The sum of the 1D magnifications along the axis of positive curvature for a smooth gravitational potential with N point perturbations

Abstract

Gravitational lensing is an important tool for determining the matter content of the universe. The locations of gravitationally lensed images tend to give us information about the overall structure of a lensing galaxy, whereas the magnifications of the images tell us about small scale structure of the galaxy such as the abundance of stars and dark matter condensations. In particular, flux ratio anomalies- disparities between predicted and observed magnifications of images- have led astronomers to study the role of perturbations in determining image brightness. In this paper, we explore the limits of demagnification due to point perturbations. We look at configurations of perturbations that are extremely improbable but that nonetheless illustrate interesting patterns in magnifications. Ultimately, we prove that for any number of point perturbations the total one dimensional magnification along the axis of curvature is constant and independent of perturbation size and location.