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Fig. 6

image

Mass-size relation of ellipsoidal clusters, shown with cloud-cluster mass ratio α∗ ,c = 1,2,3, which are plotted with blue solid, green dashed, red dot-dashed lines, respectively, using anisotropic turbulence following Kolmogorov spectrum (upper panel) and isotropic turbulence (lower panel). The turbulence efficiency ε = 0.5 is used, and the shadowed region represents the range of solutions for ε ∈ [0.2,0.7]. The elliptical patches represent the form of the clusters. With the molecular cloud density-size relation ρR-1, the clusters follow a RM0.5 trend for a given α∗ ,c. The gaseous protocluster corresponding to 104 M cloud is traced in yellow, which is indicative of an evolutionary sequence roughly following RM. The radius of the gaseous protocluster does not depend too much on the underlying assumption of the turbulent energy distribution, while the aspect ratio is smaller in the anisotropic case. The dots are the observed star-forming clumps from Fall et al. (2010) and Urquhart et al. (2014).

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