arXiv subjects

Hanlun Lei

Publications and source records attributed to Hanlun Lei.

29 records · Page 2Linked to original sources

arXiv2022

The von Zeipel-Lidov-Kozai effect inside mean motion resonances with applications to trans-Neptunian objects

Secular dynamics inside MMRs plays an essential role in governing the dynamical structure of the trans-Neptunian region and sculpting the orbital distribution of trans-Neptunian objects (TNOs). In this study, semi-analytical developments are made to explore the von Zeipel-Lidov-Kozai (ZLK) resonance inside mean motion resonances (MMRs). To this end, a semi-secular model is formulated by averaging theory and then a single-degree-of-freedom integrable model is achieved based on the adiabatic invariance approximation. In particular, we introduce a modified adiabatic invariant, which is continuous around the separatrices of MMRs. During the long-term evolution, both the resonant Hamiltonian and the adiabatic invariant remain unchanged, thus phase portraits can be produced by plotting level curves of the adiabatic invariant with given Hamiltonian. The phase portraits provide global pictures to predict long-term behaviors of the eccentricity, inclination and argument of pericenter. Applications to some representative TNOs inside MMRs (2018 VO137, 2005 SD278, 2015 PD312, Pluto, 2004 HA79, 1996 TR66 and 2014 SR373) show good agreements between the numerically propagated trajectories under the full N-body model and the level curves arising in phase portraits. Interestingly, 2018 VO137 and 2005 SD278 exhibit switching behaviors during the long-term evolution and currently they are inside 2:5 MMR with Neptune.

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arXiv2022

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

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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arXiv2022

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

Aim. 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 eccentricity--inclination 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 deg. 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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arXiv2022

A systematic study about orbit flips of test particles caused by eccentric von Zeipel-Lidov-Kozai effects

The problem of orbit flips caused by eccentric von Zeipel-Lidov-Kozai effects is systematically investigated by means of three approaches, including Poincaré sections, dynamical system theory (periodic orbits and invariant manifolds) and perturbation treatments. Poincaré sections show that orbit flips are due to the existence of islands of libration centered at inclination of $90^{\circ}$, dynamical system theory shows that orbit flips are due to the existence of polar periodic orbits and invariant manifolds, and perturbative treatments indicate that orbit flips are due to the libration of a certain critical argument. Using these approaches, the boundaries of flipping regions in the entire parameter space are produced and they are in excellent agreement with each other. Through analysis, the essence of flipping orbits is reached: (a) flipping orbits are a kind of quasi-periodic trajectories around polar periodic orbits and invariant manifolds at the same level of Hamiltonian provide boundaries of flipping regions, and (b) flipping orbits are a kind of resonant trajectories and resonant width measures the size of flipping regions.

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arXiv2021

Structures of secular resonances for inner test particles in hierarchical planetary systems

In this study, dynamics of secular resonances for inner test particles are investigated under the octupole-level approximation by taking non-perturbative approaches. In practice, webs of the major secular resonances are produced by identifying families of stable periodic orbits and the associated stable libration zones are obtained by analysing Poincaré surfaces of section. By taking different values of the factor $ε$ ($ε$ measures the contribution of octupole terms), the influences of the octupole-order terms upon the dynamical structures are evaluated. Under the condition of $ε= 0$ (no octupole-order contribution), the dynamical model is totally integrable and there is only Kozai resonance arising in the phase space. When the factor $ε$ is different from zero, the dynamical structure in the phase space becomes complicated due to varieties of secular resonances appearing. Numerical results further indicate that (a) distributions of libration centres and stable libration zones remain qualitatively similar with different values of $ε$, (b) Kozai resonance disappears due to the chaotic motion in the low-eccentricity region, and (c) the chaotic area arising in the low-eccentricity region increases with the factor $ε$. Secular resonances are the source of many important dynamical phenomena, such as chaos, orbit alignment and orbit flipping, and thus the results presented in this work could be useful to understand the secular dynamics for those high-eccentricity and/or high-inclination objects in hierarchical planetary systems.

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arXiv2021

A new expansion of planetary disturbing function and applications to interior, co-orbital and exterior resonances with planets

In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around circular orbits in the first step and then, in the second step, the resulting mutual interaction between circular orbits is expanded around a reference point. As usual, the resulting expansion is presented in the Fourier series form, where the force amplitudes are dependent on the semimajor axis, eccentricity and inclination and the harmonic arguments are linear combinations of the mean longitude, longitude of pericenter and longitude of ascending node of each mass. The resulting new expansion is valid for arbitrary inclinations and semimajor axis ratios. In the case of mean motion resonant configuration, the disturbing function can be easily averaged to produce the analytical expansion of resonant disturbing function. Based on the analytical expansion, the Hamiltonian model of mean motion resonances is formulated, and the resulting analytical developments are applied to Jupiter's inner and co-orbital resonances and Neptune's exterior resonances. Analytical expansion is validated by comparing the analytical results with the associated numerical outcomes.

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arXiv2021

Apsidal asymmetric-alignment of Jupiter Trojans

The most distant Kuiper belt objects exhibit the clustering in their orbits, and this anomalous architecture could be caused by Planet 9 with large eccentricity and high inclination. We then suppose that the orbital clustering of minor planets may be observed somewhere else in the solar system. In this paper, we consider the over 7000 Jupiter Trojans from the Minor Planet Center, and find that they are clustered in the longitude of perihelion $\varpi$, around the locations $\varpi_{\mbox{J}}+60^{\circ}$ and $\varpi_{\mbox{J}}-60^{\circ}$ ($\varpi_{\mbox{J}}$ is the longitude of perihelion of Jupiter) for the L4 and L5 swarms, respectively. Then we build a Hamiltonian system to describe the associated dynamical aspects for the co-orbital motion. The phase space displays the existence of the apsidally aligned islands of libration centered on $Δ\varpi=\varpi-\varpi_{\mbox{J}}\approx\pm60^{\circ}$, for the Trojan-like orbits with eccentricities $e<0.1$. Through a detailed analysis, we have shown that the observed Jupiter Trojans with proper eccentricities $e_p<0.1$ spend most of their time in the range of $|Δ\varpi|=0-120^{\circ}$, while the more eccentric ones with $e_p>0.1$ are too few to affect the orbital clustering within this $Δ\varpi$ range for the entire Trojan population. Our numerical results further prove that, even starting from a uniform $Δ\varpi$ distribution, the apsidal alignment of simulated Trojans similar to the observation can appear on the order of the age of the solar system. We conclude that the apsidal asymmetric-alignment of Jupiter Trojans is robust, and this new finding can be helpful to design the survey strategy in the future.

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arXiv2021

Secular resonance of inner test particles in hierarchical planetary systems

The present work studies the secular resonance associated with the critical argument $σ= \varpi$ ($\varpi$ is the longitude of pericentre) for inner test particles moving in low-eccentricity region with inclination $i$ smaller than $39^{\circ}$. To formulate the dynamical model, the double-averaged Hamiltonian is formulated up to an arbitrary order in the semimajor axis ratio, and then those high-order periodic terms are removed from the double-averaged Hamiltonian by means of Hori--Deprit transformation technique. The resulting Hamiltonian determines a resonant model with a single degree of freedom. Based on the resonant model, it becomes possible to explore the phase-space structure, resonant centre, and resonant width in an analytical manner. In particular, an excellent correspondence is found between the resonant width in terms of the eccentricity variation and the maximum variation of eccentricity ($Δe$) for test particles initially placed on quasi-circular orbits. It means that the secular dynamics in the low-eccentricity space with $i < 39^{\circ}$ is dominantly governed by the secular resonance associated with $σ= \varpi$.

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arXiv2021

Dynamical structures of retrograde resonances: analytical and numerical studies

In this work, retrograde mean motion resonances (MMRs) are investigated by means of analytical and numerical approaches. Initially, we define a new resonant angle to describe the retrograde MMRs and then perform a series of canonical transformations to formulate the resonant model, in which the phase portrait, resonant centre and resonant width can be analytically determined. To validate the analytical developments, the non-perturbative analysis is made by taking advantage of Poincaré surfaces of section. Some modifications are introduced in the production of Poincaré sections and, in particular, it becomes possible to make direct comparisons between the analytical and numerical results. It is found that there exists an excellent correspondence between the phase portraits and the associated Poincaré sections, and the analytical results agree well with the numerical results in terms of the resonant width and the location of resonant centre. Finally, the numerical approach is utilized to determine the resonant widths and resonant centres over the full range of eccentricity. In particular, seven known examples of retrograde asteroids including 2015 BZ509, 2008 SO218, 1999 LE31, 2000 DG8, 2014 AT28, 2016 LS and 2016 JK24 are found inside the libration zones of retrograde MMRs with Jupiter. The results obtained in this work may be helpful for understanding the dynamical evolution for asteroids inside retrograde MMRs.

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arXiv2020

Multi-harmonic Hamiltonian models with applications to first-order resonances

In this work, two multi-harmonic Hamiltonian models for mean motion resonances are formulated and their applications to first-order resonances are discussed. For the $k_p$:$k$ resonance, the usual critical argument $φ= k λ- k_p λ_p + (k_p - k) \varpi$ is taken as the resonant angle in the first model, while the second model is characterized by a new critical argument $σ= φ/ k_p$. Based on canonical transformations, the resonant Hamiltonians associated with these two models are formulated. It is found that the second Hamiltonian model holds two advantages in comparison to the first model: (a) providing a direct correspondence between phase portraits and Poincaré sections, and (b) presenting new phase-phase structures where the zero-eccentricity point is a visible saddle point. Then, the second Hamiltonian model is applied to the first-order inner and outer resonances, including the 2:1, 3:2, 4:3, 2:3 and 3:4 resonances. The phase-space structures of these first-order resonances are discussed in detail and then the libration centers and associated resonant widths are identified analytically. Simulation results show that there are pericentric and apocentric libration zones where the libration centers diverge away from the nominal resonance location as the eccentricity approaches zero and, in particular, the resonance separatrices do not vanish at arbitrary eccentricities for both the inner and outer (first-order) resonances.

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arXiv2020

GAUSS -- A Sample Return Mission to Ceres

The goal of Project GAUSS is to return samples from the dwarf planet Ceres. Ceres is the most accessible ocean world candidate and the largest reservoir of water in the inner solar system. It shows active cryovolcanism and hydrothermal activities in recent history that resulted in minerals not found in any other planets to date except for Earth's upper crust. The possible occurrence of recent subsurface ocean on Ceres and the complex geochemistry suggest possible past habitability and even the potential for ongoing habitability. Aiming to answer a broad spectrum of questions about the origin and evolution of Ceres and its potential habitability, GAUSS will return samples from this possible ocean world for the first time. The project will address the following top-level scientific questions: 1) What is the origin of Ceres and the origin and transfer of water and other volatiles in the inner solar system? 2) What are the physical properties and internal structure of Ceres? What do they tell us about the evolutionary and aqueous alteration history of icy dwarf planets? 3) What are the astrobiological implications of Ceres? Was it habitable in the past and is it still today? 4) What are the mineralogical connections between Ceres and our current collections of primitive meteorites? GAUSS will first perform a high-resolution global remote sensing investigation, characterizing the geophysical and geochemical properties of Ceres. Candidate sampling sites will then be identified, and observation campaigns will be run for an in-depth assessment of the candidate sites. Once the sampling site is selected, a lander will be deployed on the surface to collect samples and return them to Earth in cryogenic conditions that preserves the volatile and organic composition as well as the original physical status as much as possible.

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