A slow-down time-transformed symplectic integrator for solving the few-body problem

Abstract

An accurate and efficient method dealing with the few-body dynamics is important for simulating collisional N-body systems like star clusters and to follow the formation and evolution of compact binaries. We describe such a method which combines the time-transformed explicit symplectic integrator (Preto & Tremaine 1999; Mikkola & Tanikawa 1999) and the slow-down method (Mikkola & Aarseth 1996). The former conserves the Hamiltonian and the angular momentum for a long-term evolution, while the latter significantly reduces the computational cost for a weakly perturbed binary. In this work, the Hamilton equations of this algorithm are analyzed in detail. We mathematically and numerically show that it can correctly reproduce the secular evolution like the orbit averaged method and also well conserve the angular momentum. For a weakly perturbed binary, the method is possible to provide a few order of magnitude faster performance than the classical algorithm. A publicly available code written in the c++ language, SDAR, is available on GitHub (https://github.com/lwang-astro/SDAR). It can be used either as a stand alone tool or a library to be plugged in other $N$-body codes. The high precision of the floating point to 62 digits is also supported.

14 pages, 13 figures, accepted to MNRAS

References in corpus (3)

• MOCCA-SURVEY Database I: Coalescing Binary Black Holes Originating From Globular Clusters
• Merging black holes in young star clusters
• The survival of star clusters with black hole subsystems

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• Impact of initial mass functions on the dynamical channel of gravitational wave sources
• Investigating the UV-excess in star clusters with $N$-body simulations: predictions for future CSST observations
• Step-size effect in the time-transformed leapfrog integrator on elliptic and hyperbolic orbits