Influence of a stellar cusp on the dynamics of young stellar discs and
  the origin of the S-stars in the Galactic Centre
  Observations of the Galactic Centre show evidence of one or two disc-like
structures of very young stars orbiting the central super-massive black hole
within a distance of a few 0.1 pc. A number of analyses have been carried out
to investigate the dynamical behaviour and consequences of these discs,
including disc thickness and eccentricity growth as well as mutual interaction
and warping. However, most of these studies have neglected the influence of the
stellar cusp surrounding the black hole, which is believed to be 1-2 orders of
magnitude more massive than the disc(s).
  By means of N-body integrations using our bhint code, we study the impact of
stellar cusps of different compositions. We find that although the presence of
a cusp does have an important effect on the evolution of an otherwise isolated
flat disc, its influence on the evolution of disc thickness and warping is
rather mild in a two-disc configuration. However, we show that the creation of
highly eccentric orbits strongly depends on the graininess of the cusp (i.e.
the mean and maximum stellar masses): While Chang (2009) recently found that
full cycles of Kozai resonance are prevented by the presence of an analytic
cusp, we show that relaxation processes play an important role in such highly
dense regions and support short-term resonances. We thus find that young disc
stars on initially circular orbits can achieve high eccentricities by resonant
effects also in the presence of a cusp of stellar remnants, yielding a
mechanism to create S-stars and hyper-velocity stars.
  Furthermore, we discuss the underlying initial mass function (IMF) of the
young stellar discs and find no definite evidence for a non-canonical IMF.
