Journal Article

Shape, shear and flexion: an analytic flexion formalism for realistic mass profiles*

P. D. Lasky and C. J. Fluke

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 396, issue 4, pages 2257-2268
Published in print July 2009 | ISSN: 0035-8711
Published online July 2009 | e-ISSN: 1365-2966 | DOI:
Shape, shear and flexion: an analytic flexion formalism for realistic mass profiles*

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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 Sérsic-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; Sérsic-law profile. We quantitatively compare these mass distributions and show that the convergence and first-flexion are better indicators of the Sérsic shape parameter, while for the concentration of NFW profiles the shear and second-flexion terms are preferred.

Keywords: gravitational lensing; galaxies: haloes; dark matter

Journal Article.  7600 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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