The High-Mass Stellar Initial Mass Function in M31 Clusters

We have undertaken the largest systematic study of the high-mass stellar initial mass function (IMF) to date using the optical color-magnitude diagrams (CMDs) of 85 resolved, young (4 Myr < t < 25 Myr), intermediate mass star clusters (10^3-10^4 Msun), observed as part of the Panchromatic Hubble Andromeda Treasury (PHAT) program. We fit each cluster's CMD to measure its mass function (MF) slope for stars >2 Msun. For the ensemble of clusters, the distribution of stellar MF slopes is best described by $\Gamma=+1.45^{+0.03}_{-0.06}$ with a very small intrinsic scatter. The data also imply no significant dependencies of the MF slope on cluster age, mass, and size, providing direct observational evidence that the measured MF represents the IMF. This analysis implies that the high-mass IMF slope in M31 clusters is universal with a slope ($\Gamma=+1.45^{+0.03}_{-0.06}$) that is steeper than the canonical Kroupa (+1.30) and Salpeter (+1.35) values. Using our inference model on select Milky Way (MW) and LMC high-mass IMF studies from the literature, we find $\Gamma_{\rm MW} \sim+1.15\pm0.1$ and $\Gamma_{\rm LMC} \sim+1.3\pm0.1$, both with intrinsic scatter of ~0.3-0.4 dex. Thus, while the high-mass IMF in the Local Group may be universal, systematics in literature IMF studies preclude any definitive conclusions; homogenous investigations of the high-mass IMF in the local universe are needed to overcome this limitation. Consequently, the present study represents the most robust measurement of the high-mass IMF slope to date. We have grafted the M31 high-mass IMF slope onto widely used sub-solar mass Kroupa and Chabrier IMFs and show that commonly used UV- and Halpha-based star formation rates should be increased by a factor of ~1.3-1.5 and the number of stars with masses >8 Msun are ~25% fewer than expected for a Salpeter/Kroupa IMF. [abridged]