Equatorial Plane Research Articles

Field‐Aligned Low‐Energy O+ Flux Enhancements in the Inner Magnetosphere Observed by Arase

AbstractThe present study examines the low‐energy ion flux variations observed by the Arase satellite in the inner magnetosphere. From the magnetic field and ion flux data obtained by the fluxgate magnetometer and the low‐energy particle experiments–ion mass analyzer onboard Arase, we find 55 events of the low‐energy O+ flux enhancement accompanied with magnetic field dipolarization in the periods of April 1–October 31, 2017 and July 1, 2018–January 31, 2019. The low‐energy O+ flux enhancements (a) start a few minutes after the dipolarization onset, (b) have energy‐dispersed signatures with decreasing energy from a few keV down to ∼10 eV, (c) are observed in both storm and non‐storm periods, (d) have a field‐aligned distribution (α ∼ 0° in the southern hemisphere and α ∼ 180° in the northern hemisphere), (e) are accompanied by the low‐energy H+ flux enhancements that have lower energies than O+ by a factor of 3–10, and (f) increase the O+ density and the O+/H+ density ratio by ∼10 times and 4–5 times, respectively. We perform a numerical simulation to trace ion trajectories forward in time from the Arase positions. It is revealed that both H+ and O+ ions drift eastward and reach the dawn‐to‐morning sector without being lost in the ionosphere, if the pitch angle scattering effect is considered near the equatorial plane. This result suggests that these low‐energy field‐aligned ions can contribute to formation of the warm plasma cloak.

Analytic Inversion of Closed form Solutions of the Satellite’s J2 Problem

This report provides some closed form solutions -and their inversion- to a satellite’s bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the J2 spherical zonal harmonic. The equatorial track of satellite motion- assuming the co-latitude φ fixed at π/2- is investigated: the relevant time laws and trajectories are evaluated as combinations of elliptic integrals of first, second, third kind and Jacobi elliptic functions. The new feature of this report is: from the inverse t = t(c) we get the period T of some functions c(t) of mechanical interest and then we construct the relevant c(t) expansion in Fourier series, in such a way performing the inversion. Such approach-which led to new formulations for time laws of a J2 problem- is benchmarked by applying it to the basic case of keplerian motion, finding again the classic results through our different analytic path.

Quasiperiodic oscillations around rotating traversable wormholes

We study the quasi-periodic oscillations from the accretion disk around rotating traversable wormholes by means of the resonance models. We investigate the linear stability of the circular geodesic orbits in the equatorial plane for a general class of wormhole geometries deriving analytical expressions for the epicyclic frequencies. Since wormholes can often mimic black holes in the astrophysical observations, we analyze the properties of the quasi-circular oscillatory motion in comparison with the Kerr black hole. We demonstrate that wormholes possess distinctive features, which can be observationally significant. It is characteristic for the Kerr black hole that the orbital and the epicyclic frequencies obey a constant ordering in the whole range of the spin parameter. In contrast, for wormhole spacetimes we can have various types of orderings between the frequencies in the different regions of the parametric space. This enables the excitation of much more diverse types of resonances including parametric and forced resonances of lower order, which could lead to stronger observable signals. In addition, for co-rotating orbits the resonances can be excited in a very close neighbourhood of the wormhole throat for a wide range of values of the angular momentum, making wormholes a valuable laboratory for testing strong gravity.

Divergent reflections around the photon sphere of a black hole

From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to the last photon orbit. With simple numerical and a perturbed analytical solution to the null-geodesic equation of the Schwarzschild black hole we will reaffirm how each additional orbit is a factor e^{2 pi } closer to the black hole’s optical edge. Consequently, the surface of the black hole and any background light will be mirrored infinitely in exponentially thinner slices around the last photon orbit. Furthermore, the introduced formalism proves how the entire trajectories of light in the strong field limit is prescribed by a diverging and a converging exponential. Lastly, the existence of the exponential family is generalized to the equatorial plane of the Kerr black hole with the exponentials dependence on spin derived. Thereby, proving that the distance between subsequent images increases and decreases for respectively retrograde and prograde images. In the limit of an extremely rotating Kerr black hole no logarithmic divergence exists for prograde trajectories.

3-D global hybrid simulations of magnetospheric response to foreshock processes

It has been suggested that ion foreshock waves originating in the solar wind upstream of the quasi-parallel (Q-||) shock can impact the planetary magnetosphere leading to standing shear Alfvén waves, i.e., the field line resonances (FLRs). In this paper, we carry out simulations of interaction between the solar wind and terrestrial magnetosphere under radial interplanetary magnetic field conditions by using a 3-D global hybrid model, and show the properties of self-consistently generated field line resonances through direct mode conversion in magnetospheric response to the foreshock disturbances for the first time. The simulation results show that the foreshock disturbances from the Q-|| shock can excite magnetospheric ultralow-frequency waves, among which the toroidal Alfvén waves are examined. It is found that the foreshock wave spectrum covers a wide frequency range and matches the band of FLR harmonics after excluding the Doppler shift effects. The fundamental harmonic of field line resonances dominates and has the strongest wave power, and the higher the harmonic order, the weaker the corresponding wave power. The nodes and anti-nodes of the odd and even harmonics in the equatorial plane are also presented. In addition, as the local Alfvén speed increases earthward, the corresponding frequency of each harmonic increases. The field-aligned current in the cusp region indicative of the possibly observable aurora is found to be a result of magnetopause perturbation which is caused by the foreshock disturbances, and a global view substantiating this scenario is given. Finally, it is found that when the solar wind Mach number decreases, the strength of both field line resonance and field-aligned current decreases accordingly.

In Situ Preconcentration during the Di-(2-ethylhexyl) Phosphoric Acid-Assisted Dissolution of Uranium Trioxide in an Ionic Liquid: Spectroscopic, Electrochemical, and Theoretical Studies.

Dissolution of uranium oxide was carried out using a solution of HD2EHP in C8mim·NTf2, which was apparently facilitated by the in situ generation of water during the complex formation reaction. The dissolved complex in the ionic liquid phase led to splitting of the latter into a light phase and a heavy phase where the former contained predominantly the UO2(HL2)2 complex (HL = HD2EHP), while the latter contained the ionic liquid as supported by FTIR and UV-Visible spectral analyses. The complexation of the uranyl ion was suggested to take place in the equatorial plane where two dimeric units of the H-bonded HD2EHP molecules took part in complexation. An increase in temperature facilitated the dissolution rate with an activation energy of 31.0 ± 2.8 kJ/mol. The cyclic voltammetry studies indicated potential chances of recovery of the dissolved uranium by electrodeposition at the cathode. The proposed dimeric structure of HD2EHP in the complexation with U(VI) was supported by DFT studies also.

Qualifying ringdown and shadow of black holes under general parametrized metrics with photon orbits

The motion of photons around black holes determines the shape of shadow and match the ringdown properties of a perturbed black hole. Observations of shadows and ringdown waveforms will reveal the nature of black holes. In this paper, we study the motion of photons in a general parametrized metric beyond the Kerr hypothesis. We investigated the radius and frequency of the photon circular orbits on the equatorial plane and obtained fitted formula with varied parameters. The Lyapunov exponent which connects to the decay rate of the ringdown amplitude is also calculated. We also analyzed the shape of shadow with full parameters of the generally axisymmetric metric. Our results imply the potential constraint on black hole parameters by combining the Event Horizon Telescope and gravitational wave observations in the future.

Numerical inside view of hypermassive remnant models for GW170817

The first multimessenger observation attributed to a merging neutron star binary provided an enormous amount of observational data. Unlocking the full potential of this data requires a better understanding of the merger process and the early post-merger phase, which are crucial for the later evolution that eventually leads to observable counterparts. In this work, we perform standard hydrodynamical numerical simulations of a system compatible with GW170817. We focus on a single equation of state (EOS) and two mass ratios, while neglecting magnetic fields and neutrino radiation. We then apply newly developed postprocessing and visualization techniques to the results obtained for this basic setting. The focus lies on understanding the three-dimensional structure of the remnant, most notably the fluid flow pattern, and its evolution until collapse. We investigate the evolution of mass and angular momentum distribution up to collapse, as well as the differential rotation along and perpendicular to the equatorial plane. For the cases that we studied, the remnant cannot be adequately modeled as a differentially rotating axisymetric NS. Further, the dominant aspect leading to collapse is the GW radiation and not internal redistribution of angular momentum. We relate features of the gravitational wave signal to the evolution of the merger remnant, and make the waveforms publicly available. Finally, we find that the three-dimensional vorticity field inside the disk is dominated by medium-scale perturbances and not the orbital velocity, with potential consequences for magnetic field amplification effects.

Spatial Evolution of Wave‐Particle Interaction Region Deduced From Flash‐Type Auroras and Chorus‐Ray Tracing

AbstractIn‐situ observations of spatial variations of the wave‐particle interaction region require a large number of satellite probes. As an alternative, flash‐type auroras, a kind of pulsating aurora, driven by discrete chorus elements, can be used to investigate the interaction region with a high spatial resolution. We estimated the spatial extent of wave‐particle interaction region from ground‐based observations of flash aurora at Gakona (62.39°N, 214.78°E), Alaska at subauroral latitudes, and found that the auroral expansion was predominantly to the low‐latitude side. The spatial displacement is thought to be caused by the propagation effects of chorus waves in the magnetosphere. Using ray tracing analysis to take into account chorus wave propagation, we reconstructed the spatiotemporal evolution of the volume emission rate and confirmed that the predominant expansion is toward the lower‐latitude side in the ionosphere. This study shows that chorus wave propagation in the magnetosphere gives new insight for characterizing the transverse size (across the geomagnetic field line) of wave‐particle interaction regions. The calculated spatial scale of the column auroral emission shows a correlation with the magnetic latitude of the resonance region at magnetic latitudes within 10° of the equatorial plane of the magnetosphere. Our results suggest that the spatial scale of a flash aurora is indirectly related to the chorus amplitude because the latitudinal range of the wave‐particle interaction is important for the growth of wave amplitude.

A three-dimensional hydrodynamics simulation of oxygen-shell burning in the final evolution of a fast-rotating massive star

ABSTRACT We perform for the first time a 3D hydrodynamics simulation of the evolution of the last minutes pre-collapse of the oxygen shell of a fast-rotating massive star. This star has an initial mass of 38 M⊙, a metallicity of ∼1/50 Z⊙, an initial rotational velocity of 600 km s−1, and experiences chemically homogeneous evolution. It has a silicon- and oxygen-rich (Si/O) convective layer at (4.7–17) × 108 cm, where oxygen-shell burning takes place. The power spectrum analysis of the turbulent velocity indicates the dominance of the large-scale mode (ℓ ∼ 3), which has also been seen in non-rotating stars that have a wide Si/O layer. Spiral arm structures of density and silicon-enriched material produced by oxygen-shell burning appear in the equatorial plane of the Si/O shell. Non-axisymmetric, large-scale (m ≤ 3) modes are dominant in these structures. The spiral arm structures have not been identified in previous non-rotating 3D pre-supernova models. Governed by such a convection pattern, the angle-averaged specific angular momentum becomes constant in the Si/O convective layer, which is not considered in spherically symmetrical stellar evolution models. Such spiral arms and constant specific angular momentum might affect the ensuing explosion or implosion of the star.

Stabilization of an elusive tautomer by metal coordination.

The solid-state isolation of the different tautomers of a chemical compound can be a challenging problem. In many cases, tautomers with an energy very close to the most stable one cannot be isolated (elusive tautomers). In this article, with reference to the 4-methyl-7-(pyrazin-2-yl)-2H-[1,2,4]triazolo[3,2-c][1,2,4]triazole ligand, for which the elusive 3H-tautomer has an energy only 1.4 kcal mol-1 greater than the most stable 2H form, we show that metal complexation is a successful and reliable way for stabilizing the elusive tautomer. We have prepared two complexes of the neutral ligand with CuBr2 and ZnBr2, namely, aquabromidobis[4-methyl-7-(pyrazin-2-yl)-3H-[1,2,4]triazolo[3,2-c][1,2,4]triazole]copper(II) bromide trihydrate, [CuBr(C8H7N7)2(H2O)]Br·3H2O, and dibromido[4-methyl-7-(pyrazin-2-yl)-2H-[1,2,4]triazolo[3,2-c][1,2,4]triazole][4-methyl-7-(pyrazin-2-yl)-3H-[1,2,4]triazolo[3,2-c][1,2,4]triazole]zinc(II) monohydrate, [ZnBr2(C8H7N7)2]·H2O. The X-ray analysis shows that, in both cases, the elusive 3H-tautomer is present. The results of the crystallographic analysis of the two complexes reflect the different coordination preferences of CuII and ZnII. The copper(II) complex is homotautomeric as it only contains the elusive 3H-tautomer of the ligand. The complex can be described as octahedral with tetragonal distortion. Two 3H-triazolotriazole ligands are bis-chelated in the equatorial plane, while a water molecule and a bromide ion in elongated axial positions complete the coordination environment. The zinc(II) complex, on the other hand, is heterotautomeric and contains two bromide ions and two monodentate ligand molecules, one in the 2H-tautomeric form and the other in the 3H-tautomeric form, both coordinated to the metal in tetrahedral geometry. The observation of mixed-tautomer complexes is unprecedented for neutral ligands. The analysis of the X-ray molecular structures of the two complexes allows the deduction of possible rules for a rational design of mixed-tautomer complexes.

3D MHD simulations of accretion on to stars with tilted magnetic and rotational axes

ABSTRACT We present results of global 3D magnetohydrodynamic simulations of accretion on to magnetized stars where both the magnetic and rotational axes of the star are tilted about the rotational axis of the disc. We observed that initially the inner parts of the disc are warped, tilted, and precess due to the magnetic interaction between the magnetosphere and the disc. Later, larger tilted discs form with the size increasing with the magnetic moment of the star. The normal vector to the discs are tilted at different angles, from ∼5°–10° up to ∼30°–40°. Small tilts may result from the winding of the magnetic field lines about the rotational axis of the star and the action of the magnetic force which tends to align the disc. Another possible explanation is the magnetic Bardeen–Petterson effect in which the disc settles in the equatorial plane of the star due to precessional and viscous torques in the disc. Tilted discs slowly precess with the time-scale of the order of ∼50 Keplerian periods at the reference radius (∼3 stellar radii). Our results can be applied to different types of stars where signs of tilted discs and/or slow precession have been observed.

Orbital and epicyclic motion of charged test particles around non-rotating Einstein-Æther black holes

The study of charged test particle dynamics in the combined black hole gravitational field and magnetic field around it could provide important theoretical insight into astrophysical processes around such compact object. We have explored the orbital and epicyclic motion of charged test particles in the background of non-rotating Einstein-Æther black holes in the presence of external uniform magnetic field. We numerically integrate the equations of motion and analyze the trajectories of the charged test particles. We examined the stability of circular orbits using effective potential technique and study the characteristics of innermost stable circular orbits. We analyze the key features of quasi-harmonic oscillations of charged test particles nearby the stable circular orbits in an equatorial plane of the black hole, and investigate the radial profiles of the frequencies of latitudinal as well as radial harmonic oscillations in dependence on the strength of magnetic field, mass of the black hole and dimensionless coupling constants of the theory. We demonstrate that the magnetic field and dimensionless parameters of the theory have strong influence on charged particle motion around Einstein-Æther black holes.

Calibration of neutron detectors at ASDEX Upgrade, measurement and model

The neutron production in ASDEX Upgrade (AUG) neutral beam injection (NBI) heated discharges is dominated by beam-target fusion reactions. Hence, the neutron rate (NR) and energy distributions are footprints of the fast ion distribution. This motivates to establish a reliable neutron rate calibration. Comparisons at AUG between the experimental NR and the one predicted by the TRANSP code show systematic variations from campaign to campaign. Potential reason for this is the delicate absolute calibration of the neutron detectors. Therefore, a different calibration technique was performed, enabling longer acquisition time, uniform geometry, better statistics and thus less uncertainty. A toy train carrying a radioactive source (238Pu/B) over two radial positions on the equatorial plane shows a periodical NR on the epithermal 3He neutron detector. The calibration results are compared to a neutron transport simulation using the Monte Carlo (MC) code Serpent. Preliminary comparisons for one source position on the outer railway track show a discrepancy factor of about 130 in the position of least material inside the simulation, in the direct line of sight to the detector. For a better understanding of these results, two additional measurements were performed. The results were again compared to a detailed Serpent simulation. This paper describes the calibration set-up for the neutron measurements in AUG, provides a brief simulation background on reaction rate estimations and a survey on the comparison between the measured and calculated neutron rates.

Optimal VLBI baseline geometry for UT1-UTC Intensive observations

One of the main tasks of Very Long Baseline Interferometry (VLBI) is the rapid determination of the highly variable Earth’s rotation expressed through the difference between Universal Time UT1 and Coordinated Universal Time UTC (dUT1). For this reason, dedicated one hour, single baseline sessions, called “Intensives”, are observed on a daily basis. Thus far, the optimal geometry of Intensive sessions was understood to include a long east–west extension of the baseline to ensure a dUT1 estimation with highest accuracy. In this publication, we prove that long east–west baselines are the best choice only for certain lengths and orientations. In this respect, optimal orientations may even require significant inclination of the baseline with respect to the equatorial plane. The basis of these findings is a simulation study with subsequent investigations in the partial derivatives of the observed group delays tau with respect to dUT1 partial tau /partial dUT1. Almost 3000 baselines between artificial stations located on a regular 10 times 10 degree grid are investigated to derive a global and generally valid picture about the best length and orientation of Intensive baselines. Our results reveal that especially equatorial baselines or baselines with a center close to the equatorial plane are not suited for Intensives although they provide a good east–west extension. This is explained by the narrow right ascension band of visible sources and the resulting lack of variety in the partial derivatives. Moreover, it is shown that north–south baselines are also capable of determining dUT1 with reasonable accuracy, given that the baseline orientation is significantly different from the Earth rotation axis. However, great care must be taken to provide accurate polar motion a priori information for these baselines. Finally, we provide a better metric to assess the suitability of Intensive baselines based on the effective spread of partial tau /partial dUT1.

Limiting Behavior of Asteroid Obliquity and Spin Using a Semi-analytic Thermal Model of the YORP Effect

Abstract The Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect governs the spin evolution of small asteroids. The axial component of YORP, which alters the rotation rate of the asteroid, is mostly independent of its thermal inertia, while the obliquity component is very sensitive to the thermal model of the asteroid. Here, we develop a semi-analytic theory for the obliquity component of YORP. We integrate an approximate thermal model over the surface of an asteroid, and find an analytic expression for the obliquity component in terms of two YORP coefficients. This approach allows us to investigate the overall evolution of asteroid rotation state, and to generalize the results previously obtained in the case of zero thermal inertia. The proposed theory also explains how a nonzero obliquity component of YORP originates even for a symmetric asteroid, due to its finite thermal inertia. In many cases, this causes equatorial planes of asteroids to align with their orbital planes. The studied nontrivial behavior of YORP as a function of thermal model allows for a new kind of rotational equilibria, which can have important evolutionary consequences for asteroids.

On the edge turbulence effects on the density profile reconstruction using O-mode reflectometers

The effect of turbulence in the position measurements of the DEMO Plasma position reflectometer is evaluated at the high field side equatorial plane location using REFMULF, a 2D finite-difference time-domain full-wave code for reflectometry simulations. Different levels of turbulence (1–10%) of a Kolmogorov-like k-spectrum are analysed statistically with random generated density fluctuations. The study shows that for turbulence amplitudes in the range 1–7% most of the measurements are not affected significantly and the reflectometer can provide the position measurements within the DEMO requirements. For higher levels of turbulence, the mean error becomes negative and its absolute value and the standard deviation increases for values in the order of 0.5 cm. One of the reasons for this behavior is the deviation of the effective cut-off position. In these cases, part of the measurements are out of the requirements, and a study must be done to understand if the reconstruction of the separatrix stills possible for the order of error of the failed measurements (1–2 cm). Other possibility is to apply a correction based on the mean position value as function of the turbulence amplitude to the position measurements. This could be applied dynamically during the plasma pulse.

Timescales of the chaos onset in the general relativistic Poynting-Robertson effect

It has been proved that the general relativistic Poynting-Robertson effect in the equatorial plane of Kerr metric shows a chaotic behavior for a suitable range of parameters. As a further step, we calculate the timescale for the onset of chaos through the Lyapunov exponents, estimating how this trend impacts on the observational dynamics. We conclude our analyses with a discussion on the possibility to observe this phenomenon in neutron star and black hole astrophysical sources.

Achieving and Stabilizing Uranyl Bending via Physical Pressure.

Applying physical pressure in the uranyl-sulfate system has resulted in the formation of the first purely inorganic uranyl oxo-salt phase with a considerable uranyl bend: Na4[(UO2)(SO4)3]. In addition to a strong bend of the typically almost linear O═U═O, the typically equatorial plane is broken up by two out-of-plane oxygen positions. Computational investigations show the origin of the bending to lie in the applied physical pressure and not in the electronic influence or steric hindrance. The increase in pressure onto the system has been shown to increase uranyl bending. Furthermore, the phase formation is compared with a reference phase of a similar structure without uranyl bending, and a transition pressure of 2.5 GPa is predicted, which is well in agreement with the experimental results.

Robust Angular Anisotropy of Circularly Polarized Luminescence from a Single Twisted-Bipolar Polymeric Microsphere.

It has long been surmised that the circular polarization of luminescence (CPL) emitted by a chiral molecule or a molecular assembly should vary with the direction in which the photon is emitted. Despite its potential utility, this anisotropic CPL has not yet been demonstrated at the level of single molecules or supramolecular assemblies. Here we show that conjugated polymers bearing chiral side chains self-assemble into solid microspheres with a twisted bipolar interior, which are formed via liquid-liquid phase separation and subsequent condensation into a cholesteric lyotropic liquid crystalline mesophase. The resultant microspheres, when dispersed in methanol, exhibit CPL with a glum value as high as 0.23. The microspheres are mechanically robust enough to be handled with a microneedle under ambient conditions, allowing comprehensive examination of the angular anisotropy of CPL. The single microsphere is found to exhibit distinct angularly anisotropic birefringence and CPL with glum up to ∼0.5 in the equatorial plane, which is 2.5-fold greater than that along the polar axis. Such optically anisotropic solid materials are important for the application to next-generation microlight-emitting and visualizing devices as well as for fundamental optics studies of chiral light-matter interaction.