| Summary: | 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 <inline-formula> <math display="inline"> <semantics> <msup> <mi>μ</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics> </math> </inline-formula> for fold caustics and <inline-formula> <math display="inline"> <semantics> <msup> <mi>μ</mi> <mrow> <mo>−</mo> <mn>2.5</mn> </mrow> </msup> </semantics> </math> </inline-formula> 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 <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi>μ</mi> </mrow> <mrow> <mo>−</mo> <mn>2.5</mn> </mrow> </msup> </semantics> </math> </inline-formula> in the two-image region and <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi>μ</mi> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics> </math> </inline-formula> in the four-image region, where <inline-formula> <math display="inline"> <semantics> <mi>μ</mi> </semantics> </math> </inline-formula> is the total unsigned magnification. In both cases our results are supported both numerically and analytically.
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