The VMC Survey. XXIX. Turbulence-Controlled Hierarchical Star Formation
  in the Small Magellanic Cloud
  In this paper we report a clustering analysis of upper main-sequence stars in
the Small Magellanic Cloud, using data from the VMC survey (the VISTA
near-infrared YJKs survey of the Magellanic system). Young stellar structures
are identified as surface overdensities on a range of significance levels. They
are found to be organized in a hierarchical pattern, such that larger
structures at lower significance levels contain smaller ones at higher
significance levels. They have very irregular morphologies, with a
perimeter-area dimension of 1.44 +/- 0.02 for their projected boundaries. They
have a power-law mass-size relation, power-law size/mass distributions, and a
lognormal surface density distribution. We derive a projected fractal dimension
of 1.48 +/- 0.03 from the mass-size relation, or of 1.4 +/- 0.1 from the size
distribution, reflecting significant lumpiness of the young stellar structures.
These properties are remarkably similar to those of a turbulent interstellar
medium (ISM), supporting a scenario of hierarchical star formation regulated by
supersonic turbulence.
