The VMC Survey XXVII. Young Stellar Structures in the LMC$'$s Bar
  Star-Forming Complex
  Star formation is a hierarchical process, forming young stellar structures of
star clusters, associations, and complexes over a wide scale range. The
star-forming complex in the bar region of the Large Magellanic Cloud is
investigated with upper main-sequence stars observed by the VISTA Survey of the
Magellanic Clouds. The upper main-sequence stars exhibit highly non-uniform
distributions. Young stellar structures inside the complex are identified from
the stellar density map as density enhancements of different significance
levels. We find that these structures are hierarchically organized such that
larger, lower-density structures contain one or several smaller, higher-density
ones. They follow power-law size and mass distributions as well as a lognormal
surface density distribution. All these results support a scenario of
hierarchical star formation regulated by turbulence. The temporal evolution of
young stellar structures is explored by using subsamples of upper main-sequence
stars with different magnitude and age ranges. While the youngest subsample,
with a median age of log($\tau$/yr)~=~7.2, contains most substructure,
progressively older ones are less and less substructured. The oldest subsample,
with a median age of log($\tau$/yr)~=~8.0, is almost indistinguishable from a
uniform distribution on spatial scales of 30--300~pc, suggesting that the young
stellar structures are completely dispersed on a timescale of $\sim$100~Myr.
These results are consistent with the characteristics of the 30~Doradus complex
and the entire Large Magellanic Cloud, suggesting no significant environmental
effects. We further point out that the fractal dimension may be
method-dependent for stellar samples with significant age spreads.
