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Knowledge of mass and concentration of galaxy clusters is crucial tounderstand their formation and evolution. Unbiased estimates require theunderstanding of the shape and orientation of the halo as well as itsequilibrium status. We propose a novel method to determine the intrinsicproperties of galaxy clusters from a multi-wavelength data set spanning fromX-ray spectroscopic and photometric data to gravitational lensing to theSunyaev-Zel'dovich effect (SZe). The method relies on two quite non informativegeometrical assumptions: the distributions of total matter or gas areapproximately ellipsoidal and co-aligned; they have different, constant axialratios but share the same degree of triaxiality. Weak and strong lensing probethe features of the total mass distribution in the plane of the sky. X-ray datameasure size and orientation of the gas in the plane of the sky. Comparisonwith the SZ amplitude fixes the elongation of the gas along the line of sight.These constraints are deprojected thanks to Bayesian inference. The massdistribution is described as a Navarro-Frenk-White halo with arbitraryorientation, gas density and temperature are modelled with parametric profiles.We applied the method to Abell 1689. Independently of the priors, the clusteris massive, M_{200}=(1.3+-0.2)*10^{15}M_sun, and over-concentrated,c_{200}=8+-1, but still consistent with theoretical predictions. The totalmatter is triaxial (minor to major axis ratio ~0.5+-0.1 exploiting priors fromN-body simulations) with the major axis nearly orientated along the line ofsight. The gas is rounder (minor to major axis ratio ~0.6+-0.1) and deviatesfrom hydrostatic equilibrium. The contribution of non-thermal pressure is~20-50 per cent in inner regions, <~ 300 kpc, and ~25+-5 per cent at ~1.5 Mpc.

Mass, shape and thermal properties of A1689 by a multi-wavelength X-ray, lensing and Sunyaev-Zel'dovich analysis