Ultra-light axions as dark matter: soliton cores in isolation and around supermassive black holes

The current cosmological model ΛCDM has been remarkably successful in describing the observed large-scale structure of the Universe. On small scales, however, there are several discrepancies between observations and dark matter simulations, such as the Missing Satellite, the cusp-core and the Too-Big-to-Fail problems. Fuzzy Dark Matter (FDM) represents a compelling alternative, replacing the Weakly Interacting Massive Particles (WIMPs) with Ultra-Light Dark Matter (ULDM), described by a massive boson with mass around m ∼ (10⁻²² ÷ 10⁻¹⁸) eV, for which axions and axion-like particles are promising candidates. In this mass range, ULDM exhibits wave-like behavior, characterized by the de Broglie scale λdB ∼ 1 kpc. Below this scale, the Heisenberg uncertainty principle provides a quantum pressure that counteracts gravitational collapse, suppressing small-scale structure formation. The dynamics of FDM is governed by the Schrödinger-Poisson (SP) equations. Their ground-state, stationary solution is a soliton, which forms at the center of FDM halos. The goal of the Master Thesis is to study the properties of such solitonic structures, which constitute dense, stable, and coherent cores with flat density profiles in the innermost region, which may provide a solution to the cusp-core problem. To this end, we numerically solved the SP system to characterize the soliton density profile, both in isolation and in the presence of a central supermassive black hole (SMBH). The SMBH significantly alters the central core by compressing its density profile, accreting mass from the surrounding scalar field, or inhibiting soliton formation through dynamical heating. The interaction between SMBHs and ULDM provides a high-precision testing ground for the model. Characterizing how ultra-light axions impact the small-scale cosmological structure, particularly through SMBH-soliton interactions, thus provides a test of FDM against ΛCDM.