The distribution of stars around the Milky Way's black hole III:
  Comparison with simulations
  The distribution of stars around a massive black hole (MBH) has been
addressed in stellar dynamics for the last four decades by a number of authors.
Because of its proximity, the centre of the Milky Way is the only observational
test case where the stellar distribution can be accurately tested. Past
observational work indicated that the brightest giants in the Galactic Centre
(GC) may show a density deficit around the central black hole, not a cusp-like
distribution, while we theoretically expect the presence of a stellar cusp. We
here present a solution to this long-standing problem. We performed
direct-summation $N-$body simulations of star clusters around massive black
holes and compared the results of our simulations with new observational data
of the GC's nuclear cluster. We find that after a Hubble time, the distribution
of bright stars as well as the diffuse light follow power-law distributions in
projection with slopes of $\Gamma \approx 0.3$ in our simulations. This is in
excellent agreement with what is seen in star counts and in the distribution of
the diffuse stellar light extracted from adaptive-optics (AO) assisted
near-infrared observations of the GC. Our simulations also confirm that there
exists a missing giant star population within a projected radius of a few
arcsec around Sgr A*. Such a depletion of giant stars in the innermost 0.1 pc
could be explained by a previously present gaseous disc and collisions, which
means that a stellar cusp would also be present at the innermost radii, but in
the form of degenerate compact cores.
