From star-disc encounters to numerical solutions for a subset of the restricted three-body problem

TL;DR

This paper introduces a new parametrization and numerical solutions for a subset of the restricted three-body problem, enabling efficient prediction of perturbed trajectories in astrophysical systems.

Contribution

A novel parametrization reduces initial condition complexity, and the creation of trajectory maps offers a new perspective on perturbation effects in the restricted three-body problem.

Findings

Maps of perturbation effects on low-mass objects were created.

Different physical processes dominate perturbations by low- and high-mass perturbers.

Results can be generalized through interpolation and scaling for various scenarios.

Abstract

Various astrophysical processes are known, where the fly-by of a massive object affects matter initially supported against gravity by rotation. Examples are perturbations of galaxies, protoplanetary discs or planetary systems. We approximate such events as subset of the restricted three-body problem by considering only perturbations of non-interacting low-mass objects initially on circular Keplerian orbits. In this paper we present a new parametrisation of the initial conditions of this problem. Under certain conditions the initial positions of the low-mass objects can be specified largely independent of the initial position of the perturber. Exploiting additionally the known scalings of the problem reduces the parameter space of initial conditions for one specific perturbation to two dimensions. To this two-dimensional initial condition space we have related the final properties of the perturbed trajectories of the low-mass objects from our numerical simulations. That way, maps showing the effect of the perturbation on the low-mass objects have been created, which provide a new view on the perturbation process. Comparing the maps for different mass-ratios reveals that the perturbations by low- and high-mass perturbers are dominated by different physical processes. The equal-mass case is a complicated mixture of the other two cases. Since the final properties of trajectories with similar initial conditions are usually also similar, the results of the limited number of integrated trajectories can be generalised to the full presented parameter space by interpolation. Since our results are also unique within the accuracy strived for, they constitute general numerical solutions for this subset of the restricted three-body problem. As such, they can be used to predict the evolution of real physical problems by simple transformations like scaling and without further simulations. (...)