2002A&A...383..118K

Here we apply a recently developed maximum likelihood method for determining best-fit parameterised lens models to observations of the rich lensing cluster Abell 1689. The observations that we use were taken with the ESO/MPG Wide Field Imager. The wide field-of-view enables us to use the weakly lensed images of faint background objects on an unsurpassed range of scales, 0.12h^–1Mpc<R<1.8h^–1Mpc from the cluster centre, to determine best-fit models for the 1-parameter singular isothermal sphere (SIS), 2-parameter general power-law and NFW models, and 3-parameter singular isothermal ellipsoid (SIE). The best-fit SIS has an Einstein radius θ_E=0.37' (0.043h^–1Mpc) i.e. a velocity dispersion σ_1D=1028⁺³⁵_–42km/s in an Ω=1.0, Λ=0.0 cosmology. For the best-fit NFW profile, the virial radius r₂₀₀=1.14h^–1Mpc and the concentration parameter c=4.7, giving a virial mass M₂₀₀=5.7x10¹⁴h^–1M_☉. At q=0.88, the slope of the best-fit power-law model is slightly flatter than isothermal (q=1.0), indicating that the galaxies most important in the fitting procedure lie inside the scale radius r_s. By fitting an SIE, the deviation of the projected mass distribution from circular symmetry is evident, with a best-fit axial ratio f=0.74.