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 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. 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
($B\sim-0.1$) 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.
