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 lensing induced in background galaxies. This is the first time that a shapelet technique has been used to reconstruct the distribution of mass in this cluster and the first time that a flexion signal has been measured using cluster members as lenses. From weak shear measurements alone, we generate a nonparametric mass reconstruction, which shows significant substructure corresponding to groups of galaxies within the cluster. In addition, our galaxy-galaxy flexion signal demonstrates that the cluster galaxies can be well fit by a singular isothermal sphere model with a characteristic velocity dispersion of sigma(nu) = (295 +/- 40) km s(-1). We identify a major, distinct dark matter clump, offset by 40 h(-1) kpc from the central cluster members, which was not apparent from shear measurements alone. This secondary clump is present in a parametric mass reconstruction using flexion data alone, and its existence is suggested in a nonparametric reconstruction of the cluster using a combination of strong and weak lensing. As found in previous studies, the mass profile obtained by combining weak and strong lensing data shows a much steeper profile than that obtained from only weak lensing data.