# Magnification Cross Sections for the Elliptic Umbilic Caustic Surface

## TL;DR

This paper analyzes how the magnification volume cross section scales asymptotically near elliptic umbilic caustic surfaces, revealing specific power-law behaviors in different image regions.

## Contribution

It provides the first detailed asymptotic scaling laws for the magnification cross section near elliptic umbilic caustics.

## Key findings

- Magnification cross section scales as μ^{-2.5} in two-image regions.
- Magnification cross section scales as μ^{-2} in four-image regions.
- Results clarify the behavior of gravitational lensing near elliptic umbilic caustics.

## Abstract

We show that the asymptotic scaling of the magnification volume cross section corresponding to an elliptic umbilic caustic surface is $\mu^{-2.5}$ in the two-image region and $\mu^{-2}$ in the four-image region, where $\mu$ is the total unsigned magnification.