The Perils of Clumpfind: The Mass Spectrum of Sub-structures in Molecular Clouds

We study the mass spectrum of sub-structures in the Perseus Molecular Cloud Complex traced by 13CO (1-0), finding that $dN/dM\propto M^{-2.4}$ for the standard Clumpfind parameters. This result does not agree with the classical $dN/dM\propto M^{-1.6}$. To understand this discrepancy we study the robustness of the mass spectrum derived using the Clumpfind algorithm. Both 2D and 3D Clumpfind versions are tested, using 850 $\mu$m dust emission and 13CO spectral-line observations of Perseus, respectively. The effect of varying threshold is not important, but varying stepsize produces a different effect for 2D and 3D cases. In the 2D case, where emission is relatively isolated (associated with only the densest peaks in the cloud), the mass spectrum variability is negligible compared to the mass function fit uncertainties. In the 3D case, however, where the 13CO emission traces the bulk of the molecular cloud, the number of clumps and the derived mass spectrum are highly correlated with the stepsize used. The distinction between "2D" and "3D" here is more importantly also a distinction between "sparse" and "crowded" emission. In any "crowded" case, Clumpfind should not be used blindly to derive mass functions. Clumpfind's output in the "crowded" case can still offer a statistical description of emission useful in inter-comparisons, but the clump-list should not be treated as a robust region decomposition suitable to generate a physically-meaningful mass function. We conclude that the 13CO mass spectrum depends on the observations resolution, due to the hierarchical structure of MC.