Weak and strong lensing analysis of the triaxial matter distribution of
  A1689
  Halos formed in the standard Lambda cold dark matter framework should follow
an universal mass density profile and fit a well defined mass-concentration
relation. Lensing analyses of clusters with a large Einstein radius seem to
contradict this scenario, with the massive cluster Abell 1689 being often
claimed as a notable example of a highly over-concentrated halo. Shape and
orientation biases in lensing studies might be at the basis of this
disagreement between theory and observations. We developed a method for a full
three-dimensional analysis of strong and weak lensing data. Surface density
maps estimated from lensing are de-projected to infer the actual triaxial
structure of the cluster, whose mass distribution is approximated as an
ellipsoidal Navarro-Frenk-White halo with arbitrary orientation. Inversion is
performed under competing a priori assumptions, integrated in the method thanks
to Bayesian statistics. We applied the method to A1689. Whatever the considered
priors on shape and orientation, both weak and strong lensing analyses found
the halo to be slightly over-concentrated but still consistent with theoretical
predictions. We found some evidence for a mildly triaxial lens (minor to major
axis ratio ~ 0.5 +- 0.2) with the major axis orientated along the line of
sight. Exploiting priors from N-body simulations, we found mass M_{200} = (1.3
+- 0.4)x 10^{15}M_Sun and concentration c_{200} =10+-3 for the weak lensing
analysis of Subaru data, M_{200} = (1.7 +- 0.3)x 10^{15}M_Sun and c_{200}
=6.1+-0.9 for the strong lensing analysis of multiple image systems, and
M_{200} = (1.3 +- 0.2)\times 10^{15}M_Sun and c_{200} =7.3+-0.8 for the
combined weak plus strong analysis.
