Monte Carlo simulations of star clusters - I. First results

A revision of Stodolkiewicz's Monte Carlo code is used to simulate evolution of star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. The first calculations for isolated, equal-mass N-body systems with three-body energy generation according to Spitzer's formulae show good agreement with direct N-body calculations for N = 2000, 4096 and 10 000 particles. The density, velocity, mass distributions, energy generation, number of binaries, etc., follow the N-body results. Only the number of escapers is slightly too high compared with N-body results, and there is no level-off anisotropy for advanced post-collapse evolution of Monte Carlo models as is seen in N-body simulations for N less than or equal to 2000. For simulations with N > 10 000 gravothermal oscillations are clearly visible. The calculations of N = 2000, 4096, 10 000, 32 000 and 100 000 models take about 2, 6, 20, 130 and 2500 h, respectively. The Monte Carlo code is at least 10(5) times faster than the N-body one for N = 32768 with special-purpose hardware. Thus it becomes possible to run several different models to improve statistical quality of the data and run individual models with N as large as 100 000. The Monte Carlo scheme can be regarded as a method which lies in the middle between direct N-body and Fokker-Planck models and combines most advantages of both methods.