Journal Article

The non-resonant, relativistic dynamics of circumbinary planets

Cezary Migaszewski and Krzysztof Goździewski

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 411, issue 1, pages 565-583
Published in print February 2011 | ISSN: 0035-8711
Published online January 2011 | e-ISSN: 1365-2966 | DOI:
The non-resonant, relativistic dynamics of circumbinary planets

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We investigate a non-resonant, three-dimensional (spatial) model of a hierarchical system composed of a point-mass stellar (or substellar) binary and a low-mass companion (a circumbinary planet or a brown dwarf). We take into account the leading relativistic corrections to the Newtonian gravity. The secular model of the system relies on the expansion of the perturbing Hamiltonian in terms of the ratio of semi-major axes α, averaged over the mean anomalies. We found that a low-mass object in a distant orbit may excite a large eccentricity of the inner binary when the mutual inclination of the orbits is larger than about 60°. This is related to the strong instability caused by a phenomenon that acts similarly to the Lidov–Kozai resonance (LKR). The secular system may be strongly chaotic and its dynamics unpredictable over long-term time-scales. Our study shows that in the Jupiter- or brown-dwarf-mass regime of the low-mass companion, the restricted model does not properly describe the long-term dynamics in the vicinity of the LKR. The relativistic correction is significant for the parametric structure of a few families of stationary solutions in this problem, in particular for direct orbit configurations (with mutual inclination less than 90°). We found that the dynamics of hierarchical systems with small α∼ 0.01 may be qualitatively different in the realms of Newtonian (classic) and relativistic models. This holds true even for relatively large masses of the secondaries.

Keywords: methods: analytical; celestial mechanics; planetary systems

Journal Article.  12319 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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