Interaction of Massive Black Hole Binaries with Their Stellar Environment. II. Loss Cone Depletion and Binary Orbital Decay

We study the long-term evolution of massive black hole binaries (MBHBs) atthe centers of galaxies using detailed scattering experiments to solve the fullthree-body problem. Ambient stars drawn from a isotropic Maxwelliandistribution unbound to the binary are ejected by the gravitational slingshot.We construct a minimal, hybrid model for the depletion of the loss cone and theorbital decay of the binary, and show that secondary slingshots - starsreturning on small impact parameter orbits to have a second super-elasticscattering with the MBHB - may considerably help the shrinking of the pair inthe case of large binary mass ratios. In the absence of loss-cone refilling bytwo-body relaxation or other processes, the mass ejected before the stalling ofa MBHB is half the binary reduced mass. About 50% of the ejected stars areexpelled ejected in a "burst" lasting ~1E4 yrs M_6^1/4, where M_6 is the binarymass in units of 1E6 Msun. The loss cone is completely emptied in a few bulgecrossing timescales, 1E7 yrs M_6^1/4. Even in the absence of two-bodyrelaxation or gas dynamical processes, unequal mass and/or eccentric binarieswith M_6 >0.1 can shrink to the gravitational wave emission regime in less thana Hubble time, and are therefore "safe" targets for the planned LaserInterferometer Space Antenna (LISA).Comment: Minor revision. 10 pages, 7 figures, ApJ in pres