Structure of rst-order mean motion resonances

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Table of contents

1 Introduction 
1.1 A brief history of Planetary Science
1.1.1 The discovery of exoplanetary systems
1.1.2 The exoplanets sample
1.1.3 The Solar System in perspective and implications of the exoplanets sample
1.2 Planetary formation
1.2.1 Protoplanetary discs
1.2.2 Building the planets: Overview of accretion processes
1.2.3 Shaping the planets’ orbits during the disc phase: Planetary type-I migration and eccentricity damping
1.3 This thesis in context
2 Hamiltonian mechanics and the planetary problem 
2.1 Hamiltonian systems
2.1.1 Link with Lagrangian formalism
2.1.2 Dynamical variables
2.1.3 Canonical transformations
2.1.4 Integrable dynamics and action-angle variables
2.1.5 Equilibrium points and linear stability
2.1.6 Basic examples of Hamiltonian systems
2.2 Planetary systems in Hamiltonian mechanics
2.2.1 The two-body problem
2.2.2 The planetary problem
2.3 Elements of Hamiltonian perturbation theory
2.3.1 First order perturbation theory
2.3.2 An introduction to adiabatic theory
2.3.3 Application of the adiabatic theory to resonant capture
3 Two planets { The structure of resonant pairs and capture into mean motion resonance 
3.1 Structure of rst-order mean motion resonances
3.1.1 First and higher order expansions of the Hamiltonian in the eccentricities
3.1.2 Equilibrium points of the averaged Hamiltonian
3.1.3 Frequencies in the limit of small amplitude of libration
3.2 Capture into resonance by type-I migration
3.2.1 Convergent inward migration in disc and resonant capture
3.2.2 Planet-disc interactions and evolution in mean motion resonance
4 Three-planet systems and the near-resonant population 
4.1 The near-resonant population
4.1.1 Methods and physical setup
4.2 Analytical model for three resonant planets
4.2.1 Resonant equilibrium points
4.2.2 Resonant repulsion for three-planets systems
4.3 A scenario for dissipative evolution of three-planet systems
4.3.1 Choice of systems
4.3.2 Analytical maps
4.3.3 Numerical simulations
4.4 Results
4.4.1 Probabilistic measure of a resonant conguration in Kepler-305, YZ Cet and Kepler-
4.4.2 The 5:4 { 4:3 resonant chain on Kepler-60 and other near-resonant systems with k >
4.5 Conclusions
5 The onset of instability in resonant chains
5.1 Introduction
5.2 2 Planets
5.3 3 Planets
5.3.1 Numerical stability maps for N = 3 and k = 3
5.3.2 Numerical and analytical investigation of the phenomenon
5.3.3 Rescaled Hamiltonian and new set of canonical variables
5.3.4 Purely resonant dynamics
5.3.5 The synodic contribution
5.3.6 Dependence on k
5.4 N Planets
6 Extreme secular excitation of eccentricity inside mean motion resonance
6.1 Small bodies driven into star-grazing orbits by planetary perturbations
6.2 Planetary Hamiltonian
6.3 Studying the averaged Hamiltonian
6.4 Eect of short-range forces
6.5 Results
6.6 Conclusions
7 Conclusions 
7.1 Future perspectives