2023MNRAS.524..968R

Massive star clusters are often used as tracers of galaxy formation and assembly. In order to do so, we must understand their properties at formation, and how those properties change with time, galactic environment, and galaxy assembly history. The two most important intrinsic properties that govern star cluster evolution are mass and radius. In this paper, we investigate 10 theoretically and observationally motivated initial size-mass relations for star clusters, and evolve populations of clusters through galaxy formation models. We compare our results to each other and to observations of cluster populations in M83, M31, and the Milky Way. We find that none of our size-mass relations agree with the observations after 6-10 Gyr of evolution. We can successfully reproduce the cluster mass functions with models that have a small range of initial radii, and which do not allow cluster radii to change with time. However, these models do not agree with our understanding of cluster evolution, which does involve radius evolution, and do not match the observed distributions of radii. We note that there is a region of parameter space where clusters are optimally protected from both tidal shocks and evaporation due to two-body relaxation. Clusters that are allowed to evolve into this parameter space will likely survive. An improved understanding of both mass and radius evolution of star clusters in realistic, time-varying galactic potentials is necessary to appropriately make the connection between present-day cluster properties and their use as tracers of galaxy formation and assembly.