Parameterised models for the lensing cluster Abell 1689

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Abstract
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, 0.12Mpc/h<R<1.8Mpc/h 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 of 0.37arcmin (0.043Mpc/h) i.e. a velocity dispersion of 1028(+35,-42)km/s in an Omega=1.0, Lambda=0.0 cosmology. For the best-fit NFW profile, the virial radius r_200=1.14Mpc/h and the concentration parameter c=4.7, giving a virial mass M_200=5.7x10**14 M_solar/h. 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.

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