The Criterion for Chaos in Three-Planet Systems. (arXiv:2110.02956v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Rath_J/0/1/0/all/0/1">Jeremy Rath</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hadden_S/0/1/0/all/0/1">Sam Hadden</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lithwick_Y/0/1/0/all/0/1">Yoram Lithwick</a>
We establish the criterion for chaos in three-planet systems, for systems
similar to those discovered by the Kepler spacecraft. Our main results are as
follows: (i) The simplest criterion, which is based on overlapping mean motion
resonances MMR’s), only agrees with numerical simulations at a very crude
level. (ii) Much greater accuracy is attained by considering neighboring MMR’s
that do not overlap. We work out the width of the chaotic zones around each of
the neighbors, and also provide simple approximate expressions for the widths.
(iii) Even greater accuracy is provided by the overlap of three-body resonances
(3BR’s), which accounts for fine-grained structure seen in maps from N-body
simulations, and also predicts the Lyapunov times. Previous studies conflict on
whether overlap of MMR’s or of 3BR’s drive interplanetary chaos. We show that
both do, and in fact they are merely different ways of looking at the same
effect. (iv) We compare both criteria with high-resolution maps of chaos from
N-body simulations, and show that they agree at a high level of detail.
We establish the criterion for chaos in three-planet systems, for systems
similar to those discovered by the Kepler spacecraft. Our main results are as
follows: (i) The simplest criterion, which is based on overlapping mean motion
resonances MMR’s), only agrees with numerical simulations at a very crude
level. (ii) Much greater accuracy is attained by considering neighboring MMR’s
that do not overlap. We work out the width of the chaotic zones around each of
the neighbors, and also provide simple approximate expressions for the widths.
(iii) Even greater accuracy is provided by the overlap of three-body resonances
(3BR’s), which accounts for fine-grained structure seen in maps from N-body
simulations, and also predicts the Lyapunov times. Previous studies conflict on
whether overlap of MMR’s or of 3BR’s drive interplanetary chaos. We show that
both do, and in fact they are merely different ways of looking at the same
effect. (iv) We compare both criteria with high-resolution maps of chaos from
N-body simulations, and show that they agree at a high level of detail.
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