2015ApJ...806..198W

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 (10³-10⁴ M_☉), observed as part of the Panchromatic Hubble Andromeda Treasury program. We fit each cluster's CMD to measure its mass function (MF) slope for stars ≳2 M_☉. By modeling the ensemble of clusters, we find the distribution of MF slopes is best described by Γ = +1.45_–0.06^+0.03 with a very small intrinsic scatter and no drastic outliers. This model allows the MF slope to depend on cluster mass, size, and age, but the data imply no significant dependencies within this regime of cluster properties. The lack of an age dependence suggests that the MF slope has not significantly evolved over the first ∼25 Myr and provides direct observational evidence that the measured MF represents the IMF. Taken together, this analysis–based on an unprecedented large sample of young clusters, homogeneously constructed CMDs, well-defined selection criteria, and consistent principled modeling–implies that the high-mass IMF slope in M31 clusters is universal. The IMF has a slope (Γ = +1.45_–0.06^+0.03; statistical uncertainties) that is slightly steeper than the canonical Kroupa (+1.30) and Salpeter (+1.35) values, and our measurement of it represents a factor of ∼20 improvement in precision over the Kroupa IMF (+1.30±0.7). Using our inference model on select Milky Way (MW) and LMC high-mass IMF studies from the literature, we find Γ_MW ∼ +1.15 ± 0.1 and Γ_LMC ∼ +1.3 ± 0.1, 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 the literature of 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. To facilitate practical use over the full stellar mass spectrum, we have grafted the M31 high-mass IMF slope onto widely used sub-solar mass Kroupa and Chabrier IMFs. The increased steepness in the M31 high-mass IMF slope implies that commonly used UV- and Hα-based star formation rates should be increased by a factor of ∼1.3-1.5 and the number of stars with masses > 8 M_☉ is ∼25% fewer than expected for a Salpeter/Kroupa IMF.