Orbital Integrals Research Articles

Multiple Beads on a String: Dark-matter-deficient Galaxy Formation in a Mini-Bullet Satellite–Satellite Galaxy Collision

Dark-matter-deficient galaxies (DMDGs) discovered in the survey of ultra-diffuse galaxies (UDGs), in apparent conflict with standard cold dark matter, may be produced by high-velocity galaxy–galaxy collisions, the so-called Mini-Bullet scenario. Recent observations of an aligned trail of 7–11 UDGs near NGC 1052, including DMDGs DF2 and DF4, suggesting a common formation event, ∼8.9 ± 1.5 Gyr ago, provide a test.Hydro/N-body simulations, supplemented by galaxy orbit integrations, demonstrate that satellite–satellite collisions outside the host-galaxy virial radius can reproduce the observed UDGs in the NGC 1052 group. A trail of ∼10 DMDGs is shown to form, including 2 massive ones that replicate the observed motions of DF2 and DF4. The linear relation, v = A x + v 0, conjectured previously to relate positions ( x ) and velocities ( v ) of the aligned DMDGs as a signature of the collision event, is approximately obeyed, but individual DMDGs can deviate significantly from it. The progenitors whose collision spawned the trail of DMDGs survive the collision without themselves becoming DMDGs. We predict that one progenitor is located at the end of the trail, which can be tested by observing the difference between its stars, formed pre-collision, from those of the DMDGs, formed post-collision. By contrast, stellar ages and metallicities of the DMDGs are nearly identical. We further offer a hint that the tidal field of host NGC 1052 may contribute to making DMDGs diffuse. ΛCDM simulation in a 100 cMpc box finds our required initial conditions ∼10 times at z < 3. These results indicate current observations are consistent with the Mini-Bullet scenario.

Exotic Magnetism in Perovskite KOsO_{3}.

A new perovskite KOsO_{3} has been stabilized under high-pressure and high-temperature conditions. It is cubic at 500K (Pm-3m) and undergoes subsequent phase transitions to tetragonal at 320K (P4/mmm) and rhombohedral (R-3m) at 230K as shown from refining synchrotron x-ray powder diffraction (SXRD) data. The larger orbital overlap integral and the extended wave function of 5d electrons in the perovskite KOsO_{3} allow to explore physics from the regime where Mott and Hund's rule couplings dominate to the state where the multiple interactions are on equal footing. We demonstrate an exotic magnetic ordering phase found by neutron powder diffraction along with physical properties via a suite of measurements including magnetic and transport properties, differential scanning calorimetry, and specific heat, which provide comprehensive information for a system at the crossover from localized to itinerant electronic behavior.

What Is Missing from the Local Stellar Halo?

The Milky Way’s stellar halo, which extends to >100 kpc, encodes the evolutionary history of our Galaxy. However, most studies of the halo to date have been limited to within a few kiloparsecs of the Sun. Here, we characterize differences between this local halo and the stellar halo in its entirety. We construct a composite stellar halo model by combining observationally motivated N-body simulations of the Milky Way’s nine most massive disrupted dwarf galaxies that account for almost all of the mass in the halo. We find that (i) the representation by mass of different dwarf galaxies in the local halo compared to the whole halo can be significantly overestimated (e.g., the Helmi streams) or underestimated (e.g., Cetus) and (ii) properties of the overall halo (e.g., net rotation) inferred via orbit integration of local halo stars are significantly biased because, for example, highly retrograde debris from Gaia-Sausage-Enceladus is missing from the local halo. Therefore, extrapolations from the local to the global halo should be treated with caution. From analysis of a sample of 11 Milky Way–like simulated halos, we contextualize these results and identify a population of recently accreted (≲5 Gyrs) and disrupted galaxies on high-angular-momenta orbits that are entirely missing from local samples and likely awaiting discovery in the outer halo. Our results motivate the need for surveys of halo stars extending out to the Galaxy’s virial radius.

Via Machinae 2.0: Full-sky, model-agnostic search for stellar streams in Gaia DR2

ABSTRACT We present an update to Via Machinae, an automated stellar stream-finding algorithm based on the deep learning anomaly detector ANODE. Via Machinae identifies stellar streams within Gaia, using only angular positions, proper motions, and photometry, without reference to a model of the Milky Way potential for orbit integration or stellar distances. This new version, Via Machinae 2.0, includes many improvements and refinements to nearly every step of the algorithm, that altogether result in more robust and visually distinct stream candidates than our original formulation. In this work, we also provide a quantitative estimate of the false positive rate of Via Machinae 2.0 by applying it to a simulated Gaia-mock catalogue based on galaxia, a smooth model of the Milky Way that does not contain substructure or stellar streams. Finally, we perform the first full-sky search for stellar streams with Via Machinae 2.0, identifying 102 streams at high significance within the Gaia Data Release 2, of which only 10 have been previously identified. While follow-up observations for further confirmation are required, taking into account the false positive rate presented in this work, we expect approximately 90 of these stream candidates to correspond to real stellar structures.

Non-linear dynamics of a test particle near the Lagrange points L4 and L5 (Earth-Moon and Sun-Earth case)

The two-bodies problem can be fully solved, and was solved by Kepler (1609) and Newton (1687). The general three-body problem is often given as an example of a mathematical problem that ‘can’t be solved’. So, there is no general analytical solution. This problem can be significant and a special case of this problem is the Circular Restricted Three-Body Problem (CRTBP), which can be applied to the Earth-Moon system with a spacecraft, the Sun-Earth system with an asteroid, etc. In this paper, let’s focus on the motion of a test particle near the triangular Lagrange points L4 and L5 in the Earth-Moon and the Sun-Earth systems. Studying the movement of an object around these points is especially important for space mission design. To generate a trajectory around these points, the non-linear equations of motion for the circular restricted three-body problem were numerically integrated into MATLAB® 2023 software and the results are presented in the plane (x, y) and the phase plane (x, vx) and (y, vy). By numerical orbit integration, it is possible to investigate what happens when the displacement is relatively large or short from the Lagrange points. Then the small astronomical body may vibrate around these points. The results in this paper are shown in the rotating and inertia axes. Various initial positions near the Lagrange points and velocities are used to produce various paths the test particle can take. The same examples of numerical studies of trajectories associated with Lagrange points are shown in the inertial and the rotating coordinates system and are discussed. From the results of the numerical tests performed in MATLAB® 2023, it is possible to saw that there are different types of periodic, quasi-periodic, and chaotic orbits

Bessel functions and Kloosterman integrals on GL(n)

This paper will focus on the proof of local integrability of Bessel functions for GL(n) (p-adic case) by using the relations between Bessel functions and local Kloosterman (orbital) integrals proved in several papers of E. M. Baruch [5][6][7], the theory of the (relative) Shalika germs established by H. Jacquet and Y. Ye in [25][26] and G. Stevens' approach [35] on estimating certain GL(n) generalized Kloosterman sums.

Multi-GNSS ultra-rapid orbit determination through epoch-parallel processing

High-precision Global Navigation Satellite Systems (GNSS) orbits are critical for real-time clock estimation and precise positioning service; however, the prediction error grows gradually with the increasing prediction session. In this study, we present a new efficient precise orbit determination (POD) strategy referred to as the epoch-parallel processing to reduce the orbit update latency, in which a 24-h processing job is split into several sub-sessions that are processed in parallel and then stacked to solve and recover parameters subsequently. With a delicate handling of parameters crossing different sub-sessions, such as ambiguities, the method is rigorously equivalent to the one-session batch solution, but is much more efficient, halving the time-consuming roughly. Together with paralleling other procedures such as orbit integration and using open multi-processing (openMP), the multi-GNSS POD of 120 satellites using 90 stations can be fulfilled within 30 min. The lower update latency enables users to access orbits closer to the estimation part, that is, 30–60-min prediction with a 30-min update latency, which significantly improves the orbit quality. Compared to the hourly updated orbit, the averaged 1D RMS values of predicted orbit in terms of overlap for GPS, GLONASS, Galileo, and BDS MEO are improved by 39%, 35%, 41%, and 37%, respectively, and that of BDS GEO and IGSO satellites is improved by 47%. We also demonstrate that the boundary discontinuities of half-hourly orbit are within 2 cm for the GPS, GLONASS, and Galileo satellites, and for BDS the values are 2.6, 15.5, and 9.8 cm for MEO, GEO, and IGSO satellites, respectively. This method can also be implemented for any batch-based GNSS processing to improve the efficiency.

Oort cloud perturbations as a source of hyperbolic Earth impactors

The observation of interstellar objects 1I/’Oumuamua and 2I/Borisov suggests the existence of a larger population of smaller projectiles that impact our planet with unbound orbits. We analyze an asteroidal grazing meteor (FH1) recorded by the Finnish Fireball Network on October 23, 2022. FH1 displayed a likely hyperbolic orbit lying on the ecliptic plane with an estimated velocity excess of ∼0.7 kms−1 at impact. FH1 may either be an interstellar object, indicating a high-strength bias in this population, or an Oort cloud object, which would reinforce migration-based solar system models. Furthermore, under the calculated uncertainties, FH1 could potentially be associated with the passage of Scholz’s binary star system. Statistical evaluation of uncertainties in the CNEOS database and study of its hyperbolic fireballs reveals an anisotropic geocentric radiant distribution and low orbital inclinations, challenging the assumption of a randomly incoming interstellar population. Orbital integrations suggest that the event on March 9, 2017 (IM2) from CNEOS may have experienced gravitational perturbation during the Scholz fly-by, contingent upon velocity overestimation within the expected range. These findings suggest that apparent interstellar meteors may, in fact, be the result of accelerated meteoroid impacts caused by close encounters with massive objects within or passing through our solar system.

Role of Spin Polarization and Dynamic Correlation in Singlet-Triplet Gap Inversion of Heptazine Derivatives.

The new generation of proposed light-emitting molecules for organic light-emitting diodes (OLEDs) has raised considerable research interest due to its exceptional feature─a negative singlet-triplet (ST) gap violating Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wave function expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization decreases linearly with the increasing highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) exchange integral. Comparison of single- and multireference coupled-cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

ED-2: A cold but not so narrow stellar stream crossing the solar neighbourhood

Context. ED-2 is a stellar stream identified as a compact group in integrals-of-motion space in a local sample of halo stars from the third Gaia data release. Aims. We investigate its nature and possible association with known halo substructures. Methods. We explored the current properties of ED-2 members in phase-space and also analysed the expected distribution via orbit integration. In addition, we studied the metallicity of ED-2 using APOGEE DR17 and LAMOST DR8 (and re-calibrated DR3). Results. ED-2 forms a compact group in the x − z (or R − z) plane, showing a pancake-like structure as it crosses the solar neighbourhood. Dynamically, it is most similar to the globular clusters NGC 3201 and NGC 6101 and to the stellar streams Ylgr and Phlegethon. However, its orbit is sufficiently different for none of these objects to likely be the ED-2 progenitor. We also find ED-2 to be quite metal poor: all of its stars have [Fe/H]≤ − 2.42, with a median [Fe/H] = −2.60−0.21+0.20. At this low metallicity, it is unlikely that ED-2 stems from any known globular cluster. Instead, ED-2 seems to be in a similar category as the recently discovered Phoenix and C-19 stellar streams. We find that ED-2 members are scattered across the whole sky, which is due to its current orbital phase. We predict that as this object moves to its next apocentre, it will acquire an on-sky morphology that is similar to that of cold stellar streams. Finally, because ED-2 is nearing pericentre, we predict that additional members found below the plane will have high radial velocities of close to ∼500 km s−1 in the present-day direction of the globular cluster NGC 6101.

Nuclear and Orbital Characterization of the Transition Object (4015) 107P/Wilson–Harrington

Comet 107P/Wilson–Harrington, cross-listed as asteroid 4015, is one of the original transition objects whose properties do not neatly fit into a cometary or asteroidal origin. Discovered in a period of apparently gas-dominated activity in 1949, it was subsequently lost and recovered as the inactive asteroid 1979 VA. We obtained new and reanalyzed archival observations of the object, compared to meteorites, and conducted new orbital integrations in order to understand the nature of this object and to understand where it falls on the asteroid–comet continuum. Wilson–Harrington’s reflectance spectrum is approximately neutral from visible to near-infrared wavelengths, but has a reflectance maximum near 0.8–0.9 μm. The object’s spectrum is well matched by laboratory spectra of carbonaceous chondrite meteorites like the CM Murchison or the C i Ivuna. The object’s phase curve slope is compatible with either an asteroidal or cometary origin, and its recent orbital history has no periods with high enough temperatures to have altered its surface. While it is possible that some unknown process has acted to change the surface from an originally cometary one, we instead prefer a fundamentally asteroidal origin for Wilson–Harrington, which can explain its surface and orbital properties. However, this would require a way to maintain significant (hyper)volatile supplies on the near-Earth objects beyond what is currently expected. Wilson–Harrington’s similar meteorite affinity and possible orbital link to sample return targets (162173) Ryugu and (101955) Bennu suggest that the returned samples from the Hayabusa-2 and OSIRIS-REx missions might hold the key to understanding this object.

Rigid–Flexible Coupled System Attitude–Orbit Integration Fixed-Time Control

A diffractive imaging system consisting of two satellites is analyzed in view of dynamics. The mathematical model of rigid and flexion couples is studied to describe the relative motion of diffractive satellites and imaging satellites. Based on an integrated dynamics model with dual quaternion, a fixed-time non-singular terminal sliding mode controller is designed to meet the requirements of Earth observation. Finally, introducing the non-singular terminal sliding mode as the control group, a comparative simulation of relative motion and control is implemented to verify the controller and dynamics model.

Шаровые скопления в центральной области Млечного Пути. II. Частотный анализ орбит, построенных по данным Gaia EDR3

This work represents the second stage of research aimed at studying the influence of the bar on the orbital dynamics of globular clusters (Bajkova, Smirnov, and Bobylev, 2023). The orbits of 45 globular clusters in the central galactic region with a radius of 3.5 kpc have been analyzed by spectral dynamics methods in order to identify objects captured by the bar. Since the parameters of the bar of the Milky Way are known with a very large uncertainty, orbits were constructed and their frequency analysis was carried out with varying the mass, length and angular velocity of rotation of the bar in a wide range of values with a fairly dense grid. The orbits were integrated 2.5 billion years backward. As a result, globular clusters supporting the bar were identified for each set of bar parameters. To form the 6D phase space required for orbit integration, we used the most accurate astrometric data from the Gaia satellite (Vasiliev and Baumgardt, 2021), as well as new refined average distances to globular clusters (Baumgardt and Vasiliev, 2021).

A multi-dimensional nonlinear optimisation method for the TianQin constellation

TianQin is a geocentric space-based gravitational wave detecting mission that relies on three drag-free spacecraft with a mean inter-spacecraft distance of approximately 1.7 × 105 km. Considering the efficiency requirement of orbit optimisation, we apply a gradient descent method based on variational gradient calculation and the damped Newton iterative method to find the most stable solution of the constellation near the given initial position and velocity of the spacecraft. The efficiency was improved and the number of orbital integrals required for gradient calculation was significantly reduced by over 83%. Based on this optimisation method, we analysed the influence of perturbation on the stability of the TianQin constellation, and Moon’s three-body perturbation was the main factor. In addition, the influence of the orbit elements on the optimisation results was studied. The influence of the initial mean anomaly can be ignored, and the stability of the optimised constellation decreases with an increase in the semi-major axis. Working in the ‘3 months on +3 months off’ observation scheme for 2 years, the optimisation result is the ideal direction when the normal direction of the orbital plane of the TianQin constellation points to RXJ0806.3 + 1527.

Zeta functions of certain quadratic orders

In [10] Langlands provides a formula for certain product of orbital integrals in GL(2,Q). Its generalization has become an important question for the strategy of Beyond Endoscopy. Arthur in [1] predicts this formula should coincide with a product of polynomials associated to zeta functions of orders constructed in [15] by Zhiwei Yun. In this paper we compute, for a certain family of orders, explicit formulas for these zeta functions by a recursive method. We use these zeta functions in [5] to prove that Arthur's prediction is correct.

The cosmic waltz of Coma Berenices and Latyshev 2 (Group X)

Context. Open clusters (OCs) are fundamental benchmarks where theories of star formation and stellar evolution can be tested and validated. Coma Berenices (Coma Ber) and Latyshev 2 (Group X) are the second and third OCs closest to the Sun, making them excellent targets to search for low-mass stars and ultra-cool dwarfs. In addition, this pair will experience a flyby in 10–16 Myr, making it a benchmark to test pair interactions of OCs. Aims. We aim to analyse the membership, luminosity, mass, phase-space (i.e. positions and velocities), and energy distributions for Coma Ber and Latyshev 2 and test the hypothesis of the mixing of their populations at the encounter time. Methods. We developed a new phase-space membership methodology and applied it to Gaia data. With the recovered members, we inferred the phase-space, luminosity, and mass distributions using publicly available Bayesian inference codes. Then, with a publicly available orbit integration code and members’ positions and velocities, we integrated their orbits 20 Myr into the future. Results. In Coma Ber, we identified 302 candidate members distributed in the core and tidal tails. The tails are dynamically cold and asymmetrically populated. The stellar system called Group X is made of two structures: the disrupted OC Latyshev 2 (186 candidate members) and a loose stellar association called Mecayotl 1 (146 candidate members), and both of them will fly by Coma Ber in 11.3 ± 0.5 Myr and 14.0 ± 0.6 Myr, respectively, and each other in 8.1 ± 1.3 Myr. Conclusions. We study the dynamical properties of the core and tails of Coma Ber and also confirm the existence of the OC Latyshev 2 and its neighbour stellar association Mecayotl 1. Although these three systems will experience encounters, we find no evidence supporting the mixing of their populations.

GORILLA: Guiding-center ORbit Integration with Local Linearization Approach

GORILLA: Guiding-center ORbit Integration with Local Linearization Approach

Detection of Multiple Phase Space Overdensities of GSE Stars by Orbit Integration

In N-body simulations, nearly radial mergers can form shell-like overdensities in the sky position and phase space (r − v r ) due to the combination of dynamical friction and tidal stripping. The merger event of Gaia-Sausage-Enceladus (GSE) has provided a unique opportunity to study the shells in the phase space. To search for them, we integrate the orbits of 5949 GSE-related halo K giants from the LAMOST survey and record their positions at all time intervals in the r − v r diagram. After the subtraction of a smoothed background, we find six significant and complete thin chevron-like overdensities. The apocenters r apo of stars in the six chevrons are around 6.75, 12.75, 18.75, 25.25, 27.25, and 30.25 kpc. These chevrons reveal the multiple pileups of GSE stars at different apocenters. The application of a different Milky Way mass M vir will change the opening angles of these chevrons, while leaving their apocenters almost unchanged. By comparing with a recent study of the phase space overdensities of local halo stars from the Gaia Radial Velocity Spectrometer survey, our results are more inclined to a medium M vir of 1012 M ⊙. The application of a nonaxisymmetric Galactic potential with a steadily rotating bar has a blurring effect on the appearance of these chevron-like overdensities, especially for the chevrons with r apo > 20 kpc.

Look Up (Again) The Apophis Asteroid: Simulating and Visualizing Orbit

The asteroid Apophis, first discovered in 2004 by American astronomers, is known to have a dangerous potential for planet Earth. Many early studies predict that in 2029 it will experience a close encounter and have a possible collision with the Earth at the next close encounter due to keyhole gravity. This research will explain how to carry out an orbit simulation using an orbit integrator to review this possibility and the evolution of the Apophis asteroid orbit over the next 500 years. The results of this study are expected to provide an understanding of simulating asteroid orbit from its orbital parameters and to build awareness of the threat of danger from small solar system objects such as asteroids, comets, and meteoroids.

Retrospective Analysis of Management of Zygomatic Complex Fractures

Introduction Zygomatic bone and its surrounding bony anatomy are essential for maintaining facial contour—cheek prominence and orbital integrity. Management of the zygomatic complex (ZMC) fractures are important in the maintenance of function and facial integrity. Aim and Objectives To analyze the incidence, aetiology, surgical management, and complications encountered in the treatment of ZMC fractures in our super-specialty hospital, and to compare the number and location of fixation points and surgical access in our patient cohort with the literature. Materials and Method Retrospective analysis of all operative cases (Open Reduction and Internal Fixation) of ZMC fractures over a 3-year period (2017-2021) were reviewed. Craniofacial maxillofacial trauma patient’s medical records were collected and out which only the ZMC fracture cases were reviewed. Only the medical records from the period from 2017 to 2021 were included. The parameters such as etiology, site of the ZMC fracture, type of fracture, associated injuries, clinical findings, treated with conservative or surgical intervention, type of incisions used, number of fixation used, and any complications encountered were reviewed and analyzed. Results Out of 428 cases of craniofacial injury, 96 cases were ZMC fractures, isolated ZMC fractures accounted for 43%, 33% with associated injuries, 13% isolated arch, while 11% accounted isolated infraorbital rim fracture. Most common clinical findings were subconjunctival ecchymosis (71%), flattening of cheek (39%), malocclusion (22%), and so on. Buccal sulcus incision (66%) was mainly used, followed by upper blepharoplasty incision (59%). Depending on degree of displacement of fracture 1-point fixation (8%), 2-point fixation (30%), or 3-point fixation (27%) was performed. About 33% of cases were conservatively managed and followed up on regular intervals. Lymph edema, infra orbital paresthesia, temporary blindness, diplopia, hemianopsia were some of the complications encountered which were managed successfully and followed up. Conclusion ZMC fractures are most commonly occurring midface fractures with variable etiologies. The most common ZMC fracture pattern was tripod type of fracture. Greater portion of the patient were treated with 2-point fixation. Most of the complications were due to the impact and velocity of trauma.