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 ($M_{\rm core} 10\, M_{\odot}$) 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.