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 non-parametric mass reconstruction , which shows significant substructure corresponding to groups of galaxies within the cluster .
Additionally , 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 _ { v } = 295 \pm 40 km / s .
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 non-parametric 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 .