The link between ejected stars, hardening and eccentricity growth of super massive black holes in galactic nuclei

The hierarchical galaxy formation picture suggests that supermassive black holes (SMBHs) observed in galactic nuclei today have grown from coalescence of massive black hole binaries (MBHB) after galaxy merging. Once the components of an 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 (semimajor axis, eccentricity, and orientation). Here we present high-accuracy direct N-body simulations of spherical and axisymmetric (rotating) galactic nuclei with order of 10 ⁶ stars and two MBHs 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 MBHBs tend to switch stars with counter-rotating orbits into corotating orbits during their interactions.