Magnification Cross Sections for the Elliptic Umbilic Caustic Surface - Amir B. Aazami; Charles R. Keeton; Arlie O. Petters (Universe, 2019)
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 <semantics> μ − 2 </semantics> for fold caustics and <semantics> μ − 2.5 </semantics> 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 <semantics> μ − 2.5 </semantics> in the two-image region and <semantics> μ − 2 </semantics> in the four-image region, where <semantics> μ </semantics> is the total unsigned magnification. In both cases our results are supported both numerically and analytically.