The distribution of stars around the Milky Way's central black hole II:
  Diffuse light from sub-giants and dwarfs
  This is the second of three papers that search for the predicted stellar cusp
around the Milky Way's central black hole, Sagittarius A*, with new data and
methods. We aim to infer the distribution of the faintest stellar population
currently accessible through observations around Sagittarius A*. We use
adaptive optics assisted high angular resolution images obtained with the NACO
instrument at the ESO VLT. Through optimised PSF fitting we remove the light
from all detected stars above a given magnitude limit. Subsequently we analyse
the remaining, diffuse light density. The analysed diffuse light arises from
sub-giant and main-sequence stars with KS ~ 19 - 20 with masses of 1 - 2 Msol .
These stars can be old enough to be dynamically relaxed. The observed power-law
profile and its slope are consistent with the existence of a relaxed stellar
cusp around the Milky Way's central black hole. We find that a Nuker law
provides an adequate description of the nuclear cluster's intrinsic shape
(assuming spherical symmetry). The 3D power-law slope near Sgr A* is \gamma =
1.23 +- 0.05. At a distance of 0.01 pc from the black hole, we estimate a
stellar mass density of 2.3 +- 0.3 x 10^7 Msol pc^-3 and a total enclosed
stellar mass of 180 +- 20 Msol. These estimates assume a constant mass-to-light
ratio and do not take stellar remnants into account. The fact that no cusp is
observed for bright (Ks 16) giant stars at projected distances of roughly
0.1-0.3 pc implies that some mechanism has altered their appearance or
distribution.
