How many young star clusters exist in the Galactic center?

We study the evolution and observability of young compact star clusters within similar to 200 pc of the Galactic center. Calculations are performed using direct N-body integration on the GRAPE-4, including the effects of both stellar and binary evolution and the external influence of the Galaxy. The results of these detailed calculations are used to calibrate a simplified model applicable over a wider range of cluster initial conditions. We find that clusters within 200 pc of the Galactic center dissolve within similar to 70 Myr. However, their projected densities drop below the background density in the direction of the Galactic center within similar to 20 Myr, effectively making these clusters undetectable after that time. Clusters farther from the Galactic center but at the same projected distance are more strongly affected by this selection effect and may go undetected for their entire lifetimes. Based on these findings, we conclude that the region within 200 pc of the Galactic center could easily harbor some 50 clusters with properties similar to those of the Arches or the Quintuplet systems.