The Eccentric Kozai-Lidov Effect and Its Applications

Abstract

The hierarchical triple body approximation has useful applications to a variety of systems from planetary and stellar scales to supermassive black holes. In this approximation, the energy of each orbit is separately conserved and therefore the two semi-major axes are constants. On timescales much larger than the orbital periods, the orbits exchange angular momentum which leads to eccentricity and orientation (i.e., inclination) oscillations. The orbits' eccentricity can reach extreme values leading to a nearly radial motion, which can further evolve into short orbit periods and merging binaries. Furthermore, the orbits' mutual inclination may change dramatically from pure prograde to pure retrograde leading to misalignment and a wide range of inclinations. This dynamical behavior is coined as the "eccentric Kozai-Lidov" mechanism. The behavior of such a system is exciting, rich and chaotic in nature. Furthermore, these dynamics are accessible from a large part of the triple body parameter space and can be applied to diverse range of astrophysical settings and used to gain insights to many puzzles.Comment: 60 pages 25 figures, to appear in Annual Review of Astronomy and Astrophysics, comments welcom

The Post-periapsis Evolution of Galactic Center Source G1: The Second Case of a Resolved Tidal Interaction with a Supermassive Black Hole

“…The present high eccentricities of G1 and G2 in their respective orbits around Sgr A * are consistent with binary systems that have been affected by the eccentric Kozai-Lidov mechanism (Kozai 1962;Lidov 1962;Naoz 2016), because binary systems perturbed by a massive third body are more likely to merge on highly eccentric outer orbits (Naoz & Fabrycky 2014;Naoz 2016;Stephan et al 2016). The detailed dynamics involved in the eccentric Kozai-Lidov mechanism that can yield merger products have been discussed in detail in the literature (see the review by Naoz 2016).…”

Spin–Orbit Misalignment of Merging Black Hole Binaries with Tertiary Companions

“…Ford et al (2000); Naoz (2016)). This tends to widen the inclination window for large eccentricity excitation.…”

Throwing icebergs at white dwarfs

“…We include equilibrium tidal models for the inner binary following Hut (1980) and Kiseleva et al (1998), see Naoz (2016) for complete equations. We also implement general relativity precessions for the inner and outer binary (Naoz et al 2013b).…”

“…The majority of WD progenitors have a binary companion (Raghavan et al 2010) that can excite the eccentricities of PPs to extreme values (Naoz 2016). This can cause some of these PPs to accrete onto the primary star during its main sequence NOTE.…”