Gravitational N-body calculation in a discrete phase space

Abstract

An n-body calculation designed for astronomical studies in stellar dynamics is able to handle large number of particles by restricting the set of points over which force values are required. The resulting model can be treated exactly in a computer by using integer arithmetic; the “data” representing the physical system are modified to conform to the model. Reversibility and an exact Liouville theorem result, making the model close to the physics in the sense that exactly conserved quantities of the model correspond to essential features of the physics. The cost of this pleasing correspondence is a reduction in the accuracy of conserving some of the conventional integrals. While the formulation affords a useful viewpoint for considering the relationship between computer models and the physical systems they represent that is quite different from that underlying conventional calculations, numerical considerations differ only in that the numerical methods used are coarser than with conventional calculations. The numerical approximations and the features responsible for the exact properties are presented in detail. The calculation has been successfully used as a tool for numerical experiments on spiral structure and gravitational stability.