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

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. (...)

11 pages, 8 figures, + 2 pages appendix, published by A&A; This version includes the Corrigendum (DOI: 10.1051/0004-6361/201526068e) and changes from the editing process

References in corpus (4)

• Cross Sections for Planetary Systems Interacting with Passing Stars and Binaries
• Sizes of protoplanetary discs after star-disc encounters
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• Did a stellar fly-by shape the planetary system around Pr 0211 in the cluster M 44?
• Breaking long-period resonance chains with stellar flybys
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• Oort Cloud Ecology. III. The Sun left the parent star cluster shortly after the giant planets formed
• Scattered light signatures of flyby-induced warps in protoplanetary discs
• An Eccentric Massive Protobinary Assembled via a Core-merger Parabolic Encounter