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Simulation of binary-single star and binary-binary scattering. (English) Zbl 0585.65055

Numerical methods for integrating gravitational 3- and 4-body systems are investigated and tested. The methods employ multiple-pair regularization schemes for N-body systems which use the Kustaanheimo-Stiefel transformation for regularizing 2-body collisions, in conjunction with a number of different time transformations between ”physical” and ”parameter” time. These transformations can be chosen so as to make the singularity in the equations of motion, caused by many-body collisions, as mild as possible. The various time transformations are tested on both 3- and 4-body systems by comparing the numerical with known analytical solutions, and by time reversal of the integrations through many-body close encounters. Computer programs for binary-single star and binary- binary scattering have been developed and are described. They can be used in an extensive project for determining scattering cross sections with any of the above methods. They are used here to compare the performance of these methods, for a fixed set of initial conditions, on scattering involving ”hard” binaries, in which strong resonances can occur. It is found that the outcome of the scattering, for example, the identity of the escaping particle(s), can vary with method, thus reflecting the inherent instability of the N-body problem.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
70F10 \(n\)-body problems
70-08 Computational methods for problems pertaining to mechanics of particles and systems
70F05 Two-body problems
70F07 Three-body problems
85A05 Galactic and stellar dynamics
65L07 Numerical investigation of stability of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
70F35 Collision of rigid or pseudo-rigid bodies
70-04 Software, source code, etc. for problems pertaining to mechanics of particles and systems
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References:

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