Young stellar cluster dilution near supermassive black holes: the impact
  of Vector Resonant Relaxation on neighbour separation
  We investigate the rate of orbital orientation dilution of young stellar
clusters in the vicinity of supermassive black holes. Within the framework of
vector resonant relaxation, we predict the time evolution of the two-point
correlation function of the stellar orbital plane orientations as a function of
their initial angular separation and diversity in orbital parameters
(semi-major axis, eccentricity). As expected, the larger the spread in initial
orientations and orbital parameters, the more efficient the dilution of a given
set of co-eval stars, with a characteristic timescale set up by the coherence
time of the background potential fluctuations. A Markovian prescription which
matches numerical simulations allows us to efficiently probe the underlying
kinematic properties of the unresolved nucleus when requesting consistency with
a given dilution efficiency, imposed by the observed stellar disc within the
one arcsecond of Sgr A*. As a proof of concept, we compute maps of constant
dilution times as a function of the semi major axis cusp index and fraction of
intermediate mass black holes in the old background stellar cluster. This
computation suggests that vector resonant relaxation should prove useful in
this context since it impacts orientations on timescales comparable to the
stars' age.
