Galaxy Cluster Scaling Relations Research Articles

The physics inside the scaling relations for X-ray galaxy clusters: gas clumpiness, gas mass fraction and slope of the pressure profile

In galaxy clusters, the relations between observables in X-ray and millimetre wave bands and the total mass have normalizations, slopes and redshift evolutions that are simple to estimate in a self-similar scenario. We study these scaling relations and show that they can be efficiently expressed, in a more coherent picture, by fixing the normalizations and slopes to the self-similar predictions, and advocating, as responsible of the observed deviations, only three physical mass-dependent quantities: the gas clumpiness C, the gas mass fraction fg and the logarithmic slope of the thermal pressure profile βP. We use samples of the observed gas masses, temperature, luminosities and Compton parameters in local clusters to constrain normalization and mass dependence of these three physical quantities, and measure C0.5fg = 0.110( ± 0.002 ± 0.002)(EzM/5 × 1014 M⊙)0.198( ± 0.025 ± 0.04) and βP = −dln P/dln r = 3.14( ± 0.04 ± 0.02)(EzM/5 × 1014 M⊙)0.071( ± 0.012 ± 0.004), where both a statistical and systematic error (the latter mainly due to the cross-calibration uncertainties affecting the Chandra and XMM–Newton results used in the present analysis) are quoted. The degeneracy between C and fg is broken by using the estimates of the Compton parameters. Together with the self-similar predictions, these estimates on C, fg and βP define an intercorrelated internally consistent set of scaling relations that reproduces the mass estimates with the lowest residuals.

Initial conditions for idealized clusters mergers, simulating ‘El Gordo’

Simulations of isolated binary mergers of galaxy clusters are a useful tool to study the evolution of these objects. For exceptionally massive systems, they even represent the only viable way of simulation, because these are rare in typical cosmological simulations. We present a new practical model for these simulations based on the Hernquist dark matter profile. The hydrostatic equation is solved for a beta-model with β = 2/3 in this potential and approximate expressions for X-ray brightness and Compton-y parameter are derived. We show in detail how to setup such a system using smoothed particle hydrodynamics. The theoretical and several numerical models are compared to observed scaling relations of galaxy clusters and satisfactory agreement with the self-similar relations is found. The model is then applied to investigate the observed cluster ACT-CT J0102−4915 ‘El Gordo’, a particularly massive merging high-redshift cluster. We are able to reproduce the X-ray luminosity, Sunyaev–Zeldovich effect and dark matter core distance as well as the rough shape of the observed cluster for reasonable model parameters. The lack of sub-structure prevents us from obtaining the fluctuations observed in the wake of the system and we argue that the parent cluster of the system was highly disturbed even before the main merger observed today.

PICACS: self-consistent modelling of galaxy cluster scaling relations

In this paper, we introduce PICACS, a physically-motivated, internally consistent model of scaling relations between galaxy cluster masses and their observable properties. This model can be used to constrain simultaneously the form, scatter (including its covariance) and evolution of the scaling relations, as well as the masses of the individual clusters. In this framework, scaling relations between observables (such as that between X-ray luminosity and temperature) are modelled explicitly in terms of the fundamental mass-observable scaling relations, and so are fully constrained without being fit directly. We apply the PICACS model to two observational datasets, and show that it performs as well as traditional regression methods for simply measuring individual scaling relation parameters, but reveals additional information on the processes that shape the relations while providing self-consistent mass constraints. Our analysis suggests that the observed combination of slopes of the scaling relations can be described by a deficit of gas in low-mass clusters that is compensated for by elevated gas temperatures, such that the total thermal energy of the gas in a cluster of given mass remains close to self-similar expectations. This is interpreted as the result of AGN feedback removing low entropy gas from low mass systems, while heating the remaining gas. We deconstruct the luminosity-temperature (LT) relation and show that its steepening compared to self-similar expectations can be explained solely by this combination of gas depletion and heating in low mass systems, without any additional contribution from a mass dependence of the gas structure. Finally, we demonstrate that a self-consistent analysis of the scaling relations leads to an expectation of self-similar evolution of the LT relation that is significantly weaker than is commonly assumed.

The generalized scaling relations for X-ray galaxy clusters: the most powerful mass proxy

The application to observational data of the generalized scaling relations (gSR) presented in Ettori et al. (2012) is here discussed. We extend further the formalism of the gSR in the self-similar model for X-ray galaxy clusters, showing that for a generic relation M_tot ~ L^a M_g^b T^c, where L, M_g and T are the gas luminosity, mass and temperature, respectively, the values of the slopes lay in the plane 4*a+3*b+2*c=3. Using published dataset, we show that some projections of the gSR are the most efficient relations, holding among observed physical X-ray quantities, to recover the cluster mass. This conclusion is based on the evidence that they provide the lowest chi^2, the lowest total scatter and the lowest intrinsic scatter among the studied scaling laws on both galaxy group and cluster mass scales. By the application of the gSR, the intrinsic scatter is reduced in all the cases down to a relative error on M_tot below 16 per cent. The best-fit relations are: M_tot ~ M_g^a T^{1.5-1.5a}, with a~0.4, and M_tot ~ L^a T^{1.5-2a}, with a~0.15. As a by product of this study, we provide the estimates of the gravitating mass at Delta=500 for 120 objects (50 from the Mahdavi et al. 2013 sample, 16 from Maughan 2012; 31 from Pratt et al. 2009; 23 from Sun et al. 2009), 114 of which are unique entries. The typical relative error in the mass provided from the gSR only (i.e. not propagating any uncertainty associated with the observed quantities) ranges between 3-5 per cent on cluster scale and is about 10 per cent for galaxy groups. With respect to the hydrostatic values used to calibrate the gSR, the masses are recovered with deviations in the order of 10 per cent due to the different mix of relaxed/disturbed objects present in the considered samples. In the extreme case of a gSR calibrated with relaxed systems, the hydrostatic mass in disturbed objects is over-estimated by about 20 per cent.

Constructing mock catalogues for the REFLEX II galaxy cluster sample

We describe the construction of a suite of galaxy cluster mock catalogues from N-body simulations, based on the properties of the new ROSAT–ESO Flux Limited X-Ray (REFLEX II) galaxy cluster catalogue. Our procedure is based on the measurements of the cluster abundance, and involves the calibration of the underlying scaling relation linking the mass of dark matter haloes to the cluster X-ray luminosity determined in the ROSAT energy band 0.1–2.4keV. In order to reproduce the observed abundance in the luminosity range probed by the REFLEX II X-ray luminosity function [0.01 < LX/(1044ergs−1h−2) < 10], a mass–X-ray luminosity relation deviating from a simple power law is required. We discuss the dependence of the calibration of this scaling relation on the X-ray luminosity and the definition of halo masses and analyse the one- and two-point statistical properties of the mock catalogues. Our set of mock catalogues provides samples with self-calibrated scaling relations of galaxy clusters together with inherent properties of flux-limited surveys. This makes them a useful tool to explore different systematic effects and statistical methods involved in constraining both astrophysical and cosmological information from present and future galaxy cluster surveys.

The X-ray cluster survey with : forecasts for cosmology, cluster physics and primordial non-Gaussianity

Starting in late 2013, the telescope will survey the X-ray sky with unprecedented sensitivity. Assuming a detection limit of 50 photons in the (0.5–2.0) keV energy band with a typical exposure time of 1.6 ks, we predict that will detect ∼9.3 × 104 clusters of galaxies more massive than 5 × 1013 h−1 M⊙, with the currently planned all-sky survey. Their median redshift will be z≃ 0.35. We perform a Fisher-matrix analysis to forecast the constraining power of on the Λ cold dark matter (ΛCDM) cosmology and, simultaneously, on the X-ray scaling relations for galaxy clusters. Special attention is devoted to the possibility of detecting primordial non-Gaussianity. We consider two experimental probes: the number counts and the angular clustering of a photon-count limited sample of clusters. We discuss how the cluster sample should be split to optimize the analysis and we show that redshift information of the individual clusters is vital to break the strong degeneracies among the model parameters. For example, performing a ‘tomographic’ analysis based on photometric-redshift estimates and combining one- and two-point statistics will give marginal 1σ errors of Δσ8≃ 0.036 and ΔΩm≃ 0.012 without priors, and improve the current estimates on the slope of the luminosity–mass relation by a factor of 3. Regarding primordial non-Gaussianity, clusters alone will give ΔfNL≃ 9, 36 and 144 for the local, orthogonal and equilateral model, respectively. Measuring redshifts with spectroscopic accuracy would further tighten the constraints by nearly 40 per cent (barring fNL which displays smaller improvements). Finally, combining data with the analysis of temperature anisotropies in the cosmic microwave background by the Planck satellite should give sensational constraints on both the cosmology and the properties of the intracluster medium.

Pointing to the minimum scatter: the generalized scaling relations for galaxy clusters

We introduce a generalized scaling law, M_tot = 10^K A^a B^b, to look for the minimum scatter in reconstructing the total mass of hydrodynamically simulated X-ray galaxy clusters, given gas mass M_gas, luminosity L and temperature T. We find a locus in the plane of the logarithmic slopes $a$ and $b$ of the scaling relations where the scatter in mass is minimized. This locus corresponds to b_M = -3/2 a_M +3/2 and b_L = -2 a_L +3/2 for A=M_gas and L, respectively, and B=T. Along these axes, all the known scaling relations can be identified (at different levels of scatter), plus a new one defined as M_tot ~ (LT)^(1/2). Simple formula to evaluate the expected evolution with redshift in the self-similar scenario are provided. In this scenario, no evolution of the scaling relations is predicted for the cases (b_M=0, a_M=1) and (b_L=7/2, a_L=-1), respectively. Once the single quantities are normalized to the average values of the sample under considerations, the normalizations K corresponding to the region with minimum scatter are very close to zero. The combination of these relations allows to reduce the number of free parameters of the fitting function that relates X-ray observables to the total mass and includes the self-similar redshift evolution.

Planckearly results. X. Statistical analysis of Sunyaev-Zeldovich scaling relations for X-ray galaxy clusters

All-sky data from the Planck survey and the Meta-Catalogue of X-ray detected Clusters of galaxies (MCXC) are combined to investigate the relationship between the thermal Sunyaev-Zeldovich (SZ) signal and X-ray luminosity. The sample comprises ~ 1600 X-ray clusters with redshifts up to ~ 1 and spans a wide range in X-ray luminosity. The SZ signal is extracted for each object individually, and the statistical significance of the measurement is maximised by averaging the SZ signal in bins of X-ray luminosity, total mass, or redshift. The SZ signal is detected at very high significance over more than two decades in X-ray luminosity (10^43 erg/s < L_500 E(z)^-7/3 < 2 X 10^45 erg/s). The relation between intrinsic SZ signal and X-ray luminosity is investigated and the measured SZ signal is compared to values predicted from X-ray data. Planck measurements and X-ray based predictions are found to be in excellent agreement over the whole explored luminosity range. No significant deviation from standard evolution of the scaling relations is detected. For the first time the intrinsic scatter in the scaling relation between SZ signal and X-ray luminosity is measured and found to be consistent with the one in the luminosity -- mass relation from X-ray studies. There is no evidence of any deficit in SZ signal strength in Planck data relative to expectations from the X-ray properties of clusters, underlining the robustness and consistency of our overall view of intra-cluster medium properties.

Observational constraints on the redshift evolution of X-ray scaling relations of galaxy clusters out toz ~ 1.5

A precise understanding of the relations between observable X-ray properties of galaxy clusters and cluster mass is a vital part of the application of X-ray galaxy cluster surveys to test cosmological models. An understanding of how these relations evolve with redshift is just emerging from a number of observational data sets. The current literature provides a diverse and inhomogeneous picture of scaling relation evolution. We attempt to transform these results and the data on recently discovered distant clusters into an updated and consistent framework, and provide an overall view of scaling relation evolution. We study in particular the M-T, L_X-T, and M-L_X relation combining 14 published data sets supplemented with recently published data of distant clusters and new results from follow-up observations of the XMM-Newton Distant Cluster Project (XDCP). We find that the evolution of the M-T relation is consistent with the self-similar prediction, while the evolution of X-ray luminosity for a given temperature and mass for a given X-ray luminosity is slower than predicted. Our best fit results for the evolution factor E(z)^alpha are alpha = -1.04+-0.07 for the M-T relation, alpha = -0.23+0.12-0.62 for the L-T relation, and alpha = -0.93+0.62-0.12 for the M-L_X relation. We find that selection biases are the most likely reason for apparent inconsistencies between different published data sets. The new results provide the currently most robust calibration of high-redshift cluster mass estimates based on X-ray luminosity and temperature and help us to improve the prediction of the number of clusters to be found in future galaxy cluster X-ray surveys, such as eROSITA. The comparison of evolution results with hydrodynamical cosmological simulations suggests that early preheating of the intracluster medium provides the most suitable scenario to explain the observed evolution.

Testing for evolution in scaling relations of galaxy clusters: cross analysis between X-ray and SZ observations

We present predicted Sunyaev-Zeldovich (SZ) properties of known X-ray clusters of galaxies for which gas temperature measurements are available. The reference sample was compiled from the BAX database for X-ray clusters. The Sunyaev-Zeldovich signal is predicted according to two different scaling laws for the mass-temperature relation in clusters: a standard relation and an evolving relation that reproduces well the evolution of the X-ray temperature distribution function in a concordance cosmology. Using a Markov Chain Mote Carlo (MCMC) analysis we examine the values of the recovered parameters and their uncertainties. The evolving case can be clearly distinguished from the non-evolving case, showing that SZ measurements will indeed be efficient in constraining the thermal history of the intra-cluster gas. However, significant bias appears in the measured values of the evolution parameter for high SZ threshold owing to selection effects.

The effect of helium sedimentation on galaxy cluster masses and scaling relations

Recent theoretical studies predict that the inner regions of galaxy clusters may have an enhanced helium abundance due to sedimentation over the cluster lifetime. If sedimentation is not suppressed (e.g., by tangled magnetic fields), this may significantly affect the cluster mass estimates. We use Chandra X-ray observations of eight relaxed galaxy clusters to investigate the upper limits to the effect of helium sedimentation on the measurement of cluster masses and the best-fit slopes of the Y_X - M_500 and Y_X - M_2500 scaling relations. We calculated gas mass and total mass in two limiting cases: a uniform, un-enhanced abundance distribution and a radial distribution from numerical simulations of helium sedimentation on a timescale of 11 Gyrs. The assumed helium sedimentation model, on average, produces a negligible increase in the gas mass inferred within large radii (r < r500) (1.3 +/- 1.2 per cent) and a (10.2 +/- 5.5) per cent mean decrease in the total mass inferred within r < r500. Significantly stronger effects in the gas mass (10.5 +/- 0.8 per cent) and total mass (25.1 +/- 1.1 per cent) are seen at small radii owing to a larger variance in helium abundance in the inner region, r < 0.1 r500. We find that the slope of the Y_X -M_500 scaling relation is not significantly affected by helium sedimentation.

LoCuSS: comparison of observed X-ray and lensing galaxy cluster scaling relations with simulations (Corrigendum)

The article by Zhang et al. (2008, A&A, 482, 451) contains an error in Table A.1 in online material (p. 3). In preparing the final version of Table A.1, we inadvertently used the wrong conversion from degree to hh:mm:ss, with the result that the cluster coordinates were not correctly tabulated in Table A.1. We note that this does not affect any results in Zhang et al. (2008). Nevertheless, we regret this error and provide the actual cluster coordinates used in our analysis in Table A.1 in the following page.

HIFLUGCS: Galaxy cluster scaling relations between X-ray luminosity, gas mass, cluster radius, and velocity dispersion

We present relations between X-ray luminosity and velocity dispersion (L-sigma), X-ray luminosity and gas mass (L-Mgas), and cluster radius and velocity dispersion (r500-sigma) for 62 galaxy clusters in the HIFLUGCS, an X-ray flux-limited sample minimizing bias toward any cluster morphology. Our analysis in total is based on ~1.3Ms of clean X-ray XMM-Newton data and 13439 cluster member galaxies with redshifts. Cool cores are among the major contributors to the scatter in the L-sigma relation. When the cool-core-corrected X-ray luminosity is used the intrinsic scatter decreases to 0.27 dex. Even after the X-ray luminosity is corrected for the cool core, the scatter caused by the presence of cool cores dominates for the low-mass systems. The scatter caused by the non-cool-core clusters does not strongly depend on the mass range, and becomes dominant in the high-mass regime. The observed L-sigma relation agrees with the self-similar prediction, matches that of a simulated sample with AGN feedback disregarding six clusters with <45 cluster members with spectroscopic redshifts, and shows a common trend of increasing scatter toward the low-mass end, i.e., systems with sigma<500km/s. A comparison of observations with simulations indicates an AGN-feedback-driven impact in the low-mass regime. The best fits to the $L-M_{\rm gas}$ relations for the disturbed clusters and undisturbed clusters in the observational sample closely match those of the simulated samples with and without AGN feedback, respectively. This suggests that one main cause of the scatter is AGN activity providing feedback in different phases, e.g., during a feedback cycle. The slope and scatter in the observed r500-sigma relation is similar to that of the simulated sample with AGN feedback except for a small offset but still within the scatter.

χ2AND POISSONIAN DATA: BIASES EVEN IN THE HIGH-COUNT REGIME AND HOW TO AVOID THEM

We demonstrate that two approximations to the χ2 statistic as popularly employed by observational astronomers for fitting Poisson-distributed data can give rise to intrinsically biased model parameter estimates, even in the high-count regime, unless care is taken over the parameterization of the problem. For a small number of problems, previous studies have shown that the fractional bias introduced by these approximations is often small when the counts are high. However, we show that for a broad class of problem, unless the number of data bins is far smaller than , where Nc is the total number of counts in the data set, the bias will still likely be comparable to, or even exceed, the statistical error. Conversely, we find that fits using Cash's C-statistic give comparatively unbiased parameter estimates when the counts are high. Taking into account their well-known problems in the low-count regime, we conclude that these approximate χ2 methods should not routinely be used for fitting an arbitrary, parameterized model to Poisson-distributed data, irrespective of the number of counts per bin, and instead the C-statistic should be adopted. We discuss several practical aspects of using the C-statistic in modeling real data. We illustrate the bias for two specific problems—measuring the count rate from a light curve and obtaining the temperature of a thermal plasma from its X-ray spectrum measured with the Chandra X-ray observatory. In the context of X-ray astronomy, we argue the bias could give rise to systematically miscalibrated satellites and a ~5-10% shift in galaxy cluster scaling relations.

LoCuSS: comparison of observed X-ray and lensing galaxy cluster scaling relations with simulations

The Local Cluster Substructure Survey (LoCuSS, Smith et al.) is a systematic multi-wavelength survey of more than 100 X-ray luminous galaxy clusters in the redshift range 0.14-0.3 selected from the ROSAT All Sky Survey. We used data on 37 LoCuSS clusters from the XMM-Newton archive to investigate the global scaling relations of galaxy clusters. The scaling relations based solely on the X-ray data (S-T, S-Yx, P-Y x , M-T, M-Y x , M-Mg as , M gas -T, L-T, L-Y x , and L-M) obey empirical self-similarity and reveal no additional evolution beyond the large-scale structure growth. They also reveal up to 17 per cent segregation between all 37 clusters and non-cool core clusters. Weak lensing mass measurements are also available in the literature for 19 of the clusters with XMM-Newton data. The average of the weak lensing mass to X-ray based mass ratio is 1.09 ± 0.08, setting the limit of the non-thermal pressure support to 9 ± 8 per cent. The mean of the weak lensing mass to X-ray based mass ratio of these clusters is ∼1, indicating good agreement between X-ray and weak lensing masses for most clusters, although with 31-51 per cent scatter. The scatter in the mass-observable relations (M-Y x , M-Mg as , and M-T) is smaller using X-ray based masses than using weak lensing masses by a factor of 2. With the scaled radius defined by the Y x profile - r YX,X 500 , rY X,W1 500 , and r YX,Si 500 , we obtain lower scatter in the weak lensing mass based mass-observable relations, which means the origin of the scatter is M W1 and M X instead of Y x . The normalization of the M-Yx relation using X-ray mass estimates is lower than the one from simulations by up to 18-24 per cent at 3cr significance. This agrees with the M-Y x relation based on weak lensing masses, the normalization of the latter being ∼20 per cent lower than the one from simulations at ∼2σ significance. This difference between observations and simulations is also indicated in the M-M gas and M-T relations. Despite the large scatter in the comparison of X-ray to lensing, the agreement between these two completely independent observational methods is an important step towards controlling astrophysical and measurement systematics in cosmological scaling relations.

Effects of selection and covariance on X-ray scaling relations of galaxy clusters

Abstract We explore how the behaviour of galaxy cluster scaling relations are affected by flux-limited selection biases and intrinsic covariance among observable properties. Our models presume log-normal covariance between luminosity (L) and temperature (T) at fixed mass (M), centred on evolving, power-law mean relations as a function of host halo mass. Selection can mimic evolution; the L—M and L—T relations from shallow X-ray flux-limited samples will deviate from mass-limited expectations at nearly all scales while the relations from deep surveys (10−14 erg s−1 cm−2) become complete, and therefore unbiased, at masses above ∼2 × 1014h−1 M⊙. We derive expressions for low-order moments of the luminosity distribution at fixed temperature, and show that the slope and scatter of the L—T relation observed in flux-limited samples is sensitive to the assumed L—T correlation coefficient. In addition, L—T covariance affects the redshift behaviour of halo counts and mean luminosity in a manner that is nearly degenerate with intrinsic population evolution.

Adiabatic scaling relations of galaxy clusters

The aim of this work is to show that, contrary to popular belief, galaxy clusters are not expected to be self-similar, even when the only energy sources available are gravity and shock-wave heating. In particular, we investigate the scaling relations between mass, luminosity and temperature of galaxy groups and clusters in the absence of radiative processes. Theoretical expectations are derived from a polytropic model of the intracluster medium and compared with the results of high-resolution adiabatic gasdynamical simulations. It is shown that, in addition to the well-known relation between the mass and concentration of the dark matter halo, the effective polytropic index of the gas also varies systematically with cluster mass, and therefore neither the dark matter nor the gas profiles are exactly self-similar. It is remarkable, though, that the effects of concentration and polytropic index tend to cancel each other, leading to scaling relations whose logarithmic slopes roughly match the predictions of the most-basic self-similar models. We provide a phenomenological fit to the relation between polytropic index and concentration, as well as a self-consistent scheme to derive the non-linear scaling relations expected for any cosmology and the best-fitting normalizations of the M–T, L–T and F–T relations appropriate for a Λ cold dark matter universe. The predicted scaling relations reproduce observational data reasonably well for massive clusters, where the effects of cooling and star formation are expected to play a minor role.

Scaling relations for galaxy clusters

We use preliminary results of the WINGS survey (Fasano et al.) to obtain determinations of optical scaling relations for galaxy clusters. Passing from oneto twoparameter scaling relations we pay particular attention to the Kormendy relation (KR) and to the Fundamental Plane (FP) of galaxy clusters, comparing them with scaling relations of elliptical galaxies.

Are Clusters Standard Candles? Galaxy Cluster Scaling Relations with the Sunyaev‐Zeldovich Effect

An extensive sample of galaxy clusters will be available in the coming years, detected through their Sunyaev-Zeldovich effect (SZE). We use a semianalytic model to study the scientific yield of combining SZE data with X-ray and optical follow-up observations. If clusters at a given redshift z0 can be identified with virialized, spherical halos, they populate a well-defined fundamental plane (FP) in the parameter space of the three observables virial temperature (T), total Sunyaev-Zeldovich flux decrement (ΔSν), and angular size (θ). The location and orientation of the FP, as well as its redshift evolution, are sensitive to both the internal evolution of clusters and to the underlying cosmological parameters. We show that if clusters are not standard candles (e.g., because of feedback or energy injection), then this can be inferred from the FP. Likewise, we study the dependence of the FP on the cosmological parameters h, σ8, and Ω0, and quantify future constraints on these parameters. We also show that in the absence of any nongravitational effects, the scatter in the (ΔSν,T)-plane is significantly smaller than in either the (θ,T) or the (θ,ΔSν) planes. As a result, the ΔSν-T relation can be an exceptionally sensitive probe of both cluster physics and cosmological parameters. A comparison of the amount of scatter in these three scaling relations will test the origin (cosmological vs. stochastic) of the scatter.

The Mass‐Temperature Relation of 22 Nearby Clusters

We present a new investigation of the mass-temperature (Mtot-TX) relation of 22 nearby clusters based on the analysis of their ROSAT X-ray surface brightness profiles (SX ) and their ASCA emission-weighted temperatures. Two methods of the cluster mass estimations are employed and their results are compared: (1) the conventional β-model for gas distribution along with the isothermal and hydrostatic equilibrium assumptions, and (2) the NFW profile for dark matter distribution whose characteristic density and length are determined by the observed SX(r). These two models yield essentially the same goodness of fits for SX(r) and the similar Mtot-TX relations, with the latter demonstrating a significant departure from the simple gravitational scaling of Mtot ∝ T. It is also shown that the best-fit Mtot-TX relations could be reconciled with the theoretical expectation if the low-temperature clusters (TX < 3.5 keV) are excluded from the list, which lends support to the scenario that the intracluster medium is preheated in the early phase of cluster formation. Together with the entropy-temperature distribution, the existence of a similarity break at TX = 3-4 keV in the dynamical scaling relations for galaxy clusters has been confirmed.