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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 $alpha approx 0.2 - 0.33$. We develop a simple analytic model for the cluster mass-radius relation. We consider a galaxy disc in hydrostatic equilibrium, which hosts a population of molecular clouds that fragment into clumps undergoing cluster formation and feedback-driven expansion. The model predicts a mass-radius relation of $R_{star} propto M_{star}^{1/2}$ and a dependence on the kpc-scale gas surface density $R_{star} propto Sigma_{rm g}^{-1/2}$, which results from the formation of more compact clouds (and cluster-forming clumps within) at higher gas surface densities. This environmental dependence implies that the high-pressure environments in which the most massive clusters can form also induce the formation of clusters with the smallest radii, thereby shallowing the observed MRR at high-masses towards the observed $R_{star} propto M_{star}^{1/3}$. At low cluster masses, relaxation-driven expansion induces a similar shallowing of the MRR. We combine our predicted MRR with a simple population synthesis model and apply it to a variety of star-forming environments, finding good agreement. Our model predicts that the high-pressure formation environments of globular clusters at high redshift naturally led to the formation of clusters that are considerably more compact than those in the local Universe, thereby increasing their resilience to tidal shock-driven disruption and contributing to their survival until the present day.
Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber-Jackson relation suggests a strong positive correlation between mass and radius. O
In order to allow a better understanding of the origin of Galactic field populations, dynamical equivalence of stellar-dynamical systems has been postulated by Kroupa and Belloni et al. to allow mapping of solutions of the initial conditions of embed
We have undertaken the largest systematic study of the high-mass stellar initial mass function (IMF) to date using the optical color-magnitude diagrams (CMDs) of 85 resolved, young (4 Myr < t < 25 Myr), intermediate mass star clusters (10^3-10^4 Msun
While the stellar Initial Mass Function (IMF) appears to be close to universal within the Milky Way galaxy, it is strongly suspected to be different in the primordial Universe, where molecular hydrogen cooling is less efficient and the gas temperatur
Resolved observations of millimetre-sized dust, tracing larger planetesimals, have pinpointed the location of 26 Edgeworth-Kuiper belt analogs. We report that a belts distance $R$ to its host star correlates with the stars luminosity $L_{star}$, foll