Abstract
Star clusters are collisional and dark matter (DM) free stellar systems, where their evolution is ruled by two-body interactions and the galactic potential. Using direct summation N-body simulations, I study how the observational properties of star clusters can be used to: (i) distinguish between DM free and DM dominated objects. From observations, the nature of several faint stellar systems in the Milky Way halo is not clear, therefore, I quantify the contribution of star clusters to the faint stellar systems population. (ii) Probe the underlying DM density of their host galaxy. I apply a new method to the recently discovered Eridanus~II ultra-faint dwarf galaxy that hosts a star cluster in its centre. I find that a cored DM density profile naturally reproduces the observed properties of Eridanus II’s star cluster. (iii) Infer their progenitor properties if they are accreted star clusters, such as Crater. From its properties I find that Crater is likely to be tidally stripped from a dwarf galaxy, and it must have formed extended and with a low concentration. Throughout this thesis, the comparison of simulations and data took into consideration observational biases and uncertainties. I show that the initial conditions of star clusters can heavily influence its present-day properties, and that the stellar evolution prescriptions can also impact the final star cluster properties, such as the neutron stars natal kick distribution. I conclude, through a series of test cases, that N-body simulations can be used to reproduce the observed properties of star clusters, and these can ultimately probe their host galaxy DM distribution.