The fate of star clusters near the Galactic center I: Analytic considerations

A star cluster in a galactic nucleus sinks toward the galactic center due to dynamical friction. As it spirals inward, the cluster loses mass due to stellar evolution, relaxation driven evaporation, and tidal stripping, eventually dissolving in the galactic tidal field. We model the inspiral of dense young star clusters near the center of our Galaxy to study the extent of the region of parameter space in which the cluster can reach the inner parsec of the Galaxy within a few million years. Since we neglect changes in cluster structure due to internal evolution, the present study is most applicable to star clusters less than about one initial relaxation time old. We find that only star clusters with initial masses $\apgt 10^5$ {\msun} can reach the Galactic center from an initial distance of $\apgt 60$ pc within one initial relaxation time or a few million years, whichever is smaller.