. There have been several statistical studies focused on measuring cluster masses derived from lensing and comparing these with mass estimates from other measurements such as: richness, X-ray luminosity, X-ray temperature, velocity dispersions of cluster galaxies, and the Sunyaev-Zel'dovich decrement. These multi-wavelength comparisons enable a deeper understanding of empirically derived scaling relations between key physical properties of of clusters (e.g. Luppino & Gioia 1992, Loeb & Mao 1994, Miralda-Escude & Babul 1995, Allen 1998, Ota et al 1998, Ono et al 1999, Irgens et al 2002, Huterer & White 2002). These studies also help uncover how mass is partitioned between the different baryonic and non-baryonic components on cluster scales. Studying cluster samples allows the probing of several fundamental questions with regard to the dynamical state of clusters, namely, are clusters relaxed? How much substructure is present in clusters? How triaxial are clusters? How recently has a cluster had a major merger with another sub-cluster and what are the signatures of such an event? How important are projection effects in mass estimates? Are clusters in hydrostatic equilibrium? When did clusters start to assemble? And how have they evolved? Observationally derived answers to these questions from cluster samples can then be directly compared to numerical simulations, thus providing insights and tests of the structure formation paradigm.

4.1. Early Work

Comprehensive multi-wavelength datasets that ideally span a range of spatial scales in clusters are needed for such statistical studies. Collecting such datasets is a big challenge as it requires coordination between researchers working with a range of observational techniques deploying many different resources. Some of the first studies of cluster samples did produce interesting cosmological results, as discussed in Luppino et al (1999), Allen et al (2001, 2002), Dahle et al. (2002) and Smith et al. (2003).

One of the key challenges for these statistical studies lies in the very definition of a sample with robust criteria, that will be complete and volume limited and be representative to avoid systematic biases. Starting from simple selection criteria is therefore very important. For instance, dramatic lensing clusters imaged by HST are likely a biased sample of the most massive clusters at any redshift with enhanced strong lensing cross sections due to an excess of mass along the line of sight from either the cluster itself or the presence of other intervening structures. Most frequently cluster samples are therefore selected on the basis of their X-ray luminosities, which should minimize projection effects that typically plague optically selected clusters. Since X-ray luminosity is proportional to the square of the electron density of the Intra-Cluster-Medium (ICM), this selection should pick genuinely virialized clusters, irrespective of the line of sight distribution of cluster member galaxies or additional background structures. One of the first systematic studies that combined X-ray and lensing data was a sample of 12 z ∼ 0.2 X-ray luminous clusters of galaxies selected from the XBACS catalog (see Figures 26 and 27) with L_X > 8 × 10⁴⁴ erg/s in the 0.1-2.4 keV band. These clusters have been imaged with the WFPC2 camera (Smith et al. 2001, 2005). It is found that the fraction of strong lensing clusters in this sample is 70%. All of the cluster cores also have a significant weak lensing signal, providing independent lensing constraints on cluster masses.

Figure 26. Cluster samples: 3 of the 12 z ∼ 0.2 X-ray luminous clusters of galaxies selected from the XBACS catalog (Ebeling et al. 1996) observed with the HST/WFPC2 camera. Top row is Abell 68, second row is Abell 209 and last row Abell 267. First column is the weak shear field as measured from the HST data. The second column is a zoom of the cluster cores, and shows for Abell 68 the predicted critical lines (black lines). The third column is the strong lensing mass reconstruction and last column is the overlay of the Chandra X-ray map (Smith et al. 2003).

Figure 27. Left Panel: Central mass fraction (a measure of the dominance of the central dark matter halo), Mcen / Mtot versus central K-band luminosity fraction (measures the dominance of the central galaxy), LK,BCG / LK,tot. There is a remarkably clean separation between a homogeneous population of centrally concentrated clusters (Mcen / Mtot > 0.95, LK,BCG / LK,tot > ∼ 0.55) and a much more diverse population of less concentrated clusters. Center & Right Panels: Mass-LX and Mass-TX relations. The solid and dashed lines show the best-fit relations normalized by the relaxed and unrelaxed clusters respectively. The error bars on each line show the uncertainty on the normalizations. The scatter in the Mass-LX relation appears to be symmetric; in the mass–TX relation the normalization of the unrelaxed clusters appears to be 40% hotter than the relaxed clusters at 2σ significance. Figures from Smith et al. (2005).

Smith et al. (2005) defined a number of criteria to characterize whether clusters are relaxed and also quantified the amount of substructure in them. Out of 10 clusters, they found that three clusters form a homogeneous sub-sample that have mature, undisturbed gravitational potentials which satisfy the following criteria: a dominant central dark matter halo (M_cen / M_tot > 0.95); a dominant central cluster galaxy K-band luminosity fraction (L_K,BCG / L_K,tot > ∼ 0.5); close alignment between the center of the mass distribution and the peak of the X-ray flux (Δ r_peak < 3 kpc); a single cluster-scale dark matter halo best-fit for the lens model; and circular or mildly elliptical X-ray flux contours. The remaining seven clusters did not satisfy one or more of these criteria and were classified as disturbed. The disturbed clusters are much more diverse than the undisturbed clusters and typically have a bi- or tri-modal dark matter distribution, irregular X-ray morphology and an offset between X-ray and mass peaks. Comparison of these results with theoretical predictions indicates that the multi-modal dark matter distribution in disturbed clusters is due to recent infall of galaxy groups into the parent cluster since about z = 0.4. The exact scaling relation between lensing mass and X-ray properties appears to be strongly dependent on the dynamical state of the cluster. Relaxed and unrelaxed clusters appear to follow slightly different scaling relations. Furthermore, this sample was also observed with the wide field CFHT12k camera in three bands (B,R,I) in order to probe the wide field mass distribution using the measured weak lensing shear signal out to the virial radius. However, the comparison of the weak lensing determined mass to the cluster luminosity and X-ray mass estimates reported in Bardeau et al. (2007) [see Figure 28] does not reveal an obvious difference between relaxed or unrelaxed clusters. There are some strong limitations though with this dataset as there were scant constraints on the redshift distribution of background sources, and some lingering inconsistencies between strong and weak lensing results. These first results with only 10 clusters set the stage for the need for larger cluster samples to understand the physical origin of such differences.

Figure 28. Left Panel: Lensing 2D mass versus optical luminosity for the clusters in the Bardeau et al. (2007) sample (12 X-ray bright clusters selected to be at z ∼ 0.2). The lensing mass is computed at the virial radius r200 derived from the best weak lensing fits. The luminosity is computed in the R band for the cluster red sequence galaxies. Dashed line represents a constant M/L ratio of 133 in solar units. The solid line is the best-fit power law M ∝ L1.8. Center Panel: Weak lensing 3D virial mass M200 versus X-ray luminosity. The best-fit line has a slope α = 1.20 ± 0.16. Right Panel: Weak lensing 3D virial mass M200 versus X-ray temperature. The straight line corresponds to a M200 ∝ T3/2 relation while the dashed line corresponds to the best-fit power law relation M ∝ T4.6 ± 0.7. Temperatures are derived from XMM data (Zhang et al. 2007), including A 2219 from ASCA data (Ota et al. 2004). The 4 clusters with cooling core or relaxed properties are marked with empty boxes. (From Bardeau et al. 2007).

In a parallel paper, Hoekstra (2007) investigated the lensing versus X-ray mass relations for a sample of 20 clusters including those of Bardeau et al. (2007), although their cluster selection was primarily driven by X-ray emission. This investigation has lead to a more ambitious project known as the Canadian Cluster Comparison Project (CCCP) that will add 30 more X-ray selected clusters observed with the CFHT12k or Megacam camera to the initial set of 20 clusters. Lensing results are however still pending at the time of writing this review.

4.2. On-going and future cluster lensing surveys

Clusters of galaxies are complicated systems that are rapidly assembling and evolving, nevertheless they are considered to be very good tracers of the underlying cosmology (and in particular could probe Dark Energy) as well as a way to measure the growth of structure, thus potentially sensitive to gravity and to the nature of Dark Matter. A better understanding of clusters will be possible only with larger cluster samples, as earlier work and conclusions therefrom were limited by statistics. The number of massive clusters with published lensing data is steadily growing, as is the number of cosmological surveys in which clusters can be studied with strong and weak lensing techniques, either directly from the survey data or by further follow-ups.

Four techniques are avidly pursued to search for clusters:

• Photometric searches that use wide field imaging surveys such as the Sloan Digital Sky Survey (SDSS), the Red-sequence Cluster Survey (RCS), and the CFHT Legacy Survey (CFHTLS). Furthermore, new photometric surveys have just started or will start in the next year, namely the VST KIDS survey, the Dark Energy Survey (DES), and the Subaru Hyper-Suprime Camera (HSC) survey.
• X-ray selected cluster searches: i) based on the follow-up of the ROSAT All Sky Survey: such as the MAssive Cluster Survey (MACS) (Ebeling et al. 2001) and the REFLEX survey (Boehringer et al. 2004) ii) based on dedicated (or serendipitous) X-ray ROSAT or XMM imaging surveys such as: WARPS (Scharf et al. 1997), SHARC (Collins et al. 1997), the ROSAT Deep Cluster Survey (Rosati et al. 2001), XDCS (the XMM Deep Cluster Survey - Fassbender et al. 2008), XCS (Romer 2008); and XMM-LSS (Pierre et al. 2007).
• SZ searches: e.g. Atacama Cosmology Telescope Cluster Survey (ACT) (see e.g. Hincks et al. 2010, Marriage et al 2011, Hand et al 2011), the South Pole Telescope Cluster Survey (SPT) (e.g. Chang et al. 2009, Vanderlinde et al 2010, Plagge et al 2010) and the Planck mission (Ade, P. A. R., et al. 2011).
• Weak and Strong lensing searches based on photometric surveys, or following up X-ray or SZ selected clusters.

We focus on the latter techniques in the following sub-sections.

4.3. Targeted cluster surveys

4.3.1. The Local Cluster Substructure Survey (LoCuSS)

LoCuSS extends Smith et al.'s (2005) pilot study of 10 X-ray luminous clusters at z = 0.2 to an order of magnitude larger sample at 0.15 < z < 0.3, drawn from the ROSAT All-sky Survey Catalogues (Ebeling et al., 1998, 2000; Ebeling et al., 2004). The main lensing-related goals of LoCuSS are to measure the mass, internal structure, and thermodynamics of a complete volume-limited sample of 80 clusters observable from Mauna Kea, and thus to obtain definitive results on the mass-observable scaling relations at low redshift. The normalization, shape, scatter (and any structural segregation detected) of these scaling relations will calibrate the properties of low redshift clusters as an input to cluster-based cosmology experiments, and to help interpret high-redshift cluster samples.

To date LoCuSS has published weak lensing analysis of 30 clusters observed with Suprime-CAM on the Subaru 8.2-m telescope (Okabe et al. 2010; see also Oguri et al. 2010). The main results from this statistical study are that (i) a simple color-magnitude selection of background galaxies yields samples that are statistically consistent with negligible residual contamination by faint cluster members, albeit with large uncertainties, (ii) cluster density profiles are curved (in log-log space), and statistically compatible with the Navarro, Frenk & White (1997) profile, and (iii) based on the NFW profile model fits, the normalization of the mass-concentration relation of X-ray selected clusters is consistent with theoretical ΛCDM-based predictions, although the slope of the observed relation may be steeper than predicted. The last of these results is particularly interesting in the context of detailed studies of individual clusters selected to have a large Einstein radius. As noted in Section 7, such objects are often found to have concentrations that exceed the CDM prediction by factors of 2-3 (Comerford & Natarajan 2007; Oguri et al. 2009). Okabe et al.'s results from 30 X-ray-selected clusters indicate that the large Einstein radius selection in earlier work introduces a strong bias.

Comparison of Okabe et al.'s weak lensing mass measurements with X-ray and Sunyaev-Zel'dovich (SZ) effect probes has so far been limited by the presence of outlier clusters in the small samples for which the relevant data are available. For example, the well-known merging cluster A1914 strongly influences the results in the X-ray/lensing comparison of 12 clusters for which Subaru and XMM-Newton data are available (Okabe et al., 2010; Zhang et al., 2010). More recently, Marrone et al. (2011) presented the first weak lensing-based mass-SZ scaling relation based on Subaru and Sunyaev-Zel'dovich Array (SZA) observations of 18 clusters. Encouragingly, this relation is consistent with self-similar predictions, although it presents 20% scatter in natural log of mass at fixed integrated Y-parameter - a factor of 2 more scatter than found in studies that use X-ray data and assume hydrostatic equilibrium to infer cluster mass. Indeed, the normalization of the M_WL − Y relation at Δ = 500 (roughly 1Mpc) for undisturbed clusters is 40% higher in mass than that for disturbed clusters. Marrone et al. identified several of the undisturbed clusters as likely prolate spheroids whose major axis is closely aligned with the line of sight as being largely responsible for this segregation. These results highlight the feasibility and growing maturity of lensing-based studies of large cluster samples, and also emphasize that much important work remains to be done to fully understand the optimal methods for cluster mass measurement.

4.3.2. The MAssive Cluster Survey

The MAssive Cluster Survey (MACS) is an ongoing project aimed at the compilation and characterization of a statistically complete sample of very X-ray luminous (and thus, by inference, massive), distant clusters of galaxies. The primary goal of MACS was to increase the number of known massive clusters at z > 0.3 from a handful to a hundred. To achieve these goals, Ebeling et al. (2001) applied an X-ray flux and X-ray hardness-ratio cut to select distant cluster candidates from the ROSAT Bright Source catalog. Starting from a list of more than 5,000 X-ray sources within the survey area of 22,735 square degrees they use positional cross-correlations with public catalogs of Galactic and extragalactic objects, with reference to APM colors, visual inspection of Digitized Sky Survey images, extensive CCD imaging, and finally spectroscopic observations with the University of Hawaii's 2.2m and the Keck 10m telescopes to compile the final cluster sample. The MACS cluster sample comprises 124 spectroscopically confirmed clusters at 0.3 < z < 0.7 (Figure 29). Comprehensive follow-up observations of MACS clusters include: weak lensing mass measurements using wide-field SUBARU imaging data, virial mass estimates based on cluster galaxy velocity dispersions measured with the CFHT and Keck, SZ observations with the BIMA mm-wave radio interferometer, measurements of the cluster gas and temperature distribution with Chandra, and both deep, multi-passband and snapshot images with HST. A large number of MACS clusters are strong lenses and some of them have been studied in detail: MACS J1206-0847 (Ebeling et al. 2009); MACS J1149.5+2223 (Smith et al. 2009); MACS J1423.8+2404 (Limousin et al. 2010; Morandi et al. 2010). MACS J0025.4-1222 (Bradač et al. 2008) was identified as a merging cluster with some similarity to the “Bullet Cluster”. Zitrin et al. (2011a) presented the results of a strong lensing analysis of the complete sample of the 12 MACS clusters at z > 0.5 using HST images. The distribution of Einstein radii has a median value of ∼ 28 arcseconds (for a source redshift of z_S ∼ 2), twice as large as other lower-z samples, making the MACS sample a truly massive cluster sample confirmed by the numerous strong lensing discoveries. One of the most extreme clusters known presently is likely MACS J0717.5+3745 (Ebeling et al. 2004) which was recognized as a complex merger of 4 individual substructures, with a long tailed filamentary structure. The 4 substructures have all been identified in a recent lensing mass reconstruction by Limousin et al. (2011) and the filamentary structure was directly measured by weak lensing measurements with a 18-pointing HST mosaic (Jauzac et al. 2012). Horesh et al. (2010), investigated the statistics of strong lensed arcs in the X-ray selected MACS clusters versus the optically-selected RCS clusters (see below). They measured the lensed-arc statistics of 97 clusters imaged with HST, identifying lensed arcs using two automated arc-detection algorithms. They compile a catalog of 42 arcs in MACS and 7 arcs in the RCS. At 0.3 < z < 0.7, MACS clusters have a significantly higher mean frequency of arcs, 1.2 ± 0.2 per cluster, versus 0.2 ± 0.1 in RCS, which can easily be explained by the nature of the selection of these two different cluster samples.

Figure 29. The Luminosity versus redshift plot comparing the MACS surveys to a number of other X-ray surveys: EMSS, eBCS, WARPS, the 400 square degree survey. It is evident from this figure that MACS is very efficient in selecting the most massive X-ray clusters at z > 0.3.

4.3.3. ESO distant cluster survey

Nevertheless, optical selection is still common specially for high-redshift clusters (z > 0.6) where X-ray selection is limited. A particular focused and productive survey is the ESO distant cluster survey (EDiSC, White et al. 2005). EDiSC is a survey of 20 fields containing distant galaxy clusters (0.4 < z < 1.0) chosen amongst the brightest objects identified in the Las Campanas Distant Cluster Survey. They were confirmed by identifying red sequences in moderately deep two color data from VLT/FORS2, and further investigations with VLT in spectroscopy, the ESO Wide Field Imager, and HST/ACS mosaic images for 10 of the most distant clusters. Using the deep VLT/FORS2 data, Clowe et al. (2006) measured the masses for the EDiSC clusters. In particular, they compared the mass measurements of 13 of the EDiSC clusters with luminosity measurements from cluster galaxies selected using photometric redshifts and find evidence of a dependence of the cluster mass-to-light ratio with redshift.

4.3.4. Red-sequence cluster surveys

Another important optically selected cluster survey is the 100 deg² Red-Sequence Cluster Survey (RCS, Gladders 2002, Gladders & Yee 2005) and its 1000 deg² RCS-2 extension (Gilbank et al. 2011), that are based on shallow multi-color imaging with the CFHT12k and Megacam cameras. RCS-2 covers ∼ 1000 deg² and includes the first RCS area, it reaches 5σ point-source limiting magnitudes in [g, r, i, z] = [24.4, 24.3, 23.7, 22.8], approximately 1-2 magnitudes deeper than the SDSS. RCS-2 is designed to detect clusters over the redshift range 0.1 < z < 1, building a statistically complete, large (∼ 10⁴) sample of clusters, covering a sufficiently long redshift baseline to be able to place constraints on cosmological parameters probed via the evolution of the cluster mass function. Furthermore, a large sample of strongly lensed arcs associated with these clusters has been derived (e.g. Gladders et al. 2002, 2003), and weak lensing measurements from the most massive clusters detected in RCS-2 is likely possible.

4.3.5. The Multi-Cluster Treasury: CLASH survey

The recently approved MCT (Multi-Cluster Treasury) program on HST will achieve multi-band imaging of a sample of 25 X-ray selected clusters (Postman et al. 2011), thus providing detailed photometric redshift estimates for multiple-images. This sample with appropriate ground based follow-up is likely to provide important insights into many of the current unsolved problems in cluster assembly and evolution. Dedicated lensing studies will enable detailed investigation of their mass distributions (Zitrin et al. 2011b, 2011c) and will help find some efficient lenses that can be exploited to study the distant Universe by using them as gravitational telescopes (Richard et al. 2011) - a topic that will be discussed further in the next section.

4.4. Cluster lenses in wide cosmological surveys

The previous sub-section focused on targeted cluster surveys. However cluster lenses can also be found in wide cosmological surveys (e.g. Wittman et al. 2001, 2003; Hamana et al. 2004; Maturi et al. 2005). We briefly outline some of the most representative surveys of this decade starting from the widest to the deepest.

4.4.1. The Sloan Digital Sky Survey

The Sloan Digital Sky Survey (SDSS) is an imaging and spectroscopic survey covering 10,000 deg² (Aihara et al. 2011). Although, this survey was not designed or optimized to measure cluster lensing, interesting results have been produced from detected strong and weak lensing measurements of clusters. Estrada et al. (2007) investigated the Sloan images of 825 SDSS galaxy clusters searching for giant arcs. Both a visual inspection of the images and an automated search were performed, and no arcs were found. They nevertheless report a serendipitous discovery of a bright arc in the Sloan images of an as yet unknown cluster. Hennawi et al. (2008) presented the first results of a strong lensing imaging survey (using the WIYN and UH 2m telescope) targeting the richest clusters (with 0.1 < z < 0.6) selected from SDSS. From a total of 240 clusters followed-up, they uncovered 16 new lensing clusters with definite giant arcs, 12 systems for which the lensing interpretation is very likely, and 9 possible lenses which contain shorter arclets or candidate arcs which require further observations to confirm their lensing origin. The new lenses discovered in this survey will enable future systematic studies of the statistics of strong lensing and their implications for cosmology and the current structure formation paradigm. Kubo et al. (2009) and then Diehl et al. (2009) identified 10 strongly lensed galaxies as part of the “Sloan Bright Arcs Survey”. Follow-up imaging identified the lensing systems as group-scale lenses, an intermediate regime between isolated galaxies and galaxy clusters (see Cabanac et al. 2007). Baylis et al. (2011) presented the results from a spectroscopic program targeting 26 strong lensing clusters (0.2 < z < 0.65) visually identified in SDSS or RCS-2 revealing 69 unique background sources with redshifts as high as z = 5.2, which will enable robust strong lensing mass models to be constructed for these clusters (some of the most remarkable clusters discovered are presented in Figure 30).

Figure 30. SDSS discovered strong lensing clusters – a) Abell 1703, b) SDSS J1446+3033, c) SDSS J1531+3414, and d) SDSS J2111-0114. Color composite images are made from g, r, i imaging obtained with Subaru/SuprimeCam. All images are 75″ × 75″. Background sources are bracketed by red lines and labeled. Source labels with the same letter but different numbers (e.g. A1, A2, etc.) have the same redshifts to within the measurement errors, and are presumed to be the same source, multiply imaged (Figure from Bayliss et al. 2011).

On the weak lensing side, the first measurement was conducted by Sheldon et al (2001). Later on Rykoff et al. (2008) measured the scaling relation between X-ray luminosity and the total mass for 17,000 galaxy clusters in the SDSS maxBCG cluster sample. To achieve this, they stacked subsamples of clusters within fixed ranges of optical richness, and they measured the mean X-ray luminosity L_X, and the weak lensing mean mass, < M₂₀₀ >. For rich clusters, they found a power law correlation between L_X and M₂₀₀ with a slope compatible with previous estimates based on X-ray selected catalogs. Furthermore, Rozo et al. (2010) used the abundance and weak lensing mass measurements of the SDSS maxBCG cluster catalog to simultaneously constrain cosmology and the cluster richness-mass relation. Assuming a flat ΛCDM cosmology, they found that σ₈(Ω_m / 0.25)^0.41 = 0.832 ± 0.033. These constraints are fully consistent with those derived from WMAP five-year data. With this remarkable consistency they claim that optically selected cluster samples may produce precision constraints on cosmological parameters in future wide-field imaging cosmological surveys.

4.4.2. The CFHT-Legacy Survey

Soon after the first light of the Megacam camera at CFHT, a legacy survey (LS) was started. It comprises a deep ugriz (i ∼ 27.5) survey of 4 square degrees in four independent fields spread across the sky, and a wide synoptic u, g, r, i, z (i ∼ 24.5) survey of 170 square degrees in four patches of 25 to 72 square degrees. Due to the excellent seeing delivered by CFHT, the Legacy Survey has lead to intensive strong and weak lensing studies.

In particular, Cabanac et al. (2007) have searched for strong lensing arcs and Einstein rings around galaxies in both the deep and wide part of the CFHT-LS. Most of the systems uncovered have deflection angles ranging between 2 and 15 arcseconds. Such samples have thus uncovered a large population of strong lenses from galaxy groups with typical halo masses of about 10¹³ h⁻¹ M_⊙. The 13 most massive systems have been studied in detail by Limousin et al. (2009), and detailed analysis of the mass distribution on small and large scales has been investigated by Suyu & Halkola (2010) and Limousin et al. (2010), respectively. A weak lensing search for galaxy clusters in the 4 square degrees of the 4 CFHT-LS deep fields was performed and results are presented in Gavazzi & Soucail (2007). Using deep i-band images they performed weak lensing mass reconstructions and identified high convergence peaks. They used galaxy photometric-redshifts to improve the weak lensing analysis. Among the 14 peaks found above 3.5σ, nine were considered as secure detections upon cross-correlation studies with optical and X-ray catalogs. Berge et al. (2008) conducted a joint weak lensing and X-ray analysis of (only) 4 square degrees from the CFHTLS and XMM-LSS surveys. They identified 6 weak lensing-detected clusters of galaxies, and showed that their counts can be used to constrain the power-spectrum normalization σ₈ = 0.92_−0.30^+0.26 for Ω_m = 0.24. They showed that deep surveys should be dedicated to the study of the physics of clusters and groups of galaxies, and wide surveys are preferred for the measurement of cosmological parameters. A first catalogue of lensing selected cluster has been recently published by Shan et al. (2012) on the CFHT-LS W1 field. They perform a weak lensing mass map reconstruction and identify high signal-to-noise ratio convergence peaks, that were then correlated with the optically selected cluster catalogue of Thanjavur et al. (2011). They then used tomographic techniques to validate their most significant detections and estimate a tomographic redshift. More weak lensing cluster analyses are expected to be published from CFHT-LS in the near future.

4.4.3. The COSMOS Survey

With only 2 square degrees the COSMOS Survey focused on the relatively high-redshift Universe. Due to the relatively small volume probed, COSMOS is unlikely to find the most massive structures in the Universe, but it has delivered interesting constraints on the redshift evolution of clusters and the scaling relations between observables. Thanks to the deep X-ray observation of COSMOS fields, clusters can be efficiently selected in principle out to z ∼ 2. Taking advantage of the X-ray selected catalog, Leauthaud et al. (2010) have investigated the scaling relation between X-ray luminosity (L_X) and the weak lensing halo mass (M₂₀₀) for about 200 X-ray-selected galaxy groups. Weak lensing profiles and halo masses were derived for 9 sub-samples, narrowly binned in luminosity and redshift. The COSMOS data alone are well fit by a power law, M₂₀₀ ∝ L_X^α, with a slope α = 0.66 ± 0.14. These observations significantly extend the dynamic range for which the halo masses of X-ray-selected structures have been measured with weak gravitational lensing as shown in Figure (31). Combining with other measurements demonstrates that the M − L_X relation is well described by a single power law with α = 0.64 ± 0.03, over two decades in mass: M₂₀₀ ∼ 10^13.5 − 10^15.5 h₇₂⁻¹ M_⊙. These results confirm that clusters do not follow the self-similar evolution model with α = 0.75 proposed by Kaiser (1986).

Figure 31. The COSMOS M−LX relation from Leauthaud et al. (2010). Dark blue diamonds show individually detected clusters from Hoekstra et al. (2007) with updated masses from Madhavi et al. (2008). Sienna cross symbols show data points from Bardeau et al. (2007). Light blue plus symbols represent the Rykoff et al. (2008) results from a stacked analysis in the SDSS and black diamonds take into account a recent correction to these masses due to a new calibration of the source distribution. The upper error bars have been adjusted to account for the redshift uncertainty. Green asterisks show four data points at intermediate masses from Berge et al. (2008). Finally, the red squares depict our COSMOS results which extend previous results to lower masses and to higher redshifts. Three arrows highlight the highest redshift COSMOS data points. The grey shaded region shows the upper and lower envelope of the ensemble of lines with a slope and intercept that lie within the 68 percent confidence region.