arXiv subjects

Hanlun Lei

Publications and source records attributed to Hanlun Lei.

At least 19 recordsLinked to original sources

arXiv2026

Tidal coplanarization of circumbinary planetary systems through stellar Cassini states

Circumbinary planets (CBPs) currently identified are in nearly coplanar configurations relative to their host binaries, yet the dynamical origin of this preference remains unclear. We investigate this question by simulating the secular spin-orbit evolution of CBP systems with tidal decay. A representative case shows that the system evolves through three stages (coplanarization, spin-orbit synchronization, and spin-orbit alignment) through the angular momentum exchange between stellar spin and orbital motion. The evolution of mutual inclination is strongly coupled to stellar obliquity. Phase-space analysis and examination of stellar Cassini states reveal that arbitrary initial inclinations are gradually damped to coplanarity by tides, while stellar obliquity is adiabatically captured into Cassini states with diminishing oscillation amplitudes. This study provides a self-consistent analytical and numerical framework for determining stellar Cassini states and understanding coupled spin-orbit evolution in CBP systems. It shows that tidal dissipation, combined with adiabatic capture into Cassini states, drives the observed dynamical behavior.

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arXiv2026

Resonant Networks of Spin-Orbit Coupling in Ellipsoid-Ellipsoid Binary Asteroid Systems

The dynamical evolution of binary asteroid systems is deeply influenced by spin-orbit resonances. However, their domains of influence and mutual interactions remain elusive, in particular in the space where multiple resonant modes coexist. In such regimes, the standard single-resonance approach is intrinsically limited and fails to capture the true coupled dynamics. To overcome this, we develop a global Hamiltonian framework based on elliptic expansions of the spin-orbit coupling model, enabling the numerical construction of comprehensive resonant networks. Concentrating on a representative synchronous region that encompasses synchronous spin-orbit, spin-spin, spin-orbit-spin, and doubly synchronous resonances, we study the dynamical boundaries of different resonant modes in a systematical manner. Crucially, we identify a secondary resonance structure arising from the strong nonlinear coupling between the synchronous resonances of the primary and secondary asteroids. Ultimately, this study provides a reliable parameter-space atlas, which is helpful for predicting the long-term evolutionary pathways of binary asteroid systems.

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arXiv2026

Extensions of Brown Hamiltonian-III. Applications to irregular satellites of giant planets

Irregular satellites, orbiting at large distances from their host planets, are subject to strong solar perturbations that render long-term orbital predictions particularly challenging. Building upon the extended Brown Hamiltonian framework developed in Paper I, we introduce the modified Lidov integral ($C_{\rm ZLK}$) as a practical diagnostic index to characterize the dynamical modes. We demonstrate that a satellite is trapped inside the von Zeipel--Lidov--Kozai (ZLK) resonance when $C_{\rm ZLK} < 0$. Applying this criterion to the known population of irregular satellites, we identify 27 candidates in libration. Direct $N$-body simulations confirm 26 of these predictions, with the sole exception of S/2019 S1, whose discrepancy is attributed to its proximity to the separatrix. These results establish $C_{\rm ZLK}$ as a decisive parameter for identifying the ZLK resonance, providing an efficient tool for analyzing the secular dynamics in weakly hierarchical three-body systems.

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arXiv2026

High-order expansions of multi-revolution elliptic Halo orbits in the elliptic restricted three-body problem

Multi-revolution elliptic Halo (ME-Halo) orbits are a special class of symmetric and periodic solutions within the framework of the elliptic restricted three-body problem (ERTBP). During a single period, an M:N ME-Halo orbit completes $M$ revolutions around a libration point and the primaries revolve N times around each other. Owing to the repeated configurations, ME-Halo orbits hold great promise as nominal trajectories for space mission design. However, a major challenge associated with ME-Halo orbits lies in their mathematical description. To this end, we propose a novel method to derive high-order analytical expansions of ME-Halo orbits in the ERTBP by introducing two correction terms into the equations of motion in the y- and z-directions. Specifically, both the coordinate variables and correction terms are expanded as power series in terms of the primary eccentricity, the in-plane amplitude, and the out-of-plane amplitude. High-order approximations are constructed using a perturbation method, and their accuracy is validated through numerical analysis. Due to the inherent symmetry, ME-Halo orbits can be classified into four distinct families: southern/northern and periapsis/apoapsis groups. The analytical approximations developed in this study not only provide high-accuracy initial guesses for the numerical computation of ME-Halo orbits, but also offer new insights into the dynamical environment near collinear libration points in the ERTBP, thereby advancing practical applications in mission design.

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arXiv2025

Eccentric von Zeipel-Lidov-Kozai effects under mildly hierarchical triple systems: Influence of Brown corrections upon orbit flipping

Mildly hierarchical three-body systems are widespread in the Universe, exemplified by planets in stellar binaries and stars in black-hole binaries. In such systems, Brown Hamiltonian corrections play a crucial role in governing the long-term dynamical evolution. In this work, we extend Brown corrections to include octupole-order coupling terms, thereby formulating a more accurate dynamical model for predicting long-term dynamical behaviors. The utilization of the gauge freedom in canonical transformation shows that the quadrupole-octupole coupling term vanishes and the octupole-octupole coupling term is axisymmetric. Under triple systems with different levels of hierarchies, we systematically investigate the impact of Brown corrections on orbital flipping induced by the eccentric von Zeipel-Lidov-Kozai (ZLK) mechanism. Our analysis reveals that, as the hierarchy of triple systems becomes lower, the asymmetry in the flipping regions becomes more significant. The asymmetric structures are examined in detail using Poincare sections and perturbative techniques, showing that Brown corrections are the key factor responsible for breaking the symmetry of flipping regions. Finally, we extend the classical pendulum approximation to our refined model and demonstrate that its analytical predictions agree remarkably well with those derived from perturbative methods, particularly in the high-eccentricity regime.

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arXiv2025

Extensions of Brown Hamiltonian-II. Analytical study on the modified von Zeipel-Lidov-Kozai effects

In triple systems of weak hierarchies, nonlinear perturbations arising from the periodic oscillations associated with the inner and outer binaries play a crucial role in shaping their long-term dynamical evolution. In this context, we have developed an extended Brown Hamiltonian in Paper I, which serves as a fundamental model for describing the modified von Zeipel-Lidov-Kozai (ZLK) oscillations. The present work aims to analyze the characteristics of ZLK oscillations within this extended framework, focusing on phase-space structures, the location of ZLK center, the maximum eccentricity reached, the boundaries of librating cycles, and the critical inclination required to trigger ZLK resonance. Under the extended Hamiltonian, we introduce the Lidov integral C_ZLK, which is a combination of the Hamiltonian and the z-component of angular momentum, to characterize the modified ZLK properties. It is found that the librating and circulating cycles are separated by C_ZLK=0, which is consistent with the classical theory. Furthermore, we derive analytical expressions of these ZLK properties using perturbation techniques. Analytical predictions are compared to numerical results, showing an excellent agreement between them. Notably, the results reveal that ZLK characteristics in prograde and retrograde regimes are no longer symmetric under the influence of Brown corrections. At last, we conduct $N$-body integrations about millions of orbits to generate dynamical maps, where the numerical structures are well captured by the analytical solutions derived from the extended model.

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arXiv2025

ThermoONet -- a deep learning-based small body thermophysical network: applications to modelling water activity of comets

Cometary activity is a compelling subject of study, with thermophysical models playing a pivotal role in its understanding. However, traditional numerical solutions for small body thermophysical models are computationally intensive, posing challenges for investigations requiring high-resolution or repetitive modeling. To address this limitation, we employed a machine learning approach to develop ThermoONet - a neural network designed to predict the temperature and water ice sublimation flux of comets. Performance evaluations indicate that ThermoONet achieves a low average error in subsurface temperature of approximately 2% relative to the numerical simulation, while reducing computational time by nearly six orders of magnitude. We applied ThermoONet to model the water activity of comets 67P/Churyumov-Gerasimenko and 21P/Giacobini-Zinner. By successfully fitting the water production rate curves of these comets, as obtained by the Rosetta mission and the SOHO telescope, respectively, we demonstrate the network's effectiveness and efficiency. Furthermore, when combined with a global optimization algorithm, ThermoONet proves capable of retrieving the physical properties of target bodies.

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arXiv2025

Extensions of Brown Hamiltonian-I. A high-accuracy model for von Zeipel-Lidov-Kozai oscillations

Triple systems with low hierarchical structure are common throughout the Universe, including examples such as high-altitude lunar satellites influenced by the Earth, planetary satellites perturbed by the Sun, and stellar binaries affected by a supermassive black hole. In these systems, nonlinear perturbations are significant, making classical double-averaged models (even those incorporating the Brown Hamiltonian correction) insufficient for accurately capturing long-term dynamics. To overcome this limitation, the current study develops a high-precision dynamical model that incorporates the nonlinear effects of the quadrupole-order potential arising from both the inner and outer bodies, referred to as the extended Brown Hamiltonian model. This framework specifically expresses the Hamiltonian function and the transformation between mean and osculating orbital elements in elegant, closed forms with respect to the eccentricities of the inner and outer orbits. Practical applications to Jupiter's irregular satellites show that the long-term evolutions predicted by the extended Brown Hamiltonian model align well with the results of direct N-body simulations. The developed Hamiltonian offers a fundamental dynamical model, which is particularly well suited for describing von Zeipel-Lidov-Kozai oscillations in low-hierarchy three-body systems.

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arXiv2024

Deep operator neural network applied to efficient computation of asteroid surface temperature and the Yarkovsky effect

Surface temperature distribution is crucial for thermal property-based studies about irregular asteroids in our Solar System. While direct numerical simulations could model surface temperatures with high fidelity, they often take a significant amount of computational time, especially for problems where temperature distributions are required to be repeatedly calculated. To this end, deep operator neural network (DeepONet) provides a powerful tool due to its high computational efficiency and generalization ability. In this work, we applied DeepONet to the modelling of asteroid surface temperatures. Results show that the trained network is able to predict temperature with an accuracy of ~1% on average, while the computational cost is five orders of magnitude lower, hence enabling thermal property analysis in a multidimensional parameter space. As a preliminary application, we analyzed the orbital evolution of asteroids through direct N-body simulations embedded with instantaneous Yarkovsky effect inferred by DeepONet-based thermophysical modelling.Taking asteroids (3200) Phaethon and (89433) 2001 WM41 as examples, we show the efficacy and efficiency of our AI-based approach.

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arXiv2024

Resonant amplitude distribution of the Hilda asteroids and the free-floating planet flyby scenario

In some recent work, we provided a quantitative explanation for the number asymmetry of Jupiter Trojans by hypothesizing a free-floating planet (FFP) flyby into the Solar System. In support of that explanation, this paper examines the influence of the same FFP flyby on the Hilda asteroids, which orbit stably in the 3:2 mean motion resonance with Jupiter. The observed Hilda population exhibits two distinct resonant patterns: (1) a lack of Hildas with resonant amplitudes < 40 deg. at eccentricities < 0.1; (2) a nearly complete absence of Hildas with amplitudes < 20 deg., regardless of eccentricity. Previous models of Jupiter migration and resonance capture could account for the eccentricity distribution of Hildas but have failed to replicate the unusual absence of those with the smallest resonant amplitudes, which theoretically should be the most stable. Here we report that the FFP flyby can trigger an extremely rapid outward migration of Jupiter, causing a sudden shift in the 3:2 Jovian resonance. Consequently, Hildas with varying eccentricities would have their resonant amplitudes changed by different degrees, leading to the observed resonant patterns. We additionally show that, in our FFP flyby scenario, these patterns are consistently present across different resonant amplitude distributions of primordial Hildas arising from various formation models. We also place constraints on the potential parameters of the FFP, suggesting it should have an eccentricity of 1-1.3 or larger, an inclination up to 30 deg. or higher, and a minimum mass of about 50 Earth masses.

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arXiv2024

Spin-orbit coupling of the primary body in a binary asteroid system

Spin-orbit coupling is widespread in binary asteroid systems and it has been widely studied for the case of ellipsoidal secondary. Due to angular momentum exchange, dynamical coupling is stronger when the orbital and rotational angular momenta are closer in magnitudes. Thus, the spin-orbit coupling effects are significantly different for ellipsoidal secondaries and primaries. In the present work, a high-order Hamiltonian model in terms of eccentricity is formulated to study the effects of spin-orbit coupling for the case of ellipsoidal primary body in a binary asteroid system. Our results show that the spin-orbit coupling problem for the ellipsoidal primary holds two kinds of spin equilibrium, while there is only one for the ellipsoidal secondary. In particular, 1:1 and 2:3 spin-orbit resonances are further studied by taking both the classical pendulum approximation as well as adiabatic approximation (Wisdom's perturbative treatment). It shows that there is a critical value of total angular momentum, around which the pendulum approximation fails to work. Dynamical structures are totally different when the total angular momentum is on two sides of the critical value.

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arXiv2024

Spin-orbit coupling of the ellipsoidal secondary in a binary asteroid system

In our Solar system, spin-orbit coupling is a common phenomenon in binary asteroid systems, where the mutual orbits are no longer invariant due to exchange of angular momentum between translation and rotation. In this work, dynamical structures in phase space are explored for the problem of spin-orbit coupling by taking advantage of analytical and numerical methods. In particular, the technique of Poincaré sections is adopted to reveal numerical structures, which are dependent on the total angular momentum, the Hamiltonian, mass ratio and asphericity parameter. Analytical study based on perturbative treatments shows that high-order and/or secondary spin-orbit resonances are responsible for numerical structures arising in Poincaré sections. Analytical solutions are applied to (65803) Didymos, (80218) ${\rm VO}_{123}$ and (4383) Suruga to reveal their phase-space structures, showing that there is a high possibility for them to locate inside secondary 1:1 spin-orbit resonance.

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arXiv2024

Dynamical structures of misaligned circumbinary planets under hierarchical three-body systems

All circumbinary planets (CBPs) currently detected are located in almost co-planar configurations with respect to the binary orbit, due to the fact that CBPs with higher misalignment are more difficult to detect. However, observations of polar circumbinary gas and debris disks in recent years and long-term orbital stability of inclined planets indicate that it is possible to form misaligned CBPs around eccentricity binaries (even polar CBPs). In this work we focus on the dynamical structures of CBPs in a wide range of parameters in order to provide a guidance for the space where the binary can host planets for a long enough time. To this end, the dynamical model is approximated as a hierarchical three-body problem, and the secular approximation is formulated up to the hexadecapolar order in semimajor axis ratio. Dynamical maps show that there are complex structures in the parameter space. A web of secular resonances is produced in the entire parameter space and it can well explain those numerical structures arising in dynamical maps. Based on perturbative treatments, an adiabatic invariant is introduced and thus dynamical structures can be explored by analysing phase portraits. It is found that (a) the quadrupole-order resonance (nodal resonance) is responsible for the distribution of V-shape region, and high-order and secondary resonances dominate those structures inside or outside V-shape region, and (b) the secondary 1:1 resonance is the culprit causing symmetry breaking of dynamical structures inside polar region.

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arXiv2023

Dynamical structures associated with high-order and secondary resonances in the spin-orbit problem

In our Solar system, spin-orbit resonances are common under Sun--planet, planet--satellite and binary asteroid configurations. In this work, high-order and secondary spin-orbit resonances are investigated by taking numerical and analytical approaches. Poincaré sections as well as two types of dynamical maps are produced, showing that there are complicated structures in the phase space. To understand numerical structures, we adopt the theory of perturbative treatments to formulate resonant Hamiltonian for describing spin-orbit resonances. Results show that there is an excellent agreement between analytical and numerical structures. It is concluded that the main V-shape structure arising in the parameter space $(\dotθ,α)$ is sculpted by the synchronous primary resonance, those minute structures inside the V-shape region are dominated by secondary resonances and those structures outside the V-shape region are governed by high-order resonances. At last, the analytical approach is applied to binary asteroid systems (65803) Didymos and (4383) Suruga to reveal their phase-space structures.

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arXiv2023

Secular dynamics of stellar spin driven by planets inside Kozai-Lidov resonance

In many exoplanetary systems with `hot Jupiters', it is observed that the spin axes of host stars are highly misaligned to planetary orbital axes. In this study, a possible channel is investigated for producing such a misalignment under a hierarchical three-body system where the evolution of stellar spin is subjected to the gravitational torque induced from the planet inside Kozai--Lidov (KL) resonance. In particular, two special configurations are explored in detail. The first one corresponds to the configuration with planets at KL fixed points, and the second one corresponds to the configurations with planets moving on KL librating cycles. When the planet is located at the KL fixed point, the corresponding Hamiltonian model is of one degree of freedom and there are three branches of libration centres for stellar spin. When the planet is moving on KL cycles, the technique of Poincaré section is taken to reveal global structures of stellar spin in phase space. To understand the complex structures, perturbative treatments are adopted to study rotational dynamics. It shows that analytical structures in phase portraits under the resonant model can agree well with numerical structures arising in Poincaré sections, showing that the complicated dynamics of stellar spin are governed by the primary resonance under the unperturbed Hamiltonian model in combination with the 2:1 (high-order and/or secondary) spin-orbit resonances.

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arXiv2023

A study of the high-inclination population in the Kuiper belt -- IV. High-order mean motion resonances in the classical region

In our previous study of Neptune's 4:7 mean motion resonance (MMR), we discovered that its resonant angle can only librate within a specific eccentricity ($e$) versus inclination ($i$) region, determined by a theoretical limiting curve curve (Li et al. 2020). This ``permissible region'' is independent of time and encompasses the entire possible stable region. We now generalize this theory to investigate all high-order MMRs embedded in the main classical Kuiper belt (MCKB). We first consider the 2nd-order 3:5 MMR in the framework of planet migration and resonance capture, and have further validated our limiting curve theory for both captured and observed 3:5 resonators. It suggests that only the $(e, i)$ pairs inside the individual permissible regions should be chosen as initial conditions for studying the in-situ evolution of high-order resonators. With such a new setting, we proceed to explore the long-term stability (for 4 Gyr) of different resonant populations, and our simulations predict that: (1) the 3:5 and 4:7 resonators are comparable in number, and they could have inclinations up to $40^{\circ}$; (2) the populations of objects in the higher order 5:9, 6:11, 7:12 and 7:13 resonances is about 1/10 of the 3:5 (or 4:7) resonator population, and nearly all of them are found on the less inclined orbits with $i<10^{\circ}$; (3) for these high-order resonances, almost all resonators reside in their individual permissible regions. In summary, our results make predictions for the number and orbital distributions of potential resonant objects that will be discovered in the future throughout the MCKB.

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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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