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.