Earth Radii Research Articles

The Earth’s Outer Exospheric Density Distributions Derived From PROCYON/LAICA UV Observations

AbstractCurrent three‐dimensional, data‐based models for the terrestrial exosphere have been derived from measurements of optically thin Lyman‐alpha (Ly‐α) emissions scattered by neutral hydrogen atoms. Such models are only valid for the middle exospheric region (3–8 Earth radii geocentric distances) since the orbital paths of the space‐based platforms used to acquire Ly‐α radiance were located within the exosphere, thus precluding the proper detection of the faint outer exospheric emission. Notwithstanding, accurate specifications of density distributions beyond 8 RE are needed to support comprehensive studies of the solar‐terrestrial interactions. Two upcoming missions, the Solar wind Magnetosphere‐Ionosphere Link Explorer and the Lunar Environment Heliospheric X‐ray Imager, will image the Earth’s magnetosheath in soft X‐rays, and neutral densities are crucial to extract ion distributions through inversion of the acquired images. This work develops a technique to estimate the Earth’s outer exospheric density distributions using far‐ultraviolet wide‐field data acquired by the Lyman‐Alpha Imaging Camera (LAICA) onboard the Proximate Object Close Flyby with Optical Navigation mission. Our approach formulates an inverse problem based on the linearity between measurements of scattered Ly‐α flux and the local atomic hydrogen density, which is solved using the Bayesian approach known as Maximum a posteriori estimation. We use the LAICA image to derive global, 3‐D hydrogen density distributions at 6–20 RE geocentric distances. We find that the spatial structure of the outer exosphere agrees well with the predictions of radiation pressure theory. Further, we find that the hydrogen density at the 10 RE subsolar point is 26.51 atoms/cm3.

Power Line Harmonic Radiation Observed by the Van Allen Probes Spacecraft

AbstractWe present a systematic analysis of Power Line Harmonic Radiation (PLHR) electromagnetic wave events observed by the Van Allen Probes spacecraft over the entire duration of the mission (2012–2019). PLHR events are radiated by electric power systems on the ground at harmonics of the base power system frequency (50 or 60 Hz, depending on the region). We analyze wave intensities at frequencies corresponding to the first few harmonics and we demonstrate that they are significantly enhanced at the times when the field‐aligned magnetic footprint of the spacecraft is above industrialized areas. Considering the spacecraft locations close to the equatorial plane, this represents experimental evidence that PLHR emissions may propagate up to radial distances as large as about 4 Earth radii. Average frequency spectra above selected industrialized regions reveal increased wave intensities at the frequencies corresponding to the first and the third harmonics, in particular during the nighttime. Multicomponent wave measurements allow us to perform a detailed wave analysis of polarization and propagation properties of the events. The waves are typically right‐handed elliptically or nearly circularly polarized, propagating with oblique wave normal angles from low latitude sources and more field‐aligned wave vectors from high latitude sources. The sign of the parallel component of the Poynting flux confirms that the events indeed propagate from the anticipated ground regions. Few events observed above the United States region propagate in the opposite direction, which is interpreted as wave bouncing between the hemispheres.

Terrestrial exospheric dayside H-density profile at 3–15 <i>R</i><sub>E</sub> from UVIS/HDAC and TWINS Lyman-<i>α</i> data combined

Abstract. Terrestrial ecliptic dayside observations of the exospheric Lyman-α column intensity between 3–15 Earth radii (RE) by UVIS/HDAC (UVIS – ultraviolet imaging spectrograph; HDAC – hydrogen-deuterium absorption cell) Lyman-α photometer at CASSINI have been analyzed to derive the neutral exospheric H-density profile at the Earth's ecliptic dayside in this radial range. The data were measured during CASSINI's swing-by maneuver at the Earth on 18 August 1999 and are published by Werner et al. (2004). In this study the dayside HDAC Lyman-α observations published by Werner et al. (2004) are compared to calculated Lyman-α intensities based on the 3D H-density model derived from TWINS (Two Wide-angle Imaging Neutral-atom Spectrometers) Lyman-α observations between 2008–2010 (Zoennchen et al., 2015). It was found that both Lyman-α profiles show a very similar radial dependence in particular between 3–8 RE. Between 3.0–5.5 RE impact distance Lyman-α observations of both TWINS and UVIS/HDAC exist at the ecliptic dayside. In this overlapping region the cross-calibration of the HDAC profile against the calculated TWINS profile was done, assuming that the exosphere there was similar for both due to comparable space weather conditions. As a result of the cross-calibration the conversion factor between counts per second and rayleigh, fc=3.285 counts s−1 R−1, is determined for these HDAC observations. Using this factor the radial H-density profile for the Earth's ecliptic dayside was derived from the UVIS/HDAC observations, which constrained the neutral H density there at 10 RE to a value of 35 cm−3. Furthermore, a faster radial H-density decrease was found at distances above 8 RE (≈r-3) compared to the lower distances of 3–7 RE (≈r-2.37). This increased loss of neutral H above 8 RE might indicate a higher rate of H ionization in the vicinity of the magnetopause at 9–11 RE (near subsolar point) and beyond, because of increasing charge exchange interactions of exospheric H atoms with solar wind ions outside the magnetosphere.

Sensitivity of the Horizontal Scale of Convective Self‐Aggregation to Sea Surface Temperature in Radiative Convective Equilibrium Experiments Using a Global Nonhydrostatic Model

AbstractWe conduct radiative convection equilibrium experiments using a global nonhydrostatic model to investigate the dependence of convective self‐aggregation (CSA) on domain size and sea surface temperature (SST). We use a spherical domain with radii varying from 1 to 1/16 of Earth's radius, as well as SSTs between 290 and 310 K. A single aggregation occurs at small domain sizes, whereas multiple aggregations emerge at sufficiently large domain sizes. Domain‐averaged atmospheric temperature and humidity gradually increase with domain size until they reach convergence in cases of multiple aggregations. As domain size increases, surface wind speed increases, and the boundary layer becomes more humid. Because the radiative cooling in the free atmosphere also converges in cases of multiple aggregations, the surface evaporation must be limited due to the constraint of the energy balance. Thus, the convective region shifts from single to multiple aggregations to avoid increasing the surface wind speed. Our results show that the dependence of the horizontal scale of CSA on SST is not monotonic. This dependency is closely related to changes in the structure of the detrainment from the convective region at the melting level, resulting in enhanced radiative cooling at the top of the boundary layer near the convective region for cooler and warmer SSTs. This change in the circulation structure leads to increased surface wind speed with increasing domain size. This process affects the non‐monotonic dependence of the horizontal scale of CSA on SST.

A New Ray Tracing Method Based on Piecewise Conformal Transformations

We put forward a new ray tracing method for electromagnetic wave propagation based on piecewise conformal transformations. Our approach is based on our previous research, where conformal transformation was focused on giving an accurate formula for the effective Earth radius. In this article, according to the height interval of atmospheric refractive index data, we approximate the electromagnetic wave propagation path by the combination of circular arcs with different curvature radius and find the effective Earth radius of each arc using conformal transformations. Then, upon using the effective Earth radius, we transform the circular arc path into a straight path, thus simplifying the calculations needed to describe the propagation of electromagnetic waves. We compare our approach to the traditional ray tracing method for several typical atmospheric refractive index profiles and prove that our new method may achieve ray tracing with higher accuracy using fewer path points. We also consider nonuniform atmosphere and irregular terrain and compare the performance of our ray tracing scheme with that of the open-source software PETOOL, which is based on the parabolic equation method. Result proves that the new method may be effectively used for ray tracing in complex environments.

Investigation of the Vertical Profile Radio Refractivity Gradient and Effective Earth Radius Factor (k-factor) in Transmission Link Over Oyo, Oyo State, South Western Nigeria

Surface radio refractive gradient and k-factor are very imperative in observing propagation conditions, designing and planning of microwave communication links in the lower part of the atmospheric boundary layer. The measurement of weather variables (air temperature, atmospheric pressure, relative humidity and wind speed) were conducted in this study at the School of Science, Emmanuel Alayande College of Education, Oyo (7.83°N, 3.95°E), Oyo State, Nigeria. The research was carried out for a period of one year (January to December, 2020) using self-designed cost effective portable weather monitoring systems. The systems were sited from the ground to a height of 200 m on a 220 m Nigeria Television Authority (NTA) UHF channel 37 tower at Oke-Apitipiti in Oyo Town of Oyo State. The calculated daily and monthly averages data are employed to investigate the vertical surface radio refractivity and its refractivity gradient. The highest value of -1.093E+26 N-units/km was recorded in January, while the month of July experienced the least of about -9.305E+19 N-units/km. The months of January–July verified sub-refractive conditions with propagation conditions having varying degree of occurrence. On the other hand, super-refraction and ducting were recorded mostly between August–December from the study. The results also find applicability in radio engineering for refining VHF/UHF terrestrial links based on clear-air considerations which will support operational planning of terrestrial radio networks in Oyo, South Western Nigeria
 Keywords: Microwave; k-factor; refractivity gradient; sub-refractive; super-refraction

Deepening of radiation belt particles in South Atlantic Anomaly Region: A scenario over past 120 years

• Weakened magnetic field is pushing radiation belt particles towards the Earth in SAA. • The average deepening rate of radiation belt particles is 4.3 km/year. • The deepening is increased by 434–590 km in last 120 years. • Deepening in the SAA region is depended on its initial longitude. • Deepening in the SAA region is independent of its equatorial pitch angle. The geomagnetic field has an unusual weak spot over South America and the South Atlantic Ocean, called South Atlantic Anomaly (SAA). We know that the magnetospheric particles trapped in the geomagnetic field move to the deeper altitudes over the SAA, resulting in the lower inner boundary of the radiation belt. However, over the past 400 years, the magnetic field in the SAA region has decreased consistently. In some recent studies, a rapid decrease of the magnetic field in the SAA region and the possibility of splitting of SAA have been reported. This weakened geomagnetic field has a bearing on the lower altitudinal reach (deepening) of the radiation belt particles. In this context, we performed simulations to examine and quantify the lowest altitudes encountered by the radiation belt particles over the SAA region. We found that particles of energies 100 keV-50 MeV, initially entering from an altitudes of 1–2 Earth radii are moving closer to the Earth at the rate of 3.8 - 4.7 km/year, which results in approximately 434 - 590 kms decrease in their altitude over the SAA region during 1900 to 2020. Furthermore, we noticed that the lowest altitude encountered by the particle in the SAA region is dependent on the initial longitude and independent of its initial local pitch angle corresponding to its entry in the Earth’s magnetosphere.

Scaling Up: Molecular to Meteorological via Symmetry Breaking and Statistical Multifractality

The path from molecular to meteorological scales is traced and reviewed, beginning with the persistence of molecular velocity after collision induces symmetry breaking, from continuous translational to scale invariant, associated with the emergence of hydrodynamic behaviour in a Maxwellian (randomised) population undergoing an anisotropic flux. An empirically based formulation of entropy and Gibbs free energy is proposed and tested with observations of temperature, wind speed and ozone. These theoretical behaviours are then succeeded upscale by key results of statistical multifractal analysis of airborne observations on horizontal scales from 40 m to an Earth radius, and on vertical scales from the surface to 13 km. Radiative, photochemical and dynamical processes are then examined, with the intermittency of temperature implying significant consequences. Implications for vertical scaling of the horizontal wind are examined via the thermal wind and barometric equations. Experimental and observational tests are suggested for free running general circulation models, with the possibility of addressing the cold bias they still exhibit. The causal sequence underlying atmospheric turbulence is proposed.

Parametric Study of Magnetosheath Jets in 2D Local Hybrid Simulations

We perform 2D local hybrid simulations of collisionless shocks in order to study the properties of simulated magnetosheath jets as a function of shock properties, namely their Alfvénic Mach number (MA) and geometry (angle between the upstream magnetic field and the shock normal, θBN). In total we perform 15 simulations with inflow speeds of Vin = 3.3 CA (Alfvén velocity), 4.5 CA and 5.5 CA and θBN = 15°, 30°, 45°, 50°, and 65°. Under these conditions, the shock MA varied between 4.28 and 7.42. In order to identify magnetosheath jets in the simulation outputs, we use four different criteria, equivalent to those utilized to identify subsets of magnetosheath jets, called high-speed jets (Plaschke and Hietala and Angelopoulos, Ann. Geophys., 2013, 31, 1877–1889), transient flux enhancements (Němeček et al., Geophys. Res. Lett., 1998, 25, 1273–1276), density plasmoids (Karlsson et al., J. Geophys. Res., 2012, 117, a–n; Karlsson et al., J. Geophys. Res., 2015, 120, 7390–7403) and high-speed plasmoids (Gunell et al., Ann. Geophys., 2014, 32, 991–1009). In our simulations, the density plasmoids were produced only by shocks with MA ≥5.7, while the high-speed plasmoids only formed downstream of shocks with MA ≥6.97. We show that higher MA shocks tend to produce faster jets that tend to have larger surface area, mass, linear momentum and kinetic energy, while these quantities tend to be anticorrelated with θBN. In general, the increase of θBN to up to 45° results in increased jet formation rates. In the case of high-speed jets in runs with Vin = 3.3 CA and high-speed plasmoids, the jet formation anticorrelates with θBN. The jet production all but ceases for θBN = 65° regardless of the shock’s MA. The maximum distances of the magnetosheath jets from the shocks were ≲140 di (upstream ion intertial lengths), which, estimating 1 di ∼100–150 km at Earth, corresponds to 2.4–3.3 Earth radii. Thus, none of the simulated jets reached distances equivalent to the average extension of the Earth’s subsolar magnetosheath, which would make them the equivalents of geoeffective jets. Higher MA shocks are probably needed in order to produce such jets.

An exomoon survey of 70 cool giant exoplanets and the new candidate Kepler-1708 b-i

Exomoons represent a crucial missing puzzle piece in our efforts to understand extrasolar planetary systems. To address this deficiency, we here describe an exomoon survey of 70 cool, giant transiting exoplanet candidates found by Kepler. We identify only one exhibiting a moon-like signal that passes a battery of vetting tests: Kepler-1708 b. We show that Kepler-1708 b is a statistically validated Jupiter-sized planet orbiting a Sun-like quiescent star at 1.6 au. The signal of the exomoon candidate, Kepler-1708 b-i, is a 4.8σ effect and is persistent across different instrumental detrending methods, with a 1% false-positive probability via injection–recovery. Kepler-1708 b-i is ~2.6 Earth radii and is located in an approximately coplanar orbit at ~12 planetary radii from its ~1.6 au Jupiter-sized host. Future observations will be necessary to validate or reject the candidate.

Determination of radio wave propagation conditions in the atmosphere of Hanoi using the meteorological data

This article uses the data of radio occultation and the radiosonde data to determine radio refractive index and wave propagation conditions in the atmosphere of the Hanoi area. The content of this article uses the data of radio occultation in 2014-2016 and the radiosonde data in 2016-2018, showing that the radio refractive index tends to decrease with altitude, the maximum average value of radio refractivity is 370 N-units, the largest radio refractivity difference between years is not more than 11 N-units, at high altitudes the radio refractivity value is close to the value at standard model of the ITU-R while at a small altitude the difference between the model value and the observed value is up to 60 N-units, the vertical gradient of refractivity and the effective earth radius coefficient is independent with altitude. Based on radio refractivity, it is possible to determine tropospheric delay, which is input data for problems such as satellite positioning, altimetry satellite and under-the-horizon radar.

Probing the Innermost Regions of AGN Jets and Their Magnetic Fields with RadioAstron. V. Space and Ground Millimeter-VLBI Imaging of OJ 287

Abstract We present the first polarimetric space very long baseline interferometry (VLBI) observations of OJ 287, observed with RadioAstron at 22 GHz during a perigee session on 2014 April 4 and five near-in-time snapshots, together with contemporaneous ground VLBI observations at 15, 43, and 86 GHz. Ground-space fringes were obtained up to a projected baseline of 3.9 Earth diameters during the perigee session, and at a record 15.1 Earth diameters during the snapshot sessions, allowing us to image the innermost jet at an angular resolution of ∼50μ as, the highest ever achieved at 22 GHz for OJ 287. Comparison with ground-based VLBI observations reveals a progressive jet bending with increasing angular resolution that agrees with predictions from a supermassive binary black hole model, although other models cannot be ruled out. Spectral analyses suggest that the VLBI core is dominated by the internal energy of the emitting particles during the onset of a multiwavelength flare, while the parsec-scale jet is consistent with being in equipartition between the particles and magnetic field. Estimated minimum brightness temperatures from the visibility amplitudes show a continued rising trend with projected baseline length up to 1013 K, reconciled with the inverse-Compton limit through Doppler boosting for a jet closely oriented to the line of sight. The observed electric vector position angle suggests that the innermost jet has a predominantly toroidal magnetic field, which, together with marginal evidence of a gradient in rotation measure across the jet width, indicates that the VLBI core is threaded by a helical magnetic field, in agreement with jet formation models.

Gravity measurement to probe the depth of African-continental crust over a north-south profile: theory and modeling

Based upon gravity measurements and calculations, the depth of the African continental crust is estimated. Taking as constraints the mass and radius of earth, and measured gravity, this theoretical method explores the use of gravitational potential to calculate the absolute gravity at three locations in Africa (e.g., Cape Town at latitude -34o, central Africa at latitude 0, and Benghazi at latitude 32o). The computational method uses as input a continental crust density ρ1 = 2.65–2.75 g/cm3 while compromising the oceanic crust density ρ2 to maintain the average crust density of the planet fixed at <ρ12> = 2.60 g/cm3. Crustal depth is assumed uniform around the earth and kept as a free parameter to adjust for the best fitting of gravity but using values of less than 100 km. A solid angle αo is a solid angle whose vertex is at the center of earth used to separate continental and oceanic crusts (αo = 10o, 20o, 35o). The results obtained for the continental crust were H = 36 km near continental edges at both Benghazi and Cape Town, whereas H = 44.4 km at the center of continent. These results are in excellent agreement with those reported by Tedla and coworkers (H = 39 ± 5 km) using an Euler deconvolution method. Our theoretical results from the developed code are also corroborated by results of numerical forward modeling supporting our code's reliability for further geoscience explorations.

A new climatological electron density model for supporting space weather services

The ionosphere is the ionized part of the Earth’s atmosphere, ranging from about 60 km up to several Earth radii, whereas the upper part above about 1000 km height up to the plasmapause is usually called the plasmasphere. We present a new three-dimensional electron density model to support space weather services and mitigate propagation errors for trans-ionospheric signals. The model is developed by superposing the Neustrelitz Plasmasphere Model (NPSM) to an ionosphere model composed of separate F and E-layer distributions. It uses the Neustrelitz TEC model (NTCM), Neustrelitz Peak Density Model (NPDM), and the Neustrelitz Peak Height Model (NPHM) for the total electron content (TEC), peak ionization, and peak height information. These models describe the spatial and temporal variability of the key parameters as a function of local time, geographic/geomagnetic location, solar irradiation, and activity. The model is developed to calculate the electron concentration at any given location and time in the ionosphere for trans-ionospheric applications and named the Neustrelitz Electron Density Model (NEDM2020). A comprehensive validation study is conducted against electron density in-situ data from DMSP and Swarm, Van Allen Probes and ICON missions, and topside TEC data from COSMIC/FORMOSAT-3 mission, bottom side TEC data from TOPEX/Poseidon mission, and ground-based TEC data from International GNSS Service (IGS) covering both high and low solar activity conditions. Additionally, the model performance is compared with the 3D electron density model NeQuick2. Our investigation shows that the NEDM2020 performs better than the NeQuick2 compared with the in-situ data from Van Allen Probes and ICON satellites and TEC data from COSMIC and TOPEX/Poseidon missions. When compared with DMSP and IGS TEC data, both NEDM2020 and NeQuick2 perform very similarly.

Observation evidence for entropy switch model of substorm onset

The cause of substorm onset is not yet understood. Chen CX (2016) proposed an entropy switch model, in which substorm onset results from the development of interchange instability. In this study, we sought observational evidence for this model by using Time History of Events and Macroscale Interactions during Substorms (THEMIS) data. We examined two events, one with and the other without a streamer before substorm onset. In contrast to the stable magnetosphere, where the total magnetic field strength is a decreasing function and entropy is an increasing function of the downtail distance, in both events the total magnetic field strength and entropy were reversed before substorm onset. After onset, the total magnetic field strength, entropy, and other plasma quantities fluctuated. In addition, a statistical study was performed. By confining the events with THEMIS satellites located in the downtail region between ~8 and ~12 Earth radii, and 3 hours before and after midnight, we found the occurrence rate of the total magnetic field strength reversal to be 69% and the occurrence rate of entropy reversal to be 77% of the total 205 events.

Modeling the Varying Location of Field Line Resonances During Geomagnetic Storms

AbstractPrevious observational studies have shown that the natural Alfvén frequencies of geomagnetic field lines vary significantly over the course of a geomagnetic storm, decreasing by up to 50% from their quiet time values outside the plasmasphere. This was recently demonstrated statistically using ground magnetometer observations across 132 geomagnetic storm events (Wharton et al., 2020). This then brings into question where field line resonances (FLRs) will form in storm‐time conditions relative to quiet times. With storm‐time radiation belt dynamics depending heavily upon wave‐particle interactions, understanding how FLR locations change over the course of a storm will have important implications for this area. Using 3D magnetohydrodynamic (MHD) simulations, we investigate how changes in the Alfvén frequency continuum of the Earth's dayside magnetosphere over the course of a geomagnetic storm affect the fast‐Alfvén wave coupling. By setting the model Alfvén frequencies consistent with the observations, and permitting a modest change in the plasmapause/magnetopause locations consistent with storm‐time behavior, we show that FLR locations can change substantially during storms. The combined effects of higher fast waveguide frequencies and lower Alfvén frequencies during storm main phases, act together to move the FLR locations radially inwards compared to quiet times. FLRs outside of the plasmasphere are moved radially inward by 1.7 Earth radii for the cases considered.

ГЕОДИНАМІКА

Purpose. To investigate the features of the algorithm implementation for finding the derivatives of the spatial distribution function of the planet's masses with the use of high-order Stokes constants and, on the basis of this, to find its analytical expression. According to the given methodology, to carry out calculations with the help of which to carry on the study of dynamic phenomena occurring inside an ellipsoidal planet. The proposed method involves the determination of the derivatives of the mass distribution function by the sum, the coefficients of which are obtained from the system of equations, which is incorrect. In order to solve it, an error-resistant method for calculating unknowns was used. The implementation of the construction is carried out in an iterative way, while for the initial approximation we take the three-dimensional function of the density of the Earth's masses, built according to Stokes constants up to the second order inclusive, by dynamic compression by the one-dimensional density distribution, and we determine the expansion coefficients of the derivatives of the function in the variables to the third order inclusive. They are followed by the corresponding density function, which is then taken as the initial one. The process is repeated until the specified order of approximation is reached. To obtain a stable result, we use the Cesaro summation method (method of means).. The calculations performed with the help of programs that implement the given algorithm, while the achieved high (ninth) order of obtaining the terms of the sum of calculations. The studies of the convergence of the sum of the series have been carried out, and on this basis, a conclusion has been made about the advisability of using the generalized finding of the sums based on the Cesaro method. The optimal number of contents of the sum terms has been chosen, provides convergence both for the mass distribution function and for its derivatives. Calculations of the deviations of mass distribution from the mean value ("inhomogeneities") for extreme points of the earth's geoid, which basically show the total compensation along the radius of the Earth, have been performed. For such three-dimensional distributions, calculations were performed and schematic maps were constructed according to the taken into account values of deviations of three-dimensional distributions of the mean ("inhomogeneities") at different depths reflecting the general structure of the Earth's internal structure. The presented vector diagrams of the horizontal components of the density gradient at characteristic depths (2891 km - core-mantle, 700 km - middle of the mantle, also the upper mantle - 200, 100 km) allow us to draw preliminary conclusions about the global movement of masses. At the same time, a closed loop is observed on the “core-mantle” edge, which is an analogy of a closed electric circuit. For shallower depths, differentiation of vector motions is already taking place, which gives hope for attracting these vector-grams to the study of dynamic motions inside the Earth. In fact, the vertical component (derivative with respect to the z variable) is directed towards the center of mass and confirms the main property of mass distributions - growth when approaching the center of mass. The method of stable solution of incorrect linear systems is applied, by means of which the vector-gram of the gradient of the mass distribution function is constructed. The nature of such schemes provides a tool for possible causes of mass redistribution in the middle of the planet and to identify possible factors of tectonic processes in the middle of the Earth, i.e indirectly confirms the gravitational convection of masses. The proposed technique can be used to create detailed models of density functions and its characteristics (derivatives) of the planet's interior, and the results of numerical experiments - to solve tectonics problems.

Neutrino oscillations through the Earth’s core

Neutrinos have two properties that make them fairly unique from other known particles: extremely low cross sections and flavor changing oscillations. With a good knowledge of the oscillation parameters soon in hand, it will become possible to detect low-energy atmospheric neutrinos sensitive to the forward elastic scattering off electrons in the Earth's core providing a measurement of the core properties and the matter effect itself. As the dynamics of the Earth's core are complicated and in a difficult to probe environment, additional information from upcoming neutrino experiments will provide feedback into our knowledge of geophysics as well as useful information about exoplanet formation and various new physics scenarios including dark matter. In addition, we can probe the existence of the matter effect in the Earth and constrain the non-standard neutrino interaction parameter $\epsilon_{ee}^\oplus$. We show how DUNE's sensitivity to low-energy atmospheric neutrino oscillations can provide a novel constraint on the density and radius of the Earth's core at the 9\% level and the Earth's matter effect at the 5\% level. Finally, we illuminate the physics behind low-energy atmospheric neutrino resonances in the Earth.

Maximizing the Accuracy of Double Probe Electric Field Measurements Near Perigee: The Case of the Van Allen Probes Instruments

AbstractThe Van Allen Probes spacecraft flew through the inner radiation belt and the plasmasphere, probing the extremely dynamic coupling between the thermosphere, the ionosphere and the subauroral magnetosphere. Examining the electrodynamics of this region using Van Allen Probes data required that the ∼1 mV/m electric field (E‐field) of interest be measured in a region where the E‐field due to spacecraft motion was ∼100 mV/m. This means that the E‐field, the magnetic field, and the spacecraft velocity had to be measured to better than 1%. The instruments on board the Van Allen Probes have achieved this accuracy, delivering reliable near equatorial E‐field measurements even below three Earth radii. The objective of this commentary is to summarize the methodology developed over the years to maximize the accuracy and scientific return of these double probe E‐field measurements below L = 3.

Role of rare earth sites and vacancies in the anomalous compression of modulated scheelite tungstates RE2 ( WO4)3

X-ray powder diffraction experiments at high pressures combining conventional sources and synchrotron radiation, together with theoretical simulations have allowed us to study the anomalous compression of the entire \ensuremath{\alpha}-${RE}_{2}$(${\mathrm{WO}}_{4}{)}_{3}$ ($\mathit{RE}$ = La-Ho) family with modulated scheelite structure (\ensuremath{\alpha} phase). The investigated class of materials is of great interest due to their peculiar structural behavior with temperature and pressure, which is highly sought after for specialized high-tech applications. Experimental data were analyzed using full-profile refinements and were complemented with computational methods based on density functional theory (DFT) total energy calculations for a subset of the samples investigated. An unusual change in the compression curves of the lattice parameters $a, c$, and \ensuremath{\beta} was observed in both the experiments and theoretical simulations. In particular, in all the studied compounds the lattice parameter $a$ decreased with pressure to a minimum value and then increased upon further compression. Pressure evolution of the experimental x-ray diffraction (XRD) patterns and cell parameters is correlated with the ionic radius of the rare earth element: (1) the lighter La-Nd tungstates underwent two phase transitions, and both transition pressures decreased as the rare earth's ionic radius increased. The XRD patterns of the first high pressure phase could be indexed with propagation vectors parallel to the $a$ axis (tripling the unit cell). At higher pressures, the lattice parameters for the second phase (referred to as the preamorphous phase) showed little variation with pressure. (2) The heavier tungstates, from Sm to Dy, undergo a transition to the preamorphous phase without any intermediate phase. The reversibility of both phase transitions was investigated. DFT calculations support this unusual response of the crystal structures under pressure and shed light on the structural mechanism of negative linear compressibility (NLC) and the resulting softening. The pressure dependence of the structural modifications is related to tilting, along with small elongation and alignment, of the ${\mathrm{WO}}_{4}^{2\ensuremath{-}}$ tetrahedrons. These changes correlate with those in the alternating RE\dots{}RE\dots{}RE chains and blocks of cationic vacancies arranged along the $a$ axis. Possible stacking defects, which emerge between them, helped to explain this anomalous compression and the pressure induced amorphization. Such mechanisms were compared with other ferroelastic families of molybdates, niobates, vanadates, and other compounds with similar structural motifs classified as having ``hinge frames.''