Image-plane Analysis of n-point-mass Lens Critical Curves and Caustics

TL;DR

This paper introduces new analytical tools to map and understand the complex critical curves and caustics in n-point-mass gravitational lens systems, especially for three or more masses, advancing microlensing event interpretation.

Contribution

It develops the cusp curve and morph curve methods to analyze critical-curve topology and caustic metamorphoses in n-point-mass lenses in the image plane, a novel approach.

Findings

Mapped critical-curve topologies for multi-mass lenses.

Identified cusp-image positions using the cusp curve.

Analyzed caustic metamorphoses with the morph curve.

Abstract

The interpretation of gravitational microlensing events caused by planetary systems or multiple stars is based on the n-point-mass lens model. The first planets detected by microlensing were well described by the two-point-mass model of a star with one planet. By the end of 2014, four events involving three-point-mass lenses had been announced. Two of the lenses were stars with two planetary companions each; two were binary stars with a planet orbiting one component. While the two-point-mass model is well understood, the same cannot be said for lenses with three or more components. Even the range of possible critical-curve topologies and caustic geometries of the three-point-mass lens remains unknown. In this paper we provide new tools for mapping the critical-curve topology and caustic cusp number in the parameter space of n-point-mass lenses. We perform our analysis in the image plane of the lens. We show that all contours of the Jacobian are critical curves of re-scaled versions of the lens configuration. Utilizing this property further, we introduce the cusp curve to identify cusp-image positions on all contours simultaneously. In order to track cusp-number changes in caustic metamorphoses, we define the morph curve, which pinpoints the positions of metamorphosis-point images along the cusp curve. We demonstrate the usage of both curves on simple two- and three-point-mass lens examples. For the three simplest caustic metamorphoses we illustrate the local structure of the image and source planes.