Abridged: 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 (SBHs); this is the case, for instance, in the
Milky Way (MW). In this paper, we investigate how the presence of a SMBH at the
center of the MW 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 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. The total accumulated mass by ~10
clusters is about 1.5x10^7 Solar masses. Each cluster is disrupted by the SMBH
at a distance of roughly one parsec. 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 as 1/r^2. These properties are similar to
those of the MW NSC, with the exception of the core size, which in the MW is a
little 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 MW) of 10 Gyr as the stellar
distribution evolves toward a Bahcall-Wolf cusp. We also show that the
luminosity function of the MW NSC is consistent with the hypothesis that a
large fraction of the mass comes from (~10Gyr) old stars, brought in by
globular clusters. We conclude that a model in which a large fraction of the
mass of the MW NSC arose from infalling globular clusters is consistent with
existing observational constraints.Comment: 15 pages, 13 figures. ApJ accepte
