From NBODY1 to NBODY6: The growth of an industry

I review the development of direct N-body codes at Cambridge over nearly 40 years, highlighting the main stepping stones. The first code (NBODY1) was based on the simple concepts of a force polynomial combined with individual time steps, where numerical problems due to close encounters were avoided by a softened potential. Fortuitously, the elegant Kustaanheimo-Stiefel two -body regularization soon permitted small star clusters to be studied (NBOD Y3). Subsequent extensions to unperturbed three-body and four-body regulari zation proved beneficial in dealing with multiple interactions. Investigati ons of larger systems became possible with the Ahmad-Cohen neighbor scheme which was used more than 20 years ago for expanding universe models of 4000 galaxies (NBODY2). Combining the neighbor scheme with the regularization p rocedures enabled more realistic star clusters to be considered (NBODY5). A fter a period of simulations with no apparent technical progress, chain reg ularization replaced the treatment of compact subsystems (NBODY3, NBODY5). More recently, the Hermite integration method provided a major advance and has been implemented on the special-purpose HARP computers (NBODY4) togethe r with an alternative version for workstations and supercomputers (NBODY6). These codes also include a variety of algorithms for stellar evolution bas ed on fast lookup functions. The treatment of primordial binaries contains efficient procedures for chaotic two-body motion as well as tidal circulari zation, and special attention is paid to hierarchical systems and their sta bility. This family of N-body codes constitutes a powerful tool for dynamic al simulations which is freely available to the astronomical community, and the massive effort owes much to collaborators.