  We examine the effect of an accretion disc on the orbits of stars in the
central star cluster surrounding a central massive black hole by performing a
suite of 39 high-accuracy direct N-body simulations using state-of-the art
software and accelerator hardware, with particle numbers up to 128k. The
primary focus is on the accretion rate of stars by the black hole (equivalent
to their tidal disruption rate for black holes in the small to medium mass
range) and the eccentricity distribution of these stars. Our simulations vary
not only the particle number, but disc model (two models examined), spatial
resolution at the centre (characterised by the numerical accretion radius) and
softening length. The large parameter range and physically realistic modelling
allow us for the first time to confidently extrapolate these results to real
galactic centres. While in a real galactic centre both particle number and
accretion radius differ by a few orders of magnitude from our models, which are
constrained by numerical capability, we find that the stellar accretion rate
converges for models with N > 32k. The eccentricity distribution of accreted
stars, however, does not converge. We find that there are two competing effects
at work when improving the resolution: larger particle number leads to a
smaller fraction of stars accreted on nearly-circular orbits, while higher
spatial resolution increases this fraction. We scale our simulations to some
nearby galaxies and find that the expected boost in stellar accretion (or tidal
disruption, which could be observed as X-ray flares) in the presence of a gas
disc is about a factor of 10. Even with this boost, the accretion of mass from
stars is still a factor of ~ 100 slower than the accretion of gas from the
disc. Thus, it seems accretion of stars is not a major contributor to black
hole mass growth.
