Tracing star cluster formation and evolution with stellar kinematics

It is well established that star clusters are valuable probes in Astronomy across a wide range of disciplines from cosmology to stellar evolution. Indeed, star clusters are efficient tracers of intense star formation episodes across cosmic time and rich cradles of stellar-mass black holes (BHs), which are prime sources of gravitational waves. However, fundamental questions about the possible unifying principles governing their formation are yet unanswered. In addition, whether clusters form through the monolithic collapse of the gas cloud or the hierarchical merger of clumps is still an intense matter of debate. Despite tremendous observational and theoretical efforts, our understanding of star cluster formation and the actual role of the different underlying physical processes is still in its infancy. This thesis explores this long-standing problem with a multi-faceted approach, largely based on the dynamical study of very young clusters and associations in nearby star-forming regions and old massive clusters in the Galactic halo. Local star clusters represent the ideal laboratory for constraining the physical mechanisms at the basis of cluster formation as they can be resolved into individual stars, and thus they can be studied with a level of detail that cannot be achieved for distant systems. To this aim, this thesis uses a multi-diagnostic and multi-instrument approach, which is largely based on Gaia, Hubble Space Telescope (HST), and properly selected spectroscopic surveys (such as observations from the Multi Unit Spectroscopic Explorer, MUSE). We also used tailored N-body and Monte Carlo simulations to interpret the observed stellar cluster properties and to constrain the initial physical conditions for cluster formation and evolution. The analysis focused on two main aspects: i) the study of the early phases of cluster assembly and survival and ii) the long-term evolution of star clusters and the role of massive compact objects, such as BHs.