A reverse KAM method to estimate unknown mutual inclinations in exoplanetary systems

A reverse KAM method to estimate unknown mutual inclinations in exoplanetary systems The inclinations of exoplanets detected via radial velocity method are essentially unknown. We aim to provide estimations of the ranges of mutual inclinations that are compatible with the long-term stability of the system. Focusing on the skeleton of an extrasolar system, i.e. considering only the two most massive planets, we study the Hamiltonian of the three-body problem after the reduction of the angular momentum. Such a Hamiltonian is expanded both in Poincaré canonical variables and in the small parameter $$D_2$$ D 2 , which represents the normalised angular momentum deficit. The value of the mutual inclination is deduced from $$D_2$$ D 2 and, thanks to the use of interval arithmetic, we are able to consider open sets of initial conditions instead of single values. Looking at the convergence radius of the Kolmogorov normal form, we develop a reverse KAM approach in order to estimate the ranges of mutual inclinations that are compatible with the long-term stability in a KAM sense. Our method is successfully applied to the extrasolar systems HD 141399, HD 143761 and HD 40307. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Celestial Mechanics and Dynamical Astronomy Springer Journals

A reverse KAM method to estimate unknown mutual inclinations in exoplanetary systems

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Physics; Astrophysics and Astroparticles; Dynamical Systems and Ergodic Theory; Aerospace Technology and Astronautics; Geophysics/Geodesy; Classical Mechanics
ISSN
0923-2958
eISSN
1572-9478
D.O.I.
10.1007/s10569-018-9829-5
Publisher site
See Article on Publisher Site

Abstract

The inclinations of exoplanets detected via radial velocity method are essentially unknown. We aim to provide estimations of the ranges of mutual inclinations that are compatible with the long-term stability of the system. Focusing on the skeleton of an extrasolar system, i.e. considering only the two most massive planets, we study the Hamiltonian of the three-body problem after the reduction of the angular momentum. Such a Hamiltonian is expanded both in Poincaré canonical variables and in the small parameter $$D_2$$ D 2 , which represents the normalised angular momentum deficit. The value of the mutual inclination is deduced from $$D_2$$ D 2 and, thanks to the use of interval arithmetic, we are able to consider open sets of initial conditions instead of single values. Looking at the convergence radius of the Kolmogorov normal form, we develop a reverse KAM approach in order to estimate the ranges of mutual inclinations that are compatible with the long-term stability in a KAM sense. Our method is successfully applied to the extrasolar systems HD 141399, HD 143761 and HD 40307.

Journal

Celestial Mechanics and Dynamical AstronomySpringer Journals

Published: Apr 30, 2018

References

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