A new method to find the potential center of N-body systems

We present a new and fast method to find the potential center of an N-body distribution. The method uses an iterative algorithm which exploits the fact that the gradient of the potential is null at its center: it uses a smoothing radius to avoid getting trapped in secondary minima. We have tested this method on several random realizations of King models (in which the numerical computation of this center is rather difficult, due to the constant density within their cores), and compared its performance and accuracy against a more straightforward, but computer intensive method, based on cartesian meshes of increasing spatial resolution. In all cases, both methods converged to the same center, within the mesh resolution, but the new method is two orders of magnitude faster. We have also tested the method with one astronomical problem: the evolution of a 10(5) particle King model orbiting around a fixed potential that represents our Galaxy. We used a spherical harmonics expansion N-body code, in which the potential center determination is crucial for the correct, force computation. We compared this simulation with another one in which a method previously used to determine the expansion center is employed (White 1983). Our routine gives better results in energy conservation and mass loss