Orbital Resonance Research Articles

Origin of unique electronic structures of single-atom alloys unraveled by interpretable deep learning.

We uncover the origin of unique electronic structures of single-atom alloys (SAAs) by interpretable deep learning. The approach integrates tight-binding moment theory with graph neural networks to accurately describe the local electronic structure of transition and noble metal sites upon perturbation. We emphasize the complex interplay of interatomic orbital coupling and on-site orbital resonance, which shapes the d-band characteristics of an active site, shedding light on the origin of free-atom-like d-states that are often observed in SAAs involving d10 metal hosts. This theory-infused neural network approach significantly enhances our understanding of the electronic properties of single-site catalytic materials beyond traditional theories.

Experimental and numerical investigation of the Doppler-shifted resonance condition for high frequency Alfvén eigenmodes on ASDEX Upgrade

Abstract The Doppler-shifted resonance condition for high frequency Alfvénic eigenmodes has been extensively studied on ASDEX Upgrade in the presence of one or a combination of two neutral beam injected (NBI) fast ion populations. In general, only centrally deposited NBI sources drive these modes, while off-axis sources globally stabilize the mode activity. For the case of a single central NBI source, the observed trend is: the highest frequency modes are driven by the lowest energy and lowest pitch angle NBI sources, in line with the expectation from the Doppler-shifted resonance condition. The expected mode frequencies are determined analytically from the two-fluid cold plasma dispersion relation and the most unstable frequency relation, while the mode growth rates are estimated using the fast ion slowing down distribution functions from the ASCOT code. The overall mode frequency trend in a source-to-source variation is tracked, although a systematic overestimate of ∼1 MHz is observed. Possible causes of this overestimate include the finite size of the resonant fast ion drift orbit and non-linear effects such as mode sideband formation. Alternatively, the expected mode frequencies are determined by tracking the growth rate maxima trajectories, this method improves the agreement with the experimentally measured values. A combination of two central mode-driving NBI sources results in the suppression of the mode driven by the lowest energy and the lowest pitch angle NBI source. Computing the analytically expected mode frequency following the method outlined above, again, generally tracks the experimentally observed trend. The mode’s Alfvénic nature allows for a practical application to track the core hydrogen fraction by following the mode frequency changes in response to a varying ion mass density. Such application is demonstrated in a discharge where the average ion mass is varied from ∼2m p to ∼1.5m p (where m p is the proton mass) via a hydrogen puff in a deuterium plasma, in the presence of a strong mode activity. The expected mode frequency changes are computed from the existence of the resonance condition, and the values track the measured results with an offset of ∼0.5 MHz. Overall, the results suggest an intriguing possibility to monitor and control the D-T ion fraction in the core of a fusion reactor in real time using a non-invasive diagnostic.

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° at eccentricities <0.1; (2) a nearly complete absence of Hildas with amplitudes <20°, 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° or higher, and a minimum mass of about 50 Earth masses.

Formation of Close-in Neptunes around Low-mass Stars through Breaking Resonant Chains

Conventional planet formation theories predict a paucity of massive planets around small stars, especially very low-mass (0.1−0.3 M ⊙) mid-to-late M dwarfs. Such tiny stars are expected to form planets of terrestrial sizes but not much bigger. However, this expectation is challenged by the recent discovery of LHS 3154 b, a planet with period of 3.7 days and minimum mass of 13.2 M ⊕ orbiting a 0.11 M ⊙ star. Here, we propose that close-in Neptune-mass planets like LHS 3154 b formed through an anomalous series of mergers from a primordial compact system of super-Earths. We perform simulations within the context of the “breaking the chains” scenario, in which super-Earths initially form in tightly spaced chains of mean-motion resonances before experiencing dynamical instabilities and collisions. Planets as massive and close-in as LHS 3154 b (M p ∼ 12−20 M ⊕, P < 7 days) are produced in ∼1% of simulated systems, in broad agreement with their low observed occurrence. These results suggest that such planets do not require particularly unusual formation conditions but rather are an occasional by-product of a process that is already theorized to explain compact multiplanet systems. Interestingly, our simulated systems with LHS 3154 b-like planets also contain smaller planets at around ∼30 days, offering a possible test of this hypothesis.

Analytical calculation of the kinetic q factor and resonant response of toroidally confined plasmas

Symmetry-breaking perturbations in axisymmetric toroidal plasma configurations have a drastic impact on particle, energy, and momentum transport in fusion devices, thereby affecting their confinement properties. The perturbative modes strongly affect particles with specific kinetic characteristics through resonant mode–particle interactions. In this work, we present an analytical calculation of the kinetic q factor, enabling the identification of particles with kinetic properties that meet the resonant conditions. This allows us to predict the locations and structures of the corresponding resonant island chains, as well as the existence of transport barriers in the particle phase space. The analytical results, derived for the case of a large aspect ratio configuration, are systematically compared to numerical simulations, and their domain of validity is thoroughly investigated and explained. Our findings demonstrate that calculating the kinetic q factor and its dependence on both particle and magnetic field characteristics provides a valuable tool for understanding and predicting the resonant plasma response to non-axisymmetric perturbations. Moreover, this approach can be semi-analytically applied to generic realistic experimental equilibria, offering a low-computational-cost method for scenario investigations under various multi-scale perturbative modes.

JWST reveals the rapid and strong day-side variability of 55 Cancri e

Context. The nature of the close-in rocky planet 55 Cnce is puzzling, despite it having been observed extensively. Its optical and infrared occultation depths show temporal variability, in addition to a phase curve variability observed in the optical. Aims. We wish to explore the possibility that the variability originates from the planet being in a 3:2 spin–orbit resonance, and thus showing different sides during occultations. We proposed and were awarded Cycle 1 time at the James Webb Space Telescope (JWST) to test this hypothesis. Methods. JWST/NIRCam (Near Infrared Camera) observed five occultations (secondary eclipses) of the planet – of which four were observed within a week – simultaneously at 2.1 and 4.5 µm. While the former gives band-integrated photometry, the latter provides a spectrum between 3.9–5.0 µm. Results. We find that the occultation depths in both bandpasses are highly variable and change between a non-detection (−5 ± 6 ppm and 7 ± 9 ppm) to 96 ± 8 ppm and 119−19+34 ppm at 2.1 µm and 4.5 µm, respectively. Interestingly, the variations in both bandpasses are not correlated and do not support the 3:2 spin-orbit resonance explanation. The measured brightness temperature at 4.5 µm varies between 873–2256 K and is lower than the expected day-side temperature of bare rock with no heat redistribution (2500 K), which is indicative of an atmosphere. Our atmospheric retrieval analysis of occultation depth spectra at 4.5 µm finds that different visits statistically favour various atmospheric scenarios including a thin outgassed CO/CO2 atmosphere and a silicate rock vapour atmosphere. Some visits even support a flat line model. Conclusions. The observed variability could be explained by stochastic outgassing of CO/CO2, which is also hinted at by retrievals. Alternatively, the variability observed at both 2.1 and 4.5 µm could be the result of a circumstellar patchy dust torus generated by volcanism on the planet.

Dynamical and Secular Stability of Mutually Inclined Planetary Systems

Multiple analytical, semi-analytical, and empirical stability criteria have been derived in the literature for two-planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two-planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semimajor axis of the inner binary β = δ a 1/a 1 caused by perturbations from the companion. Stability criteria can be derived by setting a threshold on β. Focusing initially on circular orbits, we derive an analytical expression for β for coplanar prograde and retrograde orbits. For noncoplanar configurations, we evaluate a semi-analytical expression. We then generalize to orbits with arbitrary eccentricities and account for the secular effects. Our analytical and semi-analytical results are in excellent agreement with direct N-body simulations. In addition, we show that contours of β ∼ 0.01 can serve as criteria for stability. More specifically, we show that (1) retrograde orbits are generally more stable than prograde ones; (2) systems with intermediate mutual inclination are less stable due to von Ziepel–Lidov–Kozai (vZLK) dynamics; and (3) mean motion resonances (MMRs) can stabilize intermediate inclination secularly unstable regions in phase space, by quenching vZLK secular processes (4) MMRs can destabilize some of the dynamically stable regions. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems and their age.

Two-band atomic superfluidity in the presence of an orbital Feshbach resonance

Two-band atomic superfluidity in the presence of an orbital Feshbach resonance

The primary systemic vasculitis associated optic neuritis: a retrospective analysis in a single center over 10 years

ObjectivesTo investigate the clinical and image characteristics of primary systemic vasculitis-associated optic neuritis patients.MethodsThis is a retrospective study. The patients clinically diagnosed with primary system vasculitis-induced optic neuritis were recruited from March 2013 to December 2023. All cases received orbital magnetic resonance imaging scans were analyzed. The ocular findings, systemic manifestations, laboratory data and prognosis were reviewed retrospectively. In addition, the related literature was reviewed.ResultsFourteen patients (21 eyes), including 10 men and 4 women, were enrolled in this study. The ages ranged from 30 to 86 years in this cohort. Orbits MRI detects the enlargement and/or enhancement of the optic nerve. Cases 1–5 reported a confirmed diagnosis of Takayasu’s arteritis, and cases 6–8 had giant cell arteritis. Cases 9–13 were antineutrophil cytoplasmic antibody-associated vasculitis. Case 14 was Cogan’s syndrome. Mult organs and tissues, such as the kidneys, heart, paranasal sinuses, meninges, and respiratory system, were involved. In all of the 14 involved patients, the disease onset was either during the fall or winter season. There were no or only slight improvements in visual activity after conventional therapies.ConclusionsThe autoantibodies’ attack on the optic nerve, ischemic damage, or destruction of the blood–brain barrier may be the potential pathogenesis of vasculitis-associated optic neuritis. Even with prompt and aggressive clinical interventions, the prognosis remains unsatisfactory.

Fast inspirals and the treatment of orbital resonances

Abstract Extreme mass ratio inspirals (EMRIs), where a compact object orbits a massive black hole, are a key source of gravitational waves for the future Laser Interferometer Space Antenna (LISA). Due to their small mass ratio, ε ~ 10-4 -- 10-7 , the binary evolves slowly and EMRI signals will be in-band for years. Additionally, astrophysical EMRIs are expected to have complex dynamics featuring both spin-precession and eccentricity. A standard approach to modelling these inspirals is via the method of osculating geodesics (OG) which we employ along with a toy model for the gravitational self-force. Using this method requires resolving tens of thousands radial and polar orbital librations over the long duration of the signal which makes the inspiral trajectory expensive to compute.In this work we accelerate these calculations by employing Near-Identity (averaging) Transformations. &amp;#xD;However, this averaging technique breaks down at orbital resonances where the radial and polar frequencies are an integer ratio of each other. Thus, we switch to a partial averaging transformation in the vicinity of the resonance where the dynamics are characterised by the slow evolution of the so-called ``resonant phase". Additionally, we develop an optimal switching criterion to minimise the computation time while maximising accuracy. We find the error in the waveform phase is improved from O(ε-1/2) in the fully averaged scheme to O(ε4/7) in the switching scheme. At the same time, this scheme improves the scaling of the computation time from being inversely proportional to ε using OG, to a very weak scaling with ε. This results in a speed-up of at least two orders of magnitude for LISA EMRIs with room for further optimisation.

Dynamics of Two Planets near a 2:1 Resonance: Case Studies of Known and Synthetic Exosystems on a Grid of Initial Configurations

The distribution of period ratios for 580 known two-planet systems is apparently nonuniform, with several sharp peaks and troughs. In particular, the vicinity of the 2:1 commensurability seems to have a deficit of systems. Using Monte Carlo simulations and an empirically inferred population distribution of period ratios, we prove that this apparent dearth of near-resonant systems is not statistically significant. The excess of systems with period ratios in the wider vicinity of the 2:1 resonance is significant, however. Long-term WHFast integrations of a synthetic two-planet system on a grid period ratios from 1.87 through 2.12 reveal that the eccentricity and inclination exchange mechanism between non-resonant planets represents the orbital evolution very well in all cases, except at the exact 2:1 mean motion resonance. This resonance destroys the orderly exchange of eccentricity, while the exchange of inclination still takes place. Additional simulations of the Kepler-113 system on a grid of initial inclinations show that the secular periods of eccentricity and inclination variations are well fitted by a simple hyperbolic cosine function of the initial mutual inclination. We further investigate the six known two-planet systems with period ratios within 2% of the exact 2:1 resonance (TOI-216, KIC 5437945, Kepler-384, HD 82943, HD 73526, HD 155358) on a grid of initial inclinations and for two different initial periastron longitudes corresponding to the aligned and anti-aligned states. All these systems are found to be long-term stable except HD 73526, which is likely a false positive. The periodic orbital momentum exchange is still at work in some of these systems, albeit with much shorter cycling periods of a few years.

Exponentially localized interface eigenmodes in finite chains of resonators

AbstractThis paper studies wave localization in chains of finitely many resonators. There is an extensive theory predicting the existence of localized modes induced by defects in infinitely periodic systems. This work extends these principles to finite‐sized systems. We consider one‐dimensional, finite systems of subwavelength resonators arranged in dimers that have a geometric defect in the structure. This is a classical wave analog of the Su–Schrieffer–Heeger model. We prove the existence of a spectral gap for defectless finite dimer structures and find a direct relationship between eigenvalues being within the spectral gap and the localization of their associated eigenmode. Then, for sufficiently large‐size systems, we show the existence and uniqueness of an eigenvalue in the gap in the defect structure, proving the existence of a unique localized interface mode. To the best of our knowledge, our method, based on Chebyshev polynomials, is the first to characterize quantitatively the localized interface modes in systems of finitely many resonators.

Infiltrative Optic Neuropathy

Infiltrative optic neuropathies represent a subset of optic nerve disorders characterized by the infiltration of cells derived from inflammatory, infectious, or tumor metastasis sources. These conditions pose significant challenges in terms of diagnosis, management, and prognosis due to their diverse clinical presentations and potential for rapid progression. Detailed ophthalmic examinations such as visual field testing and optical coherence tomography (OCT) are necessary to provide valuable insights into the structure and function of the optic nerve. Additionally, brain and orbital magnetic resonance imaging (MRI) are essential for detecting infiltrative lesions and assessing the extent of optic nerve involvement.

Spin orbit resonance cascade via core shell model: application to Mercury and Ganymede

We discuss a model describing the spin orbit resonance cascade. We assume that the body has a two-layer (core–shell) structure; it is composed of a thin external shell and an inner and heavier solid core that are interacting due to the presence of a viscous friction. We assume two sources of dissipation: a viscous one, depending on the relative angular velocity between core and shell and a tidal one, smaller than the first, due to the viscoelastic structure of the core. We show how these two sources of dissipation are needed for the capture in spin–orbit resonance. The shell and the core fall in resonance with different time scales if the viscous coupling between them is big enough. Finally, the tidal dissipation of the viscoelastic core, decreasing the eccentricity, brings the system out of the resonance in a third very long time scale. This mechanism of entry and exit from resonance ends in the 1 : 1 stable state.

Mean-motion resonances with interfering density waves

ABSTRACT In this work, we study the dynamics of two less massive objects moving around a central massive object, which are all embedded within a thin accretion disc. In addition to the gravitational interaction between these objects, the disc–object interaction is also crucial for describing the long-term dynamics of the multibody system, especially in the regime of mean-motion resonances. We point out that near the resonance the density waves generated by the two moving objects generally coherently interfere with each other, giving rise to extra angular momentum fluxes. The resulting backreaction on the objects is derived within the thin-disc scenario, which explicitly depends on the resonant angle and sensitively depends on the smoothing scheme used in the two-dimensional theory. We have performed hydrodynamical simulations with planets embedded within a thin accretion disc and have found qualitatively agreement on the signatures of interfering density waves by measuring the torques on the embedded objects, for the cases of $2:1$ and $3:2$ resonance. By including in interference torque and the migration torques in the evolution of a pair of planets, we show that the chance of resonance trapping depends on the sign of the interference torque. For negative interference torques the pairs are more likely located at off-resonance regimes. The negative interference torques may also explain the $1~{{\ \rm per\ cent}}-2~{{\ \rm per\ cent}}$ offset (for the period ratios) from the exact resonance values as observed in Kepler multiplanet systems.

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) VO123 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.

Family of 2:1 resonant quasi-periodic distant retrograde orbits in cislunar space

Given the current enthusiasm for lunar exploration, the 2:1 resonant distant retrograde orbit (DRO) in Earth-Moon space is of interest. To gain an in-depth understanding of the complex dynamic environment in cislunar space and provide more options for parking orbits, this paper investigates the existence of quasi-periodic orbits near the 2:1 resonant DRO in the circular restricted three-body problem (CR3BP). Firstly, the numerical computation approach, continuation strategy, and stability analysis method of quasi-periodic orbits are introduced. Then, addressing the primary challenges in the continuation progress, we have developed an adaptive continuation algorithm with automatic adjustment of the step size and the number of discrete points that characterize the invariant torus. Finally, two types of 2D quasi-DROs and their linear stability properties are explored. Using Poincaré sections, we investigated the boundaries of the maximum extent attainable by both 2D quasi-DRO families in the CR3BP at a specific Jacobi energy, confirming that both types of quasi-periodic families have reached their respective boundaries. The algorithm described in this paper is beneficial for facilitating the computation of quasi-periodic families and aids in discovering additional potential dynamical structures.

Identification and analysis of interior and exterior resonant orbits in the Sun–Venus system

With Venus being Earth’s nearest neighbor and it being similar in size to Earth, it is the ideal candidate for certain mission types. These missions range from scientific, such as helio-physics and space weather monitoring, to defense focused, such as monitoring Earth’s orbital path for meteoroid threats. Limited research has been done on the periodic orbits in the Sun–Venus system. The first step to understanding which orbits could be useful for such a mission is to identify families of resonant periodic orbits in the Sun–Venus system and conduct a stability analysis on these orbits. This research work identifies 90 periodic, resonant orbits in the Sun–Venus system and their associated families of orbits. The orbits are found within the Circular Restricted 3 Body Problem (CR3BP) dynamical model with solar radiation pressure included as a perturbation. The periodic orbits are found using Poincaré maps, and the families are generated using a continuation method that steps through different Jacobi constants. The stability for each orbit in the family is calculated and the structure of the eigenvalues for each is assessed to determine when the family has crossed a bifurcation point. This research work seeks to generate a catalog of resonant orbits within the Sun–Venus system while providing stability and bifurcation information for each resonant orbit family.

A perturbative treatment of the Yarkovsky-driven drifts in the 2:1 mean motion resonance

Aims. Our aim is to gain a qualitative understanding as well as to perform a quantitative analysis of the interplay between the Yarkovsky effect and the Jovian 2:1 mean motion resonance under the planar elliptic restricted three-body problem. Methods. We adopted the semi-analytical perturbation method valid for arbitrary eccentricity to obtain the resonance structures inside the Jovian 2:1 resonance. We averaged the Yarkovsky force so it could be applied to the integrable approximations for the 2:1 resonance and the ν5 secular resonance. The rates of Yarkovsky-driven drifts in the action space were derived from the quasi-integrable approximations perturbed by the averaged Yarkovsky force. Pseudo-proper elements of test particles inside the 2:1 resonance were computed using N-body simulations incorporated with the Yarkovsky effect to verify the semi-analytical results. Results. In the planar elliptic restricted model, we identified two main types of systematic drifts in the action space: (Type I) for orbits not trapped in the ν5 resonance, the footprints are parallel to the resonance curve of the stable center of the 2:1 resonance; (Type II) for orbits trapped in the ν5 resonance, the footprints are parallel to the resonance curve of the stable center of the ν5 resonance. Using the semi-analytical perturbation method, a vector field in the action space corresponding to the two types of systematic drifts was derived. The Type I drift with small eccentricities and small libration amplitudes of 2:1 resonance can be modeled by a harmonic oscillator with a slowly varying parameter, for which an analytical treatment using the adiabatic invariant theory was carried out.

The 𝒯ℛ𝒪𝒴 project

Context. Co-orbital objects, also known as trojans, are frequently found in simulations of planetary system formation. In these configurations, a planet shares its orbit with other massive bodies. It is still unclear why there have not been any co-orbitals discovered thus far in exoplanetary systems (exotrojans) or even pairs of planets found in such a 1:1 mean motion resonance. Reconciling observations and theory is an open subject in the field. Aims. The main objective of the 𝒯ℛ𝒪𝒴 project is to conduct an exhaustive search for exotrojans using diverse observational techniques. In this work, we analyze the radial velocity time series informed by transits, focusing the search around low-mass stars. Methods. We employed the α-test method on confirmed planets searching for shifts between spectral and photometric mid-transit times. This technique is sensitive to mass imbalances within the planetary orbit, allowing us to identify non-negligible co-orbital masses. Results. Among the 95 transiting planets examined, we find one robust exotrojan candidate with a significant 3-σ detection. Additionally, 25 exoplanets show compatibility with the presence of exotrojan companions at a 1-σ level, requiring further observations to better constrain their presence. For two of those weak candidates, we find dimmings in their light curves within the predicted Lagrangian region. We established upper limits on the co-orbital masses for either the candidates and null detections. Conclusions. Our analysis reveals that current high-resolution spectrographs effectively rule out co-orbitals more massive than Saturn around low-mass stars. This work points out to dozens of targets that have the potential to better constraint their exotrojan upper mass limit with dedicated radial velocity observations. We also explored the potential of observing the secondary eclipses of the confirmed exoplanets in our sample to enhance the exotrojan search, ultimately leading to a more accurate estimation of the occurrence rate of exotrojans.