Shape, shear & flexion: An analytic flexion formalism for realistic mass profiles

Understand

Flexion is a non-linear gravitational lensing effect that arises from gradients in the convergence and shear across an image.

• We derive a formalism that describes non-linear gravitational lensing by a circularly symmetric lens in the thin-lens approximation.
• This provides us with relatively simple expressions for first- and second-flexion in terms of only the surface density and projected mass distribution of the lens.
• We give details of exact lens models, in particular providing flexion calculations for a Sersic-law profile, which has become increasingly popular over recent years.