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The radii of young (<100 Myr) star clusters correlate only weakly with theirmasses. This shallow relation has been used to argue that impulsive tidalperturbations, or `shocks', by passing giant molecular clouds (GMCs)preferentially disrupt low-mass clusters. We show that this mass-radiusrelation is in fact the result of the combined effect of two-body relaxationand repeated tidal shocks. Clusters in a broad range of environments includingthose like the solar neighbourhood evolve towards a typical radius of a fewparsecs, as observed, independent of the initial radius. This equilibriummass-radius relation is the result of a competition between expansion byrelaxation and shrinking due to shocks. Interactions with GMCs are moredisruptive for low-mass clusters, which helps to evolve the globular clustermass function (GCMF). However, the properties of the interstellar medium inhigh-redshift galaxies required to establish a universal GCMF shape are moreextreme than previously derived, challenging the idea that all GCs formed withthe same power-law mass function.

If it does not kill them, it makes them stronger: collisional evolution of star clusters with tidal shocks