A Selfconsistent Field Method for Galactic Dynamics
Abstract
An algorithm for evolving collisionless stellar systems is described. Our approach is similar to that suggested earlier by van Albada, McGlynn, and more specifically CluttonBrock, 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 wellapproximate a galaxy obeying the de Vaucouleurs R^1/4^ law in projection. Consequently, it will be possible to study the evolution of systems with density profiles like the R^1/4^ 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 onebody problems, the cpu cost scales with particle number as O(N) with a relatively small coefficient. Hence, calculations employing N ~ 10^6^10^7^ are straightforward on existing supercomputers, making possible simulations having significantly smoother fields than with direct methods such as treecodes. Even larger N should he feasible on multiplecpu 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 onebody 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 stellardynamical systems. In the present context, one finds orbits in a given static or timedependent 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 February 1992
 DOI:
 10.1086/171025
 Bibcode:
 1992ApJ...386..375H
 Keywords:

 Celestial Mechanics;
 Computational Astrophysics;
 Galaxies;
 Stellar Motions;
 Algorithms;
 Astronomical Models;
 Dynamical Systems;
 Numerical Analysis;
 Astrophysics;
 CELESTIAL MECHANICS;
 STELLAR DYNAMICS;
 METHODS: NUMERICAL