Constraints on Upper Cutoffs in the Mass Functions of Young Star Clusters

Abstract

We test claims that the power-law mass functions of young star clusters (ages $\lesssim\mbox{few}\times10^8$~yr) have physical upper cutoffs at $M_*\sim10^5~M_{\odot}$. Specifically, we perform maximum-likelihood fits of the Schechter function, $\psi(M)=dN/dM\propto M^{\beta}~\mbox{exp}(-M/M_*)$, to the observed cluster masses in eight well-studied galaxies (LMC, SMC, NGC 4214, NGC 4449, M83, M51, Antennae, and NGC 3256). In most cases, we find that a wide range of cutoff mass is permitted ($10^5~M_\odot \lesssim M_* < \infty$). We find a weak detection at $M_* \sim 10^5~M_\odot$ in one case (M51) and strong evidence against this value in two cases. However, when we include realistic errors in cluster masses in our analysis, the constraints on $M_*$ become weaker and there are no significant detections (even for M51). Our data are generally consistent with much larger cutoffs, at $M_*\sim\mbox{few}\times10^6~M_{\odot}$. This is the predicted cutoff from dynamical models in which old globular clusters and young clusters observed today formed by similar physical processes with similar initial mass functions.