Models of Galaxies with Central Black Holes: Simulation Methods
  We present a method for simulating numerically the effect of the adiabatic growth of black holes on the structure of elliptical galaxies. Using a parallel self--consistent field code, we add black holes to N--body realizations of model distribution functions for spherical galaxies, using a continuous mass--spectrum. The variable particle mass, combined with a simple multiple timestep integration scheme, makes it possible to evolve the models for many dynamical times with $N \sim 10^6-10^8$, allowing high spatial and mass resolution. This paper discusses verification of the code using analytic models for spherical galaxies, comparing our numerical results of the effect of central black holes on the structure of the galaxies with previously published models. The intrinsic and projected properties of the final particle distribution, including higher order moments of the velocity distribution, permit comparison with observed characteristics of real galaxies, and constrain the masses of any central black holes present in those galaxies. Our technique is promising and is easily extended to axisymmetric and triaxial galaxies. 
Steinn Sigurdsson, Lars Hernquist and Gerald D. Quinlan