Abstract
We have developed a new simulation code aimed at studying the stellar dynamics of a galactic central star cluster surrounding a massive black hole. In order to include all the relevant physical ingredients (2-body relaxation, stellar mass spectrum, collisions, tidal disruption, ...), we chose to revive a numerical scheme pioneered by Hénon in the 70's (Hénon [CITE],a; Hénon [CITE]. It is basically a Monte Carlo resolution of the Fokker-Planck equation. It can cope with any stellar mass spectrum or velocity distribution. Being a particle-based method, it also allows one to take stellar collisions into account in a very realistic way. This first paper covers the basic version of our code which treats the relaxation-driven evolution of a stellar cluster without a central BH. A technical description of the code is presented, as well as the results of test computations. Thanks to the use of a binary tree to store potential and rank information and of variable time steps, cluster models with up to particles can be simulated on a standard personal computer and the CPU time required scales as with the particle number . Furthermore, the number of simulated stars needs not be equal to but can be arbitrarily larger. A companion paper will treat further physical elements, mostly relevant to galactic nuclei.
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