trace: a code for time-reversible astrophysical close encounters

ABSTRACT We present trace, an almost 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 time-step symplectic method such the Wisdom–Holman map. trace switches methods time-reversibly during close encounters following the prescription of Hernandez & Dehnen. 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 12× speed-up. 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 15× speed-up. In large N systems simulating lunar accretion, trace qualitatively gives the same results as ias15 but at a 41× speed-up. 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.