The Unusual Initial Mass Function of the Arches Cluster

Abstract: As a young massive cluster in the Central Molecular Zone, the Arches cluster is a valuable probe of the stellar Initial Mass Function (IMF) in the extreme Galactic Center environment. We use multi-epoch Hubble Space Telescope observations to obtain high-precision proper motion and photometric measurements of the cluster, calculating cluster membership probabilities for stars down to 1.8 M${\odot}$ between cluster radii of 0.25 pc -- 3.0 pc. We achieve a cluster sample with just ~8% field contamination, a significant improvement over photometrically-selected samples which are severely compromised by the differential extinction across the field. Combining this sample with K-band spectroscopy of 5 cluster members, we forward model the Arches cluster to simultaneously constrain its IMF and other properties (such as age and total mass) while accounting for observational uncertainties, completeness, mass segregation, and stellar multiplicity. We find that the Arches IMF is best described by a 1-segment power law that is significantly top-heavy: $\alpha$ = 1.80 $\pm$ 0.05 (stat) $\pm$ 0.06 (sys), where dN/dm $\propto$ m$^{-\alpha}$, though we cannot discount a 2-segment power law model with a high-mass slope only slightly shallower than local star forming regions ($\alpha$ = 2.04$^{+0.14}{-0.19}$ $\pm$ 0.04) but with a break at 5.8$^{+3.2}_{-1.2}$ $\pm$ 0.02 M$_{\odot}$. In either case, the Arches IMF is significantly different than the standard IMF. Comparing the Arches to other young massive clusters in the Milky Way, we find tentative evidence for a systematically top-heavy IMF at the Galactic Center.