Secular evolution of stellar clusters

Stellar systems in the Universe are mainly driven by gravity, a long-range force affecting every massive object. Recent surveys have produced a formidable quantity of data capturing the kinetic properties of the Galaxy and its components (such as globular clusters and its nucleus). Decades of research have allowed the astrophysical community to reach a good understanding of the formation of gravitationally bound structures: the Λ-CDM model. Still, the long-term evolution of these systems remains an ongoing subject of research. My thesis is focused on the evolution of gravitational systems on such secular timescales. My triple objective is: (i) to understand the particular mechanisms which operate on these long timescales; (ii) to identify the origin of the observed differences depending on the nature of these objects (geometry, kinematics, composition, ...); (iii) to deduce diagnostics for dark matter experiments (e.g., the identification of populations of intermediate mass black holes). In practice, this thesis aims at describing the secular fate of isolated stellar clusters by relying on kinetic theory. The master equation describing self-gravitating clusters over many orbital times is the Balescu–Lenard diffusion equation. It captures perturbatively the effect of resonant interactions between noise-driven fluctuations within the system. In this thesis, I specifically study two approximations of the Balescu–Lenard equation: (i) the inhomogeneous Landau limit, in which collective amplification is neglected; (ii) the (orbit-averaged) Chandrasekhar limit, in which local, incoherent deflections dominate over long-range resonances. I apply these formalisms to a variety of systems. First, I study the Galactic nucleus, where I present a fiducial likelihood analysis to probe the presence of intermediate mass black holes around Sgr A⋆. Second, I consider globular clusters with kinematic anisotropy and ultimately rotation. I first apply the extended non-resonant approach, which I validate by using large sets of direct N-body simulations. This allows me to investigate the rate of core collapse and the diffusion of orbital inclinations. I also study the impact of resonant relaxation on the effective Coulomb logarithm which enters the non-resonant formulation. Finally, I probe the space of physical parameters of galactic discs which are prone to bi-symmetric instabilities. Using linear response theory, I study the onset of bars. This allows me to understand the lack of bars in galactic discs observed in current hydrodynamical simulations.