The Galaxy Cluster Concentration-Mass Scaling Relation

Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 23 November 2015 (MN LATEX style ﬁle v2.2)

A. M. Groener,1? D. M. Goldberg,1 M. Sereno,2 3 1Department of Physics, Drexel University Philadelphia, PA 19104 2Dipartimento di Fisica e Astronomia, Alma Mater Studiorum Universit`adi Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italia 3INAF, Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italia

ABSTRACT Scaling relations of clusters have made them particularly important cosmological probes of structure formation. In this work, we present a comprehensive study of the relation between two profile observables, concentration (cvir) and mass (Mvir). We have collected the largest known sample of measurements from the literature which make use of one or more of the following reconstruction techniques: Weak gravitational lensing (WL), strong gravitational lensing (SL), Weak+Strong Lensing (WL+SL), the Caustic Method (CM), Line-of-sight Velocity Dispersion (LOSVD), and X-ray. We find that the concentration-mass (c-M) relation is highly variable depending upon the reconstruction technique used. We also find concentrations derived from dark matter 14 only simulations (at approximately Mvir ∼ 10 M ) to be inconsistent with the WL and WL+SL relations at the 1σ level, even after the projection of triaxial halos is taken into account. However, to fully determine consistency between simulations and observations, a volume-limited sample of clusters is required, as selection effects become increasingly more important in answering this. Interestingly, we also find evidence for a steeper WL+SL relation as compared to WL alone, a result which could perhaps be caused by the varying shape of cluster isodensities, though most likely reflects differences in selection effects caused by these two techniques. Lastly, we compare concentration and mass measurements of individual clusters made using more than one technique, highlighting the magnitude of the potential bias which could exist in such observational samples. Key words: galaxies: clusters: general – cosmology: dark matter – gravitational lensing: strong – gravitational lensing: weak

1 INTRODUCTION The radial density proﬁles of clusters, well-modeled by the universal NFW proﬁle (Navarro et al. 1997), appears to Galaxy clusters have long been used as probes of cosmology. be a prevailing outcome of simulations regardless of cosmol-

arXiv:1510.01961v2 [astro-ph.CO] 20 Nov 2015 Cluster observables, like X-ray luminosity, L , optical rich- X ogy (Navarro et al. 1997; Craig 1997; Kravtsov et al. 1997; ness, and line-of-sight galaxy dispersion, σ , are closely tied v Bullock et al. 2001). to the formation and evolution of large scale structures, and δ ρ scale with redshift and the mass of the host halo (Sereno ρ(r) = c cr (1) 2 & Ettori 2015). Scaling relations of clusters also provide a r 1 + r way of testing cosmology (Vikhlinin et al. 2009; Rozo et al. rs rs 2010; Mantz et al. 2010, 2014), though are imperfect prox- 3H(z)2 ies for mass, due to the 2-Dimensional view they provide ρcr = (2) for us. Large cosmological simulations provide a detailed 3- 8πG dimensional view of the hierarchical process of structure for- However, the details of the relationship between the two mation, one that is unattainable by even the most accurate model parameters, halo mass, M, and concentration, c, is reconstruction techniques available. sensitive to small changes in initial parameters (Macci`oet al. 2008; Correa et al. 2015b). The physical interpretation of a halo’s concentration (deﬁned as the ratio of the virial ra- ? −2 [email protected] dius, Rvir, to the radius at which ρ ∝ r ; called the scale

c 0000 RAS 2 Groener, Goldberg, & Sereno radius, rs), is that it is a measure of the ‘compactness’ of the concentration, this feature disappears (see Meneghetti & Ra- halo, and determines the physical scale on which the density sia 2013). profile rises steeply. The connection between the observed concentration, The first indication of the connection between halo con- c2D, and the intrinsic concentration, c3D, is further compli- centration and mass (hereafter, the c-M relation) was discov- cated, since it has been shown that relaxed cluster isodensi- ered through simulations of structure formation by Navarro ties are not constant on all scales (Frenk et al. 1988; Cole & et al. (1997), and later confirmed by Bullock et al. (2001), Lacey 1996; Dubinski & Carlberg 1991; Warren et al. 1992; who found a strong correlation between an increasing scale Jing & Suto 2002; Hayashi et al. 2007; Groener & Gold- berg 2014). Indeed, in a previous study by Groener & Gold- density, ρs = δcρcr, for decreasing mass, Mvir. The explanation for this anti-correlation between concentration and berg (2014), it has been shown that a halo’s concentration mass is that low-mass halos tend to collapse and form re- is an ill-defined 2-dimensional quantity, without first speci- laxed structures earlier than their larger counterparts, which fying the scale on which the measurement was made. Using are still accreting massive structures until much later. A con- the MultiDark MDR1 Cosmological Simulation, Groener & sequence of early collapse is that halos will have collapsed Goldberg (2014) found a systematic shift of about ∼ 18% during a period of higher density, leading to a larger cen- in the mean value of the projected concentration, c2D, be- tral density (and hence larger concentration) as compared tween weak and strong lensing scales, for low-mass cluster 13 −1 to halos which formed later. halos (2.5 − 2.6 × 10 h M ) observed with their major axes aligned with the line-of-sight direction. Though this Many studies (most recently, e.g., Correa et al. 2015a) difference is notably smaller than the intrinsic scatter of the focus on the physical motivation for the existence of this concentration parameter (c3D) for a given halo mass, the relationship, and suggest that the mass accretion history origin of this systematic effect is solely due to the changing (MAH) of halos is the key to understanding the connection shape of cluster isodensities as a function of radius. between cluster observables and the environment in which For many objects, not only do observed concentrations they formed (Bullock et al. 2001; Wechsler et al. 2002; Zhao seem to differ substantially from those obtained in cosmolog- et al. 2003). These studies have found that while the mass ical simulations, but concentrations can also vary depend- accretion rate onto the halo is slow, the concentration tends ing on which method is used. Since different reconstruction to scale with the virial radius, c ∝ rvir (caused by a constant methods probe varying scales within the halo, it is not un- scale radius), while the concentration remains relatively con- reasonable to suspect that there exist systematic differences stant for epochs of high mass accretion. The MAH itself in the observed c-M relation caused by shape. depends upon the physical properties of the initial density peak (Dalal et al. 2008), which is a function of cosmology, In this paper, we focus on three main objectives. redshift, and mass (Diemer & Kravtsov 2015). Longstanding tension has existed between cluster con- (i) We present the current state of the observational centrations derived from simulations and observational mea- concentration-mass relation for galaxy clusters by aggregat- surements. Concentrations have been found to differ the ing all known measurements from the literature. The raw most for gravitational lensing techniques (Comerford & data are reported in Table A-1, and have been made pub- Natarajan 2007; Broadhurst et al. 2008; Oguri et al. 2009; licly available (see Appendix A). We also provide an addi- Umetsu et al. 2011a). This over-concentration in favor of tional table (available only online), where data have been observational measurements can be partially explained by normalized over differences in assumed cosmology, overden- the orientation of triaxial structure along our line-of-sight sity convention, and uncertainty type found in the original (Oguri et al. 2005; Sereno & Umetsu 2011), which has the studies. effect of enhancing the lensing properties (Hennawi et al. (ii) We model the observed concentration-mass relation 2007). Neglecting halo triaxiality (Corless et al. 2009) and for each method, and compare these to one another, high- substructure (Meneghetti et al. 2010; Giocoli et al. 2012) lighting potential differences which exist, caused by the pro- also each have significant effects on halo parameters. For its jection of structure along the line-of-sight, the varying shape effect on WL and X-ray mass estimates, see Sereno & Ettori of cluster isodensities, and the selection of clusters from the (2014). cosmic population. (iii) Using the largest cluster sample to date, we deter- Discrepancies in how measurements of the intrinsic con- mine if the observed c-M relation is consistent with the- centration are made using simulations also exist, along with ory, when taking halo triaxiality and elongation of structure studies who disagree on the inner slope of the density profile along the line-of-sight into account. (Moore et al. 1999; Ghigna et al. 2000; Navarro et al. 2004). However, the most puzzling and potentially interesting dis- In section 2, we summarize many of the most common parity between simulations is the existence of the upturn mass reconstruction techniques which are used throughout feature in the c-M relation (see for example, Fig. 12 of Prada the cluster community, and include a discussion regarding et al. 2012) at high redshift (Prada et al. 2012; Dutton & physical scales probed within the cluster using these meth- Macciò2014; Klypin et al. 2014; Diemer & Kravtsov 2015), ods. In section 3, we discuss the procedure for collecting our which some argue is an artifact caused by the selection of sample from the literature, and normalizing over conven- halos which are dynamically unrelaxed (Ludlow et al. 2012). tion, cosmology, and uncertainties. In section 4, we present This novel feature only shows up when the concentration is results for the observed c-M relation for each method, and expressed as a profile-independent halo property (in terms in section 5, we discuss the projection of triaxial halos from of the ratio of the maximum circular velocity and the virial simulations to the observed lensing relations. Lastly, in sec- velocity, Vmax/Vvir). In terms of the classical definition of tion 6, we conclude and discuss our findings.

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Table 1. Population Overview

14 14 14 Method Nmeas Ncl min(Mvir/10 M ) hMvir/10 M i max(Mvir/10 M ) min(cvir) hcviri max(cvir) min(z) hzi max(z) CM 82 79 <1.0 3.9 18.6 <2.0 8.9 36.7 0.003 0.06 0.44 LOSVD 70 59 1.3 5.8 17.1 <2.0 8.8 39.0 0.01 0.06 0.44 X-ray 290 195 <1.0 26.1 >40.0 <2.0 7.2 26.2 0.003 0.22 1.41 WL 169 111 <1.0 12.4 >40.0 <2.0 8.1 64.5 0.02 0.48 1.45 WL+SL 113 58 <1.0 8.7 31.8 2.3 10.2 30.6 0.18 0.53 1.39 SL 19 11 3.2 24.3 >40.0 3.8 11.2 27.5 0.18 0.47 0.78

Throughout this paper we adopt a ﬂat ΛCDM cosmol- −1 −1 ogy, Ωm = 0.3, ΩΛ = 0.7, and H0 = 70 km s Mpc . Generally speaking, we reserve the following colors within plots to represent the various methods: • Caustic Method (CM): blue • Line-of-sight velocity dispersion (LOSVD): orange • X-ray: green • Weak Lensing (WL): purple • Strong Lensing (SL): red • Weak + Strong Lensing (WL+SL): black Unless otherwise stated, throughout the study, uncertainties are reported as 1-σ (68.3%) Gaussian uncertainties.

2 CLUSTER MASS RECONSTRUCTION TECHNIQUES In this section, we present a brief overview of common mass reconstruction techniques and modeling of the cluster density profile. Figure 1. The full normalized observational cluster sample, col- ored by method. Uncertainties have been omitted here for clarity. 2.1 Weak Lensing (WL) Weak gravitational lensing is the process by which images more massive clusters produce larger distortions of back- of background galaxies are distorted by massive foreground ground galaxies. As a result, in a survey of clusters, the objects. Though these distortions cannot be detected for expectation is that nearly all of the most massive clusters any given source, it is possible to obtain a signal by locally would be selected from the population. However, in the low averaging the shapes (ellipticities) of galaxies. This shear mass region, clusters which are highly triaxial and elongated measurement within a given bin can be used as a direct along the line-of-sight (i.e. - larger 2D concentrations) are proxy for the lens density profile at intermediate to large more likely to pass the observational signal-to-noise thresh- radii. old than ones which are not. The net effect here is an ar- For a symmetric distribution, the azimuthally averaged tificial steepening of the c-M relation due to selection. Fur- tangential shear, hγti, as a function of radius from the clus- thermore, lensing geometry plays an additional role in how ter center can then be calculated, and relates to the conver- clusters are selected. Clusters which are too distant lack the gence, κ, in the following way: requisite number density of background galaxies to obtain high signal-to-noise (Bartelmann & Schneider 2001). Table Σ(¯ < r) − Σ(r)¯ hγti(r) = =κ ¯(< r) − κ¯(r) (3) 1 presents the range in redshift for weak lensing clusters, Σcr where most measurements are found to lie in the redshift 14 where the critical surface mass density is defined in terms range of z = 0.2 − 0.6, with Mvir & 1 × 10 M . of cosmology-dependent angular diameter distances Ds (source), D (lens to source), and D (lens): ds d 2.2 Strong Lensing (SL) 2 c Ds Σcr = (4) A natural extreme of the phenomenon of gravitational lens- 4πGDdsDd ing can occur if a background galaxy is serendipitously Expressions, specifically for the NFW profile, for the conver- aligned with the core of a cluster. In such cases, the pro- gence (Bartelmann 1996) and the tangential shear (Oaxaca jected surface mass density is so high that multiple images Wright & Brainerd 1999) have been derived, and can be used of the object are produced, commonly distorting them so for model fitting. much that they appear arc-like. Weak lensing comes with its own intrinsic biases in that A density profile can be obtained by fitting a model

c 0000 RAS, MNRAS 000, 000–000 4 Groener, Goldberg, & Sereno to the observed image positions, orientations, and fluxes, underlying gravitational potential. Assuming the distribu- though this technique constrains the cluster profile on small tion of mass follows an NFW profile, free parameters, which 1 scales (approximately the Einstein radius, θE , which is typ- include Mvir and cvir, can be fit to the observed data. ically ∼ 5% of the virial radius, rvir, or ∼ 50% of the scale The business of identifying clusters as mass over- radius, rs (Oguri & Blandford 2009)). densities, determining cluster membership, removal of in- Due to the irregular occurrence of multiple images and terlopers, and reconstruction details vary from technique to arcs, cluster measurements made with strong lensing are technique. For a more complete review of the reconstruction particularly prone to selection effects, and likely represent methods and their impact on cluster observables, see Old a biased sampling of the cosmic population. In fact, the et al. (2014). efficiency of lensing is increased with increasing mass and concentration, and a preferential line-of-sight alignment of the triaxial halo (Oguri & Blandford 2009). Concentrations 2.6 The Caustic Method (CM) derived from this method have been contentiously high as With the exception of weak lensing, the caustic method is compared to X-ray studies (Comerford & Natarajan 2007). the only other standalone method which has been success- ful in probing the density profile at large distances from 2.3 Weak+Strong Lensing (WL+SL) the cluster center (& rvir). Cluster galaxies, when plotted in line-of-sight velocity versus projected cluster-centric dis- Combining weak and strong gravitational methods con- tance phase-space, create a characteristic “trumpet shape”, strains the density profile over a wide range of scales, the boundaries of which form what is referred to as caustics and also has the ability to break the mass-sheet degener- (Kaiser 1987; Regos & Geller 1989). The existence of these acy (Schneider & Seitz 1995). Recent efforts to combine caustics mark an important boundary which envelops a vol- these methods have become more prevalent in the literature ume of space in which galaxies are gravitationally bound to (Merten et al. (2014) - CLASH; Oguri et al. (2012) - SGAS), the cluster. Outside of this turnaround radius, galaxies are and work to reconstruct the lensing potential by minimizing ultimately carried away in the Hubble flow. a combined least-squares approach. The width of the caustic (velocity) at any given pro- 2 2 2 jected radius, A(R), can then be related to the escape ve- χ (ψ) = χw(ψ) + χs (ψ). (5) locity due to the gravitational potential of the cluster, under the assumption of spherical symmetry (Diaferio & Geller 2.4 X-ray 1997). Through simulations of structure formation, Diaferio (1999) has shown that the caustic amplitude can be related Massive clusters are significant sources of X-ray radiation, to the mass interior to radius r by: due to the hot diffuse plasma (kBTe ∼ 10 keV) emitting via thermal bremsstrahlung, and can be used to determine the 1 Z r GM(< r) = A2(R) dR. (7) total distribution of mass. Under assumptions of spherical 2 0 symmetry and hydrostatic equilibrium with the underlying potential (Evrard et al. 1996), temperature and gas density The success of the caustic method is independent of any assumptions regarding dynamical equilibrium of the cluster, information, ρg, are used to determine the total mass of the and has been used to reconstruct profiles over a larger range cluster, typically at intermediate scales (∼ r500, corresponding to the radius at which the average density inside is 500 of scales: from the inner regions to a few times the virial radius (CAIRNS: Rines et al. 2003; CIRS: Rines & Diaferio times ρcr). 2006; HeCS: Rines et al. 2013). However, this technique re- kT(r) d log ρg(r) d log T(r) quires the measurements of at least 30-50 cluster members, M(r) = r + (6) Gµmp d log r d log r and thus limits this method to clusters at relatively low red- These assumptions are often violated due to non- shifts compared to lensing and X-ray techniques. More re- thermal pressure sources, temperature inhomogeneity, and cently, Rines et al. (2013) make use of this technique using to the presence of substructures further out (Rasia et al. ∼ 200 cluster members. 2012), and bias low mass estimates by 25-35%. 2.7 Hybrid Techniques 2.5 Line-of-sight Velocity Dispersion (LOSVD) The aforementioned methods represent the most commonly The distribution of mass within clusters can also be obtained applied techniques for constructing a density profile, how- by using the kinematics of cluster galaxies, specifically, by ever, they do not represent them all. Novel combinations of using the moments of the velocity distribution. Reconstruc- methods have also been used, but could not be included in tion methods, developed byLokas (2002) andLokas & Ma- a study of this kind. For instance, Lemze et al. (2008) common (2003), use the second (dispersion) and fourth (kurto- bine joint lensing and X-ray methods to make a determi- sis) moments of the velocity distribution, which relies on the nation of Abell 1689. Thanjavur et al. (2010) and Verdugo et al. (2011) use a combination of lensing and dynamics. Additionally, In an attempt to only compare methods used 1/2 1 4GM DLS The Einstein radius for a point mass is θE = 2 . in Comerford & Natarajan (2007), we consciously leave out c DLDS Though there is no corresponding functional form for an NFW measurements made with the Sunyaev-Zel’dovich (SZ) ef- profile, typical values for clusters lie in the range: 10”-45” (Kneib fect, or which use combinations of techniques one of which et al. 2003; Broadhurst et al. 2005b). uses SZ.

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Previous studies have even employed these multi- For extreme cosmologies, the correction to the concen- technique reconstructions to clusters in an attempt to break tration parameter, cvir, and mass, Mvir, are approximately the line-of-sight mass degeneracy (for a review of these tech- 5% and 10%, respectively. This correction is significantly niques, see section 2 of Limousin et al. (2013); see also smaller than other known effects. Moreover, the vast major- Ameglio et al. (2007), Sereno et al. (2012)). However, it ity of all measurements we have collected assume flat cos- is unclear if techniques such as this can adapt to arbitrar- mologies which lie in the range ΩΛ = 1 − Ωm = 0.73 − 0.68. ily complicated profiles, where shape is scale-dependent, or The corrections to the concentration and mass in this range where isodensities are not co-axial with one another (isoden- are ∼ 1%. sity twisting).

3 THE SAMPLE 3.1.3 Uncertainties The sample of clusters collected from the literature consists Another complication which must be accounted for is the us- of a total of 781 cluster measurements, reported by 81 stud- age of multiple definitions of measurement uncertainty on re- ies (Table A-2), representing the largest known collection of sulting mass and concentration estimates reported through- cluster concentration measurements to date. Of these, there out the literature. Particularly, many fitting procedures are 361 unique clusters, giving us a sizable sampling of the (namely methods which involve brute force exploration of cluster population as a whole, in addition to multiple mea- likelihood space) produce maximum-likelihood estimates of surements of individual clusters (often coming from more parameters of interest and corresponding confidence inter- than one category of reconstruction technique). vals. However, most studies do not report the marginal dis- This study builds off of work done by Comerford & tributions from their fitting procedures, and consequently, Natarajan (2007), which aggregated 182 cluster measure- limits the utility of their measurements for those looking to ments of 100 unique cluster objects. In accordance with that compare or adopt their values. study, we also report measurements of concentration (and Furthermore, the mathematical theorems which dictate mass) in the most popular conventions, c200, and cvir. the propagation of error of measurements rely on expected Table 1 presents population averages of masses and con- values and variances, rather than maximum-likelihood es- centration, as well as their range in redshift for the six re- timates and probability intervals. D’Agostini (2004) argues construction techniques we reference throughout this study. that the expected value and standard deviation should al- This information highlights the importance of the selection ways be reported, and in the event of an asymmetric distri- function of clusters, though we make no attempt in this pa- bution, one should also report shape parameters or best-fit per to distinguish between whether a lack of measurements model parameters as well. Most importantly, any published of certain values for a given method is due to its inability to result containing asymmetric uncertainties causes the value make these determinations, or whether it is simply a prefer- of the physical quantity of interest to be biased. ential selection effect. We follow the procedure outlined in D’Agostini (2004) for symmetrizing measurements with asymmetric uncertain- ∆+ ties (to first order), θm , and apply this to both cluster 3.1 Normalization Procedure ∆− mass and concentration measurements. Due to the nature of this study, cluster measurements must be properly normalized to ensure that they are compared ∆+ + ∆− to one another on equal footing. In this section, we discuss σθ ≈ (8a) the steps taken to eliminate biases due to overdensity con- 2 vention, assumed cosmology, and due to differences in the E[θ] ≈ θm + O(∆+ − ∆−) (8b) definitions of measurement uncertainty, respectively. Additionally, many studies report measurements without uncertainties altogether. For these clusters, we apply 3.1.1 Convention uncertainty based upon the estimate of the average fractional uncertainty of all other measurements of its type. Under the assumption that the radial density profile follows The most notable method having this issue is the caustic an NFW profile, Hu & Kravtsov (2003) derive a procedure method, where virtually no measurements are accompanied for the conversion of both concentration and mass between by uncertainties. In this case, we apply the same fractional any two arbitrary characteristic radii. We apply these for- uncertainty to all measurements equally, and is derived from mulae as a first round of our normalization procedure. the average fractional error of LOSVD concentration and mass measurements. Lastly, a large fraction of clusters represented in our 3.1.2 Cosmology database have multiple concentration and mass measure- Measurements taken from the literature do not always use ments, leading subsequent fits to be more sensitive to these the same fiducial cosmology, and thus are not immediately particular objects. In order to prevent fits from being dom- comparable. Because of this, we develop a procedure for con- inated by the most popular clusters (e.g. - Abell 1689, of verting measurements between any two arbitrary cosmolo- which there are 26 measurements in total), we combine sim- gies. Appendix B outlines this procedure for general lensing ilar measurements using an uncertainty-weighted average methods. value.

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Figure 2. Upper left to lower right: Individual ﬁts to CM, LOSVD, X-ray, WL, WL+SL, and SL. The shaded regions represent the 1-σ uncertainty in the best-ﬁt parameters, and includes the intrinsic scatter, σint. These relations are extrapolated over the full range of cluster masses for illustration purposes only.

Table 2. Best-Fit Concentration-Mass Relation Parameters

Method Bootstrap →

1 2 3 4 5 2 Ncl m σm b σb A σA σint χred m σm b σb A σA CM 63 0.280 0.003 -3.138 0.038 3.778 0.677 0.242 0.327 0.28 0.19 -3.16 2.73 3.59 43.43 LOSVD 58 0.010 0.002 0.728 0.025 7.256 0.861 0.228 1.000 0.13 0.17 -1.00 2.55 5.31 58.74 X-ray 149 -0.105 0.001 2.494 0.010 12.612 0.676 0.160 1.224 -0.17 0.03 3.38 0.44 13.32 25.69 WL 93 -0.379 0.001 6.576 0.014 35.246 2.213 0.118 1.302 -0.43 0.11 7.35 1.62 44.10 312.68 WL+SL 57 -0.534 0.001 8.977 0.016 77.882 5.249 0.130 1.070 -0.54 0.10 9.10 1.46 86.06 552.28 SL 10 0.097 0.004 -0.422 0.062 7.236 1.951 0.254 1.003 0.11 0.23 -0.60 3.49 7.24 109.02

All (This Work) 293 -0.152 0.001 3.195 0.007 15.071 0.703 0.146 1.354 -0.16 0.03 3.26 0.44 13.71 26.45 All (CO07.1) 62 -0.14 0.12 – – 14.8 6.1 0.15 – – – – – – –

1 The slope, m, of the linear model is exactly equivalent to the power-law index α. 2 σm = σα 3 The normalization parameter, A, depends upon both m and b: A = 10b+m log M∗ 4 Uncertainty was propagated through the expression in [3]. 5 Equivalent to the scatter in log cvir reported in previous studies.

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4 THE OBSERVED CONCENTRATION-MASS In Table 2, we present our best-fit linear model pa- RELATION rameters, and their mapping back to the original power-law model. In Figure 2, individual fits to each subsample are In Figure 1, we show the full cluster dataset after applying shown alongside normalized data points. Lensing (WL and the normalization procedures discussed in the previous sec- WL+SL) and X-ray relations show a clear trend consistent tion. Following this, we present here the results of our fitting with concentration decreasing with increasing mass. We also procedure to these data. The typical prescription for mod- include a bootstrap analysis of these fits, to reveal the sen- eling the c-M relation, is to use a double power-law model sitivity of the fits to the data. of the following form Though seemingly well-constrained, the bootstrap anal- A M α ysis reveals that our strong lensing c-M relation is highly c(M) = β (9) (1 + z) M∗ sensitive to the dataset (due to the very small sample size), and so the best-fit model parameters are likely untrustwor- where the power-law indices, α and β, control the depen- thy. dence of the concentration with respect to mass and red- General agreement between concentration and mass shift. The model parameter, A, controls the normaliza- measurements of all methods can be seen in the range tion of the relation, once a suitable M has been chosen 14.5 15 ∗ 10 − 10 M , which we also point out, is the region we 13 −1 13 (M∗ = 1.3 × 10 h M = 1.857 × 10 M ). find most consistent with simulation results. We follow convention in using the above model, but in We also compare our results to the c-M relation studied a slightly different form, with the power-law index, β, fixed by CLASH, which use a combined weak and strong lensing to unity. The particular choice of β = 1, and pivot mass technique for 19 X-ray selected galaxy clusters. The relation 13 −1 M∗ = 1.3 × 10 h M , is for ease of comparison with pre- they fit, vious large studies of the c-M relation (Comerford & Natara- B C jan 2007). We adapt this model to a linear model in the 1.37 M200 c200 = A 14 −1 (13) following way 1 + z 8 × 10 h M

Y = mX + b ± σint (10) with best-ﬁt values of A = 3.66 ± 0.16, B = −0.14 ± 0.52, and −0.32 ± 0.18, agrees well with projected simulations, where variables and model parameters relate to the initial after accounting for the X-ray selection function. Figure 3 model in the following way: shows the comparison of the CLASH c-M relation to the the lensing relations, WL and WL+SL. Our relations are signif- Y≡ log c(1 + z) (11a) icantly steeper, and have higher normalizations2, though it X ≡ log M (11b) should be noted that we do not account for the lensing se- m= α (11c) lection function, which would lower both parameters.

b= log A − α log M∗ (11d)

We introduce the intrinsic scatter, σint, as a ﬁxed pa- 5 PROJECTION, SHAPE, AND A DIRECT rameter, which we estimate from the data (independently COMPARISON OF RECONSTRUCTION from the ﬁt itself), and is assumed to be constant over the TECHNIQUES full mass range:

2 2 2 When regarded as a single population of measurements, a σint = σres − hσY i (12) linear fit to the full dataset of cluster mass and concentration pairs can be said to be, at face value, consistent where σres is the scatter in the residual between the data 2 with the results from simulations (albeit only marginally). and the best-fit model, and hσY i is the average squared- uncertainty in the dependent variable. The idea here is that In Figure 4, we show the best-fit linear model to the full the scatter in the residual must be accounted for by a com- dataset, with results from Groener & Goldberg (2014) plot- bination of scatter due to the intrinsic relation itself as well ted in pink. We also find good agreement with Comer- as the uncertainties in the measurements of the observables. ford & Natarajan (2007), who find a best-fit model of 14.8±6.1 −0.14±0.12 We also note that although the value of the redshift for any cvir = (1+z) (Mvir/M∗) . given cluster has an effect on the uncertainty of the variable When the projection of triaxial halos is taken into ac- Y, the uncertainty in the measured redshifts themselves do count, simulations become more consistent with the lensing not contribute much to the overall uncertainty of the best-fit observations. Figure 5 compares WL and WL+SL relations model parameters. to intrinsic 3D halo concentrations (pink), and to 2D con- After measurements have been normalized, we eliminate centrations due to line-of-sight projection (cyan) of Multi- extreme values of mass and concentration. Simulations tell Dark MDR1 simulation halos found previously in Groener & us that the most massive clusters which exist at present are Goldberg (2014). While projected halos in this figure repre- 15 sent a perfectly elongated cluster sample, it is unlikely that approximately a few times 10 M . Accordingly, we remove 15 all clusters with lensing analyses performed to date are ori- masses which are larger than 4 × 10 M . We also remove 14 ented in this way. Thus, projected concentrations presented masses lower than 1 × 10 M , since best fit parameters are particularly sensitive to this mass bin (representing data for low-mass galaxy clusters and galaxy groups). Lastly, concen- 2 Due to the addition of a third model parameter, the CLASH trations which are lower than 2, indicate rather poor NFW normalization is not directly comparable to ours. However, visual fits to the density profile, and will bias our inferred param- inspection of Figure 3 shows that their value is certainly lower eters. than ours.

c 0000 RAS, MNRAS 000, 000–000 8 Groener, Goldberg, & Sereno

Figure 3. A direct comparison of the concentration-Mass relations for lensing based methods (WL and WL+SL) with results from CLASH (Merten et al. 2014). The top panel shows these relations at a redshift of z = 0.2, whereas the bottom panel is at a higher redshift z = 0.5 (approximately the average redshift of WL and WL+SL measurements in our sample). Conversion from c200 to cvir was necessary for comparison purposes.

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 9

Figure 4. The concentration-mass relation observed for the full cluster dataset. Color scheme is the same, though cyan data points represent co-added cluster measurements where more than one category of reconstruction method was used. Errorbars have been omitted here for clarity.

Figure 5. WL and WL+SL relations plotted with MultiDark MDR1 Simulation results found by Groener & Goldberg (2014). Pink data points represent intrinsic 3D concentrations found in three mass bins, and cyan data points are corresponding 2D concentrations due to the projection of line-of-sight oriented halos.

c 0000 RAS, MNRAS 000, 000–000 10 Groener, Goldberg, & Sereno

Figure 6. Top: Concentration-mass relations from recent simulations (Prada et al. 2012, Dutton & Macci`o2014, Klypin et al. 2014, and Correa et al. 2015a), along with lensing (WL and WL+SL) relations found in this study. All relations are evaluated at a redshift of z = 0.5. Bottom: Simulation relations after projection eﬀects have been taken into account. Halos are assumed to be prolate spheroidal (q=0.65), oriented along the line-of-sight direction.

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 11 here can be interpreted as an upper limit, and constrains tial discrepancy. WL and WL+SL mass measurements are the ability of line-of-sight projection in easing the tension generally in very good agreement with one another (with between simulations and lensing observations. Bahéet al. a few notable exceptions), however, differences in concen- (2012) also confirm that mock weak lensing reconstructions tration do exist which are upwards of a factor of ∼ 2 in of Millennium Simulation halos produce concentrations of magnitude. X-ray and WL comparisons show discrepancies upwards of a factor of 2 for line-of-sight orientation, con- in mass (concentration) which can reach as high as a factor gruent with our analytical treatment. However, this fails to of ∼ 9 times (∼ 6 times) larger, with X-ray mass estimates completely account for the factor of ∼ 3 (∼ 4) which we find tending to be larger than WL. Galaxy-based reconstruction 14 for WL (WL+SL) clusters of mass ∼ 10 M . techniques (LOSVD/CM) tend to agree less in both mass In Figure 6, we compare our lensing relations to ones and concentration, with uncertainties which are quite large. obtained through dissipative N-body simulations found in the literature. Median simulation relations are shown (top panel) over the mass range defined by our lensing sam- 6 CONCLUSIONS AND DISCUSSIONS 14 15 ples (1 × 10 − 3 × 10 M ), and are evaluated at a redshift corresponding to the average lensing redshift (z = 0.5) In this paper, we have studied the observed concentration- of our observational sample. Generally, the intrinsic scat- mass relation using all known cluster measurements to date. ter in concentration is not shown here, but is assumed We also model individual relations for the most commonly to follow a log-normal distribution with a magnitude of used reconstruction techniques. In the present section, we discuss our results of this study. ∆(log cvir) ∼ 0.18 (Bullock et al. 2001). The relation found by Prada et al. (2012) shows the prominent upturn feature • There is an inconsistency between lensing (WL and in concentration, while other relations are monotonically de- WL+SL) concentrations and theoretical expectations from creasing functions of mass. Simulation relations and ones ob- simulations. Low to medium mass lensing measurements 14 tained in this study stand in stark contrast with one another (∼ 10 M ) are inconsistent with simulation results, even 14 for lower mass clusters (. 1 × 10 M ), however, projection when projection is taken into account. It is very likely the must be first be accounted for before any conclusions can be case that some of this difference can be generated by the ex- drawn. In the bottom panel, we compare analytical projec- istence of a strong orientation bias in the lensing cluster pop- tions of simulation relations (using the method outlined in ulation, however, the magnitude of this effect (quantified by Groener & Goldberg 2014) with WL and WL+SL relations. previous studies) cannot completely explain the difference For the purposes of understanding the magnitude of this ef- we observe here. fect, halo shapes are assumed to be well-described by prolate • We find that the concentration-mass relation from spheroidal isodensities with axis ratios of q = 0.65 (Jing & strong lensing clusters remains virtually unconstrained, due Suto 2002), with major axes in the line-of-sight direction. to the small size of the sample, as well as the insensitivity Increased scatter in projected relations are expected to be of SL reconstructions to the outer region of clusters. caused by the actual distributions of shapes and orientations • The slope of the WL+SL relation is found to be higher (which we do not account for here). Direct statistical com- (though still consistent) with WL alone over the lower half parisons of these relations is non-trivial, due to the differ- of the mass range, and may point to the existence of a new ences in relation models. However, the projection of triaxial physical feature of clusters. However, when we only look at halos was thought to be a sufficient explanation for fully clusters with both measurements, we find no evidence that describing the existence of differing observed and simulated concentrations generated by WL+SL methods are in excess cluster concentrations. It is clear that it is unlikely to be the of WL. Most likely, this tells us that the selection effects sole contributing factor. for WL+SL is most likely the cause of this difference. More- We also observe that the concentration-mass relation over, the intrinsic scatter of the concentration parameter on for combined WL+SL is steeper than WL alone (though all mass scales is observed to be larger than the proposed both relations are consistent at the 1-σ level). Cluster halo difference in projected concentration due to shape, making isodensities which are more prolate in the inner regions can this effect difficult to measure. produce larger projected concentrations for line-of-sight ha- • Lensing (WL and WL+SL) concentrations are system- los, and thus any method which makes use of information atically higher than those made with X-ray methods. In the 14 on this scale may stand to be biased high because of it. We mass range of ∼ (1 − 3) × 10 M , the WL+SL relation is find that the sign of this difference is in the right direction marginally inconsistent with X-ray measurements. Reasons for this effect, and we cannot rule out shape as one of the for a flatter X-ray relation as compared lensing methods are underlying causes. numerous. The gas distribution is rounder than the dark Though we do not possess a complete volume-limited matter mass distribution, causing projection effects to be sample of galaxy clusters for which all measurement meth- less severe for X-ray samples. X-ray masses are also bi- ods have been performed, we can begin to understand any ased low due to temperature and hydrostatic equilibrium systematic effects present in clusters with concentrations biases. Consequently, for the same nominal value of mass and masses present for various combinations. In Figure 7, (MWL = MX), X-ray clusters are likely more massive than we show clusters whose profiles have been estimated using clusters measured using WL. Because lower concentrations the following pairwise combinations of methods: i) WL and correlate with larger masses, lower concentrations are at- WL+SL, ii) X-ray and WL, and iii) CM and LOSVD. We tributed to cluster mass bins, causing the X-ray c-M relation do not detect any discernable trend in the way concentra- to have a lower normalization as compared to WL. Lastly, tions or masses are overestimated or underestimated in each at very high masses, selection effects are less effective, since comparison, however, we show the magnitude of the poten- these clusters are likely to pass observational thresholds, and

c 0000 RAS, MNRAS 000, 000–000 12 Groener, Goldberg, & Sereno

15 −1 thus are included in samples. Due to less severe selection bias (& 10 h M ) can be overestimated and underestimated, 15 at larger mass (∼ 10 M ), as well as lower concentrations respectively, by about ∼ 10%, if an NFW model is incor- as compared to WL, a bias towards flatness is expected for rectly assumed. Though this does not fix the mismatch in the X-ray c-M relation. the concentration parameter we have discussed here, it could • Out of all reconstruction methods, we also find that perhaps artificially steepen the overall slope of the relation lensing (WL and WL+SL) relations are the most inconsis- by reducing the concentrations of the most massive clusters. tent with a power-law index of zero. Another plausible explanation for the existence of this • Methods which depend upon using galaxies as tracers of new over-concentration discrepancy for clusters is that the mass show a neutral (LOSVD) or positive (CM) correla- dark matter only simulations lack important cluster physics tion between concentration and mass. The sensitivity of the which is present in real clusters. Feedback from AGN and su- slope of the caustic method c-M relation to the uncertain- pernovae, and gas cooling are mechanisms which may cause ties is minimal. Disregarding uncertainties in either mass (or prevent) further concentration of dark matter within the or concentration, we find a best fit slope and intercept of cores of clusters, and have a strong effect on their lensing m = 0.207 and b = −2.103. efficiency (Puchwein et al. 2005; Wambsganss et al. 2008; • We find the c-M relation of our X-ray sample to be con- Rozo et al. 2008). Mead et al. (2010) find that strong lens- sistent with results from DM only simulations, though with ing cross-sections for high mass clusters are boosted by up a higher normalization, and slightly higher slope. However, to 2-3 times, when including gas cooling with star formation direct comparison of these results with simulations which in- in simulations. Furthermore, they find that by adding AGN clude baryons, feedback, and star formation is necessary. Ra- feedback into the mix, this cross-section (and also the con- sia et al. (2013) performed such a study, and found that the centration parameter) decreases, as energy is injected back dependence of the c-M relation on the radial range used to into the baryonic component. derive the relation, the baryonic physics included in simula- There is a strong need to obtain low-mass 14 tions, and the selection of clusters based on X-ray luminosity (< 1 × 10 M ) lensing measurements, since our most all work to alleviate tensions between simulations and ob- contentious conclusion is that, if the relation we have servations which existed previously. Though, they also find found holds in the galaxy group region, we expect cluster that including AGN feedback brings the relation more in line concentrations to be even less consistent with theory with DM only simulations, and it remains unclear whether than they already are. Clearly this trend cannot continue or not all tensions between these relations have been identi- indefinitely, but it remains to be seen how this model breaks fied and accounted for. down. An ideal study would contain a large, complete, and volume-limited sample of clusters, which can be studied One potential source of error in the inference of the in each reconstruction method. In this way, we could slope of the c-M relation which we do not account for in hope to eliminate the dependence of the selection function this study is the covariance of the mass and concentration of clusters on the concentration-mass relation we would measurements themselves (Sereno et al. 2015b). Auger et al. measure. Lastly, since selection effects are quite difficult (2013) discovered they were unable to constrain the slope of to model, it is worth extending this study to as large of the c-M relation of a sample of 26 strongly-lensed clusters a sample as possible. Heterogeneous datasets (such as the with richness information, due to the intrinsic covariance of one compiled in this study) have the ability to compensate their mass and concentration estimates, in addition to a lim- for selection biases (Gott et al. 2001; Piffaretti et al. 2011; ited dynamic range of halo masses. Furthermore, improper Sereno & Ettori 2015). modeling of the distribution of halo masses can also significantly alter the inferred relation (i.e. - it is sensitive to the A.G. would like to thank the referee for a constructive prior). and thorough review, which significantly contributed to im- Selection effects can strongly steepen the slope of the c- proving the quality of the publication. M relation, especially for lensing clusters (Merten et al. 2014; M.S. acknowledges financial contributions from con- Meneghetti et al. 2014). The slopes of relations for clusters tracts ASI/INAF n.I/023/12/0 ‘Attivitàrelative alla fase from CLASH, LOCUSS, SGAS, and a high redshift sam- B2/C per la missione Euclid’, PRIN MIUR 2010-2011 ‘The ple (also included in this study), were all found to be much dark Universe and the cosmic evolution of baryons: from cur- steeper than that of the relation characterizing dark-matter rent surveys to Euclid’, and PRIN INAF 2012 ‘The Universe only clusters (Sereno et al. 2015b). For fixed mass, the most in the box: multiscale simulations of cosmic structure’. highly concentrated clusters are most likely to show SL fea- tures, and thus are most likely to be included in SL selected samples (Oguri & Blandford 2009). In all cases, the selection REFERENCES process of clusters tend to prefer over-concentrated halos, and depends strongly on observational selection thresholds Abdullah M. H., Ali G. B., Ismail H. A., Rassem M. 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c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 15

APPENDIX A: FULL OBSERVATIONAL due to assumed cosmological model. Beginning with the to- DATASET1 tal mass enclosed within a sphere of radius r We discuss here the details of our measurement aggregation 3 r/rs MNFW(6 r) = 4πrs ρs log (1 + r/rs) − (4) procedure. 1 + r/rs • The overwhelming majority of measurements were re- where rs is the scale radius, and is used to scale the radial ported in the one or both of the conventions shown in Table coordinate which we will denote as x = r/rs. In terms of A-1 (200, and virial). Whenever possible, we report measure- projected quantities, following Sereno et al. (2010) we can ments made by the original paper, rather than relying on the express the scale radius and scale density ρs as conversion procedure outlined in Hu & Kravtsov (2003). For Σcr ρs = κs (5) papers which report their results for only one (or neither) of rs the previously mentioned conventions, we apply the aforementioned conversion process. rs = Ddθs (6) • There are numerous deﬁnitions (and approximations) where κs is the normalization, Σcr is the critical surface mass used throughout the literature for δvir (also represented as density for lensing, Dd is the angular diameter distance to ∆v). All measurements reported using the virial overdensity the lens, and θs is the angular scale radius. convention have been converted to a consistent deﬁnition 2 c Ds (Bryan & Norman 1998), before being reported in Table A- Σcr = (7) 1: 4πGDdsDd

2 2 At this point it should be noted that the scale convergence ∆v = 18π + 82x − 39x (1) and projected (angular) scale radius do not depend upon for a flat cosmology (ΩR = 0), and where x = Ω(z) − 1. cosmology when fitting the shear profile. The mass within Furthermore, radius r∆ and its corresponding concentration c∆ can be expressed in terms of projected quantities Ω (1 + z)3 0 2 2 Ω(z) = 2 (2) c DdDsκsθs c∆ E(z) MNFW(6 r∆) = log (1 + c∆) − (8) GDds 1 + c∆ with E(z) representing the Hubble function.

2 3 2 1/3 E(z) = Ω0 (1 + z) + ΩR (1 + z) + ΩΛ (3) r∆ 1 2MNFW(6 r∆) c∆ = = 2 (9) rs Ddθs ∆ · H This approximation is accurate to 1% within the range of Ω(z) = 0.1 − 1. where ∆ is the factor by which the density inside r∆ is • All data reported in Comerford & Natarajan (2007), ∆ · ρcr, and H is the Hubble parameter. Next, by solving the were also reported in this study using their original cos- former two expressions for κs and θs (which are conserved mological model (with the exception of King et al. (2002)). measurements for any arbitrary choice of cosmology), we We follow this convention, and continued to report measure- obtain a system of equations which then relate the lensing ments in Table A-1 in the cosmology found in the source mass and concentration in any two cosmologies, Ω1 and Ω2. paper. In order to simplify the notation a bit, the mass and concen- • All new measurements added to the dataset which do tration corresponding to r∆ in cosmology Ωx, will henceforth not appear in Comerford & Natarajan (2007) received red- be expressed as M∆(Ωx) and c∆(Ωx), respectively. shifts from previous entries (if available; meaning that if the cluster already exists in the database, the first reported c (Ω )3 c (Ω )3 ∆ 2 = ∆ 1 · R (10) value of the redshift is used). Differences in these redshifts M∆(Ω2) M∆(Ω1) are minimal (∼ 1%), and do not contribute significant uncertainty to the inferred c-M relation. Right ascension (RA) f(c (Ω )) f(c (Ω )) ∆ 2 = ∆ 1 · T (11) and declination (Dec) measurements were almost exclusively M∆(Ω2) M∆(Ω1) obtained from NED2. Lastly, due to the plurality of cluster naming conventions (nearly one for each survey or study), The ratios R and T, and the function f, can be expressed cluster names were cross-matched with previous entries us- in terms of the following cosmology dependent quantities: ing NED in order to ensure that our cluster sample does not 3 2 3 contain artificially over-represented objects. Dd(Ω1) H(Ω1) ∆(Ω1) Dd(Ω1) ∆(Ω1)ρcr(Ω1) R = 3 2 = 3 · Dd(Ω2) H(Ω2) ∆(Ω2) Dd(Ω2) ∆(Ω2)ρcr(Ω1) (12) D (Ω )D (Ω ) D (Ω ) Σ (Ω ) APPENDIX B: LENSING COSMOLOGY T = s 1 d 1 ds 2 = cr 2 (13) CORRECTION Dds(Ω1) Ds(Ω2)Dd(Ω2) Σcr(Ω1) x In this section, we derive the correction to the measured f(x) = log(x) − (14) cluster concentration and mass (assuming an NFW profile), 1 + x Solving this system of equations, can be done by nu- merically solving for c (Ω ) 1 The raw data has been made publicly available (format: csv, ∆ 2 xlsx) here: http://www.physics.drexel.edu/∼groenera/ f(c∆(Ω2)) f(c∆(Ω1)) T 2 3 = 3 · (15) https://ned.ipac.caltech.edu/ c∆(Ω2) c∆(Ω1) R

c 0000 RAS, MNRAS 000, 000–000 16 Groener, Goldberg, & Sereno

Figure 7. Comparisons of concentrations and masses for clusters measured in the following pairs of measurements: i) WL and WL+SL, ii) X-ray and WL, and iii) CM and LOSVD. In all cases, the color of the scatter point indicates redshift.

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 17

Lastly, the mass M∆(Ω2) is obtained by direct substitution of the numerical result from (15).

c 0000 RAS, MNRAS 000, 000–000 18 Groener, Goldberg, & Sereno h / Λ Ω / m Ω δ Lokas et al. (2006) virial 0.3/0.7/0.7 Lokas et al. (2006) virial 0.3/0.7/0.7 Lokas & Mamon (2003) virial 0.3/0.7/0.7 Gastaldello et al. (2007a) 1250 0.3/0.7/0.7 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Ref. McLaughlin (1999)Babyk et al. 200 (2014) 0.3/0.7/0.7 200 0.27/0.73/0.73 Xu et al. (2001) 200 0.3/0.7/0.5 Babyk et al. (2014)Gastaldello et al. (2007a) 2500 200 0.3/0.7/0.7 0.27/0.73/0.73 Wojtak &Lokas (2010) Gastaldello et al. (2007a) 102 2500 0.3/0.7/0.7 0.3/0.7/0.7 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Gastaldello et al. (2007a) 1250 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Gastaldello et al. (2007a)Vikhlinin et al. (2006)Xu et al. (2001) 2500Wojtak &Lokas (2010) 500 0.3/0.7/0.7 200 102 0.3/0.7/0.71 0.3/0.7/0.5 0.3/0.7/0.7 Babyk et al. (2014)Gastaldello et al. (2007a) 1250 200 0.3/0.7/0.7 0.27/0.73/0.73 Vikhlinin et al. (2006) 500 0.3/0.7/0.71 Wojtak &Lokas (2010) 102Gastaldello et al. (2007a) 1250 0.3/0.7/0.7 0.3/0.7/0.7 Okabe et al. (2014) virial/200/500 0.27/0.73/None Voigt & Fabian (2006)Gastaldello et al. (2007a) 200/2E4 1250 0.3/0.7/0.7 0.3/0.7/0.7 al.D´emocl`eset (2010)Wojtak &Lokas (2010) 500 102 0.3/0.7/0.7 0.3/0.7/0.7 Kubo et al. (2007) 200 0.3/0.7/None Gastaldello et al. (2007a)Babyk et al. (2014) 2500Babyk et al. (2014) 200 0.3/0.7/0.7 200 0.27/0.73/0.73 0.27/0.73/0.73 Gavazzi et al. (2009) 200 0.3/0.7/0.7 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Babyk et al. (2014)Babyk et al. (2014) 200 200 0.27/0.73/0.73 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 ) 011 35 014 078 012 099 033 02 046 041 04 065 55 88 011 53 014 078 012 099 033 02 046 96 041 17 065 63 07 ......

36 32 4 25 25 35 2 31 31 53 91 05 0 3 07 39 84 39 43 27 06 2 43 76 57 67 69 0 18 37 46 0 . 1 . 0 . 0 . 0 0 . . 0 . . 0 . 0 0 . 7 0 . . . . . 1 5 ...... 9 0 78 0 7 9 1 85 2 4 . M 0 . . 0 0 0 . . 0 2 0 0 0 0 2 2 . 4 0 1 . . . . . +0 − +1 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +5 3 +0 − +8 − +0 − +2 − +7 − 0 1 0 1 3 +0 − +0 − +0 − +0 − +0 − +2 − +0 − +0 − +2 − +0 − +1 − +1 − +4 − +0 − +1 − 14 +0 − 39 +1 − +0 − +1 − 03 62 +7 − 9 9 Rines et al. (2003) 200/turn 0.3/0.7/None 91 86 ...... vir 59375 Rines & Diaferio (2006) 200 0.3/0.7/None 1909 Rines & Diaferio (2006) 200 0.3/0.7/None 87 Rines & Diaferio (2006) 200 0.3/0.7/None 4 4 58 311 79 263 51 4 3229 Rines et al. (2003) 200/turn 0.3/0.7/None 7 81 099 48 624 37 59 Rines & Diaferio (2006) 200 0.3/0.7/None 77 57154 Rines & Diaferio (2006) 200 0.3/0.7/None 54 Rines & Diaferio (2006) 200 0.3/0.7/None 45 73 11507 Rines et al. (2003) 200/turn47 0.3/0.7/None 504 68 Rines & Diaferio (2006) Rines & Diaferio (2006) 200 200 0.3/0.7/None 0.3/0.7/None 45 69 9 9726349 Abdullah et al. (2011) Rines & Diaferio (2006) virial09 2004562 0.3/0.7/None Rines et al. (2003) Rines & 0.3/0.7/None Diaferio (2006) Rines & Diaferio (2006) 200 200/turn 200 0.3/0.7/None 0.3/0.7/None 0.3/0.7/None 59 62 94 Rines & Diaferio (2006) 200 0.3/0.7/None ...... 0 4 M 5 11 4 − 9 0 2 0 2 3 0 2 1 1 − − 2 0 1 1 0 0 12 3 0 23 0 8 9 8 1 0 1 9 14 62 31 0 88 3 17 55 16 66 34 22 0 52 36 14 72 55 13 7 37 ...... 3 89 8 11 0 04 3 62 55 4 8 28 05 3 9 12 64 48 4 97 35 39 3 27 8 08 0 42 3 3 38 55 4 8 28 09 3 1 54 65 4 08 34 36 . 3 . . . . . 2 1 . . . . 4 ...... 1 4 2 . . 1 ...... 9 4 2 7 8 4 1 9 4 7 8 3 1 0 . 2 10 0 1 1 3 . 1 . 3 . 0 1 0 0 6 2 6 1 4 . 2 . . 1 1 0 0 ...... +1 − +2 − +1 − +4 − +1 − +4 − +2 − +1 − 0 3 3 0 0 3 5 +0 − +3 − +22 − +0 − +1 − +1 − +1 − +1 − +1 − +0 − +1 − +0 − +0 − +1 − +2 − +8 − +1 − +1 − +17 − +1 − +1 − +0 − +0 − 951 0 4198 0 +0 − 7 0 1 9 0 +3 − 45 46 9 +11 − 4 +0 − 8 19 3 13 2 2 6 8 8 9+0 − 6 18 11 74 +4 − +5 − 2 0 4 46 146 12 2 ...... 8 35 3 85 9 2 3 1 8 03 17 7557 0 8 2 5 17 030 0 0 7 0 382 49 13 0 9142 39 1 4 98 ...... vir 11 13 c 3 13 14 11 13 17 8 9 10 13 16 4 10 8 7 16 26 12 5 12 14 12 3 12 9 5 15 20 13 6 11 9 5 12 8 1 ) (10 009 011 06 01 077 017 036 036 054 29 92 009 011 06 01 077 017 036 036 054 18 72 ......

31 16 28 34 21 67 21 1 026 15 27 27 46 6 57 77 3 24 92 34 32 72 33 37 73 23 84 026 15 37 23 49 5 48 46 3 15 18 0 . . . 0 . 0 . . 0 . 0 . . . . 0 . . 0 . 0 . . 0 . . . 1 3 ...... 5 7 6 26 0 5 4 2 61 1 M 0 . 1 . 0 0 0 0 . 0 2 0 0 0 0 . 0 5 2 1 . 0 0 0 . . . . . +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +2 − +4 − 0 0 0 2 3 +0 − +1 − +0 − +0 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +2 − +0 − +6 − +1 − +1 − +0 − +0 − +1 − 14 +0 − +0 − +0 − +3 − 8 +6 − 8 38 94 2 13 . . . . . 200 5322 57 10 16 11 2 81 4 1 8 26 274 35 224 14 93 1 202 55 09 8 927 22 54 11 2753 15 39 135 9 25 46 5 16 9 46431 21 442 47 38 3 456 9 7 6529 301 8 6326 19 21 6 997 1 5 66 31 ...... 0 3 (10 4 9 M 3 − 8 0 2 0 2 2 2 0 1 0 − − 2 0 1 1 0 0 8 3 18 0 0 7 8 7 1 1 0 8 12 41 Cluster concentrations and masses 52 17 83 98 17 19 16 01 93 45 1 81 02 15 16 19 14 04 ...... 7 8 3 19 0 75 43 1 22 62 4 8 84 55 84 47 01 26 27 8 07 91 0 05 43 1 22 83 3 8 17 26 8 03 25 25 2 2 . 0 . . . 0 . . . . 3 ...... 1 3 2 ...... 2 7 6 7 4 5 6 6 5 0 1 2 7 6 7 7 5 6 6 2 1 0 . . 7 . 0 2 . 2 . 1 2 . 0 1 . 0 4 5 1 0 3 1 . . . 1 . 1 0 0 ...... +0 − +2 − +0 − +1 − +3 − +1 − +3 − +2 − 0 0 2 0 0 2 1 0 2 0 4 +17 − +0 − +1 − +1 − +1 − +1 − +0 − +1 − +0 − +0 − +6 − +1 − +1 − +1 − +13 − +0 − +1 − +0 − +0 − +0 − 67 +0 − 27 6 43 +0 − 0 +2 − 11 0 +8 − +0 − 9 93 +0 − 6 2 2 9+0 − 5 66 28 37 +3 − +1 − 7 3 +4 − 41 2 0 11 ...... 4 29 0 8 64 0 92 2 4 69 5 94 91 1 7 29 27 1 4 85 32 81 55 81 84 2 29 0 46 2 0 35 6 8527 0 0 38 27 37 01 11 87 0 3502 0 3 ...... 200 Table A-1: Method c . NGC 5044Abell 1060 0.009 0.01 13 15 24.0 10 36 41.8 -16 23 08 -27 31 28 X-ray LOSVD 8 10 NGC 5846 0.006 15 06 29.3 +01 36 20 CM 8 ClusterVirgoNGC 4636Abell z 1060 0.003 0.0031 RA 12 12 42 30 49.8 47.3 0.01 +02 +12 41 20 16 13 Dec 10 36 CM 41.8 X-ray -27 31 2 28 8 X-ray 10 Continued on next page VirgoAbell 1060 0.003 12 30 47.3 0.01 +12 20 13 10 36 CM 41.8 -27 31 28 0 LOSVD 10 Abell 3526 0.011 12 48 47.9 -41 18 28 X-ray 10 Abell 1060 0.01 10 36 41.8 -27 31 28 X-ray 8 NGC 1550Abell S805 0.0124 0.0139 04 19 37.9 18 47 20.0 +02 24 34 -63 20 13 X-ray LOSVD 13 6 NGC 2563Abell 262 0.0149 0.0163 08 20 35.7 01 52 46.8 +21 04 04 +36 09 05 X-ray LOSVD 7 7 Abell 262 0.0163 01 52 46.8 +36 09 05 X-ray 10 NGC 533MKW 4 0.0185 01 0.02 25 31.3 12 +01 03 45 57.7 33 +01 X-ray 53 18 13 LOSVD 7 Abell 262 0.0163 01 52 46.8 +36 09 05 LOSVD 3 Abell 262Abell 262Abell 262Abell 194MKW 4 0.0163 0.0163 01 52 46.8 0.0163 01 52 46.8 0.018 01 +36 52 09 46.8 05 +36 01 09 25 05 40.8 +36 09 X-ray 05 0.02 -01 X-ray 24 26 X-ray 6 12 03 57.7 5 CM 12 +01 53 18 6 X-ray 19 MKW 4MKW 4 0.02 0.02 12 03 57.7 12 03 57.7 +01 53 18 +01 53 18 X-ray X-ray 9 3 MKW 4Abell 3581 0.0218 0.02 14 07 28.1 12 03 57.7 -27 00 55 +01 53 18 LOSVD CM 9 11 Abell 3581NGC 5129Abell 1656 0.0218 14 07 28.1 0.023 -27 00 55 0.023 13 24 10.0 12 X-ray 59 48.7 +13 58 36 +27 9 58 50 X-ray WL 11 Abell 539 2 0.029 05 16 37.3 +06 26 16 LOSVD 9 Abell 1656 0.023 12 59 48.7 +27 58 50 WL 3 Abell 1367IC 1860MKW 11 0.022 11 0.0223 44 36.5 0.0228 02 49 13 33.7 29 +19 31.2 45 32 -31 11 +11 21 47 19 CMRXC X-ray CM J2315.7-0222MKW 16 8 7 NGC 6338 4 0.0267Abell 539 23 15 45.2 -02 22 37 0.0271 0.0286 14 40 X-ray 38.2 17 15 23.0 0.029 +03 28 11 35 +57 24 05 40 16 37.3 X-ray CM +06 26 16 15 X-ray 7 10 Abell 1656 0.023 12 59 48.7 +27 58 50 WL 5 Abell 779NGC 4325RXC J2214.8+1350MKW 8 0.0264 0.0233 22 09 14 19 52.7 49.2 0.0257Abell 539Abell 12 +13 +33 4038 23 50 45 06.7 48 37Abell 2199 +10 37 CM LOSVD 16 0.0271 4 14 40 X-ray 38.2 6 0.029 0.03 +03 8 28 35 05 16 0.03 37.3 23 47 43.2 CM +06 26 16 16 28 -28 38.0 08 29 5 CM +39 32 55 X-ray X-ray 14 9 6 Abell 1656Abell 1656Abell 779 0.023 12 0.023 59 48.7 0.0233 12 59 +27 48.7 58 09 50 19 49.2 +27 58 50 X-ray +33 45 37 LOSVD 1 LOSVD 7 6 Abell 779NGC 4325 0.0233 0.0257 09 19 12 49.2 23 06.7Abell +33 2197 45 +10 37 37 16Abell 2199 CM CM 24 4 0.03 0.03 16 28 10.4 16 28 +40 38.0 54 26 +39 32 55 CM CM 1 4 Abell 1656 0.023 12 59 48.7 +27 58 50 CM 10

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 19 h / Λ Ω / m Ω δ Lokas et al. (2006) virial 0.3/0.7/0.7 Lokas et al. (2006) virial 0.3/0.7/0.7 Xu et al. (2001)Markevitch et al. (1999) 200 200 0.3/0.7/0.50 0.3/0.7/0.5 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Ref. Babyk et al. (2014)Gastaldello et al. (2007a) 200 1250 0.27/0.73/0.73 0.3/0.7/0.7 Babyk et al. (2014)Babyk et al. (2014)Gastaldello et al. (2007a) 200 1250 200 0.27/0.73/0.73 0.3/0.7/0.7 0.27/0.73/0.73 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Xu et al. (2001)Markevitch et al. (1999) 200 200 0.3/0.7/0.50 0.3/0.7/0.5 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Xu et al. (2001)Voigt & Fabian (2006) 200/2E4 200 0.3/0.7/0.7 0.3/0.7/0.5 Babyk et al. (2014) 200 0.27/0.73/0.73 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Xu et al. (2001) 200 0.3/0.7/0.5 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014)Gastaldello et al. (2007a)Gastaldello et al. (2007a) 2500 200 500 0.3/0.7/0.7 0.27/0.73/0.73 0.3/0.7/0.7 Pointecouteau et al. (2005) 200 0.3/0.7/0.7 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Xu et al. (2001) 200 0.3/0.7/0.5 Babyk et al. (2014) 200 0.27/0.73/0.73 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Buote & Lewis (2004) 200 0.3/0.7/0.7 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Wojtak &Lokas (2010) Wojtak &Lokas (2010) 102 102 0.3/0.7/0.7 0.3/0.7/0.7 Pointecouteau et al. (2005) 200 0.3/0.7/0.7 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 ) 46 187 07 196 46 53 99 48 016 84 48 56 55 49 47 187 2 196 37 4 3 46 47 016 19 38 64 53 7 ......

87 44 58 47 77 49 487 38 34 02 44 27 82 75 74 73 01 7 62 18 49 487 38 24 31 63 37 82 73 22 . 1 0 1 . 0 . 1 . . 1 . 1 1 . 0 . 1 4 . 1 . 1 1 ...... 4 1 2 33 4 1 36 M . 0 0 0 . 0 0 . 0 0 0 0 1 0 0 . 0 0 2 . . . +2 − +0 − +1 − +0 − +1 − +2 − +1 − +1 − +0 − +1 − +4 − +2 − +1 − +2 − 2 1 1 0 +0 − +1 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +5 − 14 +3 − 65 13 46 +1 − − 22 +175 54 62 77 49 05 08 41 85 Rines et al. (2003) 200/turn 0.3/0.7/None +0 − 2 ...... vir 47003 Rines et al. (2003) Kelson et al. (2002) Rines & Diaferio (2006) 200/turn 200 200 0.3/0.7/None 0.3/0.7/0.75 0.3/0.7/None 1 81 72303 Rines & Diaferio (2006) 200 0.3/0.7/None 79 622 73 533 Rines et al. (2003) 200/turn 0.3/0.7/None 47 18 Rines & Diaferio (2006) 200 0.3/0.7/None 92 6 86 2639 Abdullah et al. (2011) Rines & Diaferio (2006) virial 200 0.3/0.7/None 0.3/0.7/None 82 282 44 44 Pratt & Arnaud (2005) 200 0.3/0.7/0.7 56 15 17 Rines & Diaferio (2006) 200 0.3/0.7/None 75 3904 Rines & Diaferio Rines (2006) & Diaferio (2006) 200 200 0.3/0.7/None 0.3/0.7/None 07 5 91 Rines & Diaferio (2006) 200 0.3/0.7/None 97 02 ...... − − 7 5 M 13 1 10 7 1 4 10 5 − − 3 5 12 − 1 2 10 − 2 12 1 0 1 1 10 35 − 1 12 8 − 12 26 2 2 1 1 5 30 85 82 07 67 8 76 65 15 78 16 6 87 76 1 55 9 92 84 04 9 62 08 ...... 5 9 66 38 01 8 67 44 3 9 86 24 09 23 96 04 99 23 31 5 17 36 63 7 8 43 51 9 86 5 12 82 0 66 93 78 34 . . . 2 1 . . 1 . . 5 . . 4 1 . 5 . 3 2 . . . . 6 ...... 8 8 3 4 5 0 9 9 3 1 1 91 8 8 4 5 0 9 9 3 1 12 91 0 7 2 . 1 . 1 . 0 2 0 . 9 0 . . . 0 . . 1 1 1 . 0 . 1 1 . 1 0 ...... +2 − +1 − +1 − +1 − +1 − +1 − +5 − +1 − +2 − +2 − 0 0 6 0 2 1 0 0 0 3 1 0 +0 − +14 − +1 − +1 − +0 − +0 − +1 − +0 − +23 − +0 − +0 − +0 − +1 − +0 − +1 − +0 − +0 − +0 − +0 − 7 0 8 1 4 04 +0 − 87 +0 − 88 1+16 − 3 5 23 2 02 +0 − 7 26 66 6 +2 − 47 3 83 +1 − +0 − +0 − 52 82 +0 − +3 − +1 − 136 10 16 1 07 3 +0 − ...... 80 5 67 6 6 1664 1 9 75 3 0 57 82 8 1 8 9 14 1 5 49 38 72 5 3239 1 8 52 9474 0 1 56 59 ...... vir 10 13 10 9 c 15 7 14 9 8 4 14 9 13 8 8 16 9 6 10 12 13 12 13 8 9 7 10 11 6 3 7 4 6 8 5 15 3 4 5 4 5 ) (10 27 146 156 28 397 012 84 29 19 18 15 146 156 5 27 397 012 75 27 16 16 ......

74 93 37 46 4 67 29 42 72 58 26 28 81 38 2 26 61 59 62 04 85 55 52 04 94 42 26 03 18 17 04 55 28 28 61 57 . 1 0 . . 0 ...... 1 0 0 . 3 . . . 1 1 . . . . . 2 ...... 8 27 7 0 3 5 19 3 3 M . 0 0 0 0 . . 0 0 1 . 0 1 . 1 0 1 0 0 0 0 0 0 . . . . +2 − +0 − +0 − +1 − +0 − +0 − +3 − +1 − +2 − +4 − 1 1 0 1 0 +0 − +1 − +0 − +0 − +0 − +1 − +1 − +0 − +1 − +1 − +0 − +2 − +1 − +0 − +0 − +0 − +0 − +0 − 14 +1 − 88 +1 − +0 − 3 − +115 93 +0 − 41 05 11 06 ...... 200 0 995 14 670 9 5 81 089 55 46 9 374 75 1 5 13 18 93 9121 14 4 48 12 9209 9 36 542 241 2 226 7 19 89 47 99 8 42 51 14 57 9119 13 27 1 4459 15 97 ...... 6 − − 4 (10 11 M 8 1 6 1 3 9 4 − − 2 5 10 − 1 2 9 − 1 10 1 0 1 1 9 30 − 1 9 6 − 10 21 2 1 1 1 3 24 16 38 81 37 33 27 76 26 17 33 83 19 83 39 81 61 ...... 02 03 03 75 6 03 33 2 68 67 41 1 91 81 92 72 81 76 49 71 23 89 02 47 9 6 09 38 48 67 46 98 37 83 61 75 83 49 69 71 25 . . 2 1 . . 0 . . 4 . . . 1 4 ...... 4 ...... 4 6 6 8 3 7 0 8 7 7 2 4 91 4 6 6 3 0 7 8 7 7 2 4 58 6 . 2 . 1 . 0 . 0 2 0 . 7 3 . . . . 0 . 2 2 . 0 0 0 . 0 0 0 1 0 . 0 ...... +2 − +1 − +0 − +1 − +1 − +3 − +1 − 0 0 0 2 0 0 2 0 4 0 0 0 0 +11 − +0 − +1 − +0 − +0 − +1 − +0 − +18 − +1 − +0 − +1 − +1 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − 0 38 0 38 25 +0 − +0 − 26 0+12 − 3 4 9535 1 +0 − 33 +2 − 4446 3 +0 − +0 − +0 − +0 − +0 − +2 − 87 9 9 14 0 64 3 +0 − ...... 79 2 37 470 4 5 8 21 968 53 1 9 0 52 36 18 41 1 9 7 7 6 41 4 05 92 57 9 49 52 9 27 28 34 0 59 54 3883 0 4 12 ...... 200 Method c Continued . Table A-1 – Abell 2199Abell 2199Abell 2199Zw1665Abell 2634 0.03 0.03 16 28 0.03 38.0 16 0.0302 28 0.031 +39 38.0 32 16 55 28 38.0 08 23 23 11.5 +39 38 32 25.7 55 LOSVD +39 32 55 +04 21 +27 21.6 7 00 X-ray 45 X-ray CM LOSVD 8 10 7 11 ClusterAbell 2199Abell 2199 zAbell 2634 0.03 0.03 16 RA 28 38.0 16 28 +39 38.0 32 55 0.031 +39 Dec 32 55 CM 23 38 25.7 LOSVD 7 4 +27 00 45 X-ray 11 Continued on next page IIIZw54ESO 5520200AWM 4 0.0311 0.0314 03 04 41 54 17.6 52.0 0.0317 +15 -18 23 06 44 56 16 04 57.0 X-ray X-ray +23 55 14 11 5 X-ray 7 NGC 6107AWM 4Abell 496 0.0311 16 17 20.1 +34 0.0317 54 07 0.0329 16 04 04 57.0 33 CM 38.4 +23 55 -13 14 15 33 6 X-ray LOSVD 6 3 Abell 496 0.0329 04 33 38.4 -13 15 33 X-ray 11 Abell 496Abell 496 0.0329 0.0329 04 33 38.4 04 33 38.4 -13 15 33 -13 15 33 CM LOSVD 6 14 Abell 496Abell 496Abell 1314 0.0329 0.0329 04 0.0334 33 38.4 04 33 11 38.4 34 50.5 -13 15 33 -13 15 +49 33 03 28 X-ray X-ray LOSVD 10 6 6 Abell 1314Abell 2063 0.0334 0.0337 11 34 50.5 15 23 01.8 +49 03 28 +08 38 22 CM LOSVD 12 10 Abell 2063 0.0337 15 23 01.8 +08 38 22 X-ray 7 2A 0335+096Abell 2052 0.0347 03 38 35.3 0.0348 15 16 +09 44.0 57 55 +07 01 07 X-ray LOSVD 8 9 Abell 2063 0.0337 15 23 01.8 +08 38 22 X-ray 5 Abell 2052 0.0348 15 16 44.0 +07 01 07 X-ray 10 Abell 1142Abell 1142Abell 2147 0.035 0.035 11 0.035 00 48.9 11 00 48.9 16 02 +10 18.7 33 35 +10 33 35 +16 01 12 LOSVD CM 6 X-ray 28 10 Abell 2052 0.0348 15 16 44.0 +07 01 07 X-ray 9 ESO 3060170RGH89 080MKW 9 0.0358 05 40 0.0379 06.6 13 20 24.9 -40 50 0.0382 12 +33 15 12 32 17 29.3 X-ray +04 X-ray 40 54 6 7 X-ray 5 MKW 9Abell 3571 0.0382 0.039 15 32 13 29.3 47 28.4 +04 40 -32 54 50 59 X-ray LOSVD 5 8 Abell 3571 0.039 13 47 28.4 -32 50 59 X-ray 8 Abell 1139 0.0398 10 58 04.3 +01 29 56 LOSVD 2 Abell 3571 0.039 13 47 28.4 -32 50 59 X-ray 4 Abell 2657 0.04 23 44 51.0 +09 08 40 X-ray 5 Abell 576 0.04 07 21 24.1 +55 44 20 LOSVD 3 Abell 2589Abell 2589 0.041 0.041 23 23 53.5 23 23 53.5 +16 48 32 +16 48 32 X-ray X-ray 4 6 Abell 576 0.04 07 21 24.1 +55 44 20 X-ray 4 Abell 2589Abell 2107 0.041 23 23 53.5 0.0411 +16 48 15 32 39 38.4 CM +21 47 20 LOSVD 6 11 Abell 576 0.04 07 21 24.1 +55 44 20 CM 10 Abell 2593Abell 160Abell 1983 0.0415 23 24 20.2 0.0432 0.0442 +14 39 01 04 12 14 51.4 52 44.0 LOSVD +15 30 +16 54 44 46 2 CM LOSVD 3 10 Abell 2593Abell 295Abell 1983 0.0415 0.0424 23 24 20.2 02 02 19.9 0.0442 +14 39 04 14 -01 52 07 44.0 13 CM +16 44 46 CM 11 X-ray 1 3 Abell 119 0.0446 00 56 18.3 -01 13 00 LOSVD 3 Abell 119 0.0446 00 56 18.3 -01 13 00 X-ray 4

c 0000 RAS, MNRAS 000, 000–000 20 Groener, Goldberg, & Sereno h / Λ Ω / m Ω δ Lokas et al. (2006) virial 0.3/0.7/0.7 Xu et al. (2001) 200 0.3/0.7/0.5 Babyk et al. (2014) 200Gastaldello et al. (2007a) 1250 0.27/0.73/0.73 0.3/0.7/0.7 Xu et al. (2001) 200 0.3/0.7/0.5 Babyk et al. (2014) 200Wojtak &Lokas (2010) 102 0.27/0.73/0.73 0.3/0.7/0.7 Ref. Babyk et al. (2014)Babyk et al. (2014) 200 200 0.27/0.73/0.73 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Xu et al. (2001) 200 0.3/0.7/0.5 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014)Xu et al. (2001) 200 200 0.27/0.73/0.73 0.3/0.7/0.5 Wojtak &Lokas (2010) Babyk et al. (2014) 102 200 0.3/0.7/0.7 0.27/0.73/0.73 Gastaldello et al. (2007a) 500 0.3/0.7/0.7 Pointecouteau et al. (2005) 200 0.3/0.7/0.7 Babyk et al. (2014)Xu et al. (2001) 200 200 0.27/0.73/0.73 0.3/0.7/0.5 Babyk et al. (2014) 200Okabe et al. (2015) 0.27/0.73/0.73 virial 0.27/0.73/0.70 Wojtak &Lokas (2010) Babyk et al. (2014) 102David et al. 200 (2001) 0.3/0.7/0.7 0.27/0.73/0.73 200 0.3/0.7/0.7 Okabe & Umetsu (2008) virial 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Wojtak &Lokas (2010) Babyk et al. (2014) 102 200 0.3/0.7/0.7 0.27/0.73/0.73 Wojtak &Lokas (2010) Xu et al. (2001) 102 0.3/0.7/0.7 200 0.3/0.7/0.5 Babyk et al. (2014)Voigt & Fabian (2006) 200 200/2E4 0.27/0.73/0.73 0.3/0.7/0.7 Babyk et al. (2014)Xu et al. (2001) 200 200 0.27/0.73/0.73 0.3/0.7/0.5 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 ) 671 66 32 49 53 52 122 71 49 97 85 33 05 71 54 671 83 66 07 83 54 122 83 45 83 88 76 23 84 16 ......

44 54 11 33 61 5 91 25 22 82 78 47 39 83 1 4 54 4 29 62 5 58 25 42 77 0 47 39 34 0 46 . 0 3 . . . 1 . 1 2 . . 1 0 . 1 . . . 1 . . 4 . 2 1 4 8 . 2 ...... 7 M 3 0 2 1 0 4 0 0 5 1 0 0 5 0 . 1 +0 − +2 − +1 − +1 − +3 − +2 − +0 − +1 − +1 − +5 − +2 − +1 − +6 − +6 − +4 − 1 +4 − +0 − +2 − +1 − +0 − +3 − +1 − +0 − +5 − +2 − +1 − +0 − +5 − +1 − +1 − 14 5 78 47 45 91 5 56 46 7 97 37 13 22 73 +10 − 86 15 ...... vir 06 Rines & Diaferio (2006) 200 0.3/0.7/None 81 Rines et al. (2003)61283 200/turn Rines & Diaferio (2006) 0.3/0.7/None 200 0.3/0.7/None 081756 Abdullah et al. (2011)25 Rines et al. (2003) virial Rines & Diaferio (2006) 200/turn 0.3/0.7/None 200 0.3/0.7/None 0.3/0.7/None 98 12 41 82 Rines & Diaferio (2006) 200 0.3/0.7/None 53 842 92 92 Pratt & Arnaud (2005) 200 0.3/0.7/0.7 5423 Rines & Diaferio (2006) Abdullah et al. (2011) 200 virial 0.3/0.7/None 0.3/0.7/None 66 933269 Abdullah et al.3 (2011) Rines & Diaferio (2006) Rines & Diaferio (2006) virial Abdullah et al. (2011) 200 200 0.3/0.7/None virial 0.3/0.7/None 0.3/0.7/None 0.3/0.7/None 51 15 54 Rines & Diaferio (2006) 200 0.3/0.7/None 09 69 Rines & Diaferio (2006) 200 0.3/0.7/None 19 08 Rines & Diaferio (2006) 200 0.3/0.7/None 7 64 ...... − 31 1 13 − 3 3 7 9 M 16 4 12 − 24 12 − 5 15 1 1 1 16 − 3 42 4 5 1 5 21 1 4 63 5 31 12 − 32 2 68 − 5 19 59 48 4 45 65 1 36 79 79 59 34 87 73 44 09 67 03 33 5 65 47 33 ...... 37 95 12 08 32 0 5 75 0 98 23 26 32 4 94 3 56 31 34 67 89 12 32 0 48 95 0 46 23 26 39 13 75 35 34 39 . 3 4 5 5 . 2 1 . . . 0 . . . . . 1 . . . . 1 . . . . 5 0 ...... 3 8 9 6 36 3 7 3 4 4 0 5 8 3 3 8 9 6 35 3 3 3 4 4 0 5 8 3 . 1 . . . . 0 . . . 3 1 . 0 . . 4 0 1 7 . 5 0 5 0 2 0 . 0 3 0 ...... +2 − +1 − +5 − +5 − +2 − +1 − +0 − +1 − +1 − +1 − +0 − 0 1 0 2 0 0 1 0 0 0 1 0 0 0 +1 − +0 − +1 − +1 − +0 − +4 − +0 − +2 − +7 − +1 − +0 − +5 − +0 − +1 − +0 − +0 − +4 − +0 − +0 − 03+1 − 2 96 +0 − +2 − 85 6 3 +0 − 26 07 36 +0 − 08 +5 − +0 − +0 − +0 − 93 +1 − 0 0 +0 − 3 22 9 61 4 33 +0 − +0 − 09 71 ...... 4 4581 3 3 25 4 4 4 8 84 5 52 3 7 3 25 9417 4 0 58 6 1 08 1752 1 3 5598 1 0 97 49 63 16 1 18 8 82 9305 4 83 6 ...... vir 4 9 6 14 8 12 9 21 c 20 3 12 6 11 2 5 8 8 6 5 10 7 5 4 15 12 15 4 1 5 12 4 9 4 8 1 7 11 10 ) (10 91 514 19 28 16 26 46 12 28 46 18 17 72 514 47 92 27 11 56 27 25 48 89 55 ......

78 18 17 47 76 09 19 43 69 41 16 68 04 82 95 03 15 47 48 34 09 19 17 88 41 71 09 38 57 26 2 0 3 . . . . 1 2 . 1 . . 1 4 . . 1 . . . 2 . 3 . . 2 ...... 47 3 77 4 47 3 77 9 M . 1 1 1 0 . 0 0 0 1 0 0 . 3 0 1 . 5 0 . . . . +3 − +0 − +2 − +0 − +3 − +2 − +1 − +4 − +1 − +2 − +4 − +3 − 0 2 4 1 +2 − +1 − +1 − +0 − +1 − +0 − +0 − +2 − +0 − +0 − +3 − +1 − +1 − +4 − +1 − 14 61 02 +0 − 6 72 27 +0 − 94 05 67 91 +4 − 3 84 68 +7 − 0 34 ...... 200 36 3 24055 1 10 07 8 5874 7 7911 10 3 6 37 0 67 09 8 51 57 57 5 7865 10 16 3 3285 23 8102 1 0954 6 3 01 15 3 23 41 7 59 3 36 5 88 ...... − 26 12 1 3 − 2 6 8 (10 M 14 3 10 − 21 9 − 4 12 1 1 1 14 − 33 2 3 5 4 18 0 1 3 40 4 26 9 25 − 2 46 − 4 16 73 13 17 63 18 16 89 13 ...... 03 46 27 01 83 38 81 25 27 37 29 5 36 18 12 22 81 36 7 22 79 22 31 26 01 33 26 02 78 44 84 25 25 35 17 5 14 18 12 27 86 25 56 26 42 27 13 25 . 2 . . 4 4 ...... 4 ...... 2 4 7 0 7 2 2 2 3 3 8 1 4 6 2 2 4 0 7 5 2 0 2 3 3 8 1 4 6 2 . 1 . 3 . . 0 . 2 . 0 . . 2 0 . 0 . 0 . 0 . 1 5 1 . 0 4 0 1 1 0 0 . 2 0 . 4 0 ...... +2 − +4 − +3 − +1 − 0 1 2 0 0 0 3 0 0 0 0 0 0 1 0 +1 − +1 − +0 − +2 − +0 − +1 − +0 − +0 − +0 − +0 − +2 − +5 − +1 − +0 − +4 − +0 − +0 − +1 − +0 − +0 − +3 − +0 − +1 − +0 − +0 − 37 +1 − +2 − 27 +0 − 35 +0 − +0 − +4 − +0 − +0 − +0 − +0 − +3 − 9 85 +0 − 3 1 4 +0 − +0 − ...... 3 38 55 2 8 91 6 37 69 2 29 4 4 13 2 19 4 6 36 37 8 9 29 12 0 836 4 21 2 26 4 74 7 32 26 9 33 1 9696 1 0 74 02 25 36 4512 1 55 5 16 528 3 8 56 11 ...... 200 Method c Continued . Table A-1 – Abell 119Abell 3376 0.0446 0.045 00 56 18.3 06 01 45.7 -01 13 00 -39 59 34 X-ray X-ray 3 7 Abell 119MKW 3S 0.0446 00MS 56 0116.3-0115 18.3Abell 957 0.045 -01 13 00 15 21 51.9 CM 0.0452 +07 42 31 01 18 53.6 2 X-ray 0.0455 -01 00 07 10 13 40.3 11 X-ray -00 54 52 4 LOSVD 9 Abell 168Abell 168Abell 168Abell 1736 0.0451 0.0451 01 15 12.0 01 0.0451 15 12.0 +00 19 01 48 15 12.0 +00 19 48 0.046 LOSVD +00 19 48 X-ray 5 13 26 54.0 CM 7 -27 11 00 7 X-ray 16 ClusterAbell 119MKW 3S z 0.0446 00 56 RA 18.3 -01 13 00Abell 957 0.045 Dec CM 15 21 51.9 +07 42 6 31 0.0455 X-ray 10 13 40.3 6 -00 54 52 CM 8 Continued on next page Abell 168Abell 1644 0.0451 01 15 12.0 +00 19 48 0.047 CM 12 57 09.7 5 -17 24 01 X-ray 15 Abell 4059 0.0478 23 57 02.3 -34 45 38 LOSVD 2 Abell 4059 0.0478 23 57 02.3 -34 45 38 X-ray 9 Abell 3558 0.048 13 27 57.5 -31 30 09 X-ray 8 Abell 4059 0.0478 23 57 02.3 -34 45 38 X-ray 4 Abell 3558Abell 376Abell 2717 0.048 13 27 57.5 0.0484 02 0.049 -31 45 30 48.5 09 00 03 +36 12.1 51 36 LOSVD -35 55 1 38 LOSVD 6 X-ray 6 Abell 3558 0.048 13 27 57.5 -31 30 09 X-ray 4 SHK 352Abell 2717 0.0484 0.049 11 21 40.3 00 03 12.1 +02 53 33 -35 55 38 CM X-ray 6 4 Abell 2717 0.049 00 03 12.1 -35 55 38 X-ray 4 Abell 2717Abell 3562 0.049 0.0499 00 03 12.1 13 33 36.3 -35 55 38 -31 39 40 X-ray X-ray 4 8 Abell 3562Abell 3395 0.0499 0.05 13 33 36.3Abell 117 06 27Hydra -31 14.4 A 39 40 -54 28 12 X-ray X-ray 5 0.0535 3 00 0.0538 56 00.9 09 18 05.7 -10 01 46 -12 05 44 LOSVD WL 7 3 Abell 671Abell 671Abell 3391Abell 1377Abell 1377 0.0503 0.0503 08 28 29.3Hydra A 08 28 29.3 0.051 +30 25 01 +30 06 0.0515 25 26 01 22.8 0.0515 LOSVD 11 46 57.9 11 -53 LOSVD 46 41 17 57.9 44 +55 11 44 20 +55 0.0538 44 20 X-ray 09 LOSVD 18 05.7 CM 9 0 -12 05 44 2 X-ray 12 Abell 671Abell 1291AAbell 757 0.0508 0.0503 11Abell 08 32 754 28 19.6 29.3 0.0514 +55 +30 58 09 25 44.0 12 01 47.3 CM +47 CM 42 38 4 0.054 CM 12 09 09 08.4 2 -09 39 58 WL 3 Abell 754 0.054 09 09 08.4 -09 39 58 X-ray 1 Abell 978Abell 3667 0.0544 10 0.055 20 28.8 20 12 -06 30.5 31 11 -56 49 55 LOSVD 4 X-ray 9 RXCJ1022.0+3830Abell 85 0.0546 10 22 04.7 +38 30 43 0.0557 CM 00 41 50.1 5 -09 18 07 LOSVD 3 Abell 85Abell 85Sersic 159 03 0.0557 00 0.0564 41 0.0557 50.1 23 13 00 58.6 41 -09 50.1 18 07 -42 44 -09 02 18 07 X-ray X-ray X-ray 3 6 7 Abell 85Abell 2319 0.0557 00 41 50.1 0.0564 19 -09 21 18 08.8 07 +43 57 30 CM X-ray 4 1 Abell 2319Abell 133 0.0564 19 0.0569 21 08.8 01 02 42.1 +43 57 30 -21 52 25 X-ray LOSVD 5 8 Abell 133 0.0569 01 02 42.1 -21 52 25 X-ray 8

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 21 h / Λ Ω / m Ω δ Lokas et al. (2006) virial 0.3/0.7/0.7 Ref. Vikhlinin et al. (2006) 500 0.3/0.7/0.71 Babyk et al. (2014)Pointecouteau et al. (2005) 200 200 0.27/0.73/0.73 0.3/0.7/0.7 Wojtak &Lokas (2010) 102Vikhlinin et al. (2006) 500 0.3/0.7/0.7 0.3/0.7/0.71 Xu et al. (2001) 200 0.3/0.7/0.5 Babyk et al. (2014) 200 0.27/0.73/0.73 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Wojtak &Lokas (2010) Wojtak &Lokas (2010) 102 102 0.3/0.7/0.7 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Voigt & Fabian (2006) 200/2E4 0.3/0.7/0.7 Babyk et al. (2014)Xu et al. (2001) 200 200 0.27/0.73/0.73 0.3/0.7/0.5 Vikhlinin et al. (2006)Xu et al. (2001) al.D´emocl`eset (2010)Babyk 500 et al. (2014) 500 200 0.3/0.7/0.71 200 0.3/0.7/0.7 0.3/0.7/0.5 Wojtak &Lokas (2010) Wojtak &Lokas (2010) 0.27/0.73/0.73 102 102 0.3/0.7/0.7 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014)Xu et al. 200 (2001) 0.27/0.73/0.73 200 0.3/0.7/0.5 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014)Wojtak &Lokas (2010) 200 102 0.27/0.73/0.73 0.3/0.7/0.7 Voigt & Fabian (2006) 200/2E4 0.3/0.7/0.7 ) 07 82 87 67 05 021 56 82 27 59 61 5 2 86 43 69 4 76 023 38 8 54 79 35 63 ......

77 22 58 3 7 4 49 84 09 03 0 01 45 0 58 05 77 22 89 3 31 6 58 38 24 03 01 57 66 35 58 4 . 8 . . . 3 1 . . . . . 2 . . 4 . 0 . 3 . . 2 1 5 3 2 ...... 2 M 0 0 0 0 3 5 0 1 1 2 7 1 1 1 5 1 . +8 − +4 − +2 − +2 − +4 − +0 − +1 − +2 − +1 − +7 − +5 − +3 − 2 +0 − +0 − +0 − +0 − +4 − +7 − +0 − +0 − +1 − +3 − +74 − +1 − +1 − +1 − +5 − +0 − 14 93 86 81 1 4 87 8 13 1 0 71 5 47 48 76 79 78 +16 − ...... vir 33 42 Rines & Diaferio (2006) 200 0.3/0.7/None 94 6894 Rines & Diaferio (2006) Pratt & Arnaud (2005) 200 200 0.3/0.7/None 0.3/0.7/0.7 63 94 33 Rines & Diaferio (2006) 200 0.3/0.7/None 23 94 Rines & Diaferio (2006) 200 0.3/0.7/None 14 96 07 6 Rines & Diaferio (2006) 200 0.3/0.7/None 5297212 Rines & Diaferio (2006)0 Rines & Diaferio (2006) Abdullah et al. (2011) Rines02 & Diaferio (2006) 20062 200 Buote et al. (2005) virial 200 Abdullah et al. (2011) 0.3/0.7/None Rines & Diaferio (2006) 0.3/0.7/None 0.3/0.7/None virial virial 0.3/0.7/None 200 0.3/0.7/0.7 0.3/0.7/None 0.3/0.7/None 27 246 4642 Abdullah et al. (2011) Rines & Diaferio (2006) virial 200 0.3/0.7/None 0.3/0.7/None 28 Rines & Diaferio (2006) 200 0.3/0.7/None 06 Rines & Diaferio (2006) 200 0.3/0.7/None 6657 Abdullah et al. (2011) Rines & Diaferio (2006) virial 200 0.3/0.7/None 0.3/0.7/None 0976 Rines & Diaferio (2006) Rines & Abdullah Diaferio et (2006) al. (2011) 200 200 virial 0.3/0.7/None 0.3/0.7/None 0.3/0.7/None 46 4 76 Abdullah et al. (2011) virial 0.3/0.7/None ...... M 5 72 1 1 3 1 38 − 12 35 15 2 5 7 23 9 10 44 5 8 − 8 10 15 11 5 − 0 4 51 23 16 52 1 48 − 3 21 4 3 2 07 65 58 67 66 96 1 39 25 71 62 96 ...... 53 39 45 54 58 12 45 63 18 98 09 37 0 33 46 55 52 46 87 77 45 0 61 05 53 53 45 97 58 11 75 14 74 09 84 35 0 33 2 9 52 51 94 88 51 0 59 82 . . . . . 1 3 . . . 3 ...... 3 . . . . . 2 . . . 0 ...... 4 3 5 2 3 4 4 2 8 4 4 5 3 5 2 3 4 4 2 8 4 4 0 0 0 . 2 0 . 1 . 1 1 1 0 3 0 3 . . . 0 2 1 . 0 . 0 0 0 . 0 . 8 1 3 ...... +1 − +1 − +1 − +3 − +2 − +0 − 0 0 2 1 0 1 0 1 2 0 2 +0 − +0 − +0 − +1 − +0 − +1 − +0 − +0 − +0 − +1 − +2 − +0 − +3 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +8 − +0 − +2 − +0 − 03 +0 − 28 +7 − 06 7 33 0 3+1 − +0 − 7 +1 − 85 +0 − +1 − 05 9 96 5 2 54 +2 − 22 0 +0 − 0 25 +2 − ...... 28 67 0456 1 5 22 2835 1 2 04 5 45 58 76 0 19 86 64 7503 4 0 0 9 32 7154 1 0 34 9756 8 9 59 5 97 66 3 27 0 32 5 7191 91 5 3 14 0 ...... vir c 6 1 7 7 8 11 5 11 3 3 3 3 10 6 5 5 3 6 6 14 5 3 9 4 2 17 13 3 4 5 12 3 9 ) (10 29 27 62 16 99 27 016 49 11 18 81 16 37 16 11 18 51 37 018 47 34 82 16 14 ......

59 18 48 24 72 0 38 42 94 58 79 89 77 11 82 59 18 75 24 17 7 45 3 07 32 5 79 13 28 94 45 5 . 5 . . . 3 1 . . . . . 2 . 2 . 1 . . 0 . 2 1 4 2 2 ...... 6 9 M 0 0 0 0 2 3 0 1 0 1 . 0 2 0 4 0 . +5 − +4 − +2 − +2 − +3 − +1 − +0 − +2 − +1 − +5 − +4 − +3 − 5 1 +0 − +0 − +0 − +0 − +3 − +1 − +0 − +0 − +1 − +2 − +0 − +1 − +1 − +3 − +0 − 14 78 25 11 8 4 34 +54 − 55 12 9 73 35 43 97 84 +13 − ...... 200 41 63 14 5 04 6365 7 43 9 4171 13 96 87 73 3 48 9 91 8 38 96270 11 14 4852 07 6 4 1119 2 1 27 7 196 6529 5 14 57 10 6 8 3551 5 23 49 33 16 2129 7 7 9 32 7 ...... (10 4 M 47 1 3 1 1 33 − 11 25 11 1 3 6 19 7 8 32 8 13 4 7 − 6 9 4 − 0 3 37 20 14 39 1 37 − 18 3 3 2 2 81 67 04 84 72 01 ...... 42 27 35 81 82 81 08 21 76 88 77 41 27 26 87 15 39 33 56 33 73 21 3 23 42 37 35 83 07 8 56 1 96 55 86 23 25 26 15 67 39 37 64 38 73 44 3 62 ...... 2 . . . . 0 2 ...... 94 3 46 2 8 4 9 2 1 3 9 2 3 9 5 4 46 2 57 4 9 2 1 3 9 2 3 9 0 0 0 . . . 0 . 2 0 . 1 1 2 0 0 2 0 0 . . . . 1 1 . 0 . 0 0 . 0 . 0 1 6 3 ...... +2 − +0 − +2 − 1 0 0 2 0 0 1 0 0 0 1 2 0 1 +0 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +0 − +0 − +2 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +6 − +3 − +1 − +0 − +0 − +0 − +0 − 12 6 36 +2 − 13+0 − +0 6 − +1 − +0 − +0 − 93 8 23 37 24 0 +2 − 5 +0 − +1 − ...... 77 16 78 5 797 4 1 12 1 36 71 9 19 5 56 66 97 861 0 45 28 19 82 5 736 6 7 3 05 65 6 45 2 9909 1 0 1215 7 49 4 38 6719 2 8 36 93 2 06 9208 4 3 4 ...... 200 Method c Continued . Table A-1 – ClusterAbell 133 z 0.0569 01 RA 02 42.1 -21 52 25 Dec X-ray 4 Continued on next page Abell 2256Abell 1991 0.058 17 03 43.5 0.0586 +78 43 03 14 54 31.4 X-ray +18 38 31 1 X-ray 5 Abell 2415Abell 2169Abell 1991Abell 1991 0.0581 22 0.0585 05 40.5 16 14 09.6 0.0586 -05 35 36 0.0586 14 54 +49 31.4 09 11 14 54 31.4 LOSVD +18 38 31 CM 5 +18 38 31 X-ray 3 X-ray 5 6 Abell 2399Abell 3266 0.0582 21 57 25.8 -07 47 41 0.0594 04 31 CM 24.1 -61 26 38 7 X-ray 8 Abell 3158 0.0597 03 42 53.9 -53 38 07 LOSVD 8 Abell 3266 0.0594 04 31 24.1 -61 26 38 X-ray 3 Abell 3158 0.0597 03 42 53.9 -53 38 07 X-ray 2 Abell 3158 0.0597 03 42 53.9 -53 38 07 LOSVD 2 Abell 602Abell 3809 0.0606 0.0623 07 53 21 24.2 46 57.8 +29 21 -43 58 54 36 CM LOSVD 2 10 Abell 2734Abell 1795 0.0625 00 11 0.063 20.7 13 -28 48 51 53.0 18 +26 35 44 LOSVD 2 LOSVD 7 RXCJ1351.7+4622Abell 1795 0.063 13 51 45.6 +46 22 00 0.063 CM 13 48 53.0 +26 35 2 44 X-ray 4 Abell 1795 0.063 13 48 53.0 +26 35 44 X-ray 4 Abell 1795 0.063 13 48 53.0 +26Abell 35 644 44 X-ray 4 0.0704 08 17 24.5 -07 30 46 X-ray 2 Abell 1795Abell 2124 0.063Abell 1066Abell 13 1066 48 53.0RXCJ1115.5+5426 +26Abell 35 644 44 0.065Abell 644 0.0701Abell X-ray 1767 15 45 00.0 11 0.0684Abell 15 1767 32.8 0.0684 4 10 +36 39Abell 03 27.9 1691 58 +54 10 26 39 06 27.9 +05 0.0704 10 X-ray 46 +05 CM 10 0.0704 46 08 17 0.0714 24.5 LOSVD 11 08 17 0.0714 24.5 13 CM 36 06.1 -07 6 8 30 13 46 36 0.072 06.1 -07 30 46 +59 12 28 11 13 +59 X-ray 11 12 23.2 28 X-ray LOSVD +39 4 12 LOSVD 05 3 4 4 LOSVD 2 Abell 1795RXC J0216.7-4749Abell 1436Abell 1436Abell 2124 0.0635Abell 2149 02 0.063 16 42.3 13 48 -47 0.0648 53.0 49 24 0.0648 12 00 22.0 +26 35 12 44 00 0.065 X-ray 22.0 0.0653 +56 13 49 15 X-ray +56 45 16 13 3 00.0 01 49Abell 38.1 1767 LOSVD 7 +36 03 +53 CMAbell 58 52 399 43 4 CM CM 1 0.0714 10 1 13 36 06.1 0.072 +59 12 02 28 57 56.4 CM +13 00 59 X-ray 6 2 Abell 2462 0.073 22 39 16.4 -17 19 46 X-ray 13 RXJ1053.7+5450 0.0727Abell 10 1569 53 43.9 +54 52 20 CM 0.074 8 12 36 18.7 +16 35 30 X-ray 10 Abell 2065 0.073 15 22 42.6 +27 43 21 X-ray 2 Abell 2067Abell 2064Abell 401 0.0737 0.0738 15 23 07.9 15 20 59.4 0.0748 +30 50 42 +48 02 38 58 17 57.5 CM +13 CM 34 46 18 X-ray 6 3 Abell 1238Abell 3112 0.0733 11 22 58.0Abell 1190 +01 05 32Abell 1205 0.075 LOSVD 03 3 17 58.5 0.0755 -44 14 20 11 11 0.0756 38.5 X-ray 11 13 +40 20.7 50 33 9 +02 31 56 LOSVD 2 LOSVD 12 Abell 401 0.0748 02 58 57.5 +13 34 46 X-ray 4 Abell 3112Abell 1424Abell 1190 0.075 03 0.0754 17 58.5 11 57 0.0755 28.7 -44 14 20 11 11 +05 38.5 03 46 X-ray +40 50 33 CM 7 CM 5 6 Abell 1424 0.0754 11 57 28.7 +05 03 46 LOSVD 5

c 0000 RAS, MNRAS 000, 000–000 22 Groener, Goldberg, & Sereno h / Λ Ω / m Ω δ Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Wojtak &Lokas (2010) Babyk et al. (2014) 102 200 0.3/0.7/0.7 0.27/0.73/0.73 Babyk et al. (2014)Babyk et al. (2014) 200 200 0.27/0.73/0.73 0.27/0.73/0.73 Babyk et al. (2014)Schmidt & Allen (2007) 200 virial 0.27/0.73/0.73 0.3/0.7/0.7 Ref. Gastaldello et al. (2007a)Vikhlinin et al. (2006) 500 500 0.3/0.7/0.7 0.3/0.7/0.71 Pointecouteau et al. (2005)Xu et al. (2001) 200 200 0.3/0.7/0.7 0.3/0.7/0.5 Voigt & Fabian (2006) 200/2E4 0.3/0.7/0.7 Babyk et al. (2014)Xu et al. (2001) 200 200 0.27/0.73/0.73 Okabe & Umetsu (2008) 0.3/0.7/0.5 virialOkabe et al. (2015) 0.3/0.7/0.7 virial 0.27/0.73/0.70 Vikhlinin et al. (2006) 500 0.3/0.7/0.71 Okabe & Umetsu (2008) virialBabyk et al. (2014) 0.3/0.7/0.7 200 0.27/0.73/0.73 Lewis et al. (2003)Xu et al. (2001) 200 200 0.3/0.7/0.7 0.3/0.7/0.5 Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Babyk et al. (2014)Wojtak &Lokas (2010) 200 102 0.27/0.73/0.73 0.3/0.7/0.7 Voigt & Fabian (2006) 200/2E4 0.3/0.7/0.7 Pointecouteau et al. (2005) 200 0.3/0.7/0.7 Vikhlinin et al. (2006) 500 0.3/0.7/0.71 Allen et al. (2003)Xu et al. (2001) 200 200 0.3/0.7/0.5 0.3/0.7/0.5 ) 87 8 42 96 536 0 69 41 33 67 17 0 88 39 11 48 52 536 0 03 7 33 22 03 88 ......

65 71 42 97 33 0 64 6 09 3 1 44 94 42 97 33 0 9 0 39 3 2 . 4 3 1 1 . 0 . 2 . 4 1 . 2 . . . 5 . . 1 ...... 89 08 M 1 . 0 0 20 2 2 3 0 2 1 33 2 3 . ∞ +4 − +5 − +1 − +1 − +0 − +3 − +5 − +1 − +3 − +5 − +1 − 0 +1 − +0 − +0 − +74 − +2 − +2 − +3 − +0 − +3 − +1 − + − +2 − +6 − 14 +1 − 52 84 53 15 0 12 48 76 1 Abdullah et al. (2011) virial 0.3/0.7/None 72 0 0 65 0 1 51 0 Pointecouteau et al. (2004) 200 0.3/0.7/0.7 6 ...... vir 2467 Rines & Diaferio (2006) Abdullah et al. (2011) 200 virial 0.3/0.7/None 0.3/0.7/None 416304 Rines & Diaferio (2006) Abdullah et al. (2011) Rines 200 & Diaferio (2006) virial 200 0.3/0.7/None 0.3/0.7/None 0.3/0.7/None 99 2 9815 Rines & Diaferio (2006) Abdullah05 et al. (2011) 200 Rines & virial Diaferio (2006) 0.3/0.7/None 200 0.3/0.7/None 0.3/0.7/None 9156 Rines & Diaferio (2006) Rines 200 & Diaferio (2006) 200 0.3/0.7/None 0.3/0.7/None 97 9 Rines & Diaferio (2006) 200 0.3/0.7/None 54 77909 Rines &13 Diaferio (2006) 200 Rines & Diaferio (2006) 200 0.3/0.7/None 1276 0.3/0.7/None 93 Rines & Diaferio Rines (2006) & Diaferio Rines (2006) & Diaferio (2006) 200 200 200 0.3/0.7/None 0.3/0.7/None 0.3/0.7/None 14 48 Rines & Diaferio (2006) 200 0.3/0.7/None 44 Rines & Diaferio (2006) 200 0.3/0.7/None 69 564773 Rines & Diaferio (2006) Abdullah et al. (2011) Rines & Diaferio (2006) 200 virial 200 0.3/0.7/None 0.3/0.7/None 0.3/0.7/None 98 Rines & Diaferio (2006)93 200 0.3/0.7/None 25 9848 Rines & Diaferio (2006) Abdullah et al. (2011) 200 virial 0.3/0.7/None 0.3/0.7/None 42 Rines & Diaferio (2006) 200 0.3/0.7/None ...... 1 7 7 8 39 4 53 12 20 8 3 M 24 0 − − 24 4 16 12 10 − 2 28 15 3 − 4 16 40 6 5 43 13 12 13 22 − 7 0 65 0 3 0 66 0 ...... 0 0 05 57 45 63 24 7 55 95 42 28 89 64 8 13 41 53 73 0 81 49 49 44 0 0 34 54 47 63 08 7 55 99 42 67 89 68 8 95 45 56 55 0 56 49 49 39 . . . 4 . 1 ...... 51 48 8 38 3 1 9 5 5 48 42 8 38 3 1 9 5 5 7 4 1 0 12 . 1 . 0 2 2 0 . 0 3 1 . 13 . 4 0 . . 0 3 0 0 1 3 3 0 0 . 0 ...... +1 − +1 − 0 0 0 0 0 1 1 0 0 +7 − +4 − +0 − +0 − +12 − +1 − +0 − +2 − +2 − +0 − +0 − +3 − +1 − +13 − +4 − +0 − +0 − +0 − +0 − +0 − +1 − +3 − +2 − +0 − +0 − +0 − 0 0 88 0 +0 − 83 +0 − 6 +0 − 9445 9 8 +0 − 0 +0 − +1 − +1 − 8 630 2 +0 − +0 − ...... 3487 6 68 1 2221 1 08 1 8 09 2 7808 4 456 2 31 0 59 74 51 7 7573 9 97 1 21 2456 3 8 4 94 3 52 9401 3 8 0 2499 87 7 2 13 45 7912 2 81 52 92 5 82 1 7 6 ...... vir 2 14 9 2 10 7 8 7 c 5 10 3 8 5 5 4 7 6 5 6 5 10 8 5 7 5 3 5 6 4 8 ) (10 12 78 22 62 0 451 17 49 08 17 29 0 51 71 74 27 25 0 451 45 52 08 62 17 51 ......

23 79 58 68 13 0 55 1 88 8 4 08 95 77 68 13 0 77 3 13 8 8 . . 4 2 1 1 . 0 2 . 3 1 . 2 . . . 4 . . 1 ...... 33 33 M 1 0 0 . 16 2 2 2 0 2 0 26 1 2 . ∞ +3 − +3 − +1 − +1 − +0 − +2 − +4 − +1 − +2 − +4 − +1 − 0 +1 − +0 − +0 − +57 − +2 − +2 − +2 − +0 − +2 − +1 − + − +1 − +4 − 14 43 44 76 62 +0 − 0 48 06 81 35 0 1 71 0 8 53 04 5 ...... 200 5398 33 7925 18 07 5 1984 7 5 7 18 66 56 4 56 3 6603 2 4 0 71 4 789 39 619 13 14 24 7 89 3 39 3 06 21 21 86 5 7 3 8822 6 07 4113 8 3 546178 8 12 12 13 6 ...... 1 5 6 7 33 3 39 10 16 7 3 (10 20 M 0 − 19 − 3 13 10 9 − 2 23 12 2 4 13 − 33 5 4 34 10 10 11 18 − 67 4 02 4 . . . . 6 78 2 43 6 37 26 09 38 5 76 43 71 71 87 48 42 33 4 31 88 39 39 35 6 25 2 41 6 35 27 11 34 5 64 43 74 71 87 51 73 36 42 18 02 39 39 31 . . . 3 ...... 1 6 95 3 2 9 5 6 4 4 4 1 6 25 3 2 9 5 6 4 4 4 5 0 3 0 9 0 1 1 0 0 1 . 0 0 . 2 . . 10 . 3 0 . . 2 0 . 0 1 . 2 0 0 . 0 ...... +1 − 2 0 0 0 0 0 1 0 2 0 0 +5 − +0 − +3 − +0 − +9 − +0 − +1 − +1 − +0 − +0 − +1 − +0 − +0 − +2 − +10 − +3 − +0 − +0 − +0 − +0 − +1 − +2 − +0 − +0 − +0 − 1 1 62 1 +2 − +0 − 931+1 − 8 7 +0 − 5 +0 − +0 − +1 − +0 − +2 − +0 − +0 − ...... 12 99 0603 5 28 933 96 1 64 0 07 1 386 1 05 3 3538 2 3 63 29 25 0 7 97 4 0 969 8 98 0 22 4251 2 4 6 95 53 2 96 2 92 4 62 89 3 359 6 2 88 7883 2 2 22 33 67 2 7 67 6 ...... 200 Method c Continued . Table A-1 – Abell 1459Abell 1650 0.0839 0.0843 12 04 15.7 12 58 41.1 +02 30 18 -01 45 25 LOSVD LOSVD 26 2 Abell 2670Abell 2670Abell 2029 0.0761 0.0761 23 54 13.7 23 54 13.7 -10 25 08 0.0767 -10 25 08 15 10 55.0 LOSVD LOSVD 14 +05 43 12 11 X-ray 6 Abell 1663Abell 1663Abell 1650Abell 2597 0.0837 0.0837 13 02 50.7 13 02 50.7 -02 0.0843 30 22 -02 30 22 12 58 0.0852 41.1 LOSVD 23 25 CM -01 20.0 45 14 25 -12 07 38 4 X-ray X-ray 2 8 Abell 1173Abell 2670RXCJ1210.3+0523Abell 0.076 2029 0.0764 11 09 18.8 12 0.0761 10 19.9 +41 33 23 45 54 13.7 +05 22 25 0.0767 CM -10 25 08 CM 15 10 55.0 5 X-ray +05 43 3 12 5 X-ray 6 Abell 2428Abell 1650 0.0836Abell 2597 22 16 15.5 -09 20 24 0.0843 CM 12 58 41.1 0.0852 23 25 -01 3 20.0 45 25 -12 07 38 CM X-ray 2 5 ClusterAbell 1205Abell 2670 z 0.0756 11Abell 13 20.7 2029 RA +02 31 56 0.0761 23 CM 54 Dec 13.7 -10 0.0767 25 08 2 15 10 55.0 CM +05 43 12 3 X-ray 4 Continued on next page RXJ1159.8+5531RXJ1159.8+5531Abell 1651 0.081MS 1306 0.081 11 59 51.4 11 59 51.4 +55 32 01 0.0825 +55 32 01 12 59 21.5 X-ray X-ray 0.0832 -04 11 8 41 13 09 2 16.99Abell 2597Abell X-ray -01 1750N 36 45.0 4 CMAbell 2249Abell 2245Abell 478 3 0.0852 0.0856 23 25 13 20.0 30 49.9 -12 07 -01 38 0.0863 52 22 0.0868 17 09 48.8 0.088 17 X-ray 02 WL 31.9 +34 04 26 13 26 6 25.6 +33 30 47 3 +10 CM 28 01 CM WL 10 11 3 Abell 2029 0.0767 15 10 55.0 +05 43 12 X-ray 6 Abell 2255Abell 2255Abell 1651RXJ1326.2+0013 0.0801 0.0801 17 12 31.0 17 12 31.0 0.0827 +64 05 33 +64 13 05 0.0825 26 33 17.6 LOSVD 12 59 21.5 +00 CM 13 17 16 -04 11 41 CM 5 Abell X-ray 1750C 2 Abell 1552 4 Abell 478 0.0856 13 30 49.9 0.0861 12 -01 29 52 50.0 22 +11 0.088 44 26 WL 04 13 25.6 CM 4 +10 28 01 2 X-ray 4 Abell 2029 0.0767 15 10 55.0 +05 43 12 X-ray 4 Abell 1809Abell 1809Abell 1035B 0.079 0.079 13 53 0.0801 06.4 13 53 06.4 10 32 14.16 +05 08 59 +05 +40 08 14 59 49.2 LOSVD CM LOSVD 4 6 4 Abell 1750Abell 478 0.0856 13 30 49.9 -01 52 22 0.088 CM 04 13 25.6 2 +10 28 01 X-ray 3 Abell 2029ZwCl 1215.1+0400Abell 1773 0.0772 12 17 0.0767 40.6 15 10 55.0 +03 39 45 0.0782 +05 43 13 12 42 X-ray 05.5 X-ray +02 5 13 39 8 LOSVD 3 Abell 2061Abell 2061Abell 1809 0.0783 0.0783 15 21 17.0 15 21 17.0 +30 0.079 38 24 +30 38 24 13 53 06.4 LOSVD CM 9 +05 08 59 6 CM 2 Abell 478 0.088 04 13 25.6 +10 28 01 X-ray 2 ZwCl 1215.1+0400Abell 1773 0.0772 12 17 40.6 +03 39 45 0.0782 13 42 CM 05.5 +02 13 39 6 CM 9 Abell 478 0.088 04 13 25.6 +10 28 01 X-ray 4 Abell 478 0.088 04 13 25.6 +10 28 01 X-ray 5 Abell 478 0.088 04 13 25.6 +10 28 01 X-ray 3 Abell 478 0.088 04 13 25.6 +10 28 01 X-ray 4 Abell 478Abell 1885 0.088 0.0882 04 14 13 13 25.6 43.5 +10 +43 28 39 01 48 X-ray CM 6 4

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 23 h / Λ Ω / m Ω δ Wojtak &Lokas (2010) 102 0.3/0.7/0.7 Ref. Umetsu et al. (2009) virial 0.3/0.7/0.7 Okabe & Umetsu (2008) virial 0.3/0.7/0.7 Babyk et al. (2014)Ettori et al. (2011) 200 200 0.27/0.73/0.73 0.3/0.7/0.7 Wojtak &Lokas (2010) Babyk et al. (2014) 102 200 0.3/0.7/0.7 0.27/0.73/0.73 Wojtak &Lokas (2010) Ettori et al. (2011) 102Ettori et al. (2011) 200 0.3/0.7/0.7 200 0.3/0.7/0.7 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014)Babyk et al. (2014) 200 200 0.27/0.73/0.73 0.27/0.73/0.73 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Voigt & Fabian (2006) 200/2E4 0.3/0.7/0.7 Pointecouteau et al. (2005) 200 0.3/0.7/0.7 Allen et al. (2003) 200 0.3/0.7/0.5 Babyk et al. (2014) 200 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011) 200 0.3/0.7/0.7 Okabe & Umetsu (2008) virial 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Khosroshahi et al. (2006) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Pointecouteau et al. (2005) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Pointecouteau et al. (2005) 200 0.3/0.7/0.7 Vikhlinin et al. (2006) 500 0.3/0.7/0.71 ) 74 29 49 84 14 25 21 76 07 0 33 81 14 8 38 56 02 23 09 23 47 35 14 49 99 6 47 18 76 85 0 45 81 14 34 57 28 02 23 4 45 47 ......

27 16 77 59 89 5 1 18 39 54 25 46 22 6 44 88 38 82 27 61 66 59 89 5 5 18 48 54 25 46 22 6 44 92 38 82 2 2 7 3 . . 2 . . . 5 4 3 1 . . 1 . . 2 6 1 . 1 . . 2 . . 2 . . 3 . 1 2 . 1 ...... 1 48 3 99 65 1 48 3 9 65 M 0 1 1 0 0 10 1 5 0 . 2 0 . 0 0 0 . 0 . . 0 0 0 0 . . . . . +2 − +3 − +7 − +2 − +2 − +6 − +4 − +3 − +5 − +1 − +2 − +6 − +3 − +1 − +3 − +2 − +3 − +1 − +3 − +1 − 7 0 1 0 0 +0 − +1 − +1 − +0 − +0 − +67 − +1 − +4 − +0 − +5 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − 14 29 29 07 14 81 98 31 71 89 0 9 7 59 +7 − 82 24 28 95 +0 − 68 +1 − +0 − +0 − 92 14 12 11 73 ...... vir 869 Rines & Abdullah Diaferio et (2006) al. (2011) 200 virial 0.3/0.7/None 0.3/0.7/None 13 Rines & Diaferio (2006) 200 0.3/0.7/None 19 1944 Rines & Diaferio (2006) Rines & Diaferio (2006) 200 200 0.3/0.7/None 0.3/0.7/None 28 235945 Rines & Diaferio (2006) Rines & Diaferio (2006) Abdullah et al. (2011) 200 200 virial 0.3/0.7/None 0.3/0.7/None 0.3/0.7/None 69 61 02 38 Rines & Diaferio (2006) 200 0.3/0.7/None 05 5 89 03 3 65 12 44 5 02 8 9 47 81 18 59 ...... 9 16 M 15 17 36 2 5 35 5 6 4 8 96 48 39 13 11 11 22 14 1 9 5 22 10 26 6 12 3 2 6 26 3 3 8 9 6 10 5 7 12 7 10 11 7 12 67 0 93 03 95 0 87 81 ...... 05 7 04 95 94 62 8 83 02 8 34 63 5 37 08 25 84 08 05 97 63 31 05 32 6 29 29 33 72 44 3 38 45 57 94 62 3 41 7 1 57 97 46 72 87 89 96 95 04 5 03 07 25 8 65 08 1 56 25 08 44 6 26 28 33 11 44 43 82 73 87 97 62 3 . . . 1 ...... 0 4 ...... 3 8 1 34 9 3 9 14 66 9 . 1 . 1 1 1 0 26 1 1 0 1 . 0 1 3 0 . . 1 0 2 0 0 1 1 0 0 1 0 5 0 0 0 0 0 0 1 0 0 0 0 0 . . . . . +1 − +0 − +4 − 1 0 1 0 1 +0 − +1 − +1 − +1 − +0 − +26 − +0 − +1 − +0 − +0 − +0 − +1 − +4 − +0 − +2 − +1 − +2 − +0 − +0 − +1 − +2 − +0 − +0 − +1 − +0 − +5 − +0 − +0 − +0 − +1 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +0 − +1 − +0 − 35 4 5 0 +1 − +0 − 89 17 +1 − 1 ...... 4 001 4 6 32 97 66 6 28 8597 1 87 9324 1183 2 2 91 3 0245 5 55 05 62 0 4 85 26 74 33 63 46 03 19 13 38 88 94 05 77 12 29 43 37 44 59 69 41 66 ...... vir 3 c 5 4 6 10 5 6 2 7 5 5 3 8 7 7 6 5 11 16 2 2 3 3 3 3 9 9 6 4 9 5 14 3 4 4 4 5 5 5 7 7 5 7 5 ) (10 07 89 7 17 77 18 17 55 15 17 37 18 19 67 17 78 59 7 47 15 16 17 7 26 17 54 34 81 67 17 ......

95 33 5 73 27 2 0 16 77 55 42 41 21 37 18 78 49 62 36 72 32 92 77 32 25 5 73 26 2 2 5 16 06 55 42 41 21 37 18 71 49 62 36 75 32 18 69 2 1 6 3 . 1 . . . . 3 3 3 . . 1 . . 2 . 1 . 1 . . . 2 ...... 2 . . . 1 ...... 23 5 4 0 48 65 23 4 0 48 65 M . 0 1 0 0 4 . 1 4 0 . 1 5 0 0 0 0 0 . . 0 0 1 0 0 0 0 1 ...... +1 − +2 − +6 − +2 − +2 − +3 − +3 − +4 − +1 − +2 − +2 − +1 − +2 − +2 − +1 − 0 4 1 0 0 8 +1 − +1 − +0 − +0 − +5 − +1 − +3 − +0 − +4 − +5 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +1 − +2 − 14 32 62 66 87 +0 − 61 9 52 52 82 +52 − 0 6 66 +4 − 64 98 07 84 +1 − +0 − 03 +0 − 67 ...... 200 77 4 96 6 9 56 2 5732 13 84 0 03 88 0261 39 3414 0 6 36 5 7 94 0 36 09 73 84 21 88 86 1 4 71 68 76 51 37 12 53 31 5 ...... 7 12 (10 12 M 13 29 1 4 29 5 3 5 6 78 36 33 11 9 10 18 12 0 7 4 17 8 19 4 11 2 2 4 22 2 3 6 7 5 8 4 6 10 6 8 9 6 10 9 18 9 8 . . . . 78 61 35 79 3 49 71 2 39 64 77 81 61 07 88 4 27 72 0 06 79 62 06 81 54 49 24 81 25 5 22 22 26 55 23 07 35 44 75 5 24 3 69 35 83 52 19 73 34 33 67 67 84 73 56 22 4 52 67 49 81 79 59 49 83 64 43 19 83 34 5 2 21 26 85 33 41 57 67 78 5 24 ...... 3 ...... 0 5 34 0 5 34 . 0 0 1 0 1 1 0 1 1 20 0 0 0 0 1 2 0 0 0 . 1 0 1 0 0 0 1 0 0 0 0 4 0 0 0 0 . 0 1 0 0 0 0 0 . . . +3 − 1 0 1 +0 − +0 − +1 − +0 − +1 − +1 − +0 − +0 − +1 − +20 − +0 − +0 − +0 − +0 − +1 − +3 − +0 − +0 − +0 − +1 − +0 − +1 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +4 − +0 − +0 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +0 − +0 − +1 − 49 4 0 77 +1 − 2 +0 − . . . . 3 24 5929 3 27 27 06 9703 4 27 5813 59 0 47 6469 1 45 2 43 45 8386 4 46 12 83 16 8 09 46 84 46 75 28 06 79 15 24 56 02 05 69 16 1 14 17 83 85 44 82 42 ...... 200 Method c Continued . Table A-1 – Abell 2142Abell 2142 0.0903 0.0903 15 58 20.6 15 58 20.6 +27 13 37 +27 13 37 LOSVD LOSVD 3 2 ClusterAbell 1728Abell 2142 z 0.0899 13 23 30.2 RA 0.0903 +11 17 46 15 58 20.6 CM Dec +27 13 37 4 WL 4 Continued on next page Abell 2142 0.0903 15 58 20.6 +27 13 37 WL 3 Abell 2142Abell 2700 0.0903 15 58 0.092 20.6 00 +27 03 13 50.6 37 +02 03 X-ray 48 5 X-ray 8 Abell 2142Abell 971Abell 954Abell 3921 0.0903 15 58 20.6 0.0923 0.0928 10 +27 19 13 46.7 37 10 0.093 13 44.8 +40 57 CM 22 55 49 -00 57.0 06 31 CM -64 25 46 1 LOSVD 4 10 X-ray 5 Abell 954Abell 2175Abell 3911Abell 2048Abell 3827 0.0928 10 0.0961 13 44.8 16 20 0.097 22.9 -00 06 31 22 0.0972 +29 46 54 18.6 54 0.098 15 CM 15 17.8 -52 43 LOSVD 22 46 01 56.0 +04 22 2 56 0 -59 X-ray 56 58 LOSVD 5 31 X-ray 4 Abell 2175Abell 2110Abell 3827 0.0961 16 20 0.0971 22.9 15 39 +29 48.7 54 54 0.098 +30 43 02 CM 22 01 56.0 CM -59 0 56 58 4 X-ray 4 Abell 2244PKS0745-191 0.0997 0.103 17 02 42.9 07 47 31.3 +34 03 43 -19 17 40 X-ray X-ray 2 6 Abell 2244PKS0745-191 0.0997 0.103 17 02 42.9 07 47 31.3 +34 03 43 -19 17 40 CM X-ray 3 5 PKS0745-191 0.103 07 47 31.3 -19 17 40 X-ray 5 PKS0745-191 0.103 07 47 31.3 -19 17 40 X-ray 5 PKS0745-191 0.103 07 47 31.3 -19 17 40 X-ray 3 Abell 1446 0.104 12 01 51.5 +58 01 18 X-ray 9 RXCJ0049.4-2931 0.108 00 49 24.0 -29 31 28 X-ray 12 ZwCl0740.4+1740 0.1114 07 43 23.16 +17 33 40.0 WL 1 ZwCl0740.4+1740 0.1114 07 43 23.16 +17 33 40.0 WL 2 Abell 2034 0.113 15 10 11.7 +33 30 53 X-ray 2 Abell 2034 0.113 15 10 11.7 +33 30 53 WL 2 Abell 2034 0.113 15 10 11.7 +33 30 53 X-ray 2 Abell 2051 0.115 15 16 34.0 -00 56 56 X-ray 2 Abell 1361 0.117 11 43 45.1 +46 21 21 X-ray 7 Abell 2050 0.118 15 16 19.2 +00 05 52 X-ray 7 Abell 3814 0.118 21 49 07.4 -30 41 55 X-ray 4 RXC J1141.4-1216 0.119 11 41 24.3 -12 16 20 X-ray 3 Abell 1664 0.128 13 03 41.8 -24 13 06 X-ray 7 Abell 1084 0.132 10 44 33.0 -07 04 22 X-ray 4 RXJ1416.4+2315 0.137 14 16 26.9 +23 15 31 X-ray 11 Abell 1068 0.1375 10 40 43.9 +39 56 53 X-ray 3 Abell 1068 0.1375 10 40 43.9 +39 56 53 X-ray 3 Abell 1068 0.1375 10 40 43.9 +39 56 53 X-ray 3 RXC J2218.6-3853 0.138 22 18 40.2 -38 53 51 X-ray 3 RXCJ0605.8-3518 0.141 06 05 52.8 -35 18 02 X-ray 4 RXCJ0605.8-3518 0.141 06 05 52.8 -35 18 02 X-ray 4 Abell 22 0.142 00 20 42.8 -25 42 37 X-ray 4 Abell 1413 0.143 11 55 18.9 +23 24 31 X-ray 5 Abell 1413 0.143 11 55 18.9 +23 24 31 X-ray 5 Abell 1413 0.143 11 55 18.9 +23 24 31 X-ray 4 Abell 1413 0.143 11 55 18.9 +23 24 31 X-ray 5 Abell 1413 0.143 11 55 18.9 +23 24 31 X-ray 4

c 0000 RAS, MNRAS 000, 000–000 24 Groener, Goldberg, & Sereno h / Λ Ω / m Ω δ Ref. Ettori et al. (2011) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Corless et al. (2009) 200 0.3/0.7/0.7 Babyk et al. (2014)Clowe (2003)Clowe & Schneider (2002)Clowe & Schneider (2001a) 200 200 200 200 0.3/0.7/None 0.3/0.7/0.7 0.27/0.73/0.73 0.3/0.7/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Pointecouteau et al. (2005) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Vikhlinin et al. (2006) 500 0.3/0.7/0.71 Babyk et al. (2014) 200 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Okabe & Umetsu (2008)Babyk et al. (2014) virial 200 0.3/0.7/0.7 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Umetsu & Broadhurst (2008) 200/virial 0.3/0.7/0.7 Umetsu & Broadhurst (2008) 200/virial 0.3/0.7/0.7 Coe et al. (2010) 200/virial 0.3/0.7/0.7 Umetsu et al. (2015) 200 0.3/0.7/0.7 Umetsu et al. (2015) 200 0.3/0.7/0.7 Umetsu et al. (2015) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Corless et al. (2009) 200 0.3/0.7/0.7 Umetsu et al. (2009) virial 0.3/0.7/0.7 Umetsu et al. (2011b) virial 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Zekser et al. (2006) 200 0.3/0.7/None Babyk et al. (2014)Broadhurst et al. (2005b)Halkola et al. (2006)Medezinski et al. (2007) 200 virial virial 200 0.27/0.73/0.73 0.3/0.7/0.7 0.3/0.7/None 0.3/0.7/0.7 Bardeau et al. (2005) 200 0.3/0.7/0.7 Broadhurst et al. (2005a) virial 0.3/0.7/0.7 0 . 82 0 61 ) . . . 35 5 77 0 59 81 8 76 3 29 51 35 98 43 5 04 0 59 82 8 76 3 57 1 35 22 ...... 7 ......

45 83 0 12 7 93 82 95 64 22 34 77 08 56 86 97 4 0 7 3 4 3 4 5 1 0 8 0 45 83 0 14 7 2 82 1 64 65 34 69 89 56 86 96 4 0 7 0 4 3 4 5 1 0 8 0 . . 1 1 2 . . . 5 . 2 . . . 1 ...... 3 ...... 2 2 6 67 1 ...... 1 4 85 8 1 4 86 8 +8 − M 1 1 . 2 2 1 . 0 . 0 0 0 . 1 1 0 21 2 4 0 0 25 6 2 1 0 4 5 4 0 3 1 5 2 . . . . +1 − +1 − +4 − +5 − +2 − +1 − +3 − +2 − +3 − +6 − +104 − +3 − 3 1 0 1 +1 − +1 − +3 − +3 − +1 − +1 − +0 − +1 − +0 − +1 − +1 − +0 − +21 − +2 − +4 − 86 +0 − +0 − +25 − +6 − +2 − +1 − +5 − +4 − +5 − +4 − +0 − +3 − 0 +1 − +7 − +2 − . . 14 55 06 +3 − 83 0 0 16 +1 − 32 +0 − 95 +1 − 9 99 6 3 7 0 0 5 0 9 4 57 31 73 44 00 Halkola et al. (2006) 200 0.3/0.7/0.7 1 3 ...... vir 73 55 3 44 1 86 7 37 62 18 2 07 45 37 37 77 52 57 36 ...... M 7 9 13 20 8 29 − − 8 14 16 5 3 15 7 7 8 9 12 5 4 8 6 32 7 8 113 5 15 7 51 14 19 21 20 20 29 23 8 14 15 18 33 18 35 151 40 − − 17 19 48 54 08 2 08 48 54 08 2 16 ...... 28 51 82 36 58 67 46 49 71 51 15 75 19 39 88 0 08 22 04 52 79 46 6 99 3 9 4 79 41 01 62 7 1 15 76 75 03 43 6 46 96 4 55 3 75 36 19 71 0 6 35 07 52 79 5 6 0 4 0 5 8 8 09 01 42 5 4 ...... 3 1 3 . . . 1 ...... 9 4 5 87 1 7 6 8 4 9 4 5 1 1 7 6 1 6 3 0 1 0 0 . 0 2 0 1 . 1 0 1 0 0 0 0 5 3 1 1 . 2 2 0 . 1 1 . . 3 0 1 0 11 2 1 . 0 . 5 . 1 ...... +3 − +1 − +3 − . +1 − 7 2 0 1 0 1 0 1 0 +2 − +0 − +0 − +0 − +0 − +3 − +0 − +2 − +2 − +0 − +1 − +0 − +0 − +0 − +0 − +5 − +5 − +1 − +1 − +3 − +2 − +0 − +1 − +3 − +5 − +1 − +1 − +0 − +11 − +4 3 +3 − +1 − +0 − +3 − +1 − +7 − 2 +2 − 7 +0 − +3 − +0 − +1 − 4 7 5 32 86 83 4 1 6 8 62 +0 − +2 − 4 2 +0 − 7 ...... 94 28 42 66 0 76 0 05 14 86 49 0 59 13 07 61 22 96 07 73 84 05 4 38 13 44 9 63 12 3 2 45 6 18 2 5 ...... vir c 2 5 5 3 9 3 8 8 5 12 5 5 7 6 3 8 6 8 4 5 10 8 5 8 1 8 4 1 7 8 8 0 3 13 12 11 13 10 12 10 19 15 12 5 10 7 8 37 27 4 13 0 0 ) (10 . . 1 19 17 15 02 47 3 28 07 06 24 8 73 17 19 16 15 02 48 3 81 07 31 76 8 81 ......

12 51 0 8 3 78 72 63 81 53 12 66 79 31 74 83 3 3 0 6 0 7 4 6 44 8 0 7 7 12 51 0 63 3 01 73 63 94 53 12 59 49 31 74 82 3 3 0 6 0 7 4 6 44 8 0 3 7 . . 1 1 2 . . . 4 . 2 . . . . 1 . . . . 5 . 3 ...... 2 2 4 1 57 ...... 7 1 4 05 7 1 4 42 M 1 1 . 2 1 1 . 0 0 0 0 0 . . 1 0 13 1 4 0 0 9 4 2 1 3 3 4 3 0 2 2 4 1 . . . . +1 − +1 − +3 − +4 − +2 − +1 − +5 − +3 − +2 − +2 − +4 − +2 − +88 − 2 1 1 1 +1 − +1 − +3 − +2 − +1 − +1 − +0 − +0 − +0 − +0 − +1 − +0 − +13 − +2 − +4 − +0 − +0 − +9 − +4 − +2 − +1 − +4 − +3 − +4 − +3 − +0 − +2 − 0 +1 − +6 − +1 − . 14 06 93 +2 − 35 0 8 42 +1 − 94 53 +1 − +1 − 6 85 87 6 3 6 6 0 3 6 3 1 99 31 16 09 0 0 7 1 3 ...... 200 96 89 2 48 3 24 54 28 34 56 6 5 08 43 34 15 76 46 36 ...... (10 5 M 7 11 15 7 23 − − 7 11 13 4 3 11 6 6 7 7 10 4 3 7 5 22 6 7 76 4 13 6 24 11 17 18 18 18 25 21 7 13 13 16 28 16 34 30 130 − − 14 17 93 86 48 . . . 21 63 28 44 16 37 16 32 39 89 6 15 3 67 4 96 81 97 26 33 48 3 55 7 7 85 26 52 63 0 82 85 7 9 63 57 02 32 92 37 31 85 42 01 6 28 15 54 37 06 83 75 26 36 46 3 34 5 8 85 26 52 64 0 82 91 9 14 66 ...... 1 ...... 17 2 9 1 4 1 4 2 6 5 5 3 59 2 9 1 4 1 4 2 34 9 5 5 . 0 . 0 0 . 0 2 0 1 . 1 0 0 0 0 0 0 . 2 0 0 . 1 2 0 1 1 1 . . 2 0 . 2 1 2 0 9 0 0 . . . 4 . 0 ...... +3 2 +2 − 1 4 0 0 1 0 0 6 1 1 1 0 +1 − +0 − +0 − +0 − +2 − +0 − +2 − +1 − +0 − +1 − +0 − +0 − +0 − +0 − +4 − +1 − +0 − +2 − +2 − +0 − +2 − +1 − +2 − +4 − +0 − +2 − +1 − +2 − +0 − +9 − +0 − +0 − +2 − +1 − +0 − +6 − +1 − +4 − +0 − +0 − +1 − 7 1 +1 − 7 3 4 56 27 +0 − +1 − +0 − 4 1 +0 − 0 ...... 23 1 14 81 1 83 3 33 75 12 59 28 5 09 39 25 21 38 86 88 5 81 58 27 0 55 21 04 26 86 33 2 5 2 69 31 28 35 7 5 0 5 ...... 200 Method c Continued . Table A-1 – ClusterAbell 2328 z 0.147 20 RA 48 10.6 -17 50 38 Dec X-ray 2 Continued on next page RXCJ0547.6-3152 0.148 05 47 38.2 -31 52 31 X-ray 4 RXCJ0547.6-3152 0.148 05 47 38.2 -31 52 31 X-ray 4 Abell 2204 0.152 16 32 46.5 +05 34 14 X-ray 2 Abell 2204 0.152 16 32 46.5 +05 34 14 WL 7 Abell 2204 0.152 16 32 46.5 +05 34 14 X-ray 2 Abell 2204Abell 2204Abell 2204Abell 2204 0.152 0.152 16 0.152 32 46.5 16 0.152 32 46.5 16 32 +05 46.5 34 16 14 32 +05 46.5 34 14 +05 34 14 WL +05 34 14 WL WL X-ray 6 6 4 9 Abell 2204 0.152 16 32 46.5 +05 34 14 X-ray 4 Abell 3888 0.153 22 34 31.0 -37 44 06 X-ray 4 Abell 2009 0.153 15 00 20.40 +21 21 43.2 WL 5 Abell 2009 0.153 15 00 20.40 +21 21 43.2 WL 5 Abell 907 0.1527 09 58 22.2 -11 03 35 X-ray 2 Abell 907 0.1527 09 58 22.2 -11 03 35 X-ray 6 Abell 907 0.1527 09 58 22.2 -11 03 35 X-ray 5 Abell 1240 0.159 11 23 32.1 +43 06 32 X-ray 6 RXCJ2014.8-2430 0.161 20 14 49.7 -24 30 30 X-ray 3 RXCJ2014.8-2430 0.161 20 14 49.7 -24 30 30 X-ray 3 RXJ1720.1+2638 0.164 17 20 08.88 +26 38 06.0 WL 8 RXJ1720.1+2638 0.164 17 20 08.88 +26 38 06.0 WL 6 Abell 3404 0.167 06 45 29.3 -54 13 08 X-ray 4 Abell 1201 0.169 11 12 54.9 +13 26 41 X-ray 6 Abell 586 0.171 07 32 22.32 +31 38 02.4 WL 1 Abell 586 0.171 07 32 22.32 +31 38 02.4 WL 6 Abell 1914 0.171 14 26 01.6 +37 49 38 WL 3 Abell 1914Abell 2218 0.171 0.175 14 26 01.6 16 35 52.4 +37 49 38 +66 12 52 X-ray X-ray 1 6 Abell 2218 0.175 16 35 52.4 +66 12 52 WL 6 Abell 2218 0.175 16 35 52.4 +66 12 52 X-ray 6 Abell 2345 0.1765 21 27 11.0 -12 09 33 WL 0 Abell 750 0.18 09 09 06.7 +11 01 48 WL 2 Abell 1689 0.18 13 11 29.5 -01 20 17 WL 10 Abell 1689 0.18 13 11 29.5 -01 20 17 WL+SL 10 Abell 1689 0.18 13 11 29.5 -01 20 17 SL 9 Abell 1689 0.18 13 11 29.5 -01 20 17 WL 10 Abell 1689 0.18 13 11 29.5 -01 20 17 SL 8 Abell 1689 0.18 13 11 29.5 -01 20 17 WL+SL 10 Abell 1689 0.18 13 11 29.5 -01 20 17 X-ray 8 Abell 1689 0.18 13 11 29.5 -01 20 17 WL 15 Abell 1689 0.18 13 11 29.5 -01 20 17 WL 12 Abell 1689 0.18 13 11 29.5 -01 20 17 WL 10 Abell 1689 0.18 13 11 29.5 -01 20 17 WL 4 Abell 1689 0.18 13 11 29.5 -01 20 17 X-ray 8 Abell 1689Abell 1689 0.18 0.18 13 11 29.5 13 11 29.5 -01 20 17 -01 20 17 SL SL 5 6 Abell 1689Abell 1689Abell 1689Abell 1689 0.18 13 11 29.5 0.18 0.18 -01 20 0.18 17 13 11 29.5 13 11 29.5 13 SL 11 -01 29.5 20 17 -01 20 17 -01 20 17 WL 6 WL WL 30 22 3 Abell 1689 0.18 13 11 29.5 -01 20 17 WL 11

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 25 h / Λ Ω / m Ω δ Clowe & SchneiderClowe (2001b) & Schneider (2001a) 200 200 0.3/0.7/None 0.3/0.7/0.7 Clowe (2003)Limousin et al. (2007)Andersson & Madejski (2004) 200 200 200 0.3/0.7/0.7 0.3/0.7/0.7 0.3/0.7/0.7 Ref. Zitrin et al. (2011) virial 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Vikhlinin et al. (2006) 500 0.3/0.7/0.71 Okabe et al. (2010) virial 0.27/0.73/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Okabe & Umetsu (2008)Babyk et al. (2014) virial 200 0.3/0.7/0.7 0.27/0.73/0.73 Okabe et al. (2011) 200/virial 0.3/0.7/None Paulin-Henriksson et al. (2007) 200 0.27/0.73/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Okabe et al. (2010) virial 0.27/0.73/0.72 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Allen et al. (2003) 200 0.3/0.7/0.5 Babyk et al. (2014) 200 0.27/0.73/0.73 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Schmidt & Allen (2007)Ettori et al. (2011) virial 200 0.3/0.7/0.7 0.3/0.7/0.7 Babyk et al. (2014)Sereno et al. (2014) 200 200 0.27/0.73/0.73 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Umetsu et al. (2009) virial 0.3/0.7/0.7 69 77 ) . . 5 51 99 63 6 8 58 14 57 51 99 91 01 3 8 12 71 9 ......

0 27 45 85 47 7 68 57 86 82 7 06 45 4 0 9 7 6 99 52 59 21 51 4 97 6 0 0 37 45 85 53 7 28 57 15 08 7 1 08 4 0 9 7 31 99 52 17 84 43 13 6 0 ...... 6 1 . . 3 2 ...... 2 . . 3 1 . . 3 ...... 3 5 1 9 3 5 1 3 5 1 9 3 5 49 +7 − M 2 1 0 . . 2 1 0 1 0 0 . 0 3 2 . 2 3 . 4 4 0 2 0 . 1 . 1 2 1 1 6 1 3 ...... +8 − +1 − +3 − +2 − +2 − +3 − +2 − +3 − 1 2 1 5 3 2 1 +2 − +1 − +0 − +2 − +2 − +0 − +3 − +0 − +1 − +1 − +3 − +3 − +4 − +3 − 0 Molikawa et al. (1999) virial 0.3/0.7/0.5 93 +4 − +4 − +0 − +3 − +0 − +1 − +2 − +3 − +2 − +2 − +17 − +1 − +3 − . . 14 00 King et al. (2002) Halkola et al. (2006) 200 200 1.0/0.0/None 0.3/0.7/0.7 1 +1 − +2 − 4 +1 − 1 +5 − 63 +5 − 59 5 5 66 01 7 0 +2 − +1 − 45 0 Molikawa et al. (1999) virial 0.3/0.7/0.5 9 34 0 Molikawa et al. (1999) virial 0.3/0.7/0.5 38 1 2 29 ...... vir 67 42 7 1 53 97 95 72 62 3 91 0 Wang et al. (2005) 200 0.3/0.7/0.7 02 0 36 77 5 34 6 41 9 96 81 14 54 ...... − − 26 15 − − M 7 5 4 9 7 6 10 7 4 3 3 2 7 10 7 8 5 8 34 145 9 10 18 28 12 15 11 14 7 9 6 9 6 8 8 10 4 20 13 17 21 23 19 52 52 . . 65 54 86 47 84 7 05 4 72 94 04 61 98 13 87 6 96 27 79 08 31 24 34 33 67 04 86 61 65 7 22 4 04 34 03 71 86 13 0 69 19 3 0 07 95 6 28 89 ...... 1 ...... 6 0 2 5 5 3 1 1 3 82 44 1 6 4 1 9 48 68 7 6 4 4 0 1 5 5 3 1 1 3 82 49 0 6 4 1 9 87 79 7 6 9 . . . 0 0 . . 0 0 . 0 0 3 5 2 . . 0 . 2 . 0 . . 0 . . 1 0 . 0 0 . 1 0 1 1 2 . 1 1 ...... +1 − 0 2 3 4 1 1 0 1 3 1 0 2 0 0 1 0 1 0 0 0 1 +0 − +0 − +0 − +0 − +0 − +0 − +5 − +5 − +5 − +1 − +5 − +0 − +0 − +1 − +1 − +0 − +1 − +1 − +1 − +1 − +0 − +1 − +1 − +1 − +0 − +2 − +2 − +4 − +1 − +1 − 2 +0 − +1 − +3 − +1 − +0 − +4 − +0 − +0 − +1 − +0 − 37 +1 − +0 − +0 − +0 − +1 − . . 0 6 5 15 10 9 6 77 35 6 8 38 48 6 78 03 87 24 1 4 36 5 69 9 884 154 7 4 87 7 8 83 04 3 71 49 6 59 57 53 16 74 3 75 5115 25 3 262 36 0 4 ...... vir 8 7 9 9 9 c 8 4 9 8 3 4 5 4 8 8 10 7 2 2 3 3 2 2 2 4 3 2 3 3 4 4 2 5 2 10 5 2 5 7 9 8 4 4 4 5 6 6 38 92 ) (10 . . 53 91 11 98 12 28 71 7 91 34 52 5 12 72 2 . 7 ......

0 11 37 09 19 34 74 7 52 95 32 7 7 83 29 91 2 8 26 27 19 6 1 4 0 2 37 09 04 56 99 92 29 24 32 7 7 83 29 24 64 05 96 75 78 1 4 ...... 4 . . 2 2 1 ...... 3 1 . . 2 ...... 0 1 7 47 9 3 0 7 23 7 6 0 1 7 47 9 3 0 3 23 7 6 +5 − M 2 1 0 . . 2 1 . 1 . 0 . 0 . 1 . 1 3 . . 2 3 . 0 . 1 0 1 1 1 2 1 5 1 2 ...... +5 − +2 − +2 − +2 − +3 − +1 − +3 − 1 2 0 0 0 2 4 2 1 0 1 +2 − +1 − +0 − +2 − +2 − +2 − +0 − +0 − +2 − +3 − +3 − 0 4 18 +2 − +3 − +0 − +1 − +1 − +1 − +3 − +1 − +1 − +1 − +13 − +1 − +2 − . . 14 02 9 +1 − +2 − +0 − +0 − +0 − +2 − +4 − 94 +4 − +1 − 4 1 27 05 +0 − 65 +1 − 5 94 0 8 09 7 0 5 7 62 ...... 200 5 6 71 43 1 9 99 63 7 62 1 13 9 49 17 8 19 4 26 86 7 6 5 17 4 66 22 25 47 04 11 97 ...... − − 23 13 (10 − − 6 M 4 4 7 5 5 8 6 4 3 2 2 6 7 5 6 4 6 26 7 111 8 14 23 10 12 9 10 6 7 5 8 5 7 7 9 3 17 10 14 17 19 16 52 69 36 68 57 4 13 7 56 48 5 33 77 67 45 76 25 99 6 88 07 77 21 09 05 53 12 54 69 47 53 57 1 95 0 86 48 57 37 67 77 52 94 25 01 75 88 78 27 53 05 49 61 52 ...... 5 6 6 42 7 2 0 4 1 9 7 6 5 3 92 9 7 6 5 3 6 7 03 7 2 0 4 1 9 7 1 5 3 92 9 7 6 5 . . . 0 . . . 0 0 . 0 0 2 . 2 . . 0 . 1 1 0 . 0 0 . . . 0 . 0 0 . 1 0 0 0 1 1 1 1 1 0 . . 1 ...... 0 1 2 0 3 1 1 4 0 0 2 1 0 0 0 0 0 0 0 +0 − +0 − +0 − +0 − +0 − +4 − +3 − +1 − +3 − +1 − +0 − +0 − +0 − +0 − +0 − +0 − +1 − +1 − +0 − +0 − +0 − +1 − +1 − +1 − +1 − +0 − +1 − +0 − +1 − +1 − +0 − +3 − +1 − +1 − +4 − +0 − +0 − +2 − +3 − +0 − +0 − +0 − +0 − +0 − +0 − +0 − 0 0 6 6 9 87 8 01 4 7 0 62 44 4 76 41 97 2 67 5 8 76 7 83 24 18 794 129 04 03 1 0 0 11 3 05 35 0 35 35 94 39 72 71 66 77 27 8533 1 22 198 31 13 ...... 200 Method c Continued . Table A-1 – Abell 1689Abell 1689Abell 1689Abell 1689 0.18 0.18 0.18 13 11 0.18 29.5 13 11 29.5 13 11 29.5 -01 20 13 17 11 -01 29.5 20 17 -01 20 17 -01 WL 20 17 WL WL+SL WL+SL 6 7 6 7 ClusterAbell 1689Abell 1689Abell 1689 zAbell 383 0.18 0.18 13 RA 11 29.5 13 11 29.5 -01 20 17 0.18 -01 20 17 Dec 0.188 WL 13 11 29.5 WL 02 48 02.00 -01 20 17 7 -03 32 15.0 4 X-ray WL+SL 7 7 Continued on next page Abell 383 0.188 02 48 02.00 -03 32 15.0 X-ray 3 Abell 383 0.188 02 48 02.00 -03 32 15.0 WL 7 Abell 383 0.188 02 48 02.00 -03 32 15.0 WL 7 Abell 383 0.188 02 48 02.00 -03 32 15.0 WL 2 Abell 383 0.188 02 48 02.00 -03 32 15.0 X-ray 3 Abell 383 0.188 02 48 02.00 -03 32 15.0 WL+SL 4 Abell 383 0.188 02 48 02.00 -03 32 15.0 X-ray 3 Abell 383 0.188 02 48 02.00 -03 32 15.0 X-ray 6 Abell 383 0.188 02 48 02.00 -03 32 15.0 WL 6 ZwCl0839.9+2937 0.194 08 42 56.07 +29 27 25.7 WL 8 ZwCl0839.9+2937 0.194 08 42 56.07 +29 27 25.7 WL 5 ZwCl0839.9+2937Abell 291 0.194 08 42 56.07 +29 27 0.196 25.7 X-ray 02 01 44.20 6 -02 12 03.0 WL 1 Abell 291 0.196 02 01 44.20 -02 12 03.0 WL 1 Abell 115 0.1971 00 55 59.76 +26 22 40.8 WL 2 Abell 115 0.1971 00 55 59.76 +26 22 40.8 WL 2 Abell 520 0.199 04 54 19.0 +02 56 49 WL 2 Abell 2163 0.203 16 15 34.1 -06 07 26 WL 2 Abell 520Abell 209 0.199 04 54 19.0 0.206 +02 56 49 01 31 53.00 X-ray -13 36 34.0 3 WL 3 Abell 2163 0.203 16 15 34.1 -06 07 26 X-ray 2 Abell 209 0.206 01 31 53.00 -13 36 34.0 X-ray 3 Abell 209 0.206 01 31 53.00 -13 36 34.0 WL 2 Abell 209 0.206 01 31 53.00 -13 36 34.0 WL 3 Abell 209 0.206 01 31 53.00 -13 36 34.0 WL 3 Abell 209 0.206 01 31 53.00 -13 36 34.0 X-ray 3 Abell 209 0.206 01 31 53.00 -13 36 34.0 WL+SL 3 Abell 209 0.206 01 31 53.00 -13 36 34.0 WL 2 Abell 963 0.206 10 17 13.9 +39 01 31 X-ray 4 Abell 963 0.206 10 17 13.9 +39 01 31 WL 2 Abell 963 0.206 10 17 13.9 +39 01 31 WL 8 Abell 963 0.206 10 17 13.9 +39 01 31 X-ray 4 Abell 963 0.206 10 17 13.9 +39 01 31 WL 1 Abell 963 0.206 10 17 13.9 +39 01 31 X-ray 4 Abell 963 0.206 10 17 13.9 +39 01 31 X-ray 5 RXJ0439.0+0520 0.208 04 39 02.2 +05 20 43 X-ray 7 RX J0439.0+0520 0.208 04 39 02.2 +05 20 43 X-ray 6 RX J1504.1-0248Abell 773 0.215 15 04 07.5 -02 0.217 48 16 09 17 59.4 X-ray +51 42 23 3 X-ray 3 MS 0735.6+7421Abell 773Abell 2261 0.216 07 41 44.8 +74 14 0.217 52 0.224 09 17 X-ray 59.4 17 22 27.60 +51 6 42 23 +32 07 37.2 X-ray WL 3 4 MS 1006.0+1202Abell 2261 0.221 10 08 47.9 0.224 +11 47 33 17 22 27.60 X-ray +32 07 37.2 4 WL 4 Abell 2261 0.224 17 22 27.60 +32 07 37.2 WL 5

c 0000 RAS, MNRAS 000, 000–000 26 Groener, Goldberg, & Sereno h / Λ Ω / m Ω δ Ref. Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Okabe et al. (2010) virial 0.27/0.73/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Umetsu et al. (2009) virial 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Okabe et al. (2010) virial 0.27/0.73/0.72 Vikhlinin et al. (2006) 500 0.3/0.7/0.71 Allen et al. (2003) 200 0.3/0.7/0.5 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Allen et al. (2003) 200 0.3/0.7/0.5 Ettori et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Gastaldello et al. (2008)Sereno et al. (2014) virial 200 0.3/0.7/0.7 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011) 200 0.3/0.7/0.7 Corless et al. (2009) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Okabe et al. (2010)Clowe (2003)Clowe & Schneider (2002)Clowe & Schneider (2001a) 200 200 virial 200 0.27/0.73/0.72 0.3/0.7/None 0.3/0.7/0.7 0.3/0.7/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Voigt & Fabian (2006) 200/2E4 0.3/0.7/0.7 Allen et al. (2003) 200 0.3/0.7/0.5 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 0 ) . 31 29 16 48 0 1 57 4 57 63 33 74 25 9 86 0 9 31 29 03 48 14 08 57 7 57 35 9 14 3 74 25 58 65 3 9 ......

8 69 84 5 06 64 88 7 43 8 53 5 96 83 21 38 26 22 8 6 9 21 7 24 8 01 84 5 54 64 08 7 43 53 5 73 21 84 29 45 8 6 2 78 11 . . . 5 . 8 4 . . . 1 . 2 . 3 2 0 1 . . . 1 ...... 1 . . 8 3 2 . . . 2 ...... 1 3 63 3 7 4 5 8 1 3 93 3 7 4 5 8 M 1 1 . 0 3 2 . 2 0 2 4 . 14 5 0 5 . . 1 3 0 . 1 . 1 1 4 4 3 6 20 3 2 ...... +5 − +8 − +6 − +1 − +2 − +4 − +2 − +0 − +3 − +1 − +1 − +8 − +3 − +3 − +2 − 3 1 1 1 0 2 2 0 +1 − +2 − +0 − +3 − +2 − +2 − +1 − +2 − +4 − +79 − +13 − +0 − +5 − +2 − +16 − +0 − +1 − +1 − +1 − +4 − +4 − +4 − +5 − +136 − +10 − +2 − 14 6 +3 − 62 4 83 75 +1 − 57 3 86 7 57 +1 − 45 9 08 32 5 4 +1 − 26 +0 − 0 Molikawa et al. (1999) virial 0.3/0.7/0.5 +2 − +2 − 66 4 5 89 65 69 8 3 0 4 67 5 +0 − ...... vir 49 8 83 11 0 59 85 2 48 0 3 71 63 77 0 56 1 04 85 3 ...... M 17 9 9 4 24 13 35 44 9 5 4 3 31 11 12 15 36 8 20 24 20 25 16 6 12 7 10 7 6 7 2 6 4 9 8 5 21 12 18 47 28 13 − − 25 29 21 12 15 2 97 03 . . 31 22 77 21 94 16 45 05 74 81 23 93 03 2 04 48 42 34 41 44 79 11 59 57 79 37 76 74 98 99 71 85 77 21 94 42 45 15 74 68 23 18 1 22 9 34 49 16 8 24 01 43 4 59 45 99 55 66 64 11 13 ...... 0 ...... 8 5 5 2 58 6 5 28 5 1 7 5 2 5 8 0 7 8 5 5 2 11 6 3 53 5 1 7 5 2 5 0 7 . 1 . 4 0 . 1 0 2 . 2 . 0 . . 1 0 . 0 1 0 0 1 0 . . 0 . 1 2 . . 1 . 0 0 . . 0 0 0 0 1 0 0 0 ...... +1 − 1 1 3 2 1 1 1 1 1 1 1 0 2 0 9 1 5 +1 − +2 − +0 − +1 − +0 − +3 − +2 − +0 − +1 − +0 − +0 − +2 − +0 − +0 − +0 − +0 − +0 − +2 − +2 − +2 − +1 − +0 − +0 − +0 − +0 − +0 − +1 − +0 − +1 − +1 − +1 − +1 − +3 − +2 − +2 − +1 − +2 − +1 − +1 − +1 − +1 − +0 − +2 − +0 − 97 +13 − +1 − +5 − . 4 04 3 28 36 2 84 42 88 4 69 0 65 6 9 56 76 2 28 04 87 94 82 67 6 3 82 6 32 09 9 789 10 52 1 06 34 8 4 27 43 35 7 7296 28 28 93 24 97 12 7 ...... vir c 4 6 3 9 3 8 4 4 6 6 5 6 2 6 6 6 2 6 3 4 2 2 3 4 2 8 4 5 3 5 7 3 3 2 13 3 3 9 3 3 3 3 3 3 5 4 3 5 3 4 9 0 ) (10 . 21 39 16 73 51 39 93 6 45 27 41 91 11 28 0 39 82 21 92 16 86 51 15 93 7 45 61 6 6 41 91 86 91 39 72 ......

7 43 74 76 7 09 75 39 6 1 55 14 19 11 13 3 3 2 03 0 7 7 74 76 7 09 91 64 94 16 19 48 16 3 3 5 62 4 . . . . . 6 3 . . 1 1 3 2 . 1 0 1 ...... 1 . . 5 3 2 . . . 2 1 ...... 1 76 0 1 44 6 1 6 7 7 96 6 1 17 0 1 44 6 1 6 7 7 14 6 M 1 1 . 0 3 2 . . 2 0 . 1 11 4 . . . 1 . 1 3 0 . 1 . 1 . 4 3 3 5 16 3 ...... +6 − +4 − +1 − +1 − +3 − +3 − +1 − +0 − +2 − +1 − +5 − +2 − +2 − +2 − +1 − 2 1 1 2 0 3 1 0 1 1 0 0 +1 − +1 − +0 − +3 − +2 − +2 − +0 − +1 − +59 − +10 − +0 − +2 − +12 − +0 − +1 − +1 − +4 − +3 − +3 − +4 − − +104 +8 − 14 2 +2 − 8 7 91 49 +2 − +1 − 71 +2 − 15 47 21 58 6 88 71 6 +0 − +3 − +1 − +0 − +1 − +1 − +1 − 53 0 0 67 86 92 8 2 0 2 44 62 +0 − ...... 200 04 9 25 8 3 89 26 7 97 4 7 1 46 1 32 46 43 9 7 5 66 9 21 6 0 ...... (10 14 M 8 7 4 19 11 29 36 7 4 3 3 24 9 11 13 28 6 16 20 15 19 13 5 9 6 8 6 5 6 2 4 3 6 7 4 17 11 15 38 22 10 − − 21 24 18 10 12 2 78 83 . . 03 63 99 73 71 01 25 04 21 43 62 01 19 02 15 85 38 33 03 97 41 12 61 09 48 44 31 44 61 78 77 34 63 99 73 7 01 66 12 85 43 52 21 19 08 17 74 27 38 67 31 41 74 78 34 9 48 35 45 37 53 88 88 ...... 0 ...... 4 2 41 9 8 3 57 2 9 4 8 4 0 8 61 7 4 2 3 9 8 3 79 2 9 4 8 4 8 77 7 . 1 . . 0 . 0 0 1 . 2 1 0 . 1 1 0 1 0 . 0 0 0 0 . . 0 . 1 1 0 . 1 . 0 0 . . 0 0 . 0 1 0 0 0 ...... +0 − 1 1 3 2 1 1 0 1 1 0 0 1 1 8 0 4 +1 − +0 − +0 − +0 − +2 − +2 − +1 − +0 − +1 − +1 − +0 − +1 − +0 − +0 − +0 − +0 − +0 − +0 − +1 − +2 − +0 − +1 − +0 − +0 − +0 − +0 − +0 − +1 − +0 − +0 − +0 − +1 − +1 − +2 − +2 − +1 − +1 − +1 − +1 − +0 − +1 − +1 − +0 − 26 +10 − +0 − +0 − +4 − . 4 75 6 5 63 6 84 44 44 1 54 73 06 3 55 26 11 89 58 2 24 25 02 71 0 7 77 3 56 07 39 1 6573 8 6 36 64 0 7 58 66 6 9 968 42 23 13 21 15 22 9 ...... 200 Method c Continued . Table A-1 – ClusterAbell 2261 z 0.224 17 RA 22 27.60 +32 07 37.2 WL+SL Dec 3 Continued on next page Abell 2261 0.224 17 22 27.60 +32 07 37.2 WL 4 ZwCl 0823.2+0425 0.2248 08 25 59.3 +04 15 47 WL 2 Abell 1763 0.228 13 35 18.2 +40 59 49 X-ray 7 Abell 1763 0.228 13 35 18.2 +40 59 49 WL 2 Abell 2219 0.2281 16 40 21.4 +46 42 21 WL 6 Abell 2219 0.2281 16 40 21.4 +46 42 21 WL 3 Abell 2219 0.2281 16 40 21.4 +46 42 21 X-ray 3 Abell 2219 0.2281 16 40 21.4 +46 42 21 WL 5 Abell 267 0.23 01 52 48.72 +01 01 08.4 WL 5 Abell 267 0.23 01 52 48.72 +01 01 08.4 WL 4 Abell 267 0.23 01 52 48.72 +01 01 08.4 WL 4 Abell 2390 0.23 21 53 35.5 +17 41 12 X-ray 2 Abell 2390 0.23 21 53 35.5 +17 41 12 WL 5 Abell 2390 0.23 21 53 35.5 +17 41 12 WL 5 Abell 2390 0.23 21 53 35.5 +17 41 12 WL 5 Abell 2390 0.23 21 53 35.5 +17 41 12 X-ray 2 Abell 2390 0.23 21 53 35.5 +17 41 12 WL 4 Abell 2390 0.23 21 53 35.5 +17 41 12 X-ray 2 Abell 2390 0.23 21 53 35.5 +17 41 12 X-ray 3 Abell 2667 0.233 23 51 40.7 -26 05 01 X-ray 2 Abell 2667 0.233 23 51 40.7 -26 05 01 X-ray 2 Abell 2667 0.233 23 51 40.7 -26 05 01 X-ray 3 RXJ2129.6+0005 0.235 21 29 37.92 +00 05 38.4 X-ray 3 RXJ2129.6+0005 0.235 21 29 37.92 +00 05 38.4 WL 2 RXJ2129.6+0005 0.235 21 29 37.92 +00 05 38.4 WL 6 RXJ2129.6+0005 0.235 21 29 37.92 +00 05 38.4 X-ray 3 RXJ2129.6+0005 0.235 21 29 37.92 +00 05 38.4 WL+SL 4 RXJ2129.6+0005 0.235 21 29 37.92 +00 05 38.4 WL 2 RXJ2129.6+0005 0.235 21 29 37.92 +00 05 38.4 X-ray 4 ZwCl 1305.4+2941Abell 2485 0.241 13 07 49.2 +29 25 0.2472 48 22 48 31.13 X-ray -16 06 25.6 6 WL 3 MS 1910.5+6736Abell 2485 0.246 19 10 27.3 0.2472 +67 41 27 22 48 31.13 X-ray -16 06 25.6 4 WL 2 Abell 521 0.2475 04 54 09.1 -10 14 19 WL 1 Abell 521 0.2475 04 54 09.1 -10 14 19 X-ray 11 Abell 521 0.2475 04 54 09.1 -10 14 19 WL 2 Abell 1835 0.2528 14 01 02.3 +02 52 48 X-ray 2 Abell 1835 0.2528 14 01 02.3 +02 52 48 WL 8 Abell 1835 0.2528 14 01 02.3 +02 52 48 WL 2 Abell 1835 0.2528 14 01 02.3 +02 52 48 WL 2 Abell 1835 0.2528 14 01 02.3 +02 52 48 X-ray 2 Abell 1835 0.2528 14 01 02.3 +02 52 48 WL 2 Abell 1835Abell 1835Abell 1835Abell 1835 0.252 0.252 14 0.252 01 02.3 14 0.252 01 02.3 14 01 +02 02.3 52 14 48 01 +02 02.3 52 48 +02 52 48 WL +02 52 48 WL WL X-ray 2 2 4 3 Abell 1835 0.252 14 01 02.3 +02 52 48 X-ray 3 Abell 1835 0.252 14 01 02.3 +02 52 48 X-ray 4 RXCJ0307.0-2840 0.253 03 07 04.1 -28 40 14 X-ray 3 RXCJ0307.0-2840 0.253 03 07 04.1 -28 40 14 X-ray 3 ZwCl0104.4+0048 0.2545 01 06 48.48 +01 02 42.0 WL 7

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 27 h / Λ Ω / m Ω δ Ref. Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Bardeau et al. (2007) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011)Schirmer et al. (2010) 200 200 0.3/0.7/0.7 0.27/0.73/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Oguri et al. (2009) virial 0.26/0.74/0.72 Oguri et al. (2009) virial 0.26/0.74/0.72 Oguri et al. (2009) virial 0.26/0.74/0.72 Zitrin et al. (2010) virial 0.3/0.7/0.7 Zitrin et al. (2010) virial 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Umetsu et al. (2011b) virial 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Okabe et al. (2010) virial 0.27/0.73/0.72 Okabe & Umetsu (2008) virial 0.3/0.7/0.7 Okabe & Umetsu (2008) virial 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Gastaldello et al. (2007b) virial 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Allen et al. (2003) 200 0.3/0.7/0.5 Sereno et al. (2014) 200 0.3/0.7/0.7 Okabe et al. (2010) virial 0.27/0.73/0.72 Ettori et al. (2011) 200 0.3/0.7/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Ettori et al. (2011) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 ) 62 98 17 63 32 21 43 36 9 56 53 57 62 98 61 92 48 68 43 8 0 56 93 53 ......

47 43 81 36 33 77 22 04 1 8 0 5 1 1 5 91 98 14 64 01 35 4 4 7 42 53 0 59 39 95 58 43 56 02 33 77 22 19 1 0 5 0 1 0 5 49 15 14 64 23 35 4 4 7 75 78 59 39 93 . . 3 ...... 2 ...... 2 1 ...... 1 2 2 2 ...... 3 1 2 ...... 3 7 4 5 7 3 3 2 3 7 4 5 7 3 3 5 M 0 2 . 1 . 1 0 0 2 . 1 2 5 5 3 2 3 2 2 0 8 1 . . 1 0 3 . 4 0 1 2 5 . . 0 20 1 0 ...... ∞ +3 − +2 − +2 − +1 − +1 − +2 − +2 − +2 − +3 − +1 − +2 − 2 2 1 1 1 2 1 1 +0 − +2 − +2 − +2 − +0 − +0 − +2 − +1 − +2 − +7 − +6 − +4 − +2 − +4 − +2 − +3 − +1 − +8 − +1 − +1 − +0 − +3 − +4 − +0 − +1 − +5 − +21 − +0 − + − +1 − +0 − 14 7 +2 − 56 +2 − 0 Molikawa et al. (1999) virial 0.3/0.7/0.5 +1 − 88 1 5 0 4 4 7 6 88 96 +1 − +1 − 2 76 36 26 64 +2 − 1 3 0 +1 − +1 − 5 89 48 89 ...... vir 73 1 49 4 45 19 94 91 3 98 88 24 51 71 1 9 49 89 8 65 83 1 4 32 28 22 ...... M 1 19 5 10 5 4 3 4 0 7 7 9 16 7 24 19 15 17 16 15 17 12 10 5 7 1 2 6 4 3 16 15 12 18 23 8 17 10 6 7 11 4 4 9 34 5 7 12 17 18 84 84 . . 43 08 82 96 63 7 11 24 5 66 7 03 84 28 95 51 89 52 69 05 85 23 94 68 7 18 32 91 94 98 2 04 36 44 65 35 33 99 5 22 36 24 14 54 95 51 71 39 85 84 87 77 06 83 7 34 19 78 55 98 . . . . . 5 ...... 6 37 4 0 22 7 1 7 0 0 9 4 9 7 0 1 27 74 3 6 37 4 0 95 7 4 2 0 0 9 4 9 7 0 1 15 81 3 3 0 . . 1 . 1 0 2 . . 0 2 . . . 0 1 . 1 1 0 2 0 6 . . 1 . . 1 0 0 0 . . . 1 1 2 4 2 0 2 . . 0 0 ...... +5 − 4 1 3 3 2 0 1 0 1 2 1 0 0 1 1 1 4 3 0 +8 − +1 − +3 − +3 − +0 − +4 − +1 − +2 − +0 − +2 − +2 − +1 − +1 − +3 − +0 − +6 − +2 − +1 − +0 − +0 − +0 − +1 − +2 − +2 − +4 − +3 − +0 − +2 − +3 − +1 − +4 − +1 − +3 − 279 15 +3 − +1 − +0 − +1 − +1 − +1 − +2 − +1 − +0 − +0 − +1 − +1 − +1 − 1 +6 − +4 − +0 − . . . 08 35 1 8 02 5 01 79 17 1 3 36 34 1 3 5 15 71 9 02 79 08 84 24 91 9 6 12 7 1 97 97 29 43 6 6 3 23 24 64 55 19 91 5 9 03 13 1 ...... vir c 8 3 6 4 4 4 4 7 11 6 8 6 2 7 5 3 6 7 7 6 7 4 7 7 0 3 1 6 7 6 3 6 2 2 2 4 5 4 4 6 5 10 6 4 2 9 9 3 3 6 ) (10 97 33 55 82 14 9 82 3 88 22 19 97 33 06 19 27 9 16 88 54 16 ......

41 81 48 11 29 66 91 83 9 0 0 8 7 0 42 85 8 63 88 4 75 6 18 11 49 84 51 81 09 65 29 66 91 83 9 2 4 8 5 0 67 0 8 63 07 4 12 6 45 68 6 49 82 . 1 ...... 2 ...... 2 1 ...... 1 . 1 1 . . . . . 2 1 2 ...... 7 0 1 89 9 3 32 7 5 9 1 04 24 7 0 1 01 9 3 32 7 5 1 3 24 M 0 . 2 1 . 1 0 0 1 . . 1 4 4 3 1 2 2 1 0 6 1 . . 0 . 2 1 . 3 . 1 2 . . . 0 16 . 0 ...... ∞ . +1 − +2 − +3 − +2 − +1 − +1 − +2 − +2 − +1 − +2 − 1 2 1 0 0 1 0 1 0 3 1 1 1 +0 − +2 − +2 − +1 − +0 − +0 − +1 − +1 − +5 − +5 − +3 − +1 − +3 − +2 − +1 − +1 − +6 − +1 − +1 − +2 − +2 − +3 − +1 − +4 − +0 − + − +0 − 14 96 +1 − +2 − 0 13 +1 − +1 − 21 2 5 9 3 4 6 41 82 +0 − +1 − +0 − 1 56 28 25 +1 − 6 +0 − +16 − +1 − +1 − 1 +1 − 44 96 12 ...... 200 51 4 86 49 7 82 66 84 81 4 5 88 52 57 74 42 6 0 89 4 78 4 5 51 81 4 7 8 79 7 38 ...... (10 1 M 15 4 8 4 3 2 3 0 6 6 8 13 6 20 15 12 15 14 13 15 10 9 4 3 1 1 6 3 3 13 13 9 14 18 7 14 8 5 6 9 3 3 7 28 4 6 10 13 16 74 06 13 43 53 51 18 77 09 82 39 82 68 68 41 52 22 54 66 97 61 22 75 26 32 03 75 77 24 56 82 13 63 69 53 52 55 04 43 92 99 92 68 41 17 11 66 67 4 72 36 68 15 31 89 82 55 24 ...... 8 8 8 5 5 9 6 4 4 8 83 6 6 3 7 04 4 8 9 9 51 8 8 8 5 5 1 0 4 8 8 84 6 6 3 7 66 4 8 9 9 05 2 0 . 1 1 . 1 0 . 2 . 1 0 1 ...... 1 0 0 . 0 5 . . 1 . . 1 0 . 0 . . . 0 1 2 . 1 0 2 . 3 0 0 0 ...... 3 2 4 2 0 0 0 0 1 0 1 1 0 0 0 0 0 3 3 1 1 +6 − +0 − +1 − +2 − +2 − +0 − +3 − +1 − +1 − +2 − +1 − +0 − +0 − +0 − +5 − +2 − +1 − +0 − +0 − +1 − +1 − +2 − +2 − +0 − +2 − +3 − +2 − +1 − +0 − +3 − +2 − +4 − 9 14 +2 − +0 − +1 − +1 − +0 − +1 − +0 − +2 − +1 − +1 − +0 − +0 − +0 − +1 − +0 − +0 − +3 − +5 − . 46 65 9 84 15 6 14 32 5 99 6 02 85 97 0 6 2 8 3 6 72 81 69 3 16 13 5 4 71 5 5 58 31 8 88 7 5 4 35 08 58 3 26 37 32 8 01 41 45 88 ...... 200 Method c Continued . Table A-1 – ClusterZwCl0104.4+0048 0.2545 01 z 06 48.48 +01 02 42.0 RA WL 6 Dec Continued on next page Abell 68 0.2546 00 37 05.28 +09 09 10.8 X-ray 2 Abell 68 0.2546 00 37 05.28 +09 09 10.8 WL 4 Abell 68 0.2546 00 37 05.28 +09 09 10.8 WL 3 Abell 68 0.2546 00 37 05.28 +09 09 10.8 WL 3 ZwCl1454.8+2233 0.2578 14 57 14.40 +22 20 38.4 WL 3 ZwCl1454.8+2233 0.2578 14 57 14.40 +22 20 38.4 WL 3 MS 1455.0+2232J0454-0309 0.259 14 57 15.1 0.26 +22 20 34 04 54 10.0 X-ray -03 09 00 6 WL 9 MS 1455.0+2232RXCJ2337.6+0016 0.259 0.273 14 57 15.1 23 37 40.6 +22 20 34 +00 16 36 X-ray X-ray 10 4 RXCJ2337.6+0016 0.273 23 37 40.6 +00 16 36 WL 6 RXCJ2337.6+0016 0.273 23 37 40.6 +00 16 36 X-ray 5 RXCJ0303.8-7752 0.274 03 03 46.4 -77 52 09 X-ray 1 RXCJ0532.9-3701 0.275 05 32 56.0 -37 01 34 X-ray 5 Abell 1703 0.277 13 15 05.24 +51 49 02.6 SL 4 Abell 1703 0.277 13 15 05.24 +51 49 02.6 WL 2 Abell 1703 0.277 13 15 05.24 +51 49 02.6 WL+SL 5 Abell 1703 0.277 13 15 05.24 +51 49 02.6 WL+SL 5 Abell 1703 0.277 13 15 05.24 +51 49 02.6 WL 6 Abell 1703 0.277 13 15 05.24 +51 49 02.6 WL 5 Abell 1703 0.277 13 15 05.24 +51 49 02.6 WL 5 Abell 1703 0.277 13 15 05.24 +51 49 02.6 WL 3 Abell 1703 0.277 13 15 05.24 +51 49 02.6 WL+SL 5 Abell 2631 0.278 23 37 40.08 +00 16 33.6 WL 6 Abell 1758N 0.279 13 32 32.1 +50 30 37 WL 0 Abell 1758S 0.279 13 32 32.1 +50 30 37 WL 3 Abell 689 0.2793 08 37 25.4 +14 58 59 WL 1 RXJ0142.0+2131 0.2803 01 42 02.64 +21 31 19.2 WL 5 RXJ0142.0+2131 0.2803 01 42 02.64 +21 31 19.2 WL 5 XMMU J131359.7-162735 0.281 13 13 59.7 -16 27 35 X-ray 5 Abell 697 0.282 08 42 56.7 +36 21 45 WL 2 Abell 697 0.282 08 42 56.7 +36 21 45 X-ray 5 Abell 697 0.282 08 42 56.7 +36 21 45 WL 2 RXCJ0232.2-4420 0.283 02 32 18.7 -44 20 41 X-ray 1 RXCJ0232.2-4420 0.283 02 32 18.7 -44 20 41 X-ray 1 Abell 611 0.288 08 00 58.9 +36 02 50 WL 3 Abell 611 0.288 08 00 58.9 +36 02 50 WL 4 Abell 611 0.288 08 00 58.9 +36 02 50 WL+SL 3 Abell 611 0.288 08 00 58.9 +36 02 50 WL 3 Abell 611 0.288 08 00 58.9 +36 02 50 X-ray 5 Abell 611 0.288 08 00 58.9 +36 02 50 X-ray 4 ZwCl1459.4+4240 0.2897 15 01 23.13 +42 20 39.6 WL 8 ZwCl1459.4+4240 0.2897 15 01 23.13 +42 20 39.6 WL 5 Zwicky 3146 0.291 10 23 39.6 +04 11 10 X-ray 3 Zwicky 3146 0.291 10 23 39.6 +04 11 10 X-ray 2 RXCJ0043.4-2037 0.292 00 43 24.4 -20 37 17 X-ray 7 RXCJ0043.4-2037 0.292 00 43 24.4 -20 37 17 X-ray 8 RXCJ0516.7-5430 0.294 05 16 35.2 -54 16 37 X-ray 2 RXCJ0516.7-5430 0.294 05 16 35.2 -54 16 37 X-ray 2 Abell 2537 0.295 23 08 23.2 -02 11 31 X-ray 4

c 0000 RAS, MNRAS 000, 000–000 28 Groener, Goldberg, & Sereno h / Λ Ω / m Ω δ Ref. Schmidt & Allen (2007)Ettori et al. (2011) virial 200 0.3/0.7/0.7 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Donnarumma et al. (2009) 200 0.3/0.7/0.7 Donnarumma et al. (2009) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Comerford & Natarajan (2007) 200/virial 0.3/0.7/0.7 Gavazzi (2005) 200 0.3/0.7/0.7 Gavazzi (2002)Gavazzi et al. (2003) 200 200 0.3/0.7/None 0.3/0.7/None Gavazzi (2005) 200 0.3/0.7/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Voigt & Fabian (2006) 200/2E4 0.3/0.7/0.7 Allen et al. (2003)Babyk et al. (2014) 200 200 0.3/0.7/0.5 0.27/0.73/0.73 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014)Babyk et al. (2014)Comerford & Natarajan (2007) 200 200/virial 200 0.3/0.7/0.7 0.27/0.73/0.73 0.27/0.73/0.73 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Oguri et al. (2009) virial 0.26/0.74/0.72 Oguri et al. (2009) virial 0.26/0.74/0.72 Oguri et al. (2009) virial 0.26/0.74/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Gruen et al. (2013) 200 0.27/0.73/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 04 0 ) . . 07 06 94 47 54 86 8 89 5 71 97 93 07 8 78 25 65 26 52 43 1 8 2 6 ......

64 58 5 51 28 9 6 61 17 0 48 65 0 51 15 44 19 01 67 4 1 2 8 0 3 28 65 52 83 28 9 6 71 17 53 94 0 96 92 38 83 33 54 05 1 2 8 0 3 . 3 2 2 ...... 2 . 2 3 5 . 3 . . . . 4 . . . . 3 . . 4 ...... 7 4 6 1 6 4 9 8 6 7 4 1 9 9 9 8 6 M 3 . 0 0 0 0 2 0 . 0 2 9 0 0 . 1 1 . 1 42 . . . 1 1 . 2 1 8 5 1 4 1 9 ...... +3 − +1 − +2 − +2 − +2 − +6 − +5 − +4 − +10 − +5 − +4 − 0 0 5 1 2 2 1 2 0 +7 − +0 − +0 − +0 − +0 − +2 − +0 − +0 − +2 − − +100 +0 − +0 − +0 − +1 − +2 − +26 − +1 − +1 − +2 − +2 − +11 − +5 − +1 − +4 − +1 − +9 − 14 0 Molikawa et al. (1999) virial 0.3/0.7/0.5 91 17 83 +0 − 7 6 +0 − 0 +39 − 0 Molikawa et al. (1999) virial 0.3/0.7/0.5 97 16 00 Molikawa et al. (1999) Molikawa et al. (1999) virial virial 0.3/0.7/0.5 0.3/0.7/0.5 96 67 +1 − 0 Molikawa et al. (1999) virial 0.3/0.7/0.5 79 9 +3 − +2 − +1 − +2 − 15 7 1 0 5 42 3 0 59 +0 − ...... vir 74 3 43 95 55 93 2 29 6 Gavazzi et al. (2003) 200 0.3/0.7/None 93 47 27 1 72 47 2 06 9 6 2 75 13 2 68 89 3 ...... M 8 13 19 28 4 3 2 4 4 11 12 3 8 8 7 10 8 5 9 4 30 5 28 54 51 5 3 30 43 5 6 7 5 5 8 6 5 12 40 14 14 17 29 11 14 38 8 79 05 1 88 0 65 17 67 52 56 86 91 0 65 44 05 5 ...... 91 95 12 22 8 35 0 0 5 71 02 1 51 09 42 4 07 16 39 04 79 69 3 78 45 58 19 8 35 0 0 5 69 87 5 02 46 48 0 27 57 89 44 2 67 45 ...... 2 1 1 . 0 . . 0 . . . . . 2 . 1 ...... 1 7 5 11 39 7 5 4 2 3 1 1 9 9 9 1 1 7 5 34 53 0 4 2 9 1 1 9 9 9 1 1 0 2 0 3 2 . . 1 7 2 10 0 3 1 1 1 0 . . . . 7 . . 2 1 . 1 1 1 . . . . 0 . . 0 ...... +4 − +1 − +0 − +0 − +0 − +2 − +2 − 1 0 0 3 0 0 1 1 1 1 3 1 1 0 3 1 +2 − +1 − +1 − +0 − +3 − +3 − +1 − +6 − +2 − +14 − +0 − +2 − +1 − +2 − +1 − +0 − +28 − +3 − +1 − +1 − +1 − +2 − +0 − +0 − 8 67 47 49 +1 − +0 − 0 34 0 1 0 11 5 9 12 16 46 +0 − +4 − 5+0 − 10 +13 − 5 +3 − +1 − +1 − +1 − +3 − +1 − +1 − +0 − +3 − +1 − ...... 93 404 39 24 22 81 4 0 75 44 69 12 99 9109 36 2 29 3 6 0 9 2 96 32 4 94 56 54 3 6 0 0 81 9 1 09 9 ...... vir c 5 3 3 2 14 8 15 11 10 6 4 16 14 14 14 14 8 6 10 9 8 10 3 10 5 9 1 3 11 7 8 5 8 5 3 5 6 3 8 4 5 2 2 7 5 3 ) (10 5 66 26 19 26 18 17 0 04 18 19 5 45 14 99 36 16 92 9 41 17 91 ......

04 51 45 46 25 4 6 54 9 42 88 31 0 88 25 05 68 44 8 3 2 9 7 88 57 47 75 25 4 6 63 9 4 47 0 84 64 02 28 58 18 12 77 6 3 2 9 7 . 2 1 2 ...... 2 . 2 3 5 ...... 4 . . . . 3 . 4 ...... 6 4 8 56 8 9 3 1 6 3 9 5 6 4 81 9 5 5 6 3 9 5 M 3 . 0 0 0 0 2 0 . 0 1 . 0 . . 0 1 . 1 2 34 . . . 1 1 . 1 1 6 4 1 3 . 7 ...... +2 − +1 − +2 − +1 − +2 − +5 − +4 − +8 − +4 − +3 − 0 0 0 4 0 2 2 1 2 0 0 7 +5 − +0 − +0 − +0 − +0 − +2 − +0 − +0 − +1 − +0 − +0 − +1 − +2 − +3 − +20 − +1 − +1 − +2 − +1 − +9 − +4 − +1 − +3 − +7 − 14 31 0 5 43 17 +0 − 2 4 +0 − +85 − +0 − +32 − 44 0 14 04 32 06 +0 − 00 5 7 8 1 +3 − +2 − +1 − +2 − 69 1 6 6 0 59 +0 − 3 78 +0 − ...... 200 58 9 03 68 11 43 9 56 923 15 3 72 7 0 25 85 5 74 2 13 3 8 4 98 54 1 58 08 0 9 ...... (10 7 11 M 15 22 3 3 2 4 4 10 10 2 7 7 7 9 7 4 8 4 27 4 25 45 46 4 2 22 35 5 5 6 4 4 7 5 5 10 33 12 11 15 23 9 12 32 6 29 74 55 71 77 0 55 ...... 59 76 67 17 2 91 91 0 0 1 0 59 52 92 23 92 77 33 36 3 68 95 12 85 51 55 24 32 16 24 15 2 73 71 0 0 1 58 41 22 64 23 99 38 67 41 4 3 66 29 52 17 86 53 36 ...... 2 . . 0 . . . 0 ...... 87 9 6 4 62 6 0 2 2 0 0 6 9 8 7 3 9 29 9 6 4 66 4 2 0 5 6 9 8 7 3 9 1 0 1 0 3 1 . 0 . . 1 6 2 8 0 2 0 1 0 1 0 1 . . 0 . . . . 1 0 . 1 0 1 . . . . 0 . . 0 ...... +3 − +0 − +0 − 0 0 0 6 1 1 1 1 2 0 0 0 3 0 0 0 2 +2 − +1 − +1 − +0 − +3 − +2 − +0 − +1 − +5 − +2 − +12 − +0 − +2 − +1 − +1 − +1 − +1 − +0 − +1 − +0 − +2 − +1 − +1 − +1 − +1 − +0 − +0 − 3 86 +1 − +0 − +0 − 0 92 5 7 0 73 4 11 +0 − +3 − 3 9 +10 − +23 − +2 − +1 − +1 − +1 − +2 − +0 − +0 − +0 − +3 − +0 − ...... 83 43 455 34 72 17 5 68 2 1 21 28 71 88 69 28 17 54 3 847 84 32 23 26 4 4 4 8 84 81 4 17 52 41 6 1 2 1 23 3 9 11 2 ...... 200 Method c Continued . Table A-1 – ClusterAbell 2537RXCJ1131.9-1955 z 0.307 0.295 11 31 54.4 23 RA 08 23.2 -19 55 42 -02 11 31 X-ray Dec X-ray 2 4 Continued on next page MS 1008.1-1224RXCJ1131.9-1955 0.301 0.307 10 10 32.2 11 31 54.4 -12 39 55 -19 55 42 X-ray X-ray 4 2 Abell 2744 0.308 00 14 18.9 -30 23 22 X-ray 1 GHO132029+3155 0.308 13 22 48.77 +31 39 17.8 WL 12 GHO132029+3155 0.308 13 22 48.77 +31 39 17.8 WL 7 GHO132029+3155 0.308 13 22 48.77 +31 39 17.8 WL+SL 12 MS 2137.3-2353 0.313 21 40 15.2 -23 39 40 SL 9 MS 2137.3-2353 0.313 21 40 15.2 -23 39 40 X-ray 8 MS 2137.3-2353 0.313 21 40 15.2 -23 39 40 WL 5 MS 2137.3-2353 0.313 21 40 15.2 -23 39 40 WL+SL 3 MS 2137.3-2353 0.313 21 40 15.2 -23 39 40 SL 13 MS 2137.3-2353 0.313 21 40 15.2 -23 39 40 SL 11 MS 2137.3-2353MS 2137.3-2353 0.313 0.313 21 40 15.2 21 40 15.2 -23 39 40 -23 39 40 SL SL 12 11 MS 2137.3-2353MS 2137.3-2353 0.313 0.313 21 40 15.2 21 40 15.2 -23 39 40 -23 39 40 WL WL+SL 11 12 MS 2137.3-2353 0.313 21 40 15.2 -23 39 40 X-ray 7 MS 2137.3-2353 0.313 21 40 15.2 -23 39 40 X-ray 5 MS 2137.3-2353MACSJ0242.6-2132 0.313 0.314 21 02 40 42 15.2 35.9 -23 -21 39 32 40 26 X-ray X-ray 8 7 MS 2137.3-2353MACSJ0242.6-2132 0.313 0.314 21 40 02 15.2 42 35.9 -23 39 -21 40 32 26 X-ray X-ray 12 6 MACSJ1427.6-2521 0.318 14 27 39.4 -25 21 02 X-ray 8 Abell 1995MACSJ2229.8-2756 0.324CL 2244-0221 0.318 22 29 45.2 14 52 56.1 -27 55 37 +58 0.33 02 56 X-ray 22 X-ray 47 12.6 8 -02 3 05 40 SL 4 MS 0353.6-3642MACSJ2229.8-2756MS 1358.4+6245 0.32 0.324RCSJ2156+0123 03 22 55 29 33.3 45.2 0.328 -36 -27 34 55 13 18 0.335 37 59 53.1 15 47 +62 34.2 X-ray X-ray 31 16 +26 38 4 7 29.0 X-ray X-ray 5 1 MS 1224.7+2007 0.327 12 27 13.5 +19 50 55 X-ray 11 SDSSJ1531+3414 0.335 15 31 10.60 +34 14 25.0 SL 2 SDSSJ1531+3414 0.335 15 31 10.60 +34 14 25.0 WL 9 SDSSJ1531+3414 0.335 15 31 10.60 +34 14 25.0 WL+SL 6 SDSSJ1531+3414 0.335 15 31 10.60 +34 14 25.0 WL 6 SDSSJ1531+3414 0.335 15 31 10.60 +34 14 25.0 WL 4 SDSSJ1531+3414 0.335 15 31 10.60 +34 14 25.0 WL+SL 6 SDSSJ1621+0607 0.342 16 21 32.36 +06 07 19.0 WL 4 SDSSJ1621+0607 0.342 16 21 32.36 +06 07 19.0 WL 3 SDSSJ1621+0607 0.342 16 21 32.36 +06 07 19.0 WL+SL 4 MACSJ0947.2+7623 0.345 09 47 13.0 +76 23 14 X-ray 5 RXCJ2248.7-4431 0.348 22 48 43.5 -44 31 44 WL 2 RXCJ2248.7-4431 0.348 22 48 43.5 -44 31 44 WL 7 RXCJ2248.7-4431 0.348 22 48 43.5 -44 31 44 WL+SL 3 MACSJ1115.8+0129 0.352 11 15 52.0 +01 29 55 WL 4 MACSJ1115.8+0129 0.352 11 15 52.0 +01 29 55 X-ray 2 MACSJ1115.8+0129 0.352 11 15 52.0 +01 29 55 WL+SL 2 MACSJ1931.8-2635 0.352 19 31 49.6 -26 34 34 WL 5 MACSJ1931.8-2635 0.352 19 31 49.6 -26 34 34 X-ray 4 MACSJ1931.8-2635 0.352 19 31 49.6 -26 34 34 WL+SL 3

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 29 h / Λ Ω / m Ω δ Ref. Schmidt & Allen (2007) virial 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Voigt & Fabian (2006) 200/2E4 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012)Umetsu et al. (2011b) virial virial 0.275/0.725/0.702 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Buckley-Geer et al. (2011) 200 0.3/0.7/0.7 Buckley-Geer et al. (2011) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Umetsu et al. (2011b) virial 0.3/0.7/0.7 Kneib et al. (2003) 200 0.3/0.7/0.65 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014)Sereno et al. (2014) 200 200 0.3/0.7/0.7 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012)Eichner et al. (2013) virial 200 0.275/0.725/0.702 0.272/0.728/0.702 Biviano et al. (2013) 200 0.3/0.7/0.7 Biviano et al. (2013) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 0 . ) 5 0 74 87 65 87 87 94 08 84 41 49 93 55 32 16 54 46 ......

44 48 22 96 61 1 28 1 46 25 39 12 25 1 64 44 3 5 9 1 33 94 19 44 8 1 3 27 07 55 71 52 05 27 1 63 28 3 5 9 1 . . . . . 3 4 . 5 3 2 . 1 . 5 3 ...... 9 7 9 3 6 5 8 1 8 27 8 4 9 7 4 5 7 6 9 7 9 3 3 3 8 2 8 5 8 4 9 7 4 5 6 M 10 . 19 . 0 0 . 3 . 1 1 . . 3 . . . 0 . . . 1 . 1 1 . . 0 0 . . 0 4 2 2 2 7 3 1 . ∞ ...... +4 − +4 − +5 − +5 − +3 − +2 − +5 − +7 − 1 0 0 2 2 2 0 1 0 0 2 1 1 1 0 2 0 1 + − +1006 − +1 − +0 − +7 − +2 − +1 − +3 − +0 − +1 − +2 − +1 − +0 − +0 − +1 − +4 − +3 − +3 − +2 − +7 − +3 − +1 − 14 2 +1 − 0 +0 − +0 − +2 − 01 76 +3 − +3 − 4 72 +0 − 31 66 +1 − +0 − +0 − +2 − 97 +1 − 34 13 +1 − +1 − +0 − +2 − +75 − 4 2 6 9 0 +1 − ...... vir 2 4 73 82 4 67 9 33 9 Molikawa et al. (1999) virial 0.3/0.7/0.5 24 7 6 8 1 1 91 8 9 6 05 3 89 76 4 Molikawa et al. (1999) virial 0.3/0.7/0.5 5 8 86 74 1 8 39 81 61 6 ...... M 19 5 23 1 0 0 6 9 7 7 6 35 56 5 5 11 46 8 10 19 6 2 0 0 8 21 9 4 50 13 5 3 3 9 1 0 0 2 0 0 11 8 8 − 15 18 14 10 7 27 16 88 56 61 13 27 43 9 92 ...... 38 0 0 0 97 0 ...... 25 7 47 1 03 85 41 04 68 0 4 03 29 33 0 1 83 74 14 22 7 56 1 39 15 28 42 25 4 17 84 66 69 1 51 69 . . 24 7 ...... 17 10 . . . . . 13 21 . 33 ...... 7 75 7 92 6 9 8 44 7 6 6 87 25 5 0 8 7 2 8 5 1 7 0 7 7 7 09 7 2 8 74 7 6 6 0 18 5 0 8 7 2 8 5 1 7 0 2 . . 4 . 1 3 2 1 . 0 . . . . . 1 1 6 4 . 2 . 1 . . . 2 1 . 4 . 6 . 1 1 ...... +12 − +22 − +0 − +12 − +18 − +0 − +0 − 2 2 1 0 2 1 1 0 1 1 1 0 1 1 2 6 1 0 2 3 2 1 1 +2 − +4 − +1 − +3 − +3 − +3 − +0 − +1 − +2 − +10 − +4 − +2 − +1 − +5 − +1 − +4 − +32 − +2 − +1 − +2 − +2 − 9 54 38 +1 − 3 +1 − +4 − +3 − +1 − +0 − +1 − 0 6 81 92 +1 − +1 − +1 − +1 − +1 − +2 − 3 89 81 +6 − 81 +1 − +0 − +2 − +3 − +2 − +1 − +1 − ...... 81 0 4 8 69 62 44 350 7 94 9 6 3 4 2 26 82 9 14 0 09 5 9 4 57 07 5 75 9 4 84 8 25 56 4 6 3 5 2 0 ...... vir c 3 9 3 14 27 17 3 5 10 5 9 7 4 5 6 7 6 5 5 8 26 15 39 26 6 4 4 9 6 5 5 4 5 9 17 20 39 7 6 39 5 5 5 4 8 5 7 5 6 0 ) (10 . 0 33 15 59 3 92 82 0 29 61 ......

6 41 44 73 7 44 6 92 3 26 25 63 97 44 26 08 62 24 4 3 14 8 8 3 24 86 96 12 61 6 17 63 28 47 82 11 84 78 34 2 4 17 88 8 8 3 ...... 3 4 . . . 2 . . . . . 3 ...... 6 6 8 0 3 2 8 0 7 4 4 6 4 4 36 11 1 1 3 6 6 8 0 9 9 8 1 7 4 4 6 4 4 66 49 1 1 3 M 8 . 16 . 0 0 . 2 . 1 1 . . 2 4 . 3 . . 0 0 . 1 . 0 4 . 1 1 . . . . . 0 0 3 2 2 1 5 3 . . ∞ ...... +3 − +3 − +3 − +6 − 1 0 0 2 2 2 0 1 0 2 1 1 1 0 0 0 2 1 1 + − − +675 +1 − +0 − +5 − +2 − +1 − +2 − +5 − +4 − +0 − +0 − +1 − +1 − +4 − +1 − +1 − +66 − +1 − +3 − +3 − +2 − +1 − +5 − +3 − 14 2 +1 − 0 +0 − +0 − +2 − 14 34 +2 − +2 − 1 7 +0 − 74 +1 − +0 − +2 − 5 +1 − 0 59 +1 − +1 − +0 − +0 − +0 − +2 − 0 7 3 3 +1 − +1 − ...... 200 7 3 68 75 3 46 1 36 59 2 9 0 9 5 01 7 9 86 75 9 0 66 6 35 26 6 7 5 8 8 7 9 71 37 69 55 6 7 ...... (10 16 M 4 19 1 0 0 5 8 7 6 5 31 48 5 4 10 40 7 9 17 5 1 0 0 7 18 8 3 44 11 4 3 3 8 1 0 0 1 0 0 10 7 7 − 13 16 13 8 6 29 49 46 36 15 26 65 85 99 ...... 14 15 0 0 0 . . . . . 88 28 0 25 77 33 36 88 41 0 8 65 1 72 07 92 82 5 44 95 87 28 0 32 91 23 61 21 89 0 8 76 57 82 01 66 39 5 48 08 4 . . . 20 6 ...... 14 9 ...... 11 18 28 ...... 3 4 6 66 53 2 6 5 4 4 3 3 7 8 69 5 2 4 0 8 5 9 3 4 6 77 6 9 7 5 4 4 3 3 7 8 5 2 4 0 8 5 9 1 . 2 4 . 1 . . . 0 0 . . . 0 . 0 1 5 3 . 1 . 1 0 1 . 1 0 . 3 . . . 1 0 ...... +10 − +18 − +0 − +10 − +15 − +0 − +0 − 2 2 1 1 2 1 1 1 1 1 1 5 0 2 3 1 1 0 1 1 5 1 +1 − +2 − +4 − +1 − +0 − +0 − +0 − +1 − +1 − +9 − +3 − +1 − +1 − +0 − +1 − +4 − +1 − +3 − +2 − +1 − +2 − 5 02 45 +1 − +2 − +2 − +2 − +3 − +2 − +1 − +1 − 0 2 62 65 +1 − +1 − +1 − +1 − 8 65 83 +5 − +27 − 83 +1 − +0 − +2 − +3 − +1 − +1 − +0 − ...... 11 5 77 0 71 6 6 8 83 8201 7 9 5 1 25 3 37 41 8 36 3 64 35 93 5 76 18 0 39 8 2 7 9 35 61 7 3 4 3 3 0 ...... 200 Method c Continued . Table A-1 – ClusterMACSJ1931.8-2635 0.352 19 z 31 49.6 -26 34 34 RA X-ray 3 Dec Continued on next page RXJ1532.9+3021 0.3615 15 32 53.8 +30 20 58 WL 7 RXJ1532.9+3021 0.3615 15 32 53.8 +30 20 58 X-ray 2 SDSSJ1152+3313 0.362 11 52 00.15 +33 13 42.1 WL 12 SDSSJ1152+3313 0.362 11 52 00.15 +33 13 42.1 WL 23 SDSSJ1152+3313 0.362 11 52 00.15 +33 13 42.1 WL+SL 14 MACSJ1532.9+3021 0.363 15 32 53.8 +30 20 58 WL+SL 3 MACSJ1532.9+3021 0.363 15 32 53.8 +30 20 58 X-ray 4 SDSSJ0851+3331 0.37 08 51 38.86 +33 31 06.1 WL 8 SDSSJ0851+3331 0.37 08 51 38.86 +33 31 06.1 WL 4 SDSSJ0851+3331Abell 370 0.37 08 51 38.86 +33 31 06.1 0.375 WL+SL 02 39 50.5 7 -01 35 08 WL 5 MS 1512.4+3647MACSJ0011.7-1523 0.372 0.379 15 14 25.1 00 11 42.9 +36 36 30 -15 23 22 X-ray X-ray 7 4 BCS J2352-5452 0.3838 23 51 38.0 -54 52 53 WL 4 BCS J2352-5452 0.3838 23 51 38.0 -54 52 53 WL+SL 5 MACSJ1720.3+3536 0.391 17 20 16.8 +35 36 26 WL 6 MACSJ1720.3+3536 0.391 17 20 16.8 +35 36 26 X-ray 5 MACSJ1720.3+3536 0.391 17 20 16.8 +35 36 26 WL+SL 4 MACSJ1720.3+3536 0.391 17 20 16.8 +35 36 26 X-ray 4 ZwCl 0024.0+1652 0.395 00 26 35.7 +17 09 46 WL 7 ZwCl 0024.0+1652 0.395 00 26 35.7 +17 09 46 WL+SL 22 SDSSJ0915+3826 0.397 09 15 39.00 +38 26 58.5 WL 13 SDSSJ0915+3826 0.397 09 15 39.00 +38 26 58.5 WL 33 SDSSJ0915+3826 0.397 09 15 39.00 +38 26 58.5 WL+SL 22 MACSJ0429.6-0253 0.399 04 29 36.0 -02 53 08 WL 5 MACSJ0429.6-0253 0.399 04 29 36.0 -02 53 08 X-ray 3 MACSJ0429.6-0253 0.399 04 29 36.0 -02 53 08 WL+SL 3 MACSJ0429.6-0253 0.399 04 29 36.0 -02 53 08 X-ray 7 MACSJ0159.8-0849 0.405 01 59 49.4 -08 49 59 X-ray 5 MACSJ0159.8-0849 0.405 01 59 49.4 -08 49 59 X-ray 4 SDSSJ1343+4155 0.418 13 43 32.85 +41 55 03.4 WL 4 SDSSJ1343+4155 0.418 13 43 32.85 +41 55 03.4 WL 3 SDSSJ1343+4155 0.418 13 43 32.85 +41 55 03.4 WL+SL 4 MACS J0416.1-2403SDSSJ1038+4849 0.42 04 16 0.43 09.9 -24 10 03 38 58 42.90 +48 49 18.7 WL WL 8 14 MS 0302.7+1658SDSSJ1038+4849 0.426 0.43 03 05 31.7 10 38 +17 42.90 10 03 +48 49 18.7 X-ray WL 7 17 SDSSJ1038+4849 0.43 10 38 42.90 +48 49 18.7 WL+SL 33 SDSSJ1226+2152 0.43 12 26 51.70 +21 52 26.0 WL 6 SDSSJ1226+2152 0.43 12 26 51.70 +21 52 26.0 WL 5 SDSSJ1226+2152 0.43 12 26 51.70 +21 52 26.0 WL+SL 33 SDSSJ1226+2149 0.435 12 26 51.11 +21 49 52.3 WL 4 SDSSJ1226+2149 0.435 12 26 51.11 +21 49 52.3 WL 4 SDSSJ1226+2149 0.435 12 26 51.11 +21 49 52.3 WL+SL 4 MACS J1206.2-0847MACS J1206.2-0847 0.439 0.439 12 06 12.2 12 06 12.2 -08 48 01 -08 48 01 SL LOSVD 7 3 MACS J1206.2-0847 0.439 12 06 12.2 -08 48 01 CM 4 MACS J1206.2-0847 0.439 12 06 12.2 -08 48 01 WL 6 MACS J1206.2-0847 0.439 12 06 12.2 -08 48 01 WL+SL 4 SDSSJ1329+2243 0.443 13 29 34.49 +22 43 16.2 WL 5

c 0000 RAS, MNRAS 000, 000–000 30 Groener, Goldberg, & Sereno h / Λ Ω / m Ω δ Ref. Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Umetsu et al. (2011b) virial 0.3/0.7/0.7 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Kling et al. (2005) 200 0.3/0.7/0.5 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Voigt & Fabian (2006) 200/2E4 0.3/0.7/0.7 Allen et al. (2003) 200 0.3/0.7/0.5 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Allen et al. (2003) 200 0.3/0.7/0.5 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Oguri et al. (2009) virial 0.26/0.74/0.72 Oguri et al. (2009) virial 0.26/0.74/0.72 Oguri et al. (2009) virial 0.26/0.74/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Babyk et al. (2014) 200 0.27/0.73/0.73 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Israel et al. (2010) 200 0.3/0.7/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Babyk et al. (2014) 200 0.27/0.73/0.73 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 ) 31 84 49 0 0 5 9 74 47 58 09 96 0 0 3 52 05 48 ......

21 31 61 81 9 7 9 5 73 12 31 98 99 4 33 07 67 76 4 26 34 49 57 95 84 8 0 38 6 85 03 9 7 9 1 92 75 25 4 17 19 4 71 31 03 86 74 58 5 38 59 56 27 8 0 . . . . . 2 1 . 3 ...... 2 2 ...... 5 ...... 14 3 9 1 8 5 2 9 6 8 6 4 5 3 1 34 3 9 1 9 0 9 6 8 6 4 3 3 1 M . 1 . 0 0 . . 1 0 8 1 15 9 21 10 0 1 3 . . . . 0 0 4 . 1 1 . 1 0 . 1 1 6 . 2 . . 2 1 . 0 5 5 ...... +2 − +2 − +3 − +3 − +3 − +5 − 1 1 1 1 2 2 2 1 1 0 1 0 3 3 1 +1 − +0 − +0 − +3 − +0 − +8 − +1 − +31 − +7 − +57 − +16 − +0 − +1 − +6 − +1 − +1 − +4 − +1 − +1 − +2 − +0 − +1 − +1 − +5 − +4 − +3 − +2 − +1 − +5 − +5 − 14 +1 − +1 − +1 − +1 − 7 22 35 8 26 5 0 1 0 3 +13 − +2 − +3 − +1 − 1 61 59 +1 − +0 − +1 − 6 +0 − +4 − +3 − 97 +1 − 0 7 ...... vir 9 62 2 97 29 5 6 48 93 14 91 3 3 3 9 07 12 6 13 79 6 68 69 4 22 98 3 02 7 1 24 75 5 77 ...... M 4 5 2 0 1 9 8 7 14 11 10 31 21 13 29 36 37 26 3 4 7 5 8 8 6 4 4 14 11 10 6 5 4 4 6 2 5 4 3 62 5 7 8 8 7 5 55 6 5 31 31 65 51 . . 0 37 8 24 0 0 3 04 39 ...... 58 81 18 7 91 09 53 17 43 57 9 02 26 2 5 9 98 23 1 2 16 1 06 05 42 22 87 66 75 91 29 18 47 7 88 52 6 14 79 87 2 01 42 4 5 23 51 07 4 2 65 1 27 94 87 6 33 92 78 81 . . 27 ...... 4 3 ...... 6 ...... 0 9 4 4 8 45 1 1 0 3 1 4 9 8 5 4 0 9 4 4 8 62 9 0 3 1 2 9 8 5 4 3 0 . 2 2 . 0 . 1 0 . 2 . 12 0 . 1 0 2 2 7 . . 4 . 0 0 . 2 1 3 1 5 3 2 0 . 1 . . 0 0 0 . 0 ...... +0 − +9 − +8 − +14 − 3 1 0 1 1 1 4 3 2 1 1 1 1 2 0 1 +7 − +1 − +4 − +2 − +0 − +1 − +0 − +3 − +74 − +0 − +1 − +1 − +2 − +3 − +28 − +4 − +1 − +1 − +4 − +1 − +3 − +1 − +5 − +7 − +5 − +0 − +1 − +1 − +0 − +0 − +0 − +3 − 81 6 +1 − +0 − +1 − +1 − 0 +1 − 7 +11 − +3 − 7 59 02 +2 − +1 − 1 65 7 +1 − +2 − +1 − +2 − +0 − +1 − ...... 89 82 2 02 7 62 3 55 47 4 08 7 68 2 49 15 29 05 1 3 5 66 25 5 17 41 92 53 51 99 3 22 4 7 66 55 98 7 92 2 1 ...... vir c 9 5 8 39 9 10 4 5 4 3 4 5 9 4 18 5 5 7 9 9 7 11 9 8 11 12 12 5 2 5 7 6 7 18 2 22 12 6 8 5 5 5 2 3 1 3 3 5 8 3 6 ) (10 17 0 0 58 71 6 0 0 2 84 72 ......

03 07 29 55 56 7 95 59 1 9 2 3 65 02 9 91 6 38 4 18 96 39 71 25 15 0 67 76 7 1 21 22 57 76 57 7 18 81 1 9 1 81 59 1 07 09 6 89 68 52 17 69 8 55 71 8 19 13 7 1 ...... 3 ...... 5 . . . 4 ...... 1 6 0 9 5 3 0 6 4 7 4 14 3 9 6 0 1 6 0 33 6 7 6 4 7 4 43 3 6 6 0 M 1 1 . 0 0 . . 1 0 1 1 7 1 14 8 18 9 0 1 . . . . . 0 0 3 2 2 . 1 0 . 1 0 . 1 . . 2 . . 2 1 . 0 4 4 ...... +3 − +4 − +4 − 1 1 1 2 2 2 2 1 1 0 1 1 0 2 2 1 +1 − +1 − +0 − +0 − +2 − +0 − +2 − +1 − +7 − +1 − +26 − +6 − +48 − +14 − +0 − +1 − +1 − +1 − +3 − +2 − +2 − +1 − +1 − +1 − +0 − +1 − +3 − +2 − +2 − +1 − +4 − +4 − 14 +1 − +1 − +1 − 7 9 33 6 0 0 0 7 +5 − +12 − +2 − +2 − +1 − 4 +1 − +0 − +1 − +1 − 11 +0 − +3 − +2 − 21 +1 − 6 4 ...... 200 44 95 0 92 16 7 3 62 49 94 57 76 1 8 5 4 3 73 77 52 29 9 55 29 3 56 51 0 77 6 6 22 2 0 64 92 7 28 ...... (10 4 M 4 2 0 1 8 7 6 12 9 8 27 19 11 27 32 33 23 3 3 7 4 7 7 6 3 3 12 9 9 5 4 4 4 5 2 5 3 3 55 4 6 7 7 5 4 48 5 5 26 28 57 38 . . 0 7 21 33 0 0 65 09 ...... 01 67 83 78 9 84 37 24 35 9 94 9 73 82 86 92 8 4 35 05 7 55 63 79 13 98 75 75 25 67 68 39 61 04 95 7 9 0 26 4 18 8 4 73 39 07 77 65 7 . . 23 ...... 3 3 . . . . . 5 ...... 6 3 6 3 44 2 5 72 0 4 6 7 1 95 58 73 0 2 6 2 4 2 6 3 6 3 5 2 5 71 5 2 7 1 36 12 03 0 8 6 2 4 2 3 0 . 1 . . 0 . 0 . . 1 . 10 0 1 1 0 . 1 . . . 3 . 0 0 . 1 0 2 . 4 . . 0 . 1 . . 0 0 0 . 0 ...... +0 − +7 − +7 − +12 − 2 2 1 0 0 1 1 6 3 2 0 2 1 1 1 1 1 0 1 1 1 1 +6 − +0 − +3 − +0 − +1 − +2 − +64 − +0 − +1 − +1 − +1 − +2 − +3 − +1 − +1 − +3 − +1 − +2 − +4 − +0 − +1 − +1 − +0 − +0 − +0 − +2 − 94 +2 − +1 − +0 − +0 − +1 − +1 − 0 +1 − +23 − +9 − +3 − 0 65 16 +1 − +1 − 6 +1 − 33 9 +6 − +5 − +1 − +1 − +1 − +1 − +0 − +1 − ...... 31 84 9 57 0 8 74 6 92 7 5 71 9 79 37 34 79 9 97 8 6 9 6 17 38 4 16 22 4 5 2 01 4 42 0 1 34 96 33 7 69 7 2 ...... 200 Method c Continued . Table A-1 – ClusterSDSSJ1329+2243 0.443 z 13 29 34.49 +22 43 16.2 RA WL 8 Dec Continued on next page SDSSJ1329+2243 0.443 13 29 34.49 +22 43 16.2 WL+SL 4 SDSSJ0957+0509 0.448 09 57 39.19 +05 09 31.9 WL 6 SDSSJ0957+0509 0.448 09 57 39.19 +05 09 31.9 WL 33 SDSSJ0957+0509 0.448 09 57 39.19 +05 09 31.9 WL+SL 7 MACSJ0329.7-0212 0.45 03 29 41.5 -02 11 46 WL 9 MACSJ0329.7-0212 0.45 03 29 41.5 -02 11 46 WL+SL 3 MACSJ0329.7-0212 0.45 03 29 41.5 -02 11 46 X-ray 4 SDSSJ1138+2754 0.451 11 38 08.95 +27 54 30.7 WL 3 SDSSJ1138+2754 0.451 11 38 08.95 +27 54 30.7 WL 2 SDSSJ1138+2754 0.451 11 38 08.95 +27 54 30.7 WL+SL 3 RXJ1347.5-1145 0.451 13 47 30.6 -11 45 10 WL 4 RXJ1347.5-1145 0.451 13 47 30.6 -11 45 10 WL 7 RXJ1347.5-1145 0.451 13 47 30.6 -11 45 10 WL+SL 3 RXJ1347.5-1145 0.451 13 47 30.6 -11 45 10 WL 15 RXJ1347.5-1145 0.451 13 47 30.6 -11 45 10 X-ray 4 RXJ1347.5-1145 0.451 13 47 30.6 -11 45 10 X-ray 4 RXJ1347.5-1145 0.451 13 47 30.6 -11 45 10 X-ray 6 3C 295 0.461 14 11 20.5 +52 12 10 X-ray 7 3C 295 0.461 14 11 20.5 +52 12 10 X-ray 7 MACSJ1621.6+3810 0.461 16 21 36.0 +38 10 00 X-ray 5 SDSSJ1446+3032 0.464 14 46 34.02 +30 32 58.2 SL 9 SDSSJ1446+3032 0.464 14 46 34.02 +30 32 58.2 WL 7 SDSSJ1446+3032 0.464 14 46 34.02 +30 32 58.2 WL+SL 6 SDSSJ1446+3032 0.464 14 46 34.02 +30 32 58.2 WL 10 SDSSJ1446+3032 0.464 14 46 34.02 +30 32 58.2 WL 10 SDSSJ1446+3032 0.464 14 46 34.02 +30 32 58.2 WL+SL 10 SDSSJ1115+5319 0.466 11 15 14.85 +53 19 54.6 WL 4 SDSSJ1115+5319 0.466 11 15 14.85 +53 19 54.6 WL 2 SDSSJ1115+5319 0.466 11 15 14.85 +53 19 54.6 WL+SL 4 RCS2J1055+5548 0.466 10 55 04.59 +55 48 23.3 WL 6 RCS2J1055+5548 0.466 10 55 04.59 +55 48 23.3 WL 5 RCS2J1055+5548 0.466 10 55 04.59 +55 48 23.3 WL+SL 6 SDSSJ1456+5702 0.484 14 56 00.78 +57 02 20.3 WL 15 SDSSJ1456+5702 0.484 14 56 00.78 +57 02 20.3 WL 2 SDSSJ1456+5702 0.484 14 56 00.78 +57 02 20.3 WL+SL 19 SDSSJ1632+3500 0.49 16 32 10.26 +35 00 29.7 WL 10 SDSSJ1632+3500 0.49 16 32 10.26 +35 00 29.7 WL 5 SDSSJ1632+3500 0.49 16 32 10.26 +35 00 29.7 WL+SL 7 MACSJ1311.0-0311 0.494 13 11 01.9 -03 10 36 X-ray 5 MACSJ1311.0-0311 0.494 13 11 01.9 -03 10 36 WL+SL 4 MACSJ1311.0-0311 0.494 13 11 01.9 -03 10 36 X-ray 4 WARP J0030.5+2618 0.5 00 30 33.2 +26 18 19 WL 2 SDSSJ1152+0930 0.517 11 52 47.38 +09 30 14.7 WL 3 SDSSJ1152+0930 0.517 11 52 47.38 +09 30 14.7 WL 1 SDSSJ1152+0930 0.517 11 52 47.38 +09 30 14.7 WL+SL 2 MACSJ1423.8+2404 0.543 14 23 47.6 +24 04 40 X-ray 3 MACSJ1423.8+2404 0.543 14 23 47.6 +24 04 40 WL+SL 4 MACSJ1423.8+2404 0.543 14 23 47.6 +24 04 40 X-ray 7 MACS J1149.5+2223 0.544 11 49 35.1 +22 24 11 WL 2 MACS J0717.5+3745 0.546 07 17 30.9 +37 45 30 WL 5

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 31 h / Λ Ω / m Ω δ Comerford & Natarajan (2007) 200/virial 0.3/0.7/0.7 Ref. Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Babyk et al. (2014) 200 0.27/0.73/0.73 Oguri et al. (2013) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Comerford & Natarajan (2007) 200/virial 0.3/0.7/0.7 Oguri et al. (2009) virial 0.26/0.74/0.72 Oguri et al. (2009) virial 0.26/0.74/0.72 Oguri et al. (2009) virial 0.26/0.74/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Oguri et al. (2012) virial 0.275/0.725/0.702 Sereno et al. (2014) 200 0.3/0.7/0.7 Oguri et al. (2012) virial 0.275/0.725/0.702 Babyk et al. (2014) 200 0.27/0.73/0.73 Oguri et al. (2012)Sereno et al. (2014) virial 200 0.275/0.725/0.702 0.3/0.7/0.7 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Schmidt & Allen (2007) virial 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Comerford & Natarajan (2007) 200/virial 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 35 96 48 07 1 . . . . . 78 ) . 9 06 46 87 5 81 07 27 0 5 12 11 . 7 ......

0 02 45 03 5 57 46 38 5 71 65 2 79 03 14 94 67 96 92 43 8 58 55 51 4 0 52 83 97 57 67 82 66 5 97 97 2 2 53 0 58 43 15 41 34 41 8 6 83 84 4 ...... 1 ...... 4 . . 1 . 3 ...... 4 8 6 6 2 3 7 2 2 2 1 1 4 8 0 7 4 8 73 6 2 3 1 1 2 1 1 4 8 0 7 +12 − +13 − +11 − M 2 . 2 1 1 0 . . 0 . 1 1 3 . 1 1 3 1 2 . . . . . 2 1 . 0 0 . 1 1 3 . 3 0 0 5 . . 22 ...... +1 − +6 − +1 − +5 − 2 0 0 1 2 0 2 3 3 3 2 2 0 0 4 0 0 Molikawa et al. (1999) virial 0.3/0.7/0.5 +2 − +2 − +1 − +0 − +0 − +0 − +1 − +1 − 61 +3 − 37 +1 − +1 − +3 − +2 − +2 − +2 − +2 − +2 − +2 − +4 − +2 − +3 − 02 +5 − +0 − +0 − +5 − +22 − . . . . 14 0 +2 − +0 − +0 − +1 − 5 +2 − 0 +0 − +13 − +4 − +4 − +3 − 25 +2 − +2 − 0 +0 − 23 99 4 49 +0 − +4 − 1 +0 − ...... vir 5 92 03 42 21 1 0 02 7 42 37 3 84 84 92 59 5 5 2 2 3 03 25 7 07 26 8 82 25 Williams & Saha (2004) 200 0.3/0.7/0.7 21 9 78 02 99 2 5 1 ...... 20 M 8 6 6 4 2 3 2 2 5 4 4 117 12 115 8 6 6 10 6 7 3 5 9 9 6 6 5 14 4 2 2 2 2 2 14 134 7 9 54 6 5 11 10 34 7 5 28 3 48 7 52 42 . . . . 02 17 1 1 56 97 33 0 9 9 92 26 87 ...... 25 25 01 5 9 1 6 82 49 14 9 67 09 31 98 5 3 01 62 82 5 74 13 19 2 41 82 52 29 3 69 59 06 9 1 46 15 9 34 86 3 32 68 16 85 5 45 61 44 85 65 29 3 . . . . . 5 4 ...... 27 15 ...... 3 5 0 3 2 3 9 9 1 1 2 2 2 9 3 5 0 3 2 3 9 9 1 1 23 2 2 9 . . 2 1 0 7 4 5 4 2 0 . 0 4 2 2 . 3 0 . 10 9 9 . 1 1 0 5 . 3 3 . 0 . 1 0 0 0 0 . . . . . 4 ...... +14 − +9 − +3 − +17 − 0 1 3 1 0 4 4 2 1 2 0 0 5 0 +3 − +1 − +0 − +14 − +4 − +5 − +15 − +14 − +0 − +0 − +4 − +5 − +4 − +6 − +1 − +24 − +25 − +25 − +1 − +3 − +0 − +5 − +30 − +11 − +0 − +1 − +0 − +0 − +0 − +0 − +4 − +0 − +1 − 7 6 48 09 1 +3 − 6 +1 − +0 − 0 1 1 +4 − 9 89 39 +4 − +2 − +1 − +2 − +0 − +0 − +5 − +0 − 6 ...... 114 105 8 75 85 02 44 66 05 4 23 24 16 0 55 57 0 9 91 79 25 7 42 32 01 4 22 8 95 81 81 66 22 1 4 8 7 1 ...... vir 6 c 7 5 7 1 25 10 11 11 14 9 9 2 8 1 11 7 7 5 9 4 5 16 14 14 5 1 4 7 13 35 22 9 4 8 8 1 4 4 2 3 3 3 4 1 3 5 1 12 15 18 26 14 82 ) (10 . . . . . 28 72 49 28 18 4 64 22 11 11 4 . . 6 ......

0 81 32 77 47 56 52 34 27 0 55 5 65 8 75 73 64 9 72 31 3 16 45 0 25 66 73 54 68 62 67 52 0 79 79 02 24 1 11 17 05 27 88 21 3 84 74 ...... 10 . 9 ...... 1 ...... 3 . 1 3 ...... 1 7 4 9 7 3 5 0 0 7 9 9 4 48 6 7 4 6 1 7 4 9 7 3 8 8 7 9 9 4 73 6 7 4 6 +8 − M 2 . 1 1 0 0 . 0 0 . 1 1 3 . 1 1 . 1 1 . . . . . 1 1 . 0 0 . 1 1 3 . 3 . 0 . . . 16 ...... +10 − +10 − +1 − +5 − +1 − +4 − 2 0 1 1 2 0 2 3 3 2 1 1 0 0 4 0 3 0 +2 − +2 − +1 − +0 − +0 − +0 − +0 − +1 − +1 − +3 − +1 − +1 − +2 − +2 − +2 − +2 − +2 − +2 − +3 − +2 − +3 − 48 +4 − +0 − +16 − . 14 0 3 5 +2 − +0 − +1 − 66 4 51 +1 − +2 − +0 − +12 − +3 − +3 − +2 − 91 +1 − +1 − 9 +0 − 64 +0 − 51 +4 − 37 +0 − +3 − 0 +0 − ...... 200 7 19 48 32 08 9 85 86 3 06 01 7 22 21 9 36 73 1 1 5 5 7 92 69 4 97 13 6 52 03 870 6 83 3 27 3 5 0 9 ...... 18 (10 7 M 6 5 3 2 2 1 1 5 4 4 96 11 89 7 6 6 8 6 6 3 5 8 8 5 4 4 12 4 1 2 2 2 2 12 7 106 8 46 5 5 10 9 28 6 5 23 2 16 75 24 26 . . . . 51 51 74 34 9 4 4 45 08 33 ...... 91 07 01 32 59 5 96 43 3 29 8 86 8 2 0 84 39 71 9 22 72 16 06 35 71 45 25 17 9 14 36 05 24 5 3 59 17 44 4 71 73 9 37 43 37 73 56 25 19 9 . . . 6 ...... 24 13 ...... 3 3 3 41 6 11 1 84 2 8 4 6 0 9 2 7 8 3 3 3 38 6 12 1 13 2 8 4 6 0 9 2 7 8 . . 1 1 0 . 4 3 4 3 2 . . . 4 2 1 . 2 . . 8 8 8 . 0 1 0 4 . 3 2 . . 0 1 0 0 0 0 . 0 . . . 3 ...... +12 − +3 − +15 − 0 1 4 0 2 0 1 0 0 2 1 1 0 4 0 3 4 +3 − +1 − +0 − +12 − +8 − +4 − +13 − +12 − +4 − +4 − +4 − +5 − +20 − +22 − +22 − +1 − +2 − +0 − +4 − +26 − +10 − +0 − +1 − +0 − +0 − +0 − +0 − +0 − +3 − +0 − +1 − 31 +4 − 3 +0 − +2 − +0 − 1 +1 − +1 − +0 − 9 2 2 +3 − 2 55 61 +4 − +2 − +1 − +1 − +0 − +4 − +0 − 3 ...... 5 377 93 89 71 82 2 89 56 12 32 7 3 0 22 15 3 24 9 3 1 59 11 24 5 81 24 1 1 001 3 32 39 28 15 78 6 18 3 0 9 ...... 200 Method c Continued . Table A-1 – MS 0451.6-0305 0.55 04 54 11.1 -03 00 54 SL 5 ClusterMS 0015.9+1609SDSSJ1209+2640 0.546 z 0.561 00 18 33.8 12 09 23.68 +16 RA 26 17 +26 40 46.7 X-ray WL Dec 4 6 Continued on next page SDSSJ1209+2640 0.561 12 09 23.68 +26 40 46.7 WL 4 SDSSJ1209+2640 0.561 12 09 23.68 +26 40 46.7 WL+SL 6 RXJ0848.7+4456 0.57 08 48 47.2 +44 56 17 X-ray 0 SDSSJ1029+2623 0.584 10 29 12.48 +26 23 32.0 WL+SL 22 SDSSJ1029+2623 0.584 10 29 12.48 +26 23 32.0 WL 9 SDSSJ1029+2623 0.584 10 29 12.48 +26 23 32.0 WL 9 SDSSJ1029+2623 0.584 10 29 12.48 +26 23 32.0 WL+SL 9 SDSSJ1315+5439 0.588 13 15 09.30 +54 37 51.8 WL 12 SDSSJ1315+5439 0.588 13 15 09.30 +54 37 51.8 WL 8 SDSSJ1315+5439 0.588 13 15 09.30 +54 37 51.8 WL+SL 8 MACSJ2129.4-0741 0.589 21 29 26.2 -07 41 26 X-ray 1 MACSJ0647.7+7015 0.59 06 47 50.5 +70 14 55 WL 7 MACSJ0647.7+7015 0.59 06 47 50.5 +70 14 55 X-ray 1 SDSSJ1050+0017 0.6 10 50 39.90 +00 17 07.1 WL 10 SDSSJ1050+0017 0.6 10 50 39.90 +00 17 07.1 WL 6 SDSSJ1050+0017 0.6 10 50 39.90 +00 17 07.1 WL+SL 6 SDSSJ1420+3955 0.607 14 20 40.33 +39 55 09.8 WL 4 SDSSJ1420+3955 0.607 14 20 40.33 +39 55 09.8 WL 8 SDSSJ1420+3955 0.607 14 20 40.33 +39 55 09.8 WL+SL 3 3C 220.1 0.62 09 32 39.6 +79 06 32 SL 4 SDSSJ2111-0114 0.638 21 11 19.34 -01 14 23.5 SL 13 SDSSJ2111-0114 0.638 21 11 19.34 -01 14 23.5 WL 12 SDSSJ2111-0114 0.638 21 11 19.34 -01 14 23.5 WL+SL 12 SDSSJ2111-0114 0.638 21 11 19.34 -01 14 23.5 WL 5 SDSSJ2111-0114 0.638 21 11 19.34 -01 14 23.5 WL 1 SDSSJ2111-0114 0.638 21 11 19.34 -01 14 23.5 WL+SL 4 RCSJ1419.2+5326 0.64 14 19 12.0 +53 26 00 X-ray 6 SDSSJ1110+6459 0.659 11 10 17.70 +64 59 47.8 WL 12 SDSSJ1110+6459 0.659 11 10 17.70 +64 59 47.8 WL 31 SDSSJ1110+6459 0.659 11 10 17.70 +64 59 47.8 WL+SL 19 SDSSJ1004+4112 0.68 10 04 34.18 +41 12 43.5 WL 8 SDSSJ1004+4112 0.68 10 04 34.18 +41 12 43.5 WL 3 SDSSJ1004+4112MACSJ0744.9+3927 0.68 0.686 10 04 07 34.18 44 52.5 +41 12 43.5 +39 27 27 WL+SL 7 WL 7 MACSJ0744.9+3927 0.686 07 44 52.5 +39 27 27 WL+SL 4 SDSSJ1004+4112MACSJ0744.9+3927 0.68 0.686 10 04 34.18 07 44 52.5 +41 12 43.5 +39 27 27 SL X-ray 5 1 MACSJ0744.9+3927 0.686 07 44 52.5 +39 27 27 X-ray 4 RXJ1221.4+4918 0.7 12 21 24.5 +49 18 13 X-ray 2 RXJ1113.1-2615 0.72 11 13 05.2 -26 15 26 X-ray 3 RCSJ1107.3-0523 0.735 11 07 22.8 -05 23 49 X-ray 3 RCSJ0224-0002 0.778 02 24 00.0 -00 02 00 X-ray 2 CLG 1137.5+6625 0.78 11 40 23.9 +66 08 19 WL 3 RCSJ2318.5+0034 0.78 23 18 31.5 +00 34 18 X-ray 1 MS 1137.5+6625 0.783 11 40 23.9 +66 08 19 SL 3 RX J1716.6+6708 0.81 17 16 49.6 +67 08 30 WL 5 MS 1054-0321 0.83 10 56 59.5 -03 37 28 WL 0 CL J0152-1357 0.84 01 52 41.0 -13 57 45 WL 11

c 0000 RAS, MNRAS 000, 000–000 32 Groener, Goldberg, & Sereno h / Λ Ω / m Ω δ Ref. Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Merten et al. (2014) 2500/200/virial 0.27/0.73/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Maughan et al. (2007) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Lerchster et al. (2011) 200 0.27/0.73/0.72 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Sereno et al. (2014) 200 0.3/0.7/0.7 Babyk et al. (2014) 200 0.27/0.73/0.73 Sereno et al. (2014) 200 0.3/0.7/0.7 81 48 52 06 . . . . ) 83 8 2 16 2 4 1 2 75 8 2 3 2 4 1 2 19 ...... 44 ......

15 6 1 3 54 13 6 1 62 76 . . . 5 . 8 ...... 3 6 0 5 6 8 6 4 6 0 8 1 5 2 5 9 1 8 8 0 2 7 7 6 0 5 6 8 6 4 6 0 8 1 5 2 5 9 1 8 8 0 2 7 +17 − +22 − M 1 2 1 . . . . 0 . 18 . 35 ...... 28 . . . 41 0 . . 20 13 ...... +4 − +6 − 1 2 1 1 4 0 0 2 2 2 0 6 1 6 1 1 2 1 2 3 2 1 +1 − +2 − +1 − 38 +0 − +18 − +35 − +28 − +41 − +0 − +20 − +13 − 98 . . 14 1 2 +1 − +2 − 74 +1 − +1 − +4 − 5 +0 − 3 +0 − +2 − +2 − +2 − +0 − +6 − 15 +1 − +6 − +1 − 8 +1 − +2 − +1 − 8 +2 − +3 − 0 9 +2 − +1 − ...... vir 35 2 2 5 2 17 7 7 7 3 6 5 0 5 5 2 2 8 4 7 37 3 6 7 8 ...... M 8 11 17 164 7 4 45 2 3 4 9 27 1 43 1 4 3 2 1 6 72 3 8 2 29 6 2 3 48 5 2 3 13 13 2 353 2 81 41 4 63 3 24 0 7 24 11 09 82 37 4 64 3 28 8 0 7 28 12 06 ...... 2 1 5 4 3 3 7 8 3 9 9 3 2 7 6 0 8 6 1 6 8 9 0 5 3 3 2 1 9 4 3 7 8 3 9 9 3 2 7 6 0 8 6 1 6 8 9 0 5 3 3 0 . . 0 . 6 0 5 . 0 . . 6 . 5 . . . . . 0 ...... 0 . . . . . 0 ...... 1 1 1 5 2 2 0 4 2 2 5 4 4 1 3 1 1 6 1 0 4 5 1 1 6 6 +0 − +0 − +6 − +0 − +5 − +0 − +6 − +5 − +0 − +0 − +0 − +1 − +1 − +1 − 5 8 +5 − +15 − +2 − 6 +0 − 8 +4 − +2 − +2 − +5 − +4 − +4 − +1 − +3 − +1 − +1 − +6 − +1 − +0 − +4 − +5 − +1 − +1 − +6 − +6 − . . . . 98 8 5 35 8 72 1 65 5 4 6 2 5 0 7 7 96 3 2 2 9 0 5 1 5 28 1 8 8 3 5 63 4 ...... vir c 4 4 4 2 8 10 3 12 8 4 4 2 12 0 12 6 4 3 8 3 2 7 2 5 0 5 6 3 0 1 3 5 0 2 7 0 9 26 84 26 27 . . . . ) (10 22 4 9 34 6 1 9 7 25 4 9 67 6 1 9 7 17 ...... 36 ......

04 3 0 27 47 02 3 0 56 66 . . . 5 . 7 ...... 2 4 9 3 2 7 6 1 3 7 7 3 3 3 3 7 9 6 4 7 0 6 6 4 9 3 2 7 6 1 3 7 7 3 3 3 3 7 9 6 4 7 0 6 +15 − +18 − M 1 2 1 . . . . 0 . 15 . 22 ...... 21 . . . 28 0 . . 15 11 ...... +4 − +5 − 1 2 0 1 4 0 0 2 2 1 0 5 1 5 1 1 1 1 2 2 2 1 +1 − +2 − +1 − 19 +0 − +15 − +22 − +21 − +28 − +0 − +15 − +11 − 15 . . 14 1 6 +1 − +2 − 96 +0 − +1 − +4 − 4 +0 − 1 +0 − +2 − +2 − +1 − +0 − +5 − 92 +1 − +5 − +1 − 4 +1 − +1 − +1 − 0 +2 − +2 − 1 7 +2 − +1 − ...... 200 57 8 0 4 0 79 8 6 6 0 3 3 9 9 3 3 0 3 3 4 67 1 4 6 7 ...... (10 7 M 10 15 143 6 4 40 2 3 3 8 24 1 34 1 4 3 2 0 5 64 3 7 2 25 6 2 3 39 4 2 3 11 12 2 293 2 71 36 55 8 21 5 2 21 1 08 72 32 56 8 25 0 5 2 25 11 05 ...... 1 9 4 8 9 0 1 6 4 1 6 4 9 9 5 3 9 7 1 0 5 4 5 9 4 9 9 1 9 7 8 9 1 6 4 1 6 4 9 9 5 3 9 7 1 0 5 4 5 9 4 9 9 0 . . 0 . . 0 4 . 0 . . 5 . 5 . . . . . 0 ...... 0 . . . . . 0 ...... 1 0 1 5 2 2 0 4 2 2 5 3 3 1 3 0 1 6 1 0 4 5 0 1 5 5 4 +0 − +0 − +0 − +4 − +0 − +5 − +5 − +0 − +0 − +0 − +1 − +0 − +1 − +5 − 5 +4 − +14 − +2 − 4 +0 − 6 +4 − +2 − +2 − +5 − +3 − +3 − +1 − +3 − +0 − +1 − +6 − +1 − +0 − +4 − +5 − +0 − +1 − +5 − +5 − . . . 38 3 0 04 9 4 27 3 12 0 1 5 6 0 7 9 3 64 6 0 7 8 6 9 8 4 14 8 3 7 1 9 55 7 ...... 200 Method c Continued . Table A-1 – ClusterRCSJ1620.2+2929 0.87 z 16 20 12.0 +29 29 RA 00 X-ray Dec 4 CLJ 1226.9+3332 0.89 12 26 58.0 +33 32 54 WL 4 CLJ 1226.9+3332 0.89 12 26 58.0 +33 32 54 WL+SL 4 CLJ 1226.9+3332 0.89 12 26 58.0 +33 32 54 X-ray 2 CLJ 1226.9+3332 0.89 12 26 58.0 +33 32 54 X-ray 7 CLJ1604+4304 0.9 16 04 25.1 +43 04 53 WL 9 RCS J2319.8+0038 0.904 23 19 53.3 +00 38 13 X-ray 3 RCS J2319.8+0038 0.904 23 19 53.3 +00 38 13 WL 11 RCSJ0439-2904 0.951 04 39 38.0 -29 04 55 WL 7 RCSJ0439-2904 0.951 04 39 38.0 -29 04 55 X-ray 4 XMMU J1230.3+1339 0.97 12 30 17.0 +13 39 01 WL 4 XMMU J1230.3+1339 0.97 12 30 17.0 +13 39 01 WL 2 RCS J1511.0+0903 0.97 15 11 03.8 +09 03 15 WL 11 XMMU J1229.4+0151 0.98 12 29 28.8 +01 51 34 WL 0 RCS 0221-0321 1.02 02 21 41 -03 21 47 WL 11 RCS J0220.9-0333 1.03 02 20 55.7 -03 33 10 WL 5 WARP J1415.1+3612 1.03 14 15 11.1 +36 12 03 WL 4 RCS J2345-3632 1.04 23 45 27.3 -36 32 50 WL 2 RCS J2156.7-0448 1.07 21 56 42.1 -04 48 04 WL 7 RCS J0337-2844 1.1 03 37 50.4 -28 44 28 WL 3 RXJ0910.7+5422 1.11 09 10 45.0 +54 22 08 X-ray 2 RXJ0910.7+5422 1.11 09 10 45.0 +54 22 08 WL 6 ISCS J1432.4+3332 1.11 14 32 29.1 +33 32 48 WL 2 XMMU J2205.8-0159 1.12 22 05 50.2 -01 59 29 WL 4 XLSS J0223-0436 1.22 02 23 03 -04 36 18 WL 0 RDCS J1252-2927 1.24 12 52 54.4 -29 27 17 WL 4 ISCS J1434.5+3427 1.24 14 34 28.5 +34 26 22 WL 5 RDCS J0849+4452 1.26 08 48 56.2 +44 52 00 WL 2 ISCS J1429.3+3437 1.26 14 29 18.5 +34 37 25 WL 0 RXJ0849+4452 1.26 08 53 43.6 +35 45 53.8 X-ray 1 RDCS J0848+4453 1.27 08 48 34.2 +44 53 35 WL 2 ISCS J1432.6+3436 1.36 14 32 38.3 +34 36 49 WL 5 ISCS J1434.7+3519 1.37 14 34 46.3 +35 19 45 WL 0 XMMU J2235.3-2557 1.39 22 35 20.6 -25 57 42 WL 2 ISCS J1438.1+3414 1.41 14 38 09.5 +34 14 19 WL 6 ISCS J1438.1+3414 1.41 14 38 09.5 +34 14 19 X-ray 0 XMMXCS J2215.9-1738 1.45 22 15 58.5 -17 38 02 WL 8

c 0000 RAS, MNRAS 000, 000–000 The Galaxy Cluster Concentration-Mass Scaling Relation 33

Table A-2: A Summary of The References

Reference # Measurements # Clusters (Unique) Method(s) Babyk et al. (2014) 128 128 X-ray Sereno et al. (2014) 109 104 WL Rines & Diaferio (2006) 72 72 CM Oguri et al. (2012) 56 28 WL+SL, WL Ettori et al. (2011) 44 44 X-ray Wojtak &Lokas (2010) 41 41 LOSVD Schmidt & Allen (2007) 31 31 X-ray Okabe et al. (2010) 26 26 WL Xu et al. (2001) 22 22 X-ray Abdullah et al. (2011) 20 20 LOSVD Merten et al. (2014) 19 19 WL+SL Gastaldello et al. (2007a) 16 16 X-ray Molikawa et al. (1999) 13 13 X-ray Voigt & Fabian (2006) 12 12 X-ray Vikhlinin et al. (2006) 12 12 X-ray Oguri et al. (2009) 12 4 WL+SL, SL, WL Bardeau et al. (2007) 11 11 WL Pointecouteau et al. (2005) 10 10 X-ray Allen et al. (2003) 10 10 X-ray Rines et al. (2003) 9 9 CM Okabe & Umetsu (2008) 9 9 WL Lokas et al. (2006) 6 6 LOSVD Umetsu et al. (2011b) 5 5 WL Comerford & Natarajan (2007) 5 5 SL Umetsu et al. (2009) 4 4 WL Umetsu et al. (2015) 3 1 WL+SL, SL, WL Pratt & Arnaud (2005) 3 3 X-ray Halkola et al. (2006) 3 1 WL+SL, SL, WL Corless et al. (2009) 3 3 WL Clowe (2003) 3 3 WL Clowe & Schneider (2001a) 3 3 WL Zitrin et al. (2010) 2 1 WL+SL, WL Umetsu & Broadhurst (2008) 2 1 WL+SL, WL Okabe et al. (2015) 2 2 WL Markevitch et al. (1999) 2 2 X-ray Gavazzi (2005) 2 1 WL+SL, SL Gavazzi et al. (2003) 2 1 SL, WL Donnarumma et al. (2009) 2 1 X-ray, SL D´emocl`eset al. (2010) 2 2 X-ray Clowe & Schneider (2002) 2 2 WL Buckley-Geer et al. (2011) 2 1 WL+SL, WL Biviano et al. (2013) 2 1 CM, LOSVD Zitrin et al. (2011) 1 1 WL+SL Zekser et al. (2006) 1 1 SL Williams & Saha (2004) 1 1 SL Wang et al. (2005) 1 1 X-ray Schirmer et al. (2010) 1 1 WL Pointecouteau et al. (2004) 1 1 X-ray Paulin-Henriksson et al. (2007) 1 1 WL Okabe et al. (2014) 1 1 WL Okabe et al. (2011) 1 1 WL Oguri et al. (2013) 1 1 WL+SL Medezinski et al. (2007) 1 1 WL McLaughlin (1999) 1 1 X-ray Maughan et al. (2007) 1 1 X-ray Lokas & Mamon (2003) 1 1 LOSVD Limousin et al. (2007) 1 1 WL+SL Lerchster et al. (2011) 1 1 WL Continued on next page

c 0000 RAS, MNRAS 000, 000–000 34 Groener, Goldberg, & Sereno

Table A-2 – Continued from previous page Reference # Measurements # Clusters (Unique) Method(s) Lewis et al. (2003) 1 1 X-ray Kubo et al. (2007) 1 1 WL Kneib et al. (2003) 1 1 WL+SL Kling et al. (2005) 1 1 WL King et al. (2002) 1 1 WL Khosroshahi et al. (2006) 1 1 X-ray Kelson et al. (2002) 1 1 LOSVD Israel et al. (2010) 1 1 WL Gruen et al. (2013) 1 1 WL Gavazzi et al. (2009) 1 1 WL Gastaldello et al. (2008) 1 1 X-ray Gastaldello et al. (2007b) 1 1 X-ray Gavazzi (2002) 1 1 SL Eichner et al. (2013) 1 1 SL David et al. (2001) 1 1 X-ray Coe et al. (2010) 1 1 SL Clowe & Schneider (2001b) 1 1 WL Buote et al. (2005) 1 1 X-ray Buote & Lewis (2004) 1 1 X-ray Broadhurst et al. (2005b) 1 1 SL Broadhurst et al. (2005a) 1 1 WL Bardeau et al. (2005) 1 1 WL Andersson & Madejski (2004) 1 1 X-ray

c 0000 RAS, MNRAS 000, 000–000