http://arxiv.org/abs/1912.05560
Young stellar clusters across nearly five orders of magnitude in mass appear to follow a simple mass-radius relationship (MRR), $R_{\star} \propto M_{\star}^{\alpha}$, with $\alpha \approx 0.2 – 0.33$. Here, we develop a simple analytic model to explain this observation. We begin by considering giant molecular clouds near virial equilibrium and subsequently relate the properties of the cluster to those of the cloud. In turn, we relate the cloud properties to those of the large-scale galactic environment. The model predicts an \textit{initial} mass-radius relation of constant surface density, $R_{\star} \propto M_{\star}^{1/2}$. It also predicts the initial cluster radius depends on the large-scale gas density $\Sigma_g$ of the ambient ISM, scaling as $R_{\star} \propto \Sigma_g^{-1/2}$. We argue that the tendency of observed clusters to fall along lines of shallower MRRs than our initial $R_{\star} \propto M_{\star}^{1/2}$ is in fact a combination of two effects. The fact that massive clusters can \textit{only} form in high gas-density environments, when combined with the $R_{\star} \propto \Sigma_g^{-1/2}$ scaling we find here, ultimately shallows the global slope at high masses to nearly $R_{\star} \propto M_{\star}^{1/3}$. Meanwhile, at low masses relaxation-driven expansion quickly shallows the MRR. We combine our predicted MRR with a simple population synthesis model and apply it to a range of star-forming environments, from nearby disc galaxies to nuclear starbursts, and find good agreement throughout. We provide quantitative predictions for the radii of proto-globular clusters (GCs) and discuss the implications of the model for GC evolution and survival across cosmic time as well as the dynamical assembly of black hole binaries in stellar clusters.
N. Choksi and J. Kruijssen
Fri, 13 Dec 19
68/75
Comments: 13 pages. MNRAS submitted. Comments welcome
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