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

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.

33 pages, 5 figures, accepted by ApJ

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• KMT-2021-BLG-1122L: The first microlensing triple stellar system
• Earth through the looking glass: how frequently are we detected by other civilisations through photometric microlensing?
• Gravitational lensing by an ellipsoidal Navarro--Frenk--White dark-matter halo: An analytic solution and its properties
• A GPU Code for Finding Microlensing Critical Curves and Caustics
• OGLE-2019-BLG-0468Lb,c: two microlensing giant planets around a G-type star