The relativistic Pythagorean three-body problem

Abstract

We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms up to 2.5 order, and the first order Taylor expansion to the Einstein-Infeld-Hoffmann equations of motion. The degree to which our system is relativistic depends on the scaling of the total mass (the unit size was 1 parsec). Using the Brutus method of convergence, we test for time-reversibility in the conservative regime, and demonstrate that we are able to obtain definitive solutions to the relativistic three-body problem. It is also confirmed that the minimal required numerical accuracy for a successful time-reversibility test correlates with the amplification factor of an initial perturbation. When we take into account dissipative effects through gravitational wave emission, we find that the duration of the resonance, and the amount of exponential growth of small perturbations depend on the mass scaling. For a unit mass <= 10 MSun, the system behavior is indistinguishable from the Newtonian case, and the resonance always ends in a binary and one escaping body. For a mass scaling up to 1e7 MSun, relativity gradually becomes more prominent, but the majority of the systems still dissolve. The first mergers start to appear for a mass of ~1e5 MSun, and between 1e7 MSun and 1e9 MSun all systems end prematurely in a merger. These mergers are preceded by a gravitational wave driven in-spiral. For a mass scaling >= 1e9 MSun, all systems result in a gravitational wave merger upon the first close encounter. Relativistic three-body encounters thus provide an efficient pathway for resolving the final parsec problem. The onset of mergers at the characteristic mass scale of 1e7 MSun potentially leaves an imprint in the mass function of supermassive black holes.

Accepted by Phys Rev D. 10 pages, 6 figures

References in corpus (13)

• Black hole mergers in the universe
• Resonant Post-Newtonian Eccentricity Excitation in Hierarchical Three-body Systems
• Dynamics of triple black hole systems in hierarchically merging massive galaxies
• The Final Parsec Problem
• Evolution of Massive Black Hole Binaries
• Interactions between multiple supermassive black holes in galactic nuclei: a solution to the final parsec problem
• Collisionless loss-cone refilling: there is no final parsec problem
• On incorporating post-Newtonian effects in N-body dynamics
• Mass Functions of Supermassive Black Holes Across Cosmic Time
• Topology of Black Hole Binary-Single Interactions
• Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length
• Properties of von Zeipel-Lidov-Kozai oscillations in triple systems at the quadrupole order: relaxing the test particle approximation
• Numerical verification of the microscopic time reversibility of Newton's equations of motion: Fighting exponential divergence

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• Reversible time-step adaptation for the integration of few-body systems
• Extreme Gravitational Interactions in the Problem of Three Black Holes in General Relativity
• Partial suppression of chaos in relativistic three-body problems
• The Steady State of Intermediate-Mass Black Holes Near a Supermassive Black Hole
• The influence of spin in black hole triplets