Journal Article

Analytic relations for magnifications and time delays in gravitational lenses with fold and cusp configurations

Arthur B. Congdon, Charles R. Keeton and C. Erik Nordgren

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 389, issue 1, pages 398-406
Published in print September 2008 | ISSN: 0035-8711
Published online August 2008 | e-ISSN: 1365-2966 | DOI:
Analytic relations for magnifications and time delays in gravitational lenses with fold and cusp configurations

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Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four-image lens. Using a perturbative expansion of the image positions, we show that the time delay between the close pair of images in a fold lens scales with the cube of the image separation, with a constant of proportionality that depends on a particular third derivative of the lens potential. We also apply our formalism to cusp lenses, where we develop perturbative expressions for the image positions, magnifications and time delays of the images in a cusp triplet. Some of these results were derived previously for a source asymptotically close to a cusp point, but using a simplified form of the lens equation whose validity may be in doubt for sources that lie at astrophysically relevant distances from the caustic. Along with the work of Keeton, Gaudi & Petters, this paper demonstrates that perturbation theory plays an important role in theoretical lensing studies.

Keywords: gravitational lensing; methods: analytical; galaxies: structure; cosmology: theory; dark matter

Journal Article.  4636 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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