A new tool to determine masses and mass profiles using gravitational
  flexion
  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 nonparametric 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 normalisation of the signal, in contrast to the
direct method.
