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Theses

Architecture and stability of planetary systems

Abstract : The architecture of a planetary systems is a signpost of their formation and history.Moreover, the large number of recent and future exoplanets discoveries allows to study the exoplanet system population.Besides, the observations of exoplanet systems has enriched the diversity of planetary system architecture, revealing that the Solar System shape is far from being the norm.However, the organization of planetary systems is heavily affected by dynamical stability, making individual studies particularly challenging.Since planets dynamics are chaotic, a detailed stability analysis study is computationally expensive.In this thesis, I develop analytic stability criteria for planet dynamics.In the secular system, the conservation of the total angular momentum and semi-major axes imply the conservation of the Angular Momentum Deficit (AMD).The AMD is a measure of a system’s eccentricities and mutual inclinations and act as a dynamical temperature of the system.Based on this consideration, we make the simplifying assumption that the dynamics can be replaced by AMD exchanges between the planets.In the first chapter we define the concept of AMD-stability. The AMD-stability criterion allows to discriminate between a priori stable planetary systems and systems for which the stability is not granted and needs further investigations.We show how AMD-stability can be used to establish a classification of the multiplanet systems in order to exhibit theplanetary systems that are long-term stable because they are AMD-stable, and those that are AMD-unstable which then require someadditional dynamical studies to conclude on their stability. We classify 131 multiplanet systems from the exoplanet.eu database with sufficiently well-known orbital elements.While the AMD criterion is rigorous, AMD conservation is only granted in absence of mean-motion resonances (MMR).If the MMR islands overlap, the system experiences chaos leading to instability.In the second chapter, we extend the AMD-stability criterion to take into account the overlap of first-order MMR.I derive analytically a new overlap criterion for first-order MMR.This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases.In the third chapter I explain how the Hill stability can be understood in the AMD framework.Widely used, the Hill stability is a topological stability criterion for the three body system.However, most studies only use the coplanar and circular orbit approximation.We show that the general Hill stability criterion can be expressed as a function of only semi-major axes, masses, and total AMD of the system.The proposed criterion is only expanded in the planets-to-star mass ratio and not in the orbital elements.When studying AMD-unstable system, numerical simulations are mandatory.However the long timescales in planet dynamics make necessary the use of symplectic methods.These methods provide very accurate and fast integration when a system is stable.Their downside is that they are limited to fixed time-step integration.For unstable systems, the integrator may fail to resolve a close encounter and become inaccurate.In the fourth chapter, I propose a time renormalization that allow to use high order symplectic integrator with adaptive time-step at close encounter.The algorithm is well-adapted to systems of few similar masses planets.In the final chapter, I revisit the planet formation toy model developed by J. Laskar.While the AMD is conserved in the secular dynamics, it decreases during planets collisions.Laskar's model can be solved analytically for the average outcome and numerical simulations are very quick allowing to build large system population.I show that this formation model is in good agreement with recent realistic planet formation simulations where the final architecture results from a giant impact phase.
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  • HAL Id : tel-02879847, version 1

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Antoine Petit. Architecture and stability of planetary systems. Other. Université Paris sciences et lettres, 2019. English. ⟨NNT : 2019PSLEO005⟩. ⟨tel-02879847⟩

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