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Measuring dark matter substructure within galaxy cluster haloes is afundamental probe of the Lambda-CDM model of structure formation. Gravitationallensing is a technique for measuring the total mass distribution which isindependent of the nature of the gravitating matter, making it a vital tool forstudying these dark-matter dominated objects. We present a new method formeasuring weak gravitational lensing flexions, the gradients of the lensingshear field, to measure mass distributions on small angular scales. Whilepreviously published methods for measuring flexions focus on measuring derivedproperties of the lensed images, such as shapelet coefficients or surfacebrightness moments, our method instead fits amass-sheet-transformation-invariant Analytic Image Model (AIM) to the eachgalaxy image. This simple parametric model traces the distortion of lensedimage isophotes and constrains the flexion fields. We test the AIM method usingsimulated data images with realistic noise and a variety of unlensed imageproperties, and show that it successfully reproduces the input flexion fields.We also apply the AIM method for flexion measurement to Hubble Space Telescopeobservations of Abell 1689, and detect mass structure in the cluster usingflexions measured with the AIM method.

Measuring Gravitational Lensing Flexions in Abell 1689 Using an Analytic Image Model