High order regularised symplectic integrator for collisional planetary systems

Abstract

We present a new mixed variable symplectic (MVS) integrator for planetary systems, that fully resolve close encounters. The method is based on a time regularisation that allows keeping the stability properties of the symplectic integrators, while also reducing the effective step size whenever two planets encounter. We use a high order MVS scheme such that it is possible to integrate with large time steps far away from close encounters. We show that this algorithm is able to resolve almost exact collisions (i.e with a mutual separation of a fraction of the physical radius) while using the same time-step as in weakly perturbed problem such as the Solar System. We demonstrate the long term behaviour on systems of six super-Earths experiencing strong scattering for 50 kyr. We compare our algorithm to hybrid methods such as MERCURY and show that for an equivalent cost we obtain much better energy conservation.

Accepted in Astronomy and Astrophysics, updated to match the published version

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• Reversible time-step adaptation for the integration of few-body systems
• Extended phase-space symplectic integration for electron dynamics
• Global time-renormalization of the gravitational $N$-body problem