Triple-Lens Gravitational Microlensing: Critical Curves for Arbitrary Spatial Configuration. (arXiv:1901.08610v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Danek_K/0/1/0/all/0/1">Kamil Danek</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Heyrovsky_D/0/1/0/all/0/1">David Heyrovsky</a>
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 all critical-curve
topologies for a triple lens with a given combination of masses in an arbitrary
spatial configuration. We compute their boundaries in parameter space, identify
the topologies in the partitioned regions, and evaluate their probabilities of
occurrence. We illustrate the analysis on three triple-lens models. For three
equal masses the computed boundary surfaces divide the parameter space into 39
regions yielding nine critical-curve topologies. The other models include a
binary star with a planet, and a hierarchical star–planet–moon combination of
masses. For both we find the same set of eleven topologies, including new
topologies with doubly-nested loops of the critical curve. 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 non-static lens configurations due to orbital motion of the
components or other parallax-type effects.
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 all critical-curve
topologies for a triple lens with a given combination of masses in an arbitrary
spatial configuration. We compute their boundaries in parameter space, identify
the topologies in the partitioned regions, and evaluate their probabilities of
occurrence. We illustrate the analysis on three triple-lens models. For three
equal masses the computed boundary surfaces divide the parameter space into 39
regions yielding nine critical-curve topologies. The other models include a
binary star with a planet, and a hierarchical star–planet–moon combination of
masses. For both we find the same set of eleven topologies, including new
topologies with doubly-nested loops of the critical curve. 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 non-static lens configurations due to orbital motion of the
components or other parallax-type effects.
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