The relation between mass and concentration in X-ray galaxy clusters at high redshift

Galaxy clusters are the most recent, gravitationally-bound products of the hierarchical mass accretion over cosmological scales. How the mass is concentrated is predicted to correlate with the total mass in the clusters halo, with systems at higher mass being less concentrated at given redshift and for any given mass, systems with lower concentration are found at higher redshifts. Through a spatial and spectral X-ray analysis, we reconstruct the total mass profile of 47 galaxy clusters observed with Chandra in the redshift range $0.4<z<1.2$, selected to have no major mergers, to investigate the relation between the mass and the dark matter concentration, and the evolution of this relation with redshift. The sample in exam is the largest one investigated so far at $z>0.4$, and is well suited to provide the first constraint on the concentration--mass relation at $z>0.7$ from X-ray analysis. Under the assumptions that the distribution of the X-ray emitting gas is spherically symmetric and in hydrostatic equilibrium, we combine the deprojected gas density and spectral temperature profiles through the hydrostatic equilibrium equation to recover the parameters that describe a NFW total mass distribution. The comparison with results from weak lensing analysis reveals a very good agreement both for masses and concentrations. Uncertainties are however too large to make any robust conclusion on the hydrostatic bias of these systems. The relation is well described by the form $c propto M^B (1+z)^C$, with $B=-0.50 pm 0.20$, $C=0.12 pm 0.61$ (at 68.3% confidence), it is slightly steeper than the one predicted by numerical simulations ($Bsim-0.1$) and does not show any evident redshift evolution. We obtain the first constraints on the properties of the concentration--mass relation at $z > 0.7$ from X-ray data, showing a reasonable good agreement with recent numerical predictions.

Mass profiles and concentration-dark matter relation in X-ray luminous galaxy clusters

(Abriged) Assuming that the hydrostatic equilibrium holds between the intracluster medium and the gravitational potential, we constrain the NFW profiles in a sample of 44 X-ray luminous galaxy clusters observed with XMM-Newton in the redshift range 0.1-0.3. We evaluate several systematic uncertainties that affect our reconstruction of the X-ray masses. We measure the concentration c200, the dark mass M200 and the gas mass fraction within R500 in all the objects of our sample, providing the largest dataset of mass parameters for galaxy clusters in this redshift range. We confirm that a tight correlation between c200 and M200 is present and in good agreement with the predictions from numerical simulations and previous observations. When we consider a subsample of relaxed clusters that host a Low-Entropy-Core (LEC), we measure a flatter c-M relation with a total scatter that is lower by 40 per cent. From the distribution of the estimates of c200 and M200, with associated statistical (15-25%) and systematic (5-15%) errors, we use the predicted values from semi-analytic prescriptions calibrated through N-body numerical runs and measure sigma_8*Omega_m^(0.60+-0.03)= 0.45+-0.01 (at 2 sigma level, statistical only) for the subsample of the clusters where the mass reconstruction has been obtained more robustly, and sigma_8*Omega_m^(0.56+-0.04) = 0.39+-0.02 for the subsample of the 11 more relaxed LEC objects. With the further constraint from the fgas distribution in our sample, we break the degeneracy in the sigma_8-Omega_m plane and obtain the best-fit values sigma_8~1.0+-0.2 (0.75+-0.18 when the subsample of the more relaxed objects is considered) and Omega_m = 0.26+-0.01.

Halo Mass-Concentration Relation at High-Mass End

The concentration-mass (c-M) relation encodes the key information of the assembly history of the dark matter halos, however its behavior at the high mass end has not been measured precisely in observations yet. In this paper, we report the measurement of halo c-M relation with galaxy-galaxy lensing method, using shear catalog of the Dark Energy Camera Legacy Survey (DECaLS) Data Release 8, which covers a sky area of 9500 deg^2. The foreground lenses are selected from redMaPPer, LOWZ, and CMASS catalogs, with halo mass range from 10^{13} to 10^{15} M_sun and redshift range from z=0.08 to z=0.65. We find that the concentration decreases with the halo mass from 10^{13} to 10^{14} M_sun, but shows a trend of upturn after the pivot point of ~10^{14} M_sun. We fit the measured c-M relation with the concentration model c(M)=C_0 (M/(10^{12} M_sun/h)^{-gamma} [1+(M/M_0)^{0.4}], and get the values (C_0, gamma, log(M_0) = (5.119_{-0.185}^{0.183}, 0.205_{-0.010}^{0.010}, 14.083_{-0.133}^{0.130}), and (4.875_{-0.208}^{0.209}, 0.221_{-0.010}^{0.010}, 13.750_{-0.141}^{0.142}) for halos with 0.08<=z<0.35 and 0.35<=z<0.65, respectively. We also show that the model including an upturn is favored over a simple power-law model. Our measurement provides important information for the recent argument of massive cluster formation process.

CLASH: The Concentration-Mass Relation of Galaxy Clusters

We present a new determination of the concentration-mass relation for galaxy clusters based on our comprehensive lensing analysis of 19 X-ray selected galaxy clusters from the Cluster Lensing and Supernova Survey with Hubble (CLASH). Our sample spans a redshift range between 0.19 and 0.89. We combine weak lensing constraints from the Hubble Space Telescope (HST) and from ground-based wide field data with strong lensing constraints from HST. The result are reconstructions of the surface-mass density for all CLASH clusters on multi-scale grids. Our derivation of NFW parameters yields virial masses between 0.53 x 10^15 and 1.76 x 10^15 M_sol/h and the halo concentrations are distributed around c_200c ~ 3.7 with a 1-sigma significant negative trend with cluster mass. We find an excellent 4% agreement between our measured concentrations and the expectation from numerical simulations after accounting for the CLASH selection function based on X-ray morphology. The simulations are analyzed in 2D to account for possible biases in the lensing reconstructions due to projection effects. The theoretical concentration-mass (c-M) relation from our X-ray selected set of simulated clusters and the c-M relation derived directly from the CLASH data agree at the 90% confidence level.

The MUSIC of CLASH: predictions on the concentration-mass relation

We present the results of a numerical study based on the analysis of the MUSIC-2 simulations, aimed at estimating the expected concentration-mass relation for the CLASH cluster sample. We study nearly 1400 halos simulated at high spatial and mass resolution, which were projected along many lines-of-sight each. We study the shape of both their density and surface-density profiles and fit them with a variety of radial functions, including the Navarro-Frenk-White, the generalised Navarro-Frenk-White, and the Einasto density profiles. We derive concentrations and masses from these fits and investigate their distributions as a function of redshift and halo relaxation. We use the X-ray image simulator X-MAS to produce simulated Chandra observations of the halos and we use them to identify objects resembling the X-ray morphologies and masses of the clusters in the CLASH X-ray selected sample. We also derive a concentration-mass relation for strong-lensing clusters. We find that the sample of simulated halos which resemble the X-ray morphology of the CLASH clusters is composed mainly by relaxed halos, but it also contains a significant fraction of un-relaxed systems. For such a sample we measure an average 2D concentration which is ~11% higher than found for the full sample of simulated halos. After accounting for projection and selection effects, the average NFW concentrations of CLASH clusters are expected to be intermediate between those predicted in 3D for relaxed and super-relaxed halos. Matching the simulations to the individual CLASH clusters on the basis of the X-ray morphology, we expect that the NFW concentrations recovered from the lensing analysis of the CLASH clusters are in the range [3-6], with an average value of 3.87 and a standard deviation of 0.61. Simulated halos with X-ray morphologies similar to those of the CLASH clusters are affected by a modest orientation bias.