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In a recent publication, an aperture mass statistic for gravitational flexion was derived and shown to be effective, at least with simulated data, in detecting massive structures and substructures within clusters of galaxies. Further, it was suggested that the radius at which the flexion aperture mass signal falls to zero might allow for estimation of the mass or density profile of the structures detected. In this paper, we more fully explore this possibility, considering the behaviour both of the peak signal and the zero‐signal contours for two mass models – the singular isothermal sphere and Navarro–Frenk–White profiles – under varying aperture size, filter shape and mass concentration parameter. We demonstrate the effectiveness of the flexion aperture mass statistic in discriminating between mass profiles and concentration parameters, and in providing an accurate estimate of the mass of the lens, to within a factor of 1.5 or better. In addition, we compare the aperture mass method to a direct non‐parametric reconstruction of the convergence from flexion measurements. We demonstrate that the aperture mass technique is much better able to constrain the shape of the central density profile, obtains much finer angular resolution in reconstructions, and does not suffer from ambiguity in the normalization of the signal, in contrast to the direct method.

A new tool to determine masses and mass profiles using gravitational flexion