A new tree code method for simulation of planetesimal dynamics

Abstract

A new tree code method for simulation of planetesimal dynamics is presented. A self-similarity argument is used to restrict the problem to a small patch of a ring of planetesimals at 1 AU from the sun. The code incorporates a sliding box model with periodic boundary conditions and surrounding ghost particles. The tree is self-repairing and exploits the flattened nature of Keplerian disks to maximize efficiency. The code uses a fourth-order force polynomial integration algorithm with individual particle time-steps. Collisions and mergers, which play an important role in planetesimal evolution, are treated in a comprehensive manner. In typical runs with a few hundred central particles, the tree code is approximately 2-3 times faster than a recent direct summation method and requires about 1 CPU day on a Sparc IPX workstation to simulate 100 yr of evolution. The average relative force error incurred in such runs is less than 0.2 per cent in magnitude. In general, the CPU time as a function of particle number varies in a way consistent with an O(N log N) algorithm. In order to take advantage of facilities available, the code was written in C in a Unix workstation environment.The unique aspects of the code are discussed in detail and the results of a number of performance tests - including a comparison with previous work - are presented.