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Magnification Cross Sections for the Elliptic Umbilic Caustic Surface

1
Department of Mathematics and Computer Science, Clark University, Worcester, MA 01610, USA
2
Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA
3
Departments of Mathematics and Physics, Duke University, Science Drive, Durham, NC 27708-0320, USA
*
Author to whom correspondence should be addressed.
Universe 2019, 5(7), 161; https://doi.org/10.3390/universe5070161
Received: 29 May 2019 / Revised: 24 June 2019 / Accepted: 25 June 2019 / Published: 2 July 2019
(This article belongs to the Special Issue Gravitational Lensing and Optical Geometry: A Centennial Perspective)
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Abstract

In gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as μ 2 for fold caustics and μ 2.5 for cusp caustics. We aim to extend the results to higher-order caustic singularities, focusing on the elliptic umbilic, which can be manifested in lensing systems with two or three galaxies. The elliptic umbilic has a caustic surface, and we show that the volume cross section scales as μ 2.5 in the two-image region and μ 2 in the four-image region, where μ is the total unsigned magnification. In both cases our results are supported both numerically and analytically. View Full-Text
Keywords: strong gravitational lensing; magnification cross sections; caustics strong gravitational lensing; magnification cross sections; caustics
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Aazami, A.B.; Keeton, C.R.; Petters, A.O. Magnification Cross Sections for the Elliptic Umbilic Caustic Surface. Universe 2019, 5, 161.

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