The S-Star Cluster at the Center of the Milky Way: On the nature of
  diffuse NIR emission in the inner tenth of a parsec
  Sagittarius A*, the super-massive black hole at the center of the Milky Way,
is surrounded by a small cluster of high velocity stars, known as the S-stars.
We aim to constrain the amount and nature of stellar and dark mass associated
with the cluster in the immediate vicinity of Sagittarius A*. We use
near-infrared imaging to determine the $K_\mathrm{s}$-band luminosity function
of the S-star cluster members, and the distribution of the diffuse background
emission and the stellar number density counts around the central black hole.
This allows us to determine the stellar light and mass contribution expected
from the faint members of the cluster. We then use post-Newtonian N-body
techniques to investigate the effect of stellar perturbations on the motion of
S2, as a means of detecting the number and masses of the perturbers. We find
that the stellar mass derived from the $K_\mathrm{s}$-band luminosity
extrapolation is much smaller than the amount of mass that might be present
considering the uncertainties in the orbital motion of the star S2. Also the
amount of light from the fainter S-cluster members is below the amount of
residual light at the position of the S-star cluster after removing the bright
cluster members. If the distribution of stars and stellar remnants is strongly
enough peaked near Sagittarius A*, observed changes in the orbital elements of
S2 can be used to constrain both their masses and numbers. Based on simulations
of the cluster of high velocity stars we find that at a wavelength of 2.2
$\mu$m close to the confusion level for 8 m class telescopes blend stars will
occur (preferentially near the position of Sagittarius A*) that last for
typically 3 years before they dissolve due to proper motions.
