Magnification Cross Sections for the Elliptic Umbilic Caustic Surface
Department of Mathematics and Computer Science, Clark University, Worcester, MA 01610, USA
Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA
Departments of Mathematics and Physics, Duke University, Science Drive, Durham, NC 27708-0320, USA
Author to whom correspondence should be addressed.
Received: 29 May 2019 / Revised: 24 June 2019 / Accepted: 25 June 2019 / Published: 2 July 2019
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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
for fold caustics and
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
in the two-image region and
in the four-image region, where
is the total unsigned magnification. In both cases our results are supported both numerically and analytically.
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MDPI and ACS Style
Aazami, A.B.; Keeton, C.R.; Petters, A.O. Magnification Cross Sections for the Elliptic Umbilic Caustic Surface. Universe 2019, 5, 161.
Aazami AB, Keeton CR, Petters AO. Magnification Cross Sections for the Elliptic Umbilic Caustic Surface. Universe. 2019; 5(7):161.
Aazami, Amir B.; Keeton, Charles R.; Petters, Arlie O. 2019. "Magnification Cross Sections for the Elliptic Umbilic Caustic Surface." Universe 5, no. 7: 161.
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