Galactic Dark Matter distribution and its implications for experimental searches

Dark Matter presents one of the key missing pieces in our understanding of the Universe. On the one hand, there is a substantial amount of independent astronomical and cosmological observations, which provide convincing evidence for its existence through various gravitational signatures. On the other hand, any non-gravitational interactions of Dark Matter remain elusive, despite more than two decades of dedicated searches in various experiments. Several of them have contended successful detection, however, such claims remain disputed, since they are in tension with null results of other related experiments and often suffer from considerable modelling uncertainties. One of the crucial unknowns entering the interpretation of direct and indirect Dark Matter searches is its distribution within galaxies. Together with rapid improvements in astronomical observations, this drives the need for accurate phase-space modelling of galactic Dark Matter distribution, which will be explored in detail throughout this thesis in various settings. First, a novel method for computing the phase-space distribution of relaxed Dark Matter component within axisymmetric systems will be presented. This method is of particular importance when addressing spiral galaxies and can have a significant impact on the interpretation of direct detection experiments, which crucially depends on the density and velocity distribution of Dark Matter in the solar neighbourhood. Therefore, the proposed phase-space distribution model will be applied to our Milky Way and carefully matched against recent measurements of the galactic kinematics. Furthermore, the corresponding impact on direct detection experiments and differences with respect to the traditional models, relying on Maxwellian velocity distribution and/or spherical symmetry, will be investigated. Regarding indirect detection, new results related to expected signals from dwarf satellite galaxies of the Milky Way will be presented, addressing the general case of velocity-dependent annihilation cross-section. Special attention will be given to a non-perturbative effect, commonly known as the Sommerfeld enhancement, which can lead to a significant boost of the annihilation signals. Similarly, as in the case of Milky Way, recent measurements of stellar kinematics within dwarf satellites will be used to bracket the astrophysical uncertainties entering the interpretation of corresponding indirect searches. Finally, a brand-new technique for detecting dark galactic subhalos will be proposed, which relies on the modern tools of machine learning and their ability to find subtle patterns in complex datasets. More precisely, the possibility of detecting tiny perturbations in stellar density and kinematics, induced by transpassing Dark Matter subhalos, will be addressed