Unveiling the three-dimensional structure of galaxy clusters: resolving the discrepancy between X-ray and lensing masses

[Abridged] We present the first determination of the intrinsic three-dimensional shapes and the physical parameters of both dark matter (DM) and intra-cluster medium (ICM) in a triaxial galaxy cluster. While most previous studies rely on the standard spherical modeling, our approach allows to infer the properties of the non-spherical intra-cluster gas distribution sitting in hydrostatic equilibrium within triaxial DM halos by combining X-ray, weak and strong lensing observations. We present an application of our method to the galaxy cluster MACS J1423.8+2404. This source is an example of a well relaxed object with a unimodal mass distribution and we infer shape and physical properties of the ICM and the DM for this source. We found that this is a triaxial galaxy cluster with DM halo axial ratios 1.53+/-0.15 and 1.44+/-0.07 on the plane of the sky and along the line of sight, respectively. We show that accounting for the three-dimensional geometry allows to solve the long-standing discrepancy between galaxy cluster masses determined from X-ray and gravitational lensing observations. We focus also on the determination of the inner slope of the DM density profile alpha, since the cuspiness of dark-matter density profiles is one of the critical tests of the cold dark matter (CDM) paradigm for structure formation: we measure alpha=0.94+/-0.09 by accounting explicitly for the 3D structure for this cluster, a value which is close to the CDM predictions, while the standard spherical modeling leads to the biased value alpha=1.24+/-0.07. Our findings provide further evidences that support the CDM scenario and open a new window in recovering the intrinsic shapes and physical parameters of galaxy clusters in a bias-free way. This has important consequences in using galaxy clusters as cosmological probes.

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