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

Spherically symmetric equal mass star clusters containing a large amount 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 (threeand 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 ten thousands of scattering events as they occur in real cluster evolution including mass segregation of binaries, gravothermal collapse and reexpansion, 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 threeand four-body encounters. It is found that a large fraction of three-body and four-body encounters results in merging. Eccentricities are generally increased in strong threeand four-body encounters and there is a characteristic scaling law ∝ exp(4efin) of the differential cross section for eccentricity changes, where efin is the final eccentricity of the binary, or harder binary for four-body encounters. Despite of 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 like formation of hierarchical triples occur.