Gravitational Flexion by Elliptical Dark Matter Haloes

We present equations for the gravitational lensing flexion expected for an elliptical lens mass distribution. These can be reduced to one-dimensional finite integrals, thus saving significant computing time over a full two-dimensional calculation. We estimate constraints on galaxy halo ellipticities for a range of potential future surveys, finding that the constraints from the two different types of flexion are comparable and are up to two orders of magnitude tighter than those from shear. Flexion therefore appears to be a very promising potential tool for constraining the shapes of galaxy haloes from future surveys.