Figure 9: Evolution of the binary semi-major axis (a) and hardening rate (b) in a set of high accuracy -body simulations; the initial galaxy model was a low-central-density Plummer sphere [20]. Units are , , with the total energy. (a) Dashed lines are simulations with binary mass and solid lines are for , in units where the total galaxy mass is one. (b) Filled (open) circles are for  . Crosses indicate the hardening rate predicted by a simple model in which the supply of stars to the binary is limited by the rate at which they can be scattered into the binary’s influence sphere by gravitational encounters. The simulations with largest () exhibit the nearly dependence expected in the “empty loss cone” regime that is characteristic of real galaxies.