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Mass Functions of Giant Molecular Clouds and Young Star Clusters in Six Nearby Galaxies

We compare the mass functions of young star clusters (ages $\leq 10$ Myr) and giant molecular clouds (GMCs) in six galaxies that cover a large range in mass, metallicity, and star formation rate (LMC, M83, M51, NGC 3627, the Antennae, and NGC 3256). We perform maximum-likelihood fits of the Schechter function, $ψ(M) = dN/dM \propto M^β \exp(-M/M_*)$, to both populations. We find that most of the GMC and cluster mass functions in our sample are consistent with a pure power-law distribution ($M_* \rightarrow \infty$). M51 is the only galaxy that shows some evidence for an upper cutoff ($M_*$) in both populations. Therefore, physical upper mass cutoffs in populations of both GMCs and clusters may be the exception rather than the rule. When we perform power-law fits, we find a range of indices $β_{\rm PL}=-2.3\pm0.3$ for our GMC sample and $β_{\rm PL}=-2.0\pm0.3$ for the cluster sample. This result, that $β_{\rm Clusters} \approx β_{\rm GMC} \approx -2$, is consistent with theoretical predictions for cluster formation and suggests that the star-formation efficiency is largely independent of mass in the GMCs.