Due to the limitations of the radial velocity method, our knowledge of the spatial configuration of the hundreds of exoplanetary systems discovered so far is limited. The aim of the present work is, through analytical study based on a secular Hamiltonian expansion and numerical explorations performed with a chaos detector, to provide constraints on the orbital inclinations and the mutual inclinations of several two-planet extrasolar systems, that ensure the long-term stability of the system. In the first part, for systems with low eccentricities, we rely on perturbation theory and apply a reverse KAM approach to determine the ranges of the mutual inclination that allow the convergence of the algorithm constructing the invariant tori. In the second part, for systems with moderate to high eccentricities, we find that long-term stable evolutions of non-coplanar configurations exist for all the selected systems, either at low mutual inclinations, or at high mutual inclinations preferentially if the system is in the Lidov-Kozai resonance. We also show how the relativistic effects influence the extent of the Lidov-Kozai resonant region for planetary systems with close-in planets.
|la date de réponse||2019|
|Sponsors||Fund for Research Training in Industry and Agriculture (FRIA)|
|Superviseur||ANNE-SOPHIE LIBERT (Promoteur), Anne Lemaitre (Président), Ugo Locatelli (Jury), Christos Efthymiopoulos (Jury) & Marco Sansottera (Jury)|