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An algorithm for evolving collisionless stellar systems is described. Our approach is similar to that suggested earlier by van Albada, McGlynn, and more specifically Clutton-Brock, in that Poisson's equation is solved by expanding the density and potential in a set of basis functions. However, the basis set used here is constructed so that the lowest order members well-approximate a galaxy obeying the de Vaucouleurs R¹/4^ law in projection. Consequently, it will be possible to study the evolution of systems with density profiles like the R¹/4^ law using only a few terms in the expansions. A good fit is also obtained for a truncated isothermal distribution and, so, our method will be quite appropriate for galaxies with flat rotation curves. Since our method is similar in spirit to solving N one-body problems, the cpu cost scales with particle number as O (N) with a relatively small coefficient. Hence, calculations employing N ~ 10⁶^-10⁷^ are straightforward on existing supercomputers, making possible simulations having significantly smoother fields than with direct methods such as tree-codes. Even larger N should he feasible on multiple-cpu computers since opportunities for parallelism abound. Moreover, the flexibility of the algorithm suggests a number of refinements that may suppress discreteness noise relative to direct N- body methods. Owing to its one-body character, our method lends itself to an iterative technique akin to those utilized by Ostriker and collaborators for nonspherical stars and by Schwarzschild for equilibrium stellar-dynamical systems. In the present context, one finds orbits in a given static or time-dependent gravitational field and then, from the resultant density, p (r, t), revises the potential, φ (r, t). However, because of Poisson noise in the representation of the density field, the convergence properties of this scheme are problematic. Possible scientific uses of our technique are discussed, including tidal perturbations of dwarf galaxies, the adiabatic growth of central masses in spheroidal galaxies, instabilities in realistic galaxy models, and secular processes in galactic evolution.
Hernquist et al. (Sat,) studied this question.