Table 2: Particle Number of Largest Simulation Feasible and GRAPE-6
Time Advantage
Table 2 gives a rough estimate of the maximum number of particles we will be able to use on both the general-purpose computers and GRAPE-6 at year 2000, based on the numbers at present. We here assumed that on both general-purpose computers and on GRAPE, we use most efficient algorithm. For collisional systems, we can expect very large gain, even if we take into account the difference in the algorithm used. For collisionless calculations, the gain is not very large, mainly because the size of the calculation is not limited by the calculation speed but by the amount of the memory available. For collisionless calculations, however, the calculation speed of GRAPE will be much faster.
In the following, we just briefly discuss the possible scientific outcomes. For globular clusters, we will be able to honestly simulate small globular clusters without cutting corners. Thus, we will be able to address the timescale problem [Heg96], which arises if we try to model globular clusters with number of particles less than that of real clusters. We will be able to understand the reason why the result of Fokker-Planck calculations and that of N-body calculations were wildly different [FH95], and to get solid understanding of the evolution of globular cluster under the effect of galactic tidal field and stellar evolution.
For planet formation, increased number of particles implies we can model a wider range in the radius with better initial mass resolution. Current simulations with GRAPE-4 are limited to very narrow range in the radius, and therefore cannot address, for example, the mechanism in which the separation of present-day planets are determined. Large scale simulations with GRAPE-6 will allow us to directly investigate the final stage of the planet formation.
Of course, what we learned from the advance in the simulation technique, and in particular from the use of GRAPE-4, is that the increase in the number of particles provided us not only quantitative improvements, but also qualitatively new results which were not anticipated beforehand. We certainly expect similar new results from GRAPE-6.