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We compare X-ray and caustic mass profiles for a sample of 16 massive galaxy clusters. We assume hydrostatic equilibrium in interpreting the X-ray data, and use large samples of cluster members with redshifts as a basis for applying the caustic technique. The hydrostatic and caustic masses agree to better than $approx20%$ on average across the radial range covered by both techniques $(sim[0.2-1.25]R_{500})$. The mass profiles were measured independently and do not assume a common functional form. Previous studies suggest that, at $R_{500}$, the hydrostatic and caustic masses are biased low and high respectively. We find that the ratio of hydrostatic to caustic mass at $R_{500}$ is $1.20^{+0.13}_{-0.11}$; thus it is larger than 0.9 at $approx3sigma$ and the combination of under- and over-estimation of the mass by these two techniques is $approx10%$ at most. There is no indication of any dependence of the mass ratio on the X-ray morphology of the clusters, indicating that the hydrostatic masses are not strongly systematically affected by the dynamical state of the clusters. Overall, our results favour a small value of the so-called hydrostatic bias due to non-thermal pressure sources.
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We present the reconstruction of hydrostatic mass profiles in 13 X-ray luminous galaxy clusters that have been mapped in their X-ray and SZ signal out to $R_{200}$ for the XMM-Newton Cluster Outskirts Project (X-COP). Using profiles of the gas temperature, density and pressure that have been spatially resolved out to (median value) 0.9 $R_{500}$, 1.8 $R_{500}$, and 2.3 $R_{500}$, respectively, we are able to recover the hydrostatic gravitating mass profile with several methods and using different mass models. The hydrostatic masses are recovered with a relative (statistical) median error of 3% at $R_{500}$ and 6% at $R_{200}$. By using several different methods to solve the equation of the hydrostatic equilibrium, we evaluate some of the systematic uncertainties to be of the order of 5% at both $R_{500}$ and $R_{200}$. A Navarro-Frenk-White profile provides the best-fit in nine cases out of 13, with the remaining four cases that do not show a statistically significant tension with it. The distribution of the mass concentration follows the correlations with the total mass predicted from numerical simulations with a scatter of 0.18 dex, with an intrinsic scatter on the hydrostatic masses of 0.15 dex. We compare them with the estimates of the total gravitational mass obtained through X-ray scaling relations applied to $Y_X$, gas fraction and $Y_{SZ}$, and from weak lensing and galaxy dynamics techniques, and measure a substantial agreement with the results from scaling laws, from WL at both $R_{500}$ and $R_{200}$ (with differences below 15%), from cluster velocity dispersions, but a significant tension with the caustic masses that tend to underestimate the hydrostatic masses by 40% at $R_{200}$. We also compare these measurements with predictions from alternative models to the Cold Dark Matter, like the Emergent Gravity and MOND scenarios.
We review the methods adopted to reconstruct the mass profiles in X-ray luminous galaxy clusters. We discuss the limitations and the biases affecting these measurements and how these mass profiles can be used as cosmological proxies.
We analyse Chandra X-ray Observatory observations of a set of galaxy clusters selected by the South Pole Telescope using a new publicly-available forward-modelling projection code, MBProj2, assuming hydrostatic equilibrium. By fitting a powerlaw plus constant entropy model we find no evidence for a central entropy floor in the lowest-entropy systems. A model of the underlying central entropy distribution shows a narrow peak close to zero entropy which accounts for 60 per cent of the systems, and a second broader peak around 130 keV cm^2. We look for evolution over the 0.28 to 1.2 redshift range of the sample in density, pressure, entropy and cooling time at 0.015 R_500 and at 10 kpc radius. By modelling the evolution of the central quantities with a simple model, we find no evidence for a non-zero slope with redshift. In addition, a non-parametric sliding median shows no significant change. The fraction of cool-core clusters with central cooling times below 2 Gyr is consistent above and below z=0.6 (~30-40 per cent). Both by comparing the median thermodynamic profiles, centrally biased towards cool cores, in two redshift bins, and by modelling the evolution of the unbiased average profile as a function of redshift, we find no significant evolution beyond self-similar scaling in any of our examined quantities. Our average modelled radial density, entropy and cooling-time profiles appear as powerlaws with breaks around 0.2 R_500. The dispersion in these quantities rises inwards of this radius to around 0.4 dex, although some of this scatter can be fit by a bimodal model.
The distribution of mass in the halos of galaxies and galaxy clusters has been probed observationally, theoretically, and in numerical simulations. Yet there is still confusion about which of several suggested parameterized models is the better representation, and whether these models are universal. We use the temperature and density profiles of the intracluster medium as measured by X-ray observations of 11 relaxed galaxy clusters to investigate mass models for the halo using a thorough Bayesian statistical analysis. We make careful comparisons between two- and three-parameter models, including the issue of a universal third parameter. We find that, of the two-parameter models, the NFW is the best representation, but we also find moderate statistical evidence that a generalized three-parameter NFW model with a freely varying inner slope is preferred, despite penalizing against the extra degree of freedom. There is a strong indication that this inner slope needs to be determined for each cluster individually, i.e. some clusters have central cores and others have steep cusps. The mass-concentration relation of our sample is in reasonable agreement with predictions based on numerical simulations.
We test the assumption of hydrostatic equilibrium in an X-ray luminosity selected sample of 50 galaxy clusters at $0.15<z<0.3$ from the Local Cluster Substructure Survey (LoCuSS). Our weak-lensing measurements of $M_{500}$ control systematic biases to sub-4 per cent, and our hydrostatic measurements of the same achieve excellent agreement between XMM-Newton and Chandra. The mean ratio of X-ray to lensing mass for these 50 clusters is $beta_{rm X}=0.95pm0.05$, and for the 44 clusters also detected by Planck, the mean ratio of Planck mass estimate to LoCuSS lensing mass is $beta_{rm P}=0.95pm0.04$. Based on a careful like-for-like analysis, we find that LoCuSS, the Canadian Cluster Comparison Project (CCCP), and Weighing the Giants (WtG) agree on $beta_{rm P}simeq0.9-0.95$ at $0.15<z<0.3$. This small level of hydrostatic bias disagrees at $sim5sigma$ with the level required to reconcile Planck cosmology results from the cosmic microwave background and galaxy cluster counts.
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