Mass, shape and thermal properties of A1689 by a multi-wavelength X-ray,
  lensing and Sunyaev-Zel'dovich analysis
  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+-0.2)*10^{15}M_sun, and over-concentrated,
c_{200}=8+-1, but still consistent with theoretical predictions. The total
matter is triaxial (minor to major axis ratio ~0.5+-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 ~0.6+-0.1) and deviates
from 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.
