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 } { Mpc } < R < 1.8 h ^ { -1 } { 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 _ { E } = 0 \arcminf 37 ( 0.043 h ^ { -1 } { Mpc } ) i.e .
a velocity dispersion \sigma _ { 1 D } = 1028 ^ { +35 } _ { -42 } { 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 } { 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 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 .