The binary gravitational lens and its extreme cases

TL;DR

This paper explores the transition of binary gravitational lenses from equal mass to planetary mass ratios, analyzing their topologies and approximations, and establishing a framework for classifying microlensing events.

Contribution

It provides a detailed analysis of the extreme cases of binary gravitational lenses, connecting different topologies and approximations, and clarifying ambiguities in lens classification.

Findings

Approach to the Chang-Refsdal lens limit for small mass ratios.

Mapping of topologies between binary and Chang-Refsdal lenses.

Identification of an ambiguity between wide and close binary lenses.

Abstract

The transition of the binary gravitational lens from the equal mass case to small (planetary) mass ratios q is studied. It is shown how the limit of a (pure shear) Chang-Refsdal lens is approached, under what conditions the Chang-Refsdal approximation is valid, and how the 3 different topologies of the critical curves and caustics for a binary lens are mapped onto the 2 different topologies for a Chang-Refsdal lens with pure shear. It is shown that for wide binaries, the lensing in the vicinity of both lens objects can be described by a Taylor-expansion of the deflection term due to the other object, where the Chang-Refsdal approximation corresponds to a truncation of this series. For close binaries, only the vicinity of the secondary, less massive, object can be described in this way. However, for image distances much larger than the separation of the lens objects, any binary lens can be approximated by means of multipole expansion, where the first non-trivial term is the quadrupole term. It is shown that an ambiguity exists between wide and close binary lenses, where the shear at one of the objects due to the other object for the wide binary is equal to the absolute value of the eigenvalues of the quadrupole moment for the close binary. This analysis provides the basis for a classification of binary lens microlensing events, especially of planetary events, and an understanding of present ambiguities.