The Link Between Ejected Stars, Hardening and Eccentricity Growth of
  Super Massive Black Holes in Galactic Nuclei
  The hierarchical galaxy formation picture suggests that super massive black
holes (MBHs) observed in galactic nuclei today have grown from coalescence of
massive black hole binaries (MBHB) after galaxy merging. Once the components of
a MBHB become gravitationally bound, strong three-body encounters between the
MBHB and stars dominate its evolution in a "dry" gas free environment, and
change the MBHB's energy and angular momentum (semi-major axis, eccentricity
and orientation). Here we present high accuracy direct N-body simulations of
spherical and axisymmetric (rotating) galactic nuclei with order a million
stars and two massive black holes that are initially unbound. We analyze the
properties of the ejected stars due to slingshot effects from three-body
encounters with the MBHB in detail. Previous studies have investigated the
eccentricity and energy changes of MBHs using approximate models or Monte-Carlo
three body scatterings. We find general agreement with the average results of
previous semi-analytic models for spherical galactic nuclei, but our results
show a large statistical variation. Our new results show many more phase space
details of how the process works, and also show the influence of stellar system
rotation on the process. We detect that the angle between the orbital plane of
the MBHBs and that of the stellar system (when it rotates) influences the
phase-space properties of the ejected stars. We also find that massive MBHB
tend to switch stars with counter-rotating orbits into co-rotating orbits
during their interactions.
