Abstract
The radii of young (. 100 Myr) star clusters correlate only weakly with their masses. This shallow relation has been used to argue that impulsive tidal perturbations, or ‘shocks’, by passing giant molecular clouds (GMCs) preferentially disrupt low-mass clusters. We show that this mass-radius relation is in fact the result of the combined effect of two-body relaxation and repeated tidal shocks. Clusters in a broad range of environments including those like the solar neighbourhood evolve towards a typical radius of a few parsecs, as observed, independent of the initial radius. This equilibrium mass-radius relation is the result of a competition between expansion by relaxation and shrinking due to shocks. Interactions with GMCs are more disruptive for low-mass clusters, which helps to evolve the globular cluster mass function (GCMF). However, the properties of the interstellar medium in high-redshift galaxies required to establish a universal GCMF shape are more extreme than previously derived, challenging the idea that all GCs formed with the same power-law mass function.