Gravitational Shear, Flexion, and Strong Lensing in Abell 1689

We present a gravitational lensing analysis of the galaxy cluster Abell 1689,incorporating measurements of the weak shear, flexion, and strong lensinginduced in background galaxies. This is the first time that a shapelettechnique has been used to reconstruct the distribution of mass in thiscluster, and the first time that a flexion signal has been measured usingcluster members as lenses. From weak shear measurements alone, we generate anon-parametric mass reconstruction, which shows significant substructurecorresponding to groups of galaxies within the cluster. Additionally, ourgalaxy-galaxy flexion signal demonstrates that the cluster galaxies can bewell-fit by a singular isothermal sphere model with a characteristic velocitydispersion of $\sigma_v = 295\pm 40 km/s $. We identify a major, distinct darkmatter clump, offset by 40$h^{-1}$kpc from the central cluster members, whichwas not apparent from shear measurements alone. This secondary clump is presentin a parametric mass reconstruction using flexion data alone, and its existenceis suggested in a non-parametric reconstruction of the cluster using acombination of strong and weak lensing. As found in previous studies, the massprofile obtained by combining weak and strong lensing data shows a much steeperprofile than that obtained from only weak lensing data.Comment: 17 pages, 12 figures, accepted for publication in Ap