Galaxies with Supermassive Binary Black Holes: (II) A Model with Cuspy
  Galactic Density Profiles
  The existence and uniqueness of equilibrium points, including Lagrange Points
and Jiang-Yeh Points, of a galactic system with supermassive binary black holes
embedded in a centrally cuspy galactic halo are investigated herein. Differing
from the previous results of non-cuspy galactic profiles that Jiang-Yeh Points
only exist under a particular condition, it is found here that the Lagrange
Points, L2, L3, L4 and L5, Jiang-Yeh Points, JY1 and JY2, exist under general
conditions. The stability analysis shows that L2, L3, JY1 and JY2 are unstable.
However, L4 and L5 are only unstable when the galactic total mass is smaller
than a critical mass; otherwise they become neutrally stable centers. These
results will be important for further studies on the cores of early-type
galaxies.
