Monte Carlo simulations of star clusters - I. First Results

Abstract

A revision of Stodó lkiewicz'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 10000 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 to 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 > 10000 gravothermal oscillations are clearly visible. The calculations of N = 2000, 4096, 10000, 32000 and 100000 models take about 2, 6 20, 130 and 2500 hours, respectively. The Monte-Carlo code is at least 10 5 times faster than the N -body one for N = 32768 with special-purpose hardware (Makino 1996ab). 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 100000. The MonteCarlo 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.

A new Monte Carlo method for dynamical evolution of non-spherical stellar systems

“…(Note that there exist simulation methods that rely on "orbit-orbit", as opposed to "particle-particle" interactions, which are used for stars on near-Keplerian orbits around a massive black hole (Touma et The energies of particles also need to be corrected after reinitialization of the potential, to account for the time dependence of the potential. We adopt the method used by Stodó lkiewicz (1982) and Giersz (1998), which states that the energy correction for a given particle is ∆Ẽi = 1 2 ∆Φ(r i,old ) + ∆Φ(ri,new) ,…”

Young Massive Star Clusters

“…Of these, the most widely used are the N-body codes NBODY (Hurley et al 2001, Aarseth 2003, kira which is part of the starlab package (e.g. Portegies Zwart et al 2001), and the Monte Carlo codes developed by Giersz (Giersz 1998, …”

“…The early techniques developed in the 1970s and 1980s (Spitzer & Hart 1971, Henon 1973, Spitzer 1975, Stodolkiewicz 1982) fall into the former category, but recent studies, in particular (Giersz 1998;Joshi, Rasio & Portegies Zwart 2000; A.4 Parallelization Individual time step schemes are generally hard to optimize on parallel machines. For those architectures, block time step schemes (McMillan 1986) offer substantially better performance.…”

Gravitational dynamics of large stellar systems

“…Of these, the most widely used are the N-body codes NBODY (Aarseth 2003) and kira (e.g. Portegies Zwart et al 2001), and the Monte-Carlo codes developed by Giersz (Giersz 1998; see also Giersz and Heggie 2008), Freitag , and by Rasio and coworkers (e.g. Fregeau et al 2003).…”