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

Mara Volpi, Ugo Locatelli, Marco Sansottera

Research output: Contribution to journalArticlepeer-review

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 Poincar\'e canonical variables and in the small parameter $D_2$, which represents the normalised Angular Momentum Deficit. The value of the mutual inclination is deduced from $D_2$ 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.
Original languageEnglish
Article number36
JournalCelestial Mechanics & Dynamical Astronomy
Volume130
Issue number5
DOIs
Publication statusPublished - 1 May 2018
Externally publishedYes

Keywords

  • Celestial Mechanics
  • Exoplanets
  • KAM theory
  • n-Body planetary problem

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