High-Mass Star Formation. III. The Functional Form of the Submillimeter Clump Mass Function

We investigate the mass function of cold, dusty clumps in 11 low- and high-mass star-forming regions. Using a homogeneous fitting technique, we analyze the shape of each region's clump mass function and examine the commonalities among them. We find that the submillimeter continuum clump mass function in low-mass star-forming regions is typically best fitted by a lognormal distribution, while that in high-mass star-forming regions is better fitted by a double power law. A single power-law clump mass distribution is ruled out in all cases. Fitting all of the regions with a double power law, we find that the mean power-law exponent at the high-mass end of each mass function is αhigh = -2.4 ± 0.1, consistent with the Salpeter result of α = -2.35. We find no region-to-region trend in αhigh with the mass scale of the clumps in a given region, as characterized by their median mass. Similarly, nonparametric tests show that the shape of the clump mass function does not change much from region to region, despite the obvious changes in the intrinsic mass scale. This result is consistent with the hypothesis that the clump mass distribution is determined by a highly stochastic process, such as turbulent fragmentation. It may also suggest that the data reduction and analysis techniques strongly affect the shape of the derived mass function.