Magnification Cross Sections for the Elliptic Umbilic Caustic Surface

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.