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

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.