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Register a new userA detailed statistical analysis of the mass profiles of galaxy clusters
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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.
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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 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.
Many galaxy clusters host Mpc scale diffuse radio sources called radio halos. Their origin is connected to the processes that lead to the formation of clusters themselves. In order to unveil this connection, statistical studies of radio halos are necessary. We selected a sample of galaxy clusters with M500>6e14Msun and z=0.08-0.33 from the Planck SZ catalogue. In paper I, we presented the radio and X-ray data analysis that we carried out on these clusters. Here, we study the radio properties of the sample, in connection to the mass and dynamical state of clusters. We used the dynamical information derived from the X-ray data to assess the role of mergers in the origin of radio halos. We studied the distribution of clusters in the radio power-mass diagram and the role of dynamics on the radio luminosity and emissivity of radio halos. We measured the occurrence of radio halos as a function of the cluster mass and we compared it with the expectations of turbulent acceleration models. We found that more than the 90% of radio halos are in merging clusters and that their radio power correlates with the mass of the host clusters. The correlation shows a large dispersion. Interestingly, we showed that cluster dynamics contributes significantly to this dispersion with more disturbed clusters being more radio luminous. Clusters without radio halos are generally relaxed and the upper limits to their diffuse emission lie below the correlation. We showed that the radio emissivity of clusters exhibits an apparent bimodality, with the emissivity of radio halos being at least 5 times larger than the non-emission associated with more relaxed clusters. We found that the fraction of radio halos drops from ~70% in high mass clusters to ~35% in the lower mass systems of the sample and we showed that this result is in good agreement with the expectations from turbulent re-acceleration models.
We jointly analyze Bolocam Sunyaev-Zeldovich (SZ) effect and Chandra X-ray data for a set of 45 clusters to derive gas density and temperature profiles without using spectroscopic information. The sample spans the mass and redshift range $3 times 10^{14} M_{odot} le M_{500} le 25 times 10^{14} M_{odot}$ and $0.15le z le 0.89$. We define cool-core (CC) and non-cool core (NCC) subsamples based on the central X-ray luminosity, and 17/45 clusters are classified as CC. In general, the profiles derived from our analysis are found to be in good agreement with previous analyses, and profile constraints beyond $r_{500}$ are obtained for 34/45 clusters. In approximately 30% of the CC clusters our analysis shows a central temperature drop with a statistical significance of $>3sigma$; this modest detection fraction is due mainly to a combination of coarse angular resolution and modest S/N in the SZ data. Most clusters are consistent with an isothermal profile at the largest radii near $r_{500}$, although 9/45 show a significant temperature decrease with increasing radius. The sample mean density profile is in good agreement with previous studies, and shows a minimum intrinsic scatter of approximately 10% near $0.5 times r_{500}$. The sample mean temperature profile is consistent with isothermal, and has an intrinsic scatter of approximately 50% independent of radius. This scatter is significantly higher compared to earlier X-ray-only studies, which find intrinsic scatters near 10%, likely due to a combination of unaccounted for non-idealities in the SZ noise, projection effects, and sample selection.
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.
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