A stochastic Monte Carlo approach to modelling real star cluster evolution - III. Direct integration of three- and four-body interactions

Spherically symmetric equal-mass star clusters containing a large number of primordial binaries are studied using a hybrid method, consisting of a gas dynamical model for single stars and a Monte Carlo treatment for relaxation of binaries and the setup of close resonant and fly-by encounters of single stars with binaries and binaries with each other (three- and four-body encounters). What differs from our previous work is that each encounter is being integrated using a highly accurate direct few-body integrator which uses regularized variables. Hence we can study the systematic evolution of individual binary orbital parameters (eccentricity, semi-major axis) and differential and total cross-sections for hardening, dissolution or merging of binaries (minimum distance) from a sampling of several tens of thousands of scattering events as they occur in real cluster evolution, including mass segregation of binaries, gravothermal collapse and re-expansion, a binary burning phase and ultimately gravothermal oscillations. For the first time we are able to present empirical cross-sections for eccentricity variation of binaries in close three- and four-body encounters. It is found that a large fraction of three-and four-body encounters result in merging. Eccentricities are generally increased in strong three- and four-body encounters and there is a characteristic scaling law α exp (4e f i n ) of the differential cross-section for eccentricity changes, where e f i n is the final eccentricity of the binary, or harder binary for four-body encounters. Despite these findings the overall eccentricity distribution remains thermal for all binding energies of binaries, which is understood from the dominant influence of resonant encounters. Previous cross-sections obtained by Spitzer and Gao for strong encounters can be reproduced, while for weak encounters non-standard processes such as the formation of hierarchical triples occur.