Dissipationless Formation and Evolution of the Milky Way Nuclear Star Cluster

In one widely discussed model for the formation of nuclear star clusters (NSCs), massive globular clusters spiral into the center of a galaxy and merge to form the nucleus. It is now known that at least some NSCs coexist with supermassive black holes (SMBHs); this is the case, for instance, in the Milky Way. In this paper, we investigate how the presence of an SMBH at the center of the Milky Way impacts the merger hypothesis for the formation of its NSC. Starting from a model consisting of a low-density nuclear stellar disk and the SMBH, we use direct N-body simulations to follow the successive inspiral and merger of globular clusters. The clusters are started on circular orbits of radius 20 pc, and their initial masses and radii are set up in such a way as to be consistent with the galactic tidal field at that radius. These clusters, decayed orbitally in the central region due to their large mass, were followed in their inspiral events; as a result, the total accumulated mass by approximate to 10 clusters is about 1.5 x 10(7)M(circle dot). Each cluster is disrupted by the SMBH at a distance of roughly 1 pc. The density profile that results after the final inspiral event is characterized by a core of roughly this radius and an envelope with density that falls off rho similar to r(-2). These properties are similar to those of the Milky Way NSC, with the exception of the core size, which in the Milky Way is somewhat smaller. But by continuing the evolution of the model after the final inspiral event, we find that the core shrinks substantially via gravitational encounters in a time (when scaled to the Milky Way) of 10 Gyr as the stellar distribution evolves toward a Bahcall-Wolf cusp. We also show that the luminosity function of the Milky Way NSC is consistent with the hypothesis that 1/2 of the mass comes from old (similar to 10 Gyr) stars, brought in by globular clusters, with the other half due to continuous star formation. We conclude that a model in which a large fraction of the mass of the Milky Way NSC is due to infalling globular clusters is consistent with existing observational constraints.