Network of Star Formation: Fragmentation controlled by scale-dependent
  turbulent pressure and accretion onto the massive cores revealed in the
  Cygnus-X GMC complex
  Molecular clouds have complex density structures produced by processes
including turbulence and gravity. We propose a triangulation-based method to
dissect the density structure of a molecular cloud and study the interactions
between dense cores and their environments. In our {approach}, a Delaunay
triangulation is constructed, which consists of edges connecting these cores.
Starting from this construction, we study the physical connections between
neighboring dense cores and the ambient environment in a systematic fashion. We
apply our method to the Cygnus-X massive GMC complex and find that the core
separation is related to the mean surface density by $\Sigma_{\rm edge} \propto
l_{\rm core }^{-0.28 }$, which can be explained by {fragmentation controlled by
a scale-dependent turbulent pressure (where the pressure is a function of
scale, e.g. $p\sim l^{2/3}$)}. We also find that the masses of low-mass cores
($M_{\rm core} < 10\, M_{\odot}$) are determined by fragmentation, whereas
massive cores ($M_{\rm core} > 10\, M_{\odot}$) grow mostly through accretion.
The transition from fragmentation to accretion coincides with the transition
from a log-normal core mass function (CMF) to a power-law CMF. By constructing
surface density profiles measured along edges that connect neighboring cores,
we find evidence that the massive cores have accreted a significant fraction of
gas from their surroundings and thus depleted the gas reservoir. Our analysis
reveals a picture where cores form through fragmentation controlled by
scale-dependent turbulent pressure support, followed by accretion onto the
massive cores, {and the method can be applied to different regions to achieve
deeper understandings in the future.
