  We investigate the dynamical interaction of a central star cluster
surrounding a super-massive black hole and a central accretion disk. The
dissipative force acting on stars in the disk leads to an enhanced mass flow
towards the super-massive black hole and to an asymmetry in the phase space
distribution due to the rotating accretion disk. The accretion disk is
considered as a stationary Keplerian rotating disk, which is vertically
extended in order to employ a fully self-consistent treatment of stellar
dynamics including the dissipative force originating from star-gas ram pressure
effects. The stellar system is treated with a direct high-accuracy N-body
integration code. A star-by-star representation, desirable in N-body
simulations, cannot be extended to real particle numbers yet. Hence, we
carefully discuss the scaling behavior of our model with regard to particle
number and tidal accretion radius. The main idea is to find a family of models
for which the ratio of two-body relaxation time and dissipation time (for
kinetic energy of stellar orbits) is constant, which then allows us to
extrapolate our results to real parameters of galactic nuclei. Our model is
derived from basic physical principles and as such it provides insight into the
role of physical processes in galactic nuclei, but it should be regarded as a
first step towards more realistic and more comprehensive simulations.
Nevertheless, the following conclusions appear to be robust: the star accretion
rate onto the accretion disk and subsequently onto the super-massive black hole
is enhanced by a significant factor compared to purely stellar dynamical
systems neglecting the disk. This process leads to enhanced fueling of central
disks in active galactic nuclei and to an enhanced rate of tidal stellar
disruptions. [Abridged]
