Creating images by adding masses to gravitational point lenses

TL;DR

This paper explores how adding small masses to gravitational point lenses can create additional images, expanding the known configurations and providing new models for maximal gravitational lensing effects.

Contribution

It provides a mathematical characterization of the image-creating effect of adding small masses to gravitational lenses and introduces new maximal lens models beyond Rhie's symmetric construction.

Findings

Characterization of image creation when adding small masses

Examples of new maximal lens models without symmetry

Conditions for constructing maximal lenses from fewer masses

Abstract

A well-studied maximal gravitational point lens construction of S. H. Rhie produces $5n$ images of a light source using $n+1$ deflector masses. The construction arises from a circular, symmetric deflector configuration on $n$ masses (producing only $3n+1$ images) by adding a tiny mass in the center of the other mass positions (and reducing all the other masses a little bit). In a recent paper we studied this "image creating effect" from a purely mathematical point of view (S\`ete, Luce & Liesen, Comput. Methods Funct. Theory 15(1):9-35, 2015). Here we discuss a few consequences of our findings for gravitational microlensing models. We present a complete characterization of the effect of adding small masses to these point lens models, with respect to the number of images. In particular, we give several examples of maximal lensing models that are different from Rhie's construction and that do not share its highly symmetric appearance. We give generally applicable conditions that allow the construction of maximal point lenses on $n+1$ masses from maximal lenses on $n$ masses.