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

TL;DR

This paper develops an analytic formalism for non-linear gravitational lensing effects, specifically flexion, for various realistic mass profiles, simplifying calculations and enabling better interpretation of lensing observations.

Contribution

It introduces a formalism that provides simple expressions for flexion based on surface density, including detailed models for common mass profiles like Sersic, NFW, and SIS.

Findings

Flexion expressions derived for multiple mass profiles.

Flexion and convergence better indicate Sersic shape parameters.

Shear and second-flexion are more sensitive to NFW concentration.

Abstract

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. We further provide a single resource for the analytic forms of convergence, shear, first- and second-flexion for the following mass distributions: a point mass, singular isothermal sphere (SIS); Navarro-Frenk-White (NFW) profile; Sersic-law profile. We quantitatively compare these mass distributions and show that the convergence and first-flexion are better indicators of the Sersic shape parameter, while for the concentration of NFW profiles the shear and second-flexion terms are preferred.