A new Monte Carlo code for star cluster simulations - I. Relaxation

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 Henon in the 70's (Henon 1971b,a; Henon 1973. 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 2 x 10(6) particles can be simulated on a standard personal computer and the CPU time required scales as N-p ln(N-p) with the particle number N-p. Furthermore, the number of simulated stars needs not be equal to N-p but can be arbitrarily larger. A companion paper will treat further physical elements, mostly relevant to galactic nuclei.