Roulettes: A weak lensing formalism for strong lensing - II. Derivation and analysis

TL;DR

This paper extends weak lensing formalism to describe strong lensing effects by solving the geodesic deviation equation iteratively, enabling detailed modeling of complex lensed images beyond traditional convergence, shear, and flexion descriptions.

Contribution

It introduces a series expansion approach to model strong lensing by decomposing lensing maps into independent spin modes, providing a comprehensive framework for complex image formation.

Findings

Series expansion captures large strong lensing effects.

Decomposition into spin modes models roulettes distortions.

Method surpasses convergence, shear, and flexion limitations.

Abstract

We present a new extension of the weak lensing formalism capable of describing strongly lensed images. This paper accompanies Paper I, arXiv:1603.04698 where we provided a condensed overview of the approach and illustrated how it works. Here we give all the necessary details, together with some more explicit examples. We solve the non-linear geodesic deviation equation order-by-order, keeping the leading derivatives of the optical tidal matrix, giving rise to a series of maps from which a complete strongly lensed image is formed. The family of maps are decomposed by separating the trace and trace-free parts of each map. Each trace-free tensor represents an independent spin mode, which distort circles into a variety of roulettes in the screen-space. It is shown how summing this series expansion allows us to create large strongly lensed images in regions where convergence, shear and flexion are not sufficient. This paper is a detailed exposition of Paper I which presents the key elements of the subject matter in a wider context.