Triple-lens Gravitational Microlensing: Critical Curves for Arbitrary Spatial Configuration

Abstract

Since the first observation of triple-lens gravitational microlensing in 2006, analyses of six more events have been published by the end of 2018. In three events the lens was a star with two planets; four involved a binary star with a planet. Other possible triple lenses, such as triple stars or stars with a planet with a moon, are yet to be detected. The analysis of triple-lens events is hindered by the lack of understanding of the diversity of their caustics and critical curves. We present a method for identifying the full range of critical curves for a triple lens with a given combination of masses in an arbitrary spatial configuration. We compute their boundaries in parameter space, identify the critical-curve topologies in the partitioned regions, and evaluate their probabilities of occurrence. We demonstrate the analysis on three triple-lens models. For three equal masses the computed boundaries divide the parameter space into 39 regions yielding nine different critical-curve topologies. The other models include a binary star with a planet, and a hierarchical star-planet-moon combination of masses. Both have the same set of 11 topologies, including new ones with doubly nested critical-curve loops. The number of lensing regimes thus depends on the combination of masses -unlike in the double lens, which has the same three regimes for any mass ratio. The presented approach is suitable for further investigations, such as studies of the changes occurring in nonstatic lens configurations due to orbital motion of the components or other parallax-type effects.

Detection of exoplanet as a binary source of microlensing events in WFIRST survey

“…Here we took, the two major configurations in microlensing events: single and binary-lens systems in which the source star has an exoplanet. However, there are some possibility to have more than two lens objects (Daněk & Heyrovský 2019) and also, some non-negligible possibility to have the multi-planetary systems such as solar system. We only assume the source star has an exoplanet and do not consider the possibility of the detection of exoplanets when it contributes as one of the lens objects in the binary lens system.…”

OGLE-2019-BLG-0304: Competing Interpretations between a Planet-binary Model and a Binary-source + Binary-lens model

“…other caustic induced by a planet companion, although there exist some deviations from the superposition due to the twisting and intersection of the caustics caused by the interference between the two caustics (Gaudi et al 1998;Rhie 2002;Danȇk & Heyrovský 2015, 2019.…”

An optical n-body gravitational lens analogy

“…13,14 For three-mass lenses, extensive studies exist as well, although the system is already hardly tractable. 34,35 Thus, only scenarios up to n = 3 have been considered experimentally here.…”

“…For three point masses, the phenomenology becomes even richer 34,35 . Already, there are five parameters required to fully describe the situation: two mass ratios (menisci height ratios) along with three relative positions defining the two-dimensional configuration of the FIG.…”