N-body integrators for planets in binary star systems

TL;DR

This paper discusses the development and adaptation of symplectic N-body integrators for studying planetary systems in binary star environments, focusing on their theory, implementation, and limitations.

Contribution

It introduces new coordinate systems and improvements for symplectic integrators tailored to binary star systems, enhancing their efficiency and applicability.

Findings

Adapted symplectic algorithms for wide and close binary systems.

Improved performance using symplectic correctors.

Identified limitations during close encounters with binary members.

Abstract

Symplectic integrators are the tool of choice for many researchers studying dynamical systems because of their good long-term energy conservation properties. For systems with a dominant central mass, symplectic integrators are also highly efficient. In this chapter, I describe the theory of symplectic integrators in terms of Lie series. I show how conventional symplectic algorithms have been adapted for use in binary-star systems to study problems such as the dynamical stability of multi-planet systems and the accretion of planets from planetesimals. This is achieved by devising new coordinate systems for the wide-binary and close-binary cases separately. I show how the performance of these algorithms can be improved at little extra cost using symplectic correctors. Finally, I discuss drawbacks of these algorithms, in particular in dealing with close encounters with one or both members of the binary, and the prospects for overcoming these problems.