Hardening in a Time--Evolving Stellar Background: Hyper--Velocity Stars, Orbital Decay and Prediction for Lisa

We study the long-term evolution of massive black hole binaries (MBHBs) at the centers of galaxies using detailed full three-body scattering experiments. Stars, drawn from a distribution unbound to the binary, are ejected by the gravitational slingshot. We quantify the effect of secondary slingshots -- stars returning on small impact parameter orbits to have a second super-elastic scattering with the MBHB -- on binary separation. Even in the absence of two-body relaxation or gas dynamical processes, very unequal mass binaries of mass M=10^7 solar masses can shrink to the gravitational wave emission regime in less than a Hubble time, and are therefore a target for the planned Laser Interferometer Space Antenna (LISA). Three-body interactions create a subpopulation of hypervelocity stars on nearly radial, corotating orbits, with a spatial distribution that is initially highly flattened in the inspiral plane of the MBHB, but becomes more isotropic with decreasing binary separation. The mass ejected is ~0.7 times the binary reduced mass, and most of the stars are ejected in an initial burst lasting much less than a bulge crossing time.