Monte Carlo simulations of star clusters — I. First Results

A revision of Stodoíkiewicz'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  ≤ 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  = 32 768 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.