The Milky Way's nuclear star cluster: Old, metal-rich, and cuspy
  (abridged) We provide Ks photometry for roughly 39,000 stars and H-band
photometry for about 11,000 stars within a field of about 40"x40", centred on
Sgr A*. In addition, we provide Ks photometry of about 3,000 stars in a very
deep central field of 10"x10", centred on Sgr A*. We find that the Ks
luminosity function (KLF) is rather homogeneous within the studied field and
does not show any significant changes as a function of distance from the
central black hole on scales of a few 0.1 pc. By fitting theoretical luminosity
functions to the KLF, we derive the star formation history of the nuclear star
cluster. We find that about 80% of the original star formation took place 10
Gyr ago or longer, followed by a largely quiescent phase that lasted for more
than 5 Gyr. We clearly detect the presence of intermediate-age stars of about 3
Gyr in age. This event makes up about 15% of the originally formed stellar mass
of the cluster. A few percent of the stellar mass formed in the past few 100
Myr. Our results appear to be inconsistent with a quasi-continuous star
formation history. The stellar density increases exponentially towards Sgr A*
at all magnitudes between Ks=15 to 19. We also show that the precise properties
of the stellar cusp around Sgr A* are hard to determine because the star
formation history suggests that the star counts can be significantly
contaminated, at all magnitudes, by stars that are too young to be dynamically
relaxed. We find that the probability of observing any young (non-millisecond)
pulsar in a tight orbit around Sgr A* and beamed towards Earth is very low. We
argue that typical globular clusters, such as they are observed in and around
the Milky Way today, have probably not contributed to the nuclear cluster's
mass in any significant way. The nuclear cluster may have formed following
major merger events in the early history of the Milky Way.
