The Panchromatic Hubble Andromeda Treasury: Triangulum Extended Region (PHATTER). VI. The High-Mass Stellar Initial Mass Function of M33

We measure the high-mass stellar initial mass function (IMF) from resolved stars in M33 young stellar clusters. Leveraging Hubble Space Telescope's high resolving power, we fully model the IMF probabilistically. We first model the optical CMD of each cluster to constrain its power-law slope Γ, marginalized over other cluster parameters in the fit (e.g., cluster age, mass, and radius). We then probabilistically model the distribution of MF slopes for a highly strict cluster sample of 9 clusters more massive than log(Mass/M_⊙)=3.6; above this mass, all clusters have well-populated main sequences of massive stars and should have accurate recovery of their MF slopes, based on extensive tests with artificial clusters. We find the ensemble IMF is best described by a mean high-mass slope of Γ = 1.49±0.18, with an intrinsic scatter of σ^2_Γ = 0.02^+0.16_0.00, consistent with a universal IMF. We find no dependence of the IMF on environmental impacts such as the local star formation rate or galactocentric radius within M33, which serves as a proxy for metallicity. This Γ measurement is consistent with similar measurements in M31, despite M33 having a much higher star formation rate intensity. While this measurement is formally consistent with the canonical Kroupa (Γ = 1.30) IMF, as well as the Salpeter (Γ = 1.35)) value, it is the second Local Group cluster sample to show evidence for a somewhat steeper high-mass IMF slope. We explore the impacts a steeper IMF slope has on a number of astronomical sub-fields.