Dynamical Evolution of Elliptical Galaxies with Central Singularities

We study the effect of a massive central singularity on the structure of a triaxial galaxy using N-body simulations. Starting from a single initial model, we grow black holes with various final masses Mh and at various rates, ranging from impulsive to adiabatic. In all cases, the galaxy achieves a final shape that is nearly spherical at the center and close to axisymmetric throughout. However, the rate of change of the galaxy’s shape depends strongly on the ratio Mh/Mg of black hole mass to galaxy mass. When Mh/Mg < ∼ 0.3%, the galaxy evolves in shape on a timescale that exceeds 10 orbital periods, or roughly a galaxy lifetime. When Mh/Mg > ∼ 2%, the galaxy becomes axisymmetric in little more than a crossing time. We propose that the rapid evolution toward axisymmetric shapes that occurs when Mh/Mg >∼ 10 −2 provides a negative feedback mechanism which limits the mass of central black holes by cutting off their supply of fuel.