THE DYNAMICAL EVOLUTION OF MASSIVE BLACK-HOLE BINARIES .1. HARDENING IN A FIXED STELLAR BACKGROUND

The stellar ejection rate and the rates of change of the binary semima jor axis and eccentricity are derived from scattering experiments for the restricted three-body problem. They are used to study the evolutio n of binaries in simple models for galactic nuclei, starting soon afte r the black holes become bound and continuing until the evolution is d ominated by the emission of gravitational radiation or until the eject ed mass is too large for the galaxy to be considered fixed. The eccent ricity growth is found to be unimportant unless the binary forms with a large eccentricity. The scattering results suggest that a binary wit h masses m(1) greater than or equal to m(2) should not be considered h ard until its orbital velocity exceeds the background velocity dispers ion by a factor that scales as (1 + m(1)/m(2))(1/2). The results are c ompared with predictions from Chandrasekhar's dynamical-friction formu la and with previous work on the capture and scattering of comets by p lanetary systems.