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Register a new userThe Kozai-Lidov Mechanism in Hydrodynamical Disks
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We use three dimensional hydrodynamical simulations to show that a highly misaligned accretion disk around one component of a binary system can exhibit global Kozai-Lidov cycles, where the inclination and eccentricity of the disk are interchanged periodically. This has important implications for accreting systems on all scales, for example, the formation of planets and satellites in circumstellar and circumplanetary disks, outbursts in X-ray binary systems and accretion on to supermassive black holes.
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The secular approximation of the hierarchical three body systems has been proven to be very useful in addressing many astrophysical systems, from planets, stars to black holes. In such a system two objects are on a tight orbit, and the tertiary is on a much wider orbit. Here we study the dynamics of a system by taking the tertiary mass to zero and solve the hierarchical three body system up to the octupole level of approximation. We find a rich dynamics that the outer orbit undergoes due to gravitational perturbations from the inner binary. The nominal result of the precession of the nodes is mostly limited for the lowest order of approximation, however, when the octupole-level of approximation is introduced the system becomes chaotic, as expected, and the tertiary oscillates below and above 90deg, similarly to the non-test particle flip behavior (e.g., Naoz 2016). We provide the Hamiltonian of the system and investigate the dynamics of the system from the quadrupole to the octupole level of approximations. We also analyze the chaotic and quasi-periodic orbital evolution by studying the surfaces of sections. Furthermore, including general relativity, we show case the long term evolution of individual debris disk particles under the influence of a far away interior eccentric planet. We show that this dynamics can naturally result in retrograde objects and a puffy disk after a long timescale evolution (few Gyr) for initially aligned configuration.
A disk around one component of a binary star system with sufficiently high inclination can undergo Kozai-Lidov (KL) oscillations during which the disk inclination and disk eccentricity are exchanged. Previous studies show that without a source of accretion, KL unstable disks exhibit damped oscillations, due to viscous dissipation, that leave the disk stable near or below the critical inclination for KL oscillations. With three-dimensional hydrodynamical simulations we show that a highly misaligned circumbinary disk that flows onto the binary components forms highly inclined circumstellar disks around each component. We show that a continuous infall of highly inclined material allows the KL oscillations to continue. The KL disk oscillations produce shocks and eccentricity growth in the circumstellar disks that affect the conditions for planet formation.
As the discoveries of more minor bodies in retrograde resonances with giant planets, such as 2015 BZ509 and 2006 RJ2, our curiosity about the Kozai-Lidov dynamics inside the retrograde resonance has been sparked. In this study, we focus on the 3D retrograde resonance problem and investigate how the resonant dynamics of a minor body impacts on its own Kozai-Lidov cycle. Firstly we deduce the action-angle variables and canonical transformations that deal with the retrograde orbit specifically. After obtaining the dominant Hamiltonian of this problem, we then carry out the numerical averaging process in closed form to generate phase-space portraits on a $e-omega$ space. The retrograde 1:1 resonance is particularly scrutinized in detail, and numerical results from a CRTBP model shows a great agreement with the our semi-analytical portraits. On this basis, we inspect two real minor bodies currently trapped in retrograde 1:1 mean motion resonance. It is shown that they have different Kozai-Lidov states, which can be used to analyze the stability of their unique resonances. In the end, we further inspect the Kozai-Lidov dynamics inside the 2:1 and 2:5 retrograde resonance, and find distinct dynamical bifurcations of equilibrium points on phase-space portraits.
The stability of planets in the alpha-Centauri AB stellar system has been studied extensively. However, most studies either focus on the orbital plane of the binary or consider inclined circular orbits. Here, we numerically investigate the stability of a possible planet in the alpha-Centauri AB binary system for S-type orbits in an arbitrary spatial configuration. In particular, we focus on inclined orbits and explore the stability for different eccentricities and orientation angles. We show that large stable and regular regions are present for very eccentric and inclined orbits, corresponding to libration in the Lidov-Kozai resonance. We additionally show that these extreme orbits can survive over the age of the system, despite the effect of tides. Our results remain qualitatively the same for any compact binary system.
The so-called Lidov-Kozai oscillation is very well known and applied to various problems in solar system dynamics. This mechanism makes the orbital inclination and eccentricity of the perturbed body in the circular restricted three-body system oscillate with a large amplitude under certain conditions. It is widely accepted that the theoretical framework of this phenomenon was established independently in the early 1960s by a Soviet Union dynamicist (Michail Lvovich Lidov) and by a Japanese celestial mechanist (Yoshihide Kozai). A large variety of studies has stemmed from the original works by Lidov and Kozai, now having the prefix of Lidov-Kozai or Kozai- Lidov. However, from a survey of past literature published in late nineteenth to early twentieth century, we have confirmed that there already existed a pioneering work using a similar analysis of this subject established in that period. This was accomplished by a Swedish astronomer, Edvard Hugo von Zeipel. In this monograph, we first outline the basic framework of the circular restricted three-body problem including typical examples where the Lidov-Kozai oscillation occurs. Then, we introduce what was discussed and learned along this line of studies from the early to mid-twentieth century by summarizing the major works of Lidov, Kozai, and relevant authors. Finally, we make a summary of von Zeipels work, and show that his achievements in the early twentieth century already comprehended most of the fundamental and necessary formulations that the Lidov-Kozai oscillation requires. By comparing the works of Lidov, Kozai, and von Zeipel, we assert that the prefix von Zeipel-Lidov-Kozai should be used for designating this theoretical framework, and not just Lidov-Kozai or Kozai-Lidov.
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