The Lives and Deaths of Star Clusters near the Galactic Center

We study the evolution and observability of young, compact star clusters near the Galactic center, such as the Arches and Quintuplet systems. The clusters are modeled by integrating the equations of motion of all stars while accounting for the internal evolution of stars and binaries, as well as the effect of the Galactic tidal field. We find that clusters within 150 pc of the Galactic center dissolve within ~55 Myr, but their projected densities drop below the background density in the direction of the Galactic center within only a few megayears, effectively making these clusters undetectable after that time. Detailed observations of the Arches cluster, taken at face value, suggest that its mass function is unusually flat and that the cluster contains an overabundance of stars more massive than 20 M☉. Our dynamical analysis, however, shows that the observed characteristics of the Arches cluster are consistent with a perfectly normal initial mass function. The observed anomalies are then caused by a combination of observational selection effects and the dynamical evolution of the cluster. We calibrate the current parameters of the Arches cluster using a normal initial mass function and conclude that the cluster is more massive than 40,000 M☉, has a half-mass radius of about 0.35 pc, and is located between 50 and 90 pc from the Galactic center.