A New Tree Code Method for Simulating Planetesimal Dynamics

A new tree code method for simulating 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 attened nature of Keplerian disks to maximize eciency. 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 years of evolution. The average relative force error incurred in such runs is less than 0.2% 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.