Estimation of halo ellipticity using spin-3 flexion
  Estimating the ellipticity of dark matter haloes at the galaxy or
galaxy-cluster scale can provide important constraints on the formation of
galaxies or clusters, as well as on the nature of dark matter. We show in this
paper that the spin-3 gravitational flexion can add useful information on the
ellipticity of lensing haloes. We introduce a general formalism to decompose
fields with arbitrary spin into radial and tangential components. The ratio of
the tangential and radial flexion components directly estimates the lens
ellipticity. We point out that any centroid offset will significantly bias our
estimate, which on the other hand can be used to determine the centre of the
lens halo.
