La description de l’évolution à long-terme des systèmes astrophysiques auto-gravitants tels que les disques stellaires, fait aujourd’hui l’objet d’un regain d’intérêt sous l’impulsion de deux développements récents. Cela repose tout d’abord sur le succès de la théorie Lambda-CDM pour décrire la formation des grandes structures et leurs interactions avec le milieu circum-galactique. En outre, de nouveaux développements théoriques permettent maintenant de décrire précisément l’amplification des perturbations extérieures ou internes, et leurs effets sur la structure orbitale d’un système sur les temps cosmiques. Ces progrès complémentaires nous permettent d’aborder la question lancinante des rôles respectifs de l’inné et de l’acquis sur les propriétés observées des systèmes auto-gravitants. Cette thèse est consacrée à la description de ces dynamiques séculaires, notamment lorsque l’auto-gravité joue un rôle important. Deux formalismes de diffusion, externe et interne, seront présentés en détail, et appliqués à différents problèmes astrophysiques. Dans un premier temps, nous étudierons les disques stellaires discrets infiniment fins, et retrouverons la formation d’étroites arêtes d’orbites résonantes en accord avec les observations et les simulations numériques, par le biais de la première mise en oeuvre de l’équation de Balescu-Lenard. Nous considérerons ensuite le mécanisme d’épaississement spontané des disques stellaires sous l’effet du bruit de Poisson. Enfin, nous illustrerons comment ces formalismes permettent également de décrire la dynamique des étoiles orbitant un trou noir supermassif dans les centres galactiques. / Understanding the long-term evolution of self-gravitating astrophysical systems, such as for example stellar discs, is now a subject of renewed interest, motivated by the combination of two factors. On the one hand, we now have at our disposal the well established Lambda-CDM model to describe the formation of structures and their interactions with the circum-galactic environment. On the other hand, recent theoretical works now provide a precise description of the amplification of external disturbances and discreteness noise, as well as their effects on a system’s orbital structure over cosmic time. These two complementary developments now allow us to address the pressing question of the respective roles of nature vs. nurture in the establishment of the observed properties of self-gravitating systems. The purpose of the present thesis is to describe such secular dynamics in contexts where self-gravity is deemed important. Two frameworks of diffusion, either external or internal, will be presented in detail, and applied to various astrophysical systems. This thesis will first investigate the secular evolution of discrete razor-thin stellar discs and recover the formation of narrow ridges of resonant orbits in agreement with observations and numerical simulations, thanks to the first implementation of the Balescu-Lenard equation. The spontaneous thickening of stellar discs as a result of Poisson shot noise will also be investigated. Finally, we will illustrate how the same formalisms allow us to describe the dynamics of stars orbiting a central super massive black hole in galactic centres.

Orientador: Ernesto Vieira Neto / Resumo: O estudo da formação e evolução do Sistema Solar é uma fonte de informação para entender sob quais condições a vida poderia surgir e evoluir. Nós apresentamos, nesta Tese de doutorado, um estudo numérico da fase final de acresção dos planetas gigantes do Sistema Solar durante e após a fase do disco de gás protoplanetário. Em nossas simulações, utilizamos um modelo recente e confiável para a formação de Urano e Netuno para esculpir as propriedades do disco trans-Netuniano original (Izidoro et al. , 2015a). Nós fizemos este estudo de uma maneira autoconsistente considerando os efeitos do gás e da evolução dos embriões planetários que formam Urano e Netuno por colisões gigantescas. Consideramos diferentes histórias de migração de Júpiter, devido a incerteza de como Júpiter migrou, durante a fase de gás. As nossas simulações permitiram obter pela primeira vez as propriedades orbitais do disco trans-Netuniano original. Então, calculamos o tempo de instabilidade dos planetas gigantes a partir de sistemas planetários que formam similares Urano e Netuno. Nossos resultados indicam fortemente que a instabilidade dos planetas gigantes acontecem cedo em até 500 milhões de anos e mais provável ainda ter acontecido em 136 milhões de anos após a dissipação do gás. Nós também realizamos simulações para discutir alguns efeitos dinâmicos que acontecem na região do cinturão de Kuiper. Estes efeitos acontecem quando Netuno esteve em alta excentricidade durante a instabilidade planetária. Para es... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: A study of the formation and evolution of the Solar System is a source of information for an understanding of what conditions life could arise and evolve. We present a numerical study of the final stage of accretion of the giant planets of the Solar System during and after the protoplanetary gas disc phase. In our simulations, we use a recent and reliable model for the formation of Uranus and Neptune to sculpt the properties of the original trans-Neptunian disk (Izidoro et al. , 2015a). We have done this study in a self-consistent way considering the effects of gas and the evolution of planetary embryos which form Uranus and Neptune by mutual giant collisions. We considered different Jupiter migration stories due to the uncertainty of how Jupiter’s migration was during the gas phase. Our simulations provide for the first time to obtain the orbital properties of the original trans-Neptunian disk. We then calculate the instability time of the giant planets from planetary systems which form similar Uranus and Neptune. Our results strongly indicate that the instability of the giant planets occurs early within 500 million years and even more likely to happen at 136 million years after gas dissipation. We also perform simulations to discuss some dynamical effects that happen in the Kuiper belt region. These effects happen when Neptune was in high eccentricity during planetary instability. For this problem, we use the simulations performed by Gomes et al. (2018) who investigated the... (Complete abstract click electronic access below) / Doutor