Parameterised models for the lensing cluster Abell 1689

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, $0.12\,h^{-1}\,{\rm Mpc} < R < 1.8\,h^{-1}\,{\rm Mpc}$ 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 $\theta_{\rm E}=0\hbox{$.\!\!^{\prime}$}37$ $(0.043\,h^{-1}\,{\rm Mpc})$ i.e. a velocity dispersion $\sigma_{\rm 1D}=1028^{+35}_{-42}\,{\rm km\,s^{-1}}$ in an $\Omega=1.0$, $\Lambda=0.0$ cosmology. For the best-fit NFW profile, the virial radius $r_{200}=1.14\,h^{-1}\,{\rm Mpc}$ and the concentration parameter $c=4.7$, giving a virial mass $M_{200}=5.7\times 10^{14}\,h^{-1}\,M_{\odot}$. 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 rs. By fitting an SIE, the deviation of the projected mass distribution from circular symmetry is evident, with a best-fit axial ratio $f=0.74$