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TRACE: a Time-Reversible Algorithm for Close Encounters

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arXiv:2405.03800v1 Announce Type: cross
Abstract: We present TRACE, a time-reversible hybrid integrator for the planetary N-body problem. Like hybrid symplectic integrators, TRACE can resolve close encounters between particles while retaining many of the accuracy and speed advantages of a fixed timestep symplectic method such the Wisdom-Holman map. TRACE switches methods time-reversibly during close encounters following the prescription of Hernandez and Dehnen (2023). In this paper we describe the derivation and implementation of TRACE and study its performance for a variety of astrophysical systems. In all our test cases TRACE is at least as accurate and fast as the hybrid symplectic integrator MERCURIUS. In many cases TRACE's performance is vastly superior to that of MERCURIUS. In test cases with planet-planet close encounters, TRACE is as accurate as MECURIUS with a 13x speedup. If close encounters with the central star are considered, TRACE achieves good error performance while MERCURIUS fails to give qualitatively correct results. In ensemble tests of violent scattering systems, TRACE matches the high-accuracy IAS15 while providing a 20x speed-up. In large N systems simulating lunar accretion, TRACE qualitatively gives the same results as IAS15 but at a 47x speedup. We also discuss some cases such as von Zeipel-Lidov-Kozai cycles where hybrid integrators perform poorly and provide some guidance on which integrator to use for which system. TRACE is freely available within the REBOUND package.

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