Fractal statistics in young star clusters: structural parameters and dynamical evolution

We used fractal statistics to quantify the degree of observed substructures in a sample of 50 embedded clusters and more evolved open clusters (<100 Myr) found in different galactic regions. The observed fractal parameters were compared with N-body simulations from the literature, which reproduce star-forming regions under different initial conditions and geometries that are related to the cluster's dynamical evolution. Parallax and proper motion from Gaia-DR2 were used to accurately determine cluster membership by using the Bayesian model and cross-entropy technique. The statistical parameters Q, <(m)over bar> and (s) over bar were used to compare observed cluster structure with simulations. A low level of substructures (Q < 0.8) is found for most of the sample that coincides with simulations of regions showing fractal dimension D similar to 2-3. Few clusters (<20 per cent) have uniform distribution with a radial density profile (alpha < 2). A comparison of 0 with mass segregation (Lambda(MSR)) and local density as a function of mass (Sigma(LDR)) shows the clusters coinciding with models that adopt supervirial initial conditions. The age-crossing time plot indicates that our objects are dynamically young, similar to the unbound associations found in the Milky Way. We conclude that this sample may be expanding very slowly. The flat distribution in the Q-age plot and the absence of trends in the distributions of Lambda(MSR) and Sigma(LDR) against age show that in the first 10 Myr the clusters did not change structurally and seem not to have expanded from a much denser region.