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We present reconstructions of galaxy-cluster-scale mass distributions from simulated gravitational lensing data sets including strong lensing, weak lensing shear, and measurements of quadratic image distortions - flexion. The lensing data is constructed to make a direct comparison between mass reconstructions with and without flexion. We show that in the absence of flexion measurements, significant galaxy-group scale substructure can remain undetected in the reconstructed mass profiles, and that the resulting profiles underestimate the aperture mass in the substructure regions by ~25-40 per cent. When flexion is included, subhaloes down to a mass of ~3 × 1012 M⊙ can be detected at an angular resolution smaller than 10 arcsec. Aperture masses from profiles reconstructed with flexion match the input distribution values to within an error of ~13 per cent, including both statistical error and scatter. This demonstrates the important constraint that flexion measurements place on substructure in galaxy clusters and its utility for producing high-fidelity mass reconstructions. [ABSTRACT FROM AUTHOR]

Measuring dark matter substructure within galaxy cluster halos is a fundamental probe of the ACDM model of structure formation. Gravitational lensing is a technique for measuring the total mass distribution which is independent of the nature of the gravitating matter, making it a vital tool for studying these dark-matter-dominated objects. We present a new method for measuring weak gravitational lensing flexion fields, the gradients of the lensing shear field, to measure mass distributions on small angular scales. While previously published methods for measuring flexion focus on measuring derived properties of the lensed images, such as shapelet coefficients or surface brightness moments, our method instead fits a mass-sheet transformation invariant Analytic Image Model (AIM) to each galaxy image. This simple parametric model traces the distortion of lensed image isophotes and constrains the flexion fields. We test the AIM method using simulated data images with realistic noise and a variety of unlensed image properties, and show that it successfully reproduces the input flexion fields. We also apply the AIM method for flexion measurement to Hubble Space Telescope observations of A 1689 and detect mass structure in the cluster using flexion measured with this method. We also estimate the scatter in the measured flexion fields due to the unlensed shape of the background galaxies and find values consistent with previous estimates. [ABSTRACT FROM AUTHOR]