Parametric Strong Gravitational Lensing Analysis of Abell 1689

(Abridged) We measure the mass distribution of galaxy cluster Abell 1689 within 0.3 Mpc/h_70 of the cluster centre using its strong lensing effect on 32 background galaxies. The multiple images are based on those of Broadhurst et al. 2005 with some modifications. The cluster profile is explored further out to ~2.5 Mpc/h_70 with weak lensing shear measurements from Broadhurst et al. 2005b. The masses of ~200 cluster galaxies are measured with Fundamental Plane in order to accurately model the small scale mass structure in the cluster. The galaxies are modelled as elliptical truncated isothermal spheres. The dark matter component of the cluster is described by either non-singular isothermal ellipsoids (NSIE) or elliptical versions of the universal dark matter profile (ENFW). We use two dark matter haloes to model the smooth DM in the cluster. The total mass profile is well described by either an NSIS profile with sigma=1514+-18 km/s and core radius of r_c=71+-5kpc/h_70, or an NFW profile with C=6.0+-0.5 and r_200=2.82+-0.11 Mpc/h_70. The errors are assumed to be due to the error in assigning masses to the individual galaxies in the galaxy component. The derived total mass is in good agreement with the mass profile of Broadhurst et al. 05. Using also weak lensing we can constrain the profile further out to r~2.5 Mpc/h_70. The best fit parameters are then sigma=1499+-15 km/s and r_c=66+-5 kpc/h_70 for the NSIS profile and C=7.6+-0.5 and r_200=2.55+-0.07 Mpc/h_70 for the NFW profile. Using the same image configuration as Broadhurst et al. 2005 we obtain a strong lensing model that is superior to that of Broadhurst et al. 2005 (rms of 2.7'' compared to 3.2'').