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

Context. 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 halo of the cluster, wherein systems at higher mass are less concentrated at given redshift and, for any given mass, systems with lower concentration are found at higher redshifts. Aims. 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, which we selected to exclude major mergers, to investigate the relation between the mass and dark matter concentration and the evolution of this relation with redshift. This sample is the largest investigated so far at z> 0.4, and is well suited to providing the first constraint on the concentration-mass relation at z> 0.7 from X-ray analysis. Methods. Under the assumption that the distribution of the X-ray emitting gas is spherically symmetric and in the hydrostatic equilibrium with the underlined gravitational potential, we combine the deprojected gas density and spectral temperature profiles through the hydrostatic equilibrium equation to recover the parameters that describe a Navarro-Frenk-White total mass distribution. The comparison with results from weak-lensing analysis reveals a very good agreement both for masses and concentrations. The uncertainties are however too large to make any robust conclusion about the hydrostatic bias of these systems. Results. The distribution of concentrations is well approximated by a log-normal function in all the mass and redshift ranges investigated. The relation is well described by the form c ∝ MB(1 + z)C with B = -0.50 ± 0.20, C = 0.12 ± 0.61 (at 68.3% confidence). This relation is slightly steeper than that predicted by numerical simulations (B ~ -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.