The Panchromatic Hubble Andromeda Treasury: Triangulum Extended Region (PHATTER). III. The Mass Function of Young Star Clusters in M33

We measure the star cluster mass function for the Local Group galaxy M33. We use the catalog of stellar clusters selected from the Panchromatic Hubble Andromeda Treasury: Triangulum Extended Region (PHATTER) survey. We analyze 711 clusters in M33 with $\rm 7.0 < log(Age/yr) < 8.5$, and log($M/M_{\odot}$) $>$ 3.0 as determined from color-magnitude diagram fits to individual stars. The M33 cluster mass function is best described by a Schechter function with power law slope $\alpha = -2.06^{+0.14}_{-0.13}$, and truncation mass log($M_c/M_{\odot}$) $= 4.24^{+0.16}_{-0.13}$. The data show strong evidence for a high-mass truncation, thus strongly favoring a Schechter function fit over a pure power law. M33's truncation mass is consistent with the previously identified linear trend between $M_c$, and star formation rate surface density, \SigSFR. We also explore the effect that individual cluster mass uncertainties have on derived mass function parameters, and find evidence to suggest that large cluster mass uncertainties have the potential to bias the truncation mass of fitted mass functions on the one sigma level.