RESONANT POST-NEWTONIAN ECCENTRICITY EXCITATION IN HIERARCHICAL THREE-BODY SYSTEMS

By S. Naoz, B. Kocsis, Abraham Loeb, N. Yunes. 2012

173 citations recorded by the source corpus.

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.

Subfields: Aerospace Engineering, Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4009de504a0940d52b89664993188f2e02629d8f

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Citations in the corpus

Merging Binaries in the Galactic Center: The eccentric Kozai-Lidov mechanism with stellar evolution (2016, methodology): “4 Numerically, this is very similar to the Mardling & Aarseth (2001) nominal triple stars stability criterion, as shown in Naoz et al. (2013b).”
Rapid Eccentricity Oscillations and the Mergers of Compact Objects in Hierarchical Triples (2013, methodology): “This timescale is given by Katz et al. (2011) and Naoz et al. (2013a) as tEKM ∼ tKL ǫoct , where ǫoct is the strength of the octupole-order term in the expansion of the three-body Hamiltonian.”
REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations (2019, background): “Naoz et al. (2013) provide the full Hamiltonian for a triple system (see also Schäfer 1987).”
Rapid and Bright Stellar-mass Binary Black Hole Mergers in Active Galactic Nuclei (2016, background): “…in dense stellar systems including globular clusters and galactic nuclei (Portegies Zwart & McMillan 2002; Miller & Hamilton 2002; Portegies Zwart et al. 2004; O’Leary et al. 2009; Kocsis & Levin 2012; Naoz et al. 2013; Antonini et al. 2014; Antognini et al. 2014; Morscher et al. 2015).”
ECCENTRICITY GROWTH AND ORBIT FLIP IN NEAR-COPLANAR HIERARCHICAL THREE-BODY SYSTEMS (2013, methodology): “When the outer orbit is non-circular, the octupole approximation is needed, inducing variations in eccentricity and inclination on longer timescales, and causes excursions to even higher eccentricities and inclinations above 90◦ (Naoz et al. 2011, 2013a).”
Secular Dynamics in Hierarchical Three-Body Systems (2011, background): “In such systems, the outer star completely dominates the orbital angular momentum, and the problem reduces to test-particle evolution (see Lithwick and Naoz 2011; Katz et al. 2011; Naoz et al. 2012a).”
Timescales of Kozai-Lidov oscillations at quadrupole and octupole order in the test particle limit (2015, background): “…has appeared in the literature, although several studies have asserted that tEKM ∼ tKL/ǫoct is a plausible timescale (e.g., Katz et al. 2011; Naoz et al. 2013b; Li et al. 2015), where ǫoct measures the strength of the octupole order term relative to the quadrupole order term of the…”
BLACK HOLE TRIPLE DYNAMICS: A BREAKDOWN OF THE ORBIT AVERAGE APPROXIMATION AND IMPLICATIONS FOR GRAVITATIONAL WAVE DETECTIONS (2013, background): “However, if the relativistic precession timescales are comparable or lower than the secular Newtonian timescales, then around some critical value of a2 it is possible that the maximum achievable eccentricity is increased with respect to the Newtonian case (Ford et al. 2000; Naoz et al. 2013).”
Black Hole Mergers in Galactic Nuclei Induced by the Eccentric Kozai–Lidov Effect (2017, methodology): “We include the secular equations up to the octupole-level of approximation (e.g., Naoz 2016), general relativity precession of the inner and outer orbits (e.g., Naoz et al. 2013), and gravitational wave emission (Peters 1964).”
Deep Learning for Real-time Gravitational Wave Detection and Parameter Estimation with Advanced LIGO Data (2017, methodology): “However, matched-filtering, the most sensitive search algorithm used by LIGO, targets only a 3D parameter space (spin-aligned binaries on quasi-circular orbits) [8, 9, 10]—a subset of the over 8D parameter space of GW signals [11, 12, 13, 14, 15].”
The Eccentric Kozai-Lidov Effect and Its Applications (2016, methodology): “…the 1st PN three body Hamiltonian in semi-major axes ratio up to the octupole level of approximation reveals another term which describes www.annualreviews.org • The EKL Effect and Its Applications 25 the general relativity interaction between the inner and outer orbits (Naoz et al. 2013b).”