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 cluster ’ s 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 .

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 , 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 .

Methods : Under the assumptions 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 .
Uncertainties are however too large to make any robust conclusion on the hydrostatic bias of these systems .

Results : The distribution of concentrations is well approximated by a lognormal function in all the mass and redshift ranges investigated .
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 ) .
This relation is slightly steeper than the one predicted by numerical simulations ( B \sim - 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 .

Conclusions :