Mass-size scaling M~ r^1.67 of massive star-forming clumps -- evidences
  of turbulence-regulated gravitational collapse
  We study the fragmentation of eight massive clumps using data from ATLASGAL
870 $\mu$m, SCUBA 850 and 450 $\mu$m, PdBI 1.3 and 3.5 mm, and probe the
fragmentation from 1 pc to 0.01 pc scale. We find that the masses and the sizes
of our objects follow $M \sim r^{1.68\pm0.05}$. The results are in agreements
with the predictions of Li (2017) where $M \sim r^{5/3}$. Inside each object,
the densest structures seem to be centrally condensed, with $\rho(r)\sim
r^{-2}$. Our observational results support a scenario where molecular gas in
the Milky Way is supported by a turbulence characterized by a constant energy
dissipation rate, and gas fragments like clumps and cores are structures which
are massive enough to be dynamically detached from the ambient medium.
