A Systematic Study about Orbit Flips of Test Particles Caused by Eccentric Von Zeipel–Lidov–Kozai Effects

Lei, Hanlun

doi:10.3847/1538-3881/ac5fa8

Cited by 10 publications

(22 citation statements)

References 49 publications

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“…In this section, we produce phase portraits and then analyse the phase portraits to estimate resonant width (Lei 2021a;Lei & Li 2021;Lei 2022). At last, we construct a connection between the libration zones of apsidal resonance and numerical distributions of resonant orbit (or flipping orbit).…”

Section: Resultsmentioning

confidence: 99%

“…In this work, secular resonances are investigated for an inner test particle moving around a central star under the gravitational perturbation from a distant planet 1 . Such a dynamical model is called restricted hierarchical planetary system, which is widely adopted as the basic dynamical model to study secular dynamics in varieties of astrophysical systems Li et al 2014a,b;Sidorenko 2018;Luo et al 2016;Lei et al 2018;Lei 2019;Katz et al 2011;Antognini 2015;Lei 2021bLei ,a, 2022.…”

Section: Hamiltonian Modelmentioning

confidence: 99%

“…For simplicity, we denote the critical argument of apsidal resonance as σ = h * + sign(H * )g * in the test-particle limit 8 . Based on the set of Delaunay variables (g, h, G, H), Sidorenko (2018) defined the critical argument as σ = h + sign(H)g, which is also adopted by Lei (2022) in his study. Additionally, Katz et al (2011) introduced the longitude Ω e = Ω + arctan (tan ω cos i) to describe the very long-term behaviours caused by eccentric ZLK effect.…”

Section: Nominal Location Of Apsidal Resonancementioning

confidence: 99%

“…Additionally, Katz et al (2011) introduced the longitude Ω e = Ω + arctan (tan ω cos i) to describe the very long-term behaviours caused by eccentric ZLK effect. Discussions about the relation between Ω e and σ = h + sign(H)g are made in Lei (2022).…”

Section: Nominal Location Of Apsidal Resonancementioning

confidence: 99%

“…It is noted that a similar transformation to Eq. ( 11) is introduced by Sidorenko (2018) and Lei (2022) but based on the set of canonical variables (g, h, G, H).…”

Section: Resonant Hamiltonian Of Apsidal Resonancementioning

confidence: 99%

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Dynamical essence of the eccentric von Zeipel-Lidov-Kozai effect in restricted hierarchical planetary systems

Lei,

Gong

2022

Preprint

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Aims. The eccentric von Zeipel-Lidov-Kozai (ZLK) effect is widely used to explain dynamical phenomena in varieties of astrophysical systems. The purpose of this work is to make clear the dynamical essence of the eccentric ZLK effect by constructing an inherent connection between such an effect and dynamics of secular resonance in restricted hierarchical planetary systems. Methods. Dynamical structures of apsidal resonance are analytically studied by means of perturbative treatments. The resonant model is formulated by averaging the Hamiltonian (up to octupole order) over rotating ZLK cycles, producing an additional motion integral. The phase portraits under the resonant model can be used to analyse dynamical structures, including resonant centres, dynamical separatrices and islands of libration. Results. By analysing phase portraits, five branches of libration centres and eight libration zones are found in the eccentricityinclination space. There is an excellent agreement between analytical results of libration zone and numerical distributions of resonant orbit, indicating that the resonant model for apsidal resonances is valid and applicable. Additionally, it is found that, in the test-particle limit, distributions of flipping orbits are dominated by those apsidal resonances centred at the inclination of i = 90 • . Conclusions. The eccentric ZLK effect is dynamically equivalent to the effect of apsidal resonance in restricted hierarchical planetary systems. The dynamical response of the eccentric ZLK effect (or effect of apsidal resonance) is to significantly excite eccentricities and/or inclinations of test particles in the very long-term evolution.

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Section: Resultsmentioning

confidence: 99%

Section: Hamiltonian Modelmentioning

confidence: 99%

Section: Nominal Location Of Apsidal Resonancementioning

confidence: 99%

Section: Nominal Location Of Apsidal Resonancementioning

confidence: 99%

“…It is noted that a similar transformation to Eq. ( 11) is introduced by Sidorenko (2018) and Lei (2022) but based on the set of canonical variables (g, h, G, H).…”

Section: Resonant Hamiltonian Of Apsidal Resonancementioning

confidence: 99%

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Dynamical essence of the eccentric von Zeipel-Lidov-Kozai effect in restricted hierarchical planetary systems

Lei,

Gong

2022

Preprint

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Dynamical essence of the eccentric von Zeipel-Lidov-Kozai effect in restricted hierarchical planetary systems

Lei

Gong

2022

A&A

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Aims. The eccentric von Zeipel–Lidov–Kozai (ZLK) effect is widely used to explain dynamical phenomena in a variety of astrophysical systems. The purpose of this work is to clarify the dynamical essence of the eccentric ZLK effect by constructing an inherent connection between this effect and the dynamics of secular resonance in restricted hierarchical planetary systems. Methods. Dynamical structures of apsidal resonance were studied analytically by means of perturbative treatments. The resonant model was formulated by averaging the Hamiltonian (up to octupole order) over rotating ZLK cycles, producing an additional motion integral. The phase portraits under the resonant model can be used to analyse dynamical structures, including resonant centres, dynamical separatrices, and islands of libration. Results. By analysing phase portraits, five branches of libration centres and eight libration zones are found in eccentricity-inclination space. The analytical results of the libration zone and the numerical distributions of the resonant orbit agree very well, indicating that the resonant model for apsidal resonances is valid and applicable. Additionally, we found that in the test-particle limit, the distributions of flipping orbits are dominated by the apsidal resonances that are centred at an inclination of i = 90°. Conclusions. The eccentric ZLK effect is dynamically equivalent to the effect of apsidal resonance in restricted hierarchical planetary systems. The dynamical response of the eccentric ZLK effect (or of the effect of apsidal resonance) is to significantly excite the eccentricities and/or inclinations of test particles in the very long-term evolution.

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Quadrupole and octupole order resonances in non-restricted hierarchical planetary systems

Lei

Huang

2022

Monthly Notices of the Royal Astronomical Society

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Nonrestricted hierarchical three-body configurations are common in various scales of astrophysical systems. Dynamical structures of the quadrupole-order resonance (the von Zeipel–Lidov–Kozai resonance) and the octupole-order resonance (the apsidal resonance) under the nonrestricted hierarchical planetary systems are investigated in this work by taking advantage of perturbative treatments. Under the quadrupole-order Hamiltonian model, the distribution of libration and circulation regions as well as the distribution of flipping region are analytically explored in the parameter space spanned by the conserved quantities. The fundamental frequencies of system are produced and then the nominal location of octupole-order resonance is identified. From the viewpoint of perturbative theory, the quadrupole-order Hamiltonian determines the unperturbed dynamical model and the octupole-order Hamiltonian plays an role of perturbation to the quadrupole-order dynamics. The resonant Hamiltonian for octupole-order resonances is formulated by means of averaging theory, giving rise to a new constant of motion. Phase portraits are produced to analyse dynamical structures of octupole-order resonance, including resonant centres, saddle points, dynamical separatrices and islands of libration. By analysing phase portraits, it is found that there are four branches of libration centre and eight libration zones in the considered space. Applications to orbit flips show that there are five flipping regions.

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A Systematic Study about Orbit Flips of Test Particles Caused by Eccentric Von Zeipel–Lidov–Kozai Effects

Cited by 10 publications

References 49 publications

Dynamical essence of the eccentric von Zeipel-Lidov-Kozai effect in restricted hierarchical planetary systems

Dynamical essence of the eccentric von Zeipel-Lidov-Kozai effect in restricted hierarchical planetary systems

Dynamical essence of the eccentric von Zeipel-Lidov-Kozai effect in restricted hierarchical planetary systems

Quadrupole and octupole order resonances in non-restricted hierarchical planetary systems

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