A CFH12k lensing survey of X-ray luminous galaxy clusters - I: Weak lensing methodology

We present the weak lensing methodology applied to our multi-colour imaging survey of X-ray luminous galaxy clusters conducted with the wide field CFH12k camera. This method, which is converting a fully reduced CFH12k image into cluster mass constraints, is done in two steps that we explain in detail: (1) determination of the "true" shape of faint (lensed) galaxies which involves: object detection strategy, point spread function (PSF) determination, galaxy shapes measurements with errors; (2) conversion of the faint galaxies catalogue into useful mass constraints which is done by different lensing techniques using 1D and/or 2D mass estimates. Finally, we compare the cluster mass model to the light distribution of cluster members as observed on 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 to the edge of the image at 3 sigma significance. The two-dimensional mass reconstruction has a ~10 sigma significance mass peak centered on the brightest cluster galaxy. The weak lensing constraints are well fitted by a NFW mass profile with $M_{200} = 14.1^{+6.3}_{-4.7}\times 10^{14} M_\sun$, and $c = 3.5^{+0.5}_{-0.3}$ (chi^2=0.33), or by a power law (PL) profile with q=0.75 +- 0.07 and theta_E = 14.6"+-0.3" (chi^2=0.64). The mass-to-light ratio is found to be almost constant with radius with a mean value of M/L_R = 150 h (M/L)_\sun. We compare these results to other weak lensing analyses of Abell 1689 presented in the literature and find good agreements in terms of the shear measurement as well as the final mass estimate.