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

• Published in: arXiv.org
• Main Author: Clarkson, Chris
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 14.11.2016
• Subjects: Formalism; Physics - Cosmology and Nongalactic Astrophysics; Physics - General Relativity and Quantum Cosmology; Series expansion; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1603.04652

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.