Gravitational Relaxation and Kinetic Theory in Fuzzy Dark Matter

Fuzzy Dark Matter (FDM), composed of ultra-light bosons with a de Broglie wavelength on galactic scales, offers an intriguing alternative to traditional cold dark matter models. On large scales, FDM behaves similarly to cold dark matter, but on the scale of its de Broglie wavelength, it exhibits unique wave-like density fluctuations that influence gravitational dynamics. These stochastic density fluctuations scatter stars and black holes, causing relaxation processes that can be described by the dynamics classical two-body interactions. In this thesis, we study the relaxation dynamics of FDM halos using the Fokker–Planck equation to describe the statistical evolution of test particles in the fluctuating potential of an FDM halo. We derive the kinetic equations for FDM and solve them to analyze the evolution of velocity distributions, the dielectric function, and the dispersion relation for linear waves in FDM systems. The implications of these processes on astrophysical phenomena, including core formation and dynamical friction, are explored, offering novel insights into the behavior of FDM on small scales and its role in shaping galactic structures.