The mass profile and dynamical status of the z~0.8 galaxy cluster LCDCS
  0504
  Constraints on the mass distribution in high-redshift clusters of galaxies
are not currently very strong. We aim to constrain the mass profile, M(r), and
dynamical status of the $z \sim 0.8$ LCDCS 0504 cluster of galaxies
characterized by prominent giant gravitational arcs near its center. Our
analysis is based on deep X-ray, optical, and infrared imaging, as well as
optical spectroscopy. We model the mass distribution of the cluster with three
different mass density profiles, whose parameters are constrained by the strong
lensing features of the inner cluster region, by the X-ray emission from the
intra-cluster medium, and by the kinematics of 71 cluster members. We obtain
consistent M(r) determinations from three methods (dispersion-kurtosis,
caustics and MAMPOSSt), out to the cluster virial radius and beyond. The mass
profile inferred by the strong lensing analysis in the central cluster region
is slightly above, but still consistent with, the kinematics estimate. On the
other hand, the X-ray based M(r) is significantly below both the kinematics and
strong lensing estimates. Theoretical predictions from $\Lambda$CDM cosmology
for the concentration--mass relation are in agreement with our observational
results, when taking into account the uncertainties in both the observational
and theoretical estimates. There appears to be a central deficit in the
intra-cluster gas mass fraction compared to nearby clusters. Despite the
relaxed appearance of this cluster, the determinations of its mass profile by
different probes show substantial discrepancies, the origin of which remains to
be determined. The extension of a similar dynamical analysis to other clusters
of the DAFT/FADA survey will allow to shed light on the possible systematics
that affect the determination of mass profiles of high-z clusters, possibly
related to our incomplete understanding of intracluster baryon physics.
