Estimate of dark halo ellipticity by lensing flexion
  Aims. The predictions of the ellipticity of the dark matter halos from models
of structure formation are notoriously difficult to test with observations. A
direct measurement would give important constraints on the formation of
galaxies, and its effect on the dark matter distribution in their halos. Here
we show that galaxy-galaxy flexion provides a direct and potentially powerful
method for determining the ellipticity of (an ensemble of) elliptical lenses.
Methods. We decompose the spin-1 flexion into a radial and a tangential
component. Using the ratio of tangential-to- radial flexion, which is
independent of the radial mass profile, the mass ellipticity can be estimated.
Results. An estimator for the ellipticity of the mass distribution is derived
and tested with simulations. We show that the estimator is slightly biased. We
quantify this bias, and provide a method to reduce it. Furthermore, a
parametric fitting of the flexion ratio and orientation provides another
estimate for the dark halo ellipticity, which is more accurate for individual
lenses Overall, galaxy-galaxy flexion appears as a powerful tool for
constraining the ellipticity of mass distributions.
