Degeneracies in triple gravitational microlensing

Abstract

We study microlensing light curves by a triple lens, in particular, by a primary star plus two planets. A four-fold degeneracy is confirmed in the light curves, similar to the close and wide degeneracy found in a double lens. Furthermore, we derive a set of equations for triple-lens in the external shear approximation. By using these external shear equations, we identify two kinds of continuous degeneracies which may confused double and triple lenses, i.e. the continuous external shear degeneracy among triple-lens systems and the double-triple lens degeneracy. These degeneracies are particularly important in high magnification events, and thus some caution needs to be applied when one infers the fraction of stars hosting multiple planets from microlensing. We study the dependence of the degeneracies on the lensing parameters (e.g., source trajectory) and give recipes about how the degeneracies should be explored with real data.

14 pages, 8 figures, 1 table, MNRAS accepted

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• Caustic Structures and Detectability of Circumbinary Planets in Microlensing
• Empirical Study of Simulated Two-planet Microlensing Event
• OGLE-2015-BLG-1459L: The Challenges of Exo-Moon Microlensing
• Triple-lens Gravitational Microlensing: Critical Curves for Arbitrary Spatial Configuration
• Image-plane Analysis of n-point-mass Lens Critical Curves and Caustics
• OGLE-2018-BLG-0532Lb: Cold Neptune With Possible Jovian Sibling
• A Mathematical Treatment of the Offset Microlensing Degeneracy
• Light Curve Calculations for Triple Microlensing Systems
• Constraint on Additional Planets in Planetary Systems Discovered through the Channel of High-magnification Gravitational Microlensing Events
• MAGIC: Microlensing Analysis Guided by Intelligent Computation
• Simulations of Triple Microlensing Events I: Detectability of a scaled Sun-Jupiter-Saturn System