Knowledge of mass and concentration of galaxy clusters is crucial to understand their formation and evolution .
Unbiased estimates require the understanding of the shape and orientation of the halo as well as its equilibrium status .
We propose a novel method to determine the intrinsic properties of galaxy clusters from a multi-wavelength data set spanning from X-ray spectroscopic and photometric data to gravitational lensing to the Sunyaev-Zel ’ dovich effect ( SZe ) .
The method relies on two quite non informative geometrical assumptions : the distributions of total matter or gas are approximately ellipsoidal and co-aligned ; they have different , constant axial ratios but share the same degree of triaxiality .
Weak and strong lensing probe the features of the total mass distribution in the plane of the sky .
X-ray data measure size and orientation of the gas in the plane of the sky .
Comparison with the SZ amplitude fixes the elongation of the gas along the line of sight .
These constraints are deprojected thanks to Bayesian inference .
The mass distribution is described as a Navarro-Frenk-White halo with arbitrary orientation , gas density and temperature are modelled with parametric profiles .
We applied the method to Abell 1689 .
Independently of the priors , the cluster is massive , M _ { 200 } = ( 1.3 \pm 0.2 ) \times 10 ^ { 15 } M _ { \odot } , and over-concentrated , c _ { 200 } = 8 \pm 1 , but still consistent with theoretical predictions .
The total matter is triaxial ( minor to major axis ratio \sim 0.5 \pm 0.1 exploiting priors from N -body simulations ) with the major axis nearly orientated along the line of sight .
The gas is rounder ( minor to major axis ratio \sim 0.6 \pm 0.1 ) and deviates from hydrostatic equilibrium .
The contribution of non-thermal pressure is \sim 20–50 per cent in inner regions , \mathrel { \lower 2.58 pt \hbox { $ \buildrel \textstyle < \over { \scriptstyle \sim } $ } } 300 % ~ { } \mathrm { kpc } , and \sim 25 \pm 5 per cent at \sim 1.5 ~ { } \mathrm { Mpc } .
This picture of A1689 was obtained with a small number of assumptions and in a single framework suitable to application to a large variety of clusters .