Properties of hierarchically forming star clusters
  We undertake a systematic analysis of the early (< 0.5 Myr) evolution of
clustering and the stellar initial mass function in turbulent fragmentation
simulations. These large scale simulations for the first time offer the
opportunity for a statistical analysis of IMF variations and correlations
between stellar properties and cluster richness. The typical evolutionary
scenario involves star formation in small-n clusters which then progressively
merge; the first stars to form are seeds of massive stars and achieve a
headstart in mass acquisition. These massive seeds end up in the cores of
clusters and a large fraction of new stars of lower mass is formed in the outer
parts of the clusters. The resulting clusters are therefore mass segregated at
an age of 0.5 Myr, although the signature of mass segregation is weakened
during mergers. We find that the resulting IMF has a smaller exponent
(alpha=1.8-2.2) than the Salpeter value (alpha=2.35). The IMFs in subclusters
are truncated at masses only somewhat larger than the most massive stars (which
depends on the richness of the cluster) and an universal upper mass limit of
150 Msun is ruled out. We also find that the simulations show signs of the
IGIMF effect proposed by Weidner & Kroupa, where the frequency of massive stars
is suppressed in the integrated IMF compared to the IMF in individual clusters.
We identify clusters through the use of a minimum spanning tree algorithm which
allows easy comparison between observational survey data and the predictions of
turbulent fragmentation models. In particular we present quantitative
predictions regarding properties such as cluster morphology, degree of mass
segregation, upper slope of the IMF and the relation between cluster richness
and maximum stellar mass. [abridged]
