Dinamica degli ammassi stellari giovani e della loro popolazione di buchi neri

Young star clusters are key objects to interpret a large number of astrophysical processes, from star and binary formation to the hierarchical assembly of the Milky Way. The spatial distribution and motions of young stars reflect the processes of cluster formation, while the kinematics of more evolved systems and the age dependence of their mass function inform us on how star clusters progressively dissolve into the field of the Galaxy. Finally, being the place where the most massive stars form, star clusters are building blocks for our comprehension of the formation of compact objects, which we can detect through gravitational-wave observations. Direct N-body simulations are usually adopted to integrate the evolution of star clusters since their earliest phases, but we often assume quite unrealistic initial conditions for such simulations. In Chapter 2, I provide an accurate modeling of the very first phases of the cluster's life. First, I make use of hydro-dynamical simulations of collapsing molecular clouds, which, coupled with appropriate recipes for star formation, yield realistic initial conditions. Then, I introduce a new algorithm to associate a primordial binary star population to such hydro-dynamical simulations. Finally, I quantify the impact of such primordial binaries on the global evolution of the cluster. I find that primordial binaries accelerate the star cluster dissolution, and enhance the formation of a hot core of massive objects. Hydro-dynamical simulations are an accurate method to obtain realistic initial conditions for star forming regions. However, producing large sets of hydro-dynamical simulations is prohibitively expensive in terms of computational time. In Chapter 3, I address this issue by introducing a novel algorithm to generate new star clusters from a given set of star masses, positions and velocities from a hydro-dynamical simulation. This method is based on a hierarchical clustering algorithm that learns a tree representation of the cluster phase-space. This is later turned into new realizations by modifying the initial branches of the tree, while preserving the characteristics of small scale structure responsible for most of the dynamical evolution. The new realizations qualitatively resemble the original simulation, and show a realistic evolution at all scales. In Chapter 4, I explore how dynamical interactions within young star clusters affect the properties of BBH mergers. I find that dynamically active environments produce more massive BBH mergers thanks to the high rate of dynamical exchanges, which favor the coupling of the most massive BHs. Also, the high initial cluster densities trigger a large number of stellar collisions. This, in turn, leads to a non-negligible number of BBH mergers with primary mass in the pair-instability mass gap, where BHs are not expected to form via isolated stellar evolution. In Chapter 5, I look for signatures of the presence of BHs the Hyades cluster, by comparing accurate $N-$body models to precise measurements from Gaia. I find that even a few BHs can affect the properties of visible stars in a quantifiable way, leading to less concentrated distributions. For the case of the Hyades, 3 BHs are favored to match the observed properties of the cluster. In massive star clusters, BHs born by the merger of other BHs can be retained, dynamically form new BBHs, and merge again. This hierarchical merger process can repeat several times and lead to a significant BH mass growth. In Chapter 6, I explore the process of hierarchical mergers in globular clusters. I investigate the importance of stellar evolution, two-body relaxation and tidal stripping by the host galaxy. My results indicate that globular clusters can only host hierarchical BH mergers up to the third generation, i.e. at least one generation less than what previously thought.