Gargantuan chaotic gravitational three-body systems II. Dependence on angular momentum and astrophysical scale

Monthly Notices of the Royal Astronomical Society, vol. 536, pp. 2993–3006

Abstract

ABSTRACT Recently, we estimated that about 5 per cent of unstable supermassive black hole triple systems are fundamentally unpredictable. These gargantuan chaotic systems are able to exponentially magnify Planck length perturbations to astronomical scales within their dynamical lifetime. These results were obtained in the zero angular momentum limit, which we naively expected to be the most chaotic. Here, we generalize to weakly and non-hierarchical triple systems with a range of non-zero angular momenta by systematically varying the initial virial ratio. We find the surprising result that increasing the angular momentum enhances their ability to amplify small perturbations, which we tracked up to 90 orders of magnitude using the arbitrary-precision N-body code brutus. This result is partially explained by the fact that triples with higher angular momenta have longer lifetimes, allowing for a prolonged exponential growth. However, we also find that for a fixed lifetime, triples with higher angular momenta can amplify perturbations to larger values, indicating that the Lyapunov exponent is also a function of angular momentum. These empirical results provide targets for three-body theories which invoke chaos drivers such as resonance overlap and punctuated chaos. Comparing the zero angular momentum case to our new ensembles with higher angular momenta, we conclude that the percentage of unpredictable supermassive black hole triples increases up to about 30 per cent. A further increase up to about 50 per cent is reached when considering triples on smaller astrophysical scales. Fundamental unpredictability is thus a generic feature of chaotic, self-gravitating triple populations.

Authors 2

1. Tjarda Boekholt corresponding

   University of Oxford · Ames Research Center

   Affiliation as printed

   NASA Ames Research Center , Moffett Field, CA 94035 ,

   Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, University of Oxford , Parks Road, Oxford, OX1 3PU ,

   NASA Ames Research Center, Moffett Field, CA 94035, USA

   Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK

2. Simon Portegies Zwart corresponding Aachen Leiden Observatory

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University , PO Box 9513, NL-2300 RA, Leiden ,

   Leiden Observatory, Leiden University, PO Box 9513, 2300 RA, Leiden, The Netherlands