Gas is hierarchical in space and time, presumably because the gas is
compressed by turbulent motions in a scale-free fashion. The
self-gravitational force is scale free also at masses far above the
thermal Jeans mass (~ 1
M
). For
a typical relationship between velocity dispersion and size that scales as
R1/2, clouds of all masses at constant pressure have
the same degree of gravitational self-binding.
Hierarchical cloud structure means that stars form in hierarchical patterns, and it follows then that the efficiency of star formation (Mstars / Mtotal) increases with the average density. Bound star clusters, which require a high efficiency, therefore form at high density. This explains at a very fundamental level why bound clusters form in the first place. Variations in the fraction of star formation that goes into bound clusters may be explained in the same way, with pressure playing an important role.
Hierarchical structure ensures that the clusters start with a mass function that is a power law with a slope close to -2. There could be an upper mass cut off.