Evolution of the mass-radius relation of expanding very young star clusters

The initial mass–radius relation of embedded star clusters is an essential boundary condition for understanding the evolution of embedded clusters in which stars form to their release into the galactic field via an open star cluster phase. The initial mass–radius relation of embedded clusters deduced by Marks & Kroupa (2012, A&A, 543, A8) is significantly different from the relation suggested by Pfalzner et al. (2016, A&A, 586, A68). Here, we use direct N-body simulations to model the early expansion of embedded clusters after the expulsion of their residual gas. The observationally deduced radii of clusters up to a few million years old, compiled from various sources, are well fitted by N-body models, implying that these observed very young clusters are most likely in an expanding state. We show that the mass–radius relation of Pfalzner et al. (2016) reflects the expansion of embedded clusters following the initial mass–radius relation of Marks & Kroupa (2012). We also suggest that even the embedded clusters in ATLASGAL clumps with HII regions are probably already in expansion. All the clusters collected here from different observations show a mass-radius relation with a similar slope, which may indicate that all clusters were born with a profile resembling that of the Plummer phase-space distribution function.