2005A&A...434..433B

We describe the weak lensing methodology we have applied to multi-colour CFH12k imaging of a homogeneously-selected sample of luminous X-ray clusters at z∼0.2. The aim of our survey is to understand the variation in cluster structure and dark matter profile within rich clusters. The method we describe converts a fully reduced CFH12k image into constraints on the cluster mass distribution in two steps: (1) determination of the ``true'' shape of faint (lensed) galaxies, including object detection, point spread function (PSF) determination, galaxy shape measurement with errors; (2) conversion of the faint galaxy catalogue into reliable mass constraints using a range of 1D and 2D lensing techniques. Mass estimates are derived independently from each of the three images taken in separate filters to quantify the systematic uncertainties. Finally, we compare the cluster mass model to the light distribution of cluster members as derived from our imaging data. To illustrate the method, we apply it to the well-studied cluster Abell 1689 (z=0.184). In this cluster, we detect the gravitational shear signal out to ∼3Mpc at >3-σ significance. The two-dimensional mass reconstruction has a ∼10-σ significance peak centered on the brightest cluster galaxy. The weak lensing profile is well fitted by a NFW mass profile with M₂₀₀=14.1^+6.3_–4.7x10¹⁴M_☉, and c=3.5^+0.5_–0.3 (χ²=0.33), or by a power law profile with q=0.75±0.07 and θ_E=14.6"±0.3" (χ²=0.64). The mass-to-light ratio is found to be almost constant with radius with a mean value of M/L_R=150h(M/L)_☉. We compare these results to other weak lensing analyses of Abell 1689 from the literature and find good agreements in terms of the shear measurement as well as the final mass estimate.