On the initial mass–radius relation of stellar clusters

ABSTRACT Young stellar clusters across nearly five orders of magnitude in mass appear to follow a power-law mass–radius relationship (MRR), $R_{\star }\propto M_{\star }^{\alpha }$, with α ≈ 0.2–0.33. We develop simple analytic model for the cluster relation. consider galaxy disc hydrostatic equilibrium, which hosts population molecular clouds that fragment into clumps undergoing formation and feedback-driven expansion. The predicts relation }^{1/2}$ dependence on kpc-scale gas surface density \Sigma _{\rm g}^{-1/2}$, results from more compact (and cluster-forming within) at higher densities. This environmental implies high-pressure environments most massive can form also induce smallest radii, thereby shallowing observed MRR high-masses towards }^{1/3}$. At low masses, relaxation-driven expansion induces similar MRR. combine our predicted synthesis apply it variety star-forming environments, finding good agreement. Our globular high redshift naturally led are considerably than those local Universe, increasing their resilience tidal shock-driven disruption contributing survival until present day.