The spatial distribution of stars in open clusters
  The analysis of the distribution of stars in open clusters may yield
important information on the star formation process and early dynamical
evolution of stellar clusters. Here we address this issue by systematically
characterizing the internal spatial structure of 16 open clusters in the Milky
Way spanning a wide range of ages. Cluster stars have been selected from a
membership probability analysis based on a non-parametric method that uses both
positions and proper motions and does not make any a priori assumption on the
underlying distributions. The internal structure is then characterized by means
of the minimum spanning tree method (Q parameter), King profile fitting, and
the correlation dimension (Dc) for those clusters with fractal patterns. On
average, clusters with fractal-like structure are younger than those exhibiting
radial star density profiles and an apparent trend between Q and age is
observed in agreement with previous ideas about the dynamical evolution of the
internal spatial structure of stellar clusters. However, some new results are
obtained from a more detailed analysis: (a) a clear correlation between Q and
the concentration parameter of the King model for those cluster with radial
density profiles, (b) the presence of spatial substructure in clusters as old
as 100 Myr, and (c) a significant correlation between fractal dimension and age
for those clusters with internal substructure. Moreover, the lowest fractal
dimensions seem to be considerably smaller than the average value measured in
galactic molecular cloud complexes.
