Caustics in gravitational lensing by mixed binary systems

TL;DR

This paper studies gravitational lensing caustics in binary systems with mixed power-law potentials, providing a comprehensive analysis of critical curves, caustics, and topological transitions, including analytic approximations for specific cases.

Contribution

It offers the first complete atlas of critical curves and caustics for mixed binary lenses with different power-law potentials, including topology transition analysis and analytic approximations.

Findings

Complete atlas of critical curves and caustics for mixed binaries

Identification of topology transition regimes

Analytic approximations for wide and extreme unequal-strength cases

Abstract

We investigate binary lenses with $1/r^n$ potentials in the asymmetric case with two lenses with different indexes $n$ and $m$. These kinds of potentials have been widely used in several contexts, ranging from galaxies with halos described by different power laws to lensing by wormholes or exotic matter. In this paper, we present a complete atlas of critical curves and caustics for mixed binaries, starting from the equal-strength case, and then exploring unequal-strength systems. We also calculate the transitions between all different topology regimes. Finally we find some useful analytic approximations for the wide binary case and for the extreme unequal-strength case.