Resonant post-Newtonian eccentricity excitation in hierarchical three-body systems

Smadar Naoz, Bence Kocsis, Abraham Loeb, Nicolás Yunes

Research output: Contribution to journalArticlepeer-review


We study the secular, hierarchical three-body problem to first-order in a post-Newtonian expansion of general relativity (GR). We expand the first-order post-Newtonian Hamiltonian to leading-order in the ratio of the semi-major axis of the two orbits. In addition to the well-known terms that correspond to the GR precession of the inner and outer orbits, we find a new secular post-Newtonian interaction term that can affect the long-term evolution of the triple. We explore the parameter space for highly inclined and eccentric systems, where the Kozai-Lidov mechanism can produce large-amplitude oscillations in the eccentricities. The standard lore, i.e., that GR effects suppress eccentricity, is only consistent with the parts of phase space where the GR timescales are several orders of magnitude shorter than the secular Newtonian one. In other parts of phase space, however, post-Newtonian corrections combined with the three-body ones can excite eccentricities. In particular, for systems where the GR timescale is comparable to the secular Newtonian timescales, the three-body interactions give rise to a resonant-like eccentricity excitation. Furthermore, for triples with a comparable-mass inner binary, where the eccentric Kozai-Lidov mechanism is suppressed, post-Newtonian corrections can further increase the eccentricity and lead to orbital flips even when the timescale of the former is much longer than the timescale of the secular Kozai-Lidov quadrupole perturbations.

Original languageEnglish (US)
Article number187
JournalAstrophysical Journal
Issue number2
StatePublished - Aug 20 2013
Externally publishedYes


  • pulsars: general
  • stars: evolution
  • stars: kinematics and dynamics

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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