Dynamical Evolution of Elliptical Galaxies with Central Singularities

We study the effect of a massive central singularity on the structure of atriaxial galaxy using N-body simulations. Starting from a single initial model,we grow black holes with various final masses Mh and at various rates, rangingfrom impulsive to adiabatic. In all cases, the galaxy achieves a final shapethat 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 ratioMh/Mg of black hole mass to galaxy mass. When Mh/Mg < 0.3%, the galaxy evolvesin shape on a timescale that exceeds 100 orbital periods, or roughly a galaxylifetime. When Mh/Mg > 2%, the galaxy becomes axisymmetric in little more thana crossing time. We propose that the rapid evolution toward axisymmetric shapesthat occurs when Mh/Mg > 2% provides a negative feedback mechanism which limitsthe mass of central black holes by cutting off their supply of fuel.Comment: 27 Latex pages, 9 Postscript figures, uses aastex.sty. Accepted for Publication in The Astrophysical Journal, Nov. 26, 199