THE ECCENTRIC KOZAI MECHANISM FOR A TEST PARTICLE

By Y. Lithwick, S. Naoz. 2011

166 citations recorded by the source corpus.

We study the dynamical evolution of a test particle that orbits a star in the presence of an exterior massive planet, considering octupole-order secular interactions. In the standard Kozai mechanism (SKM), the planet's orbit is circular and so the particle conserves vertical angular momentum. As a result, the particle's orbit oscillates periodically, exchanging eccentricity for inclination. However, when the planet's orbit is eccentric, the particle's vertical angular momentum varies and its Kozai oscillations are modulated on longer timescales—we call this the eccentric Kozai mechanism (EKM). The EKM can lead to behavior that is dramatically different from the SKM. In particular, the particle's orbit can flip from prograde to retrograde and back again, and it can reach arbitrarily high eccentricities given enough time. We map out the conditions under which this dramatic behavior (flipping and extreme eccentricities) occurs and show that when the planet's eccentricity is sufficiently high, it occurs quite generically. For example, when the planet's eccentricity exceeds a few percent of the ratio of semimajor axes (outer to inner), around half of randomly oriented test particle orbits will flip and reach extreme eccentricities. The SKM has often been invoked for bringing pairs of astronomical bodies (star–star, planet–star, compact–object pairs) close together. Including the effect of the EKM will enhance the rate at which such matchmaking occurs.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/0d906b49f84113aa0ac36633480c4beeab0aea59

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In Astronomy and Astrophysics

1. S. Naoz
2. F. Antonini
3. B. Kocsis
4. Joseph M. Antognini
5. F. Rasio
6. S. Toonen
7. T. Thompson
8. Adrian S. Hamers

Citations in the corpus

• RESONANT POST-NEWTONIAN ECCENTRICITY EXCITATION IN HIERARCHICAL THREE-BODY SYSTEMS (2012, background): “However, as demonstrated in Lithwick & Naoz (2011), although the system is chaotic when the octupole terms are included, there are two general features in the evolution: one associated with an octupole timescale, defined below, and a shorter one (see for example their Fig.”
• BLACK HOLE TRIPLE DYNAMICS: A BREAKDOWN OF THE ORBIT AVERAGE APPROXIMATION AND IMPLICATIONS FOR GRAVITATIONAL WAVE DETECTIONS (2013, background): “…at the quadrupole level orbits maintain their sense of rotation, in the octupole potential excursions to very high eccentricities can be accompanied by a “flip” of the orbit with respect to the direction of the total angular momentum (Naoz et al. 2011a; Lithwick & Naoz 2011; Naoz et al. 2011b).”
• Suppression of extreme orbital evolution in triple systems with short-range forces (2014, methodology): “…mechanism, either numerically (e.g., Naoz et al. 2011, 2013b; Teyssandier et al. 2013) or semi-analytically (e.g., Katz, Dong, & Malhotra 2011; Lithwick & Naoz 2011), and explored their implications for the formation of hot Jupiters and the resulting spin-orbit misalignments (e.g., Naoz et…”
• ON THE FORMATION OF HOT JUPITERS IN STELLAR BINARIES (2012, background): “Most of the systems that form HJs lie within the bounds of an analytic criterion for determining the regions of parameter space associated with flipping the inner orbit in the test particle approximation (Lithwick & Naoz 2011; Katz et al. 2011).”
• The Eccentric Kozai-Lidov Effect and Its Applications (2016, methodology): “it is a test particle, (i.e., either m 1 or m 2 are zero). In the second we will allow for all three masses to be non-negligible. 2.2.1.Axisymmetric Potential and Inner Test Particle - TPQ. Following Lithwick and Naoz (2011) we call this case the test particle approximation quadrupole (TPQ). Without”
• Greatly Enhanced Merger Rates of Compact-object Binaries in Non-spherical Nuclear Star Clusters (2017, background): “This behavior resembles the orbit flips in the three-body interactions with octupole-level perturbations (e.g., Katz et al. 2011; Lithwick & Naoz 2011) and are due to the forcing of jz, which periodically changes sign (panel c).”
• Timescales of Kozai-Lidov oscillations at quadrupole and octupole order in the test particle limit (2015, methodology): “Strong octupole-order effects occur in many triple systems with ǫoct = 10 −2, but these effects are much weaker for most triples when ǫoct = 10 −3 (e.g., Lithwick & Naoz 2011).”
• The evolution of hierarchical triple star-systems (2016, background): “the octupole level of approximation, even richer dynamical behaviour is expected than for the quadrupole approximation (e.g. Blaes et al., 2002; Ford et al., 2000; Lithwick and Naoz, 2011; Naoz et al., 2013; Shappee and Thompson, 2013; Teyssandier et al., 2013).”
• ECCENTRICITY GROWTH AND ORBIT FLIP IN NEAR-COPLANAR HIERARCHICAL THREE-BODY SYSTEMS (2013, methodology): “This test particle approximation in hierarchical 3-body systems was studied extensively in the past (Lithwick & Naoz 2011; Katz et al. 2011), but only in the regime of large inclinations between the inner and outer orbit’s (and for small initial inner eccentricity e1 < 0.5 Lithwick & Naoz 2011).”
• Secular Dynamics in Hierarchical Three-Body Systems (2011, background): “However, if the companion is assumed to be eccentric ǫM is not negligible, and the system is more appropriately described with the test particle octupole– level approximation (e.g., Lithwick and Naoz 2011; Katz et al. 2011).”
• Rapid Eccentricity Oscillations and the Mergers of Compact Objects in Hierarchical Triples (2013, background): “Lithwick & Naoz (2011) and Katz et al. (2011) explored the implications of these equations and showed that the octupole-order terms can lead to substantially larger eccentricities of the inner binary.”