Panchromatic Hubble Andromeda Treasury XVIII. The High-mass Truncation of the Star Cluster Mass Function

We measure the mass function for a sample of 840 young star clusters with ages between 10-300 Myr observed by the Panchromatic Hubble Andromeda Treasury (PHAT) survey in M31. The data show clear evidence of a high-mass truncation: only 15 clusters more massive than $10^4$ $M_{\odot}$ are observed, compared to $\sim$100 expected for a canonical $M^{-2}$ pure power-law mass function with the same total number of clusters above the catalog completeness limit. Adopting a Schechter function parameterization, we fit a characteristic truncation mass of $M_c = 8.5^{+2.8}_{-1.8} \times 10^3$ $M_{\odot}$. While previous studies have measured cluster mass function truncations, the characteristic truncation mass we measure is the lowest ever reported. Combining this M31 measurement with previous results, we find that the cluster mass function truncation correlates strongly with the characteristic star formation rate surface density of the host galaxy, where $M_c \propto$ $\langle \Sigma_{\mathrm{SFR}} \rangle^{\sim1.1}$. We also find evidence that suggests the observed $M_c$-$\Sigma_{\mathrm{SFR}}$ relation also applies to globular clusters, linking the two populations via a common formation pathway. If so, globular cluster mass functions could be useful tools for constraining the star formation properties of their progenitor host galaxies in the early Universe.