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At least 343 records · Page 19

Detection of a Superluminous Spiral Galaxy in the Heart of a Massive Galaxy Cluster

It is well established that brightest cluster galaxies (BCGs), residing in the centers of galaxy clusters, are typically massive and quenched galaxies with cD or elliptical morphology. An optical survey suggested that an exotic galaxy population, superluminous spiral and lenticular galaxies, could be the BCGs of some galaxy clusters. Because the cluster membership and the centroid of a cluster cannot be accurately determined based solely on optical data, we followed up a sample of superluminous disk galaxies and their environments using XMM-Newton X-ray observations. Specifically, we explored seven superluminous spiral and lenticular galaxies that are candidate BCGs. We detected massive galaxy clusters around five superluminous disk galaxies and established that one superluminous spiral, 2MASX J16273931+3002239, is the central BCG of a galaxy cluster. The temperature and total mass of the cluster are ${{kT}}_{500}={3.55}_{-0.20}^{+0.18}$ keV and M 500 = (2.39 ± 0.19) × 10 14 M ⊙ . We identified the central galaxies of the four clusters that do not host superluminous disk galaxies at their cores, and established that the centrals are massive elliptical galaxies. However, for two of the clusters, the offset superluminous spirals are brighter than the central galaxies, implying that the superluminous disk galaxies are the brightest cluster galaxies. Our results demonstrate that superluminous disk galaxies are rarely the central systems of galaxy clusters. This is likely because galactic disks are destroyed by major mergers, which are more frequent in high-density environments. We speculate that the disks of superluminous disk galaxies in cluster cores may have been reformed due to mergers with gas-rich satellites.

79 ASTRONOMY AND ASTROPHYSICS↗

Pegasus IV: Discovery and Spectroscopic Confirmation of an Ultra-faint Dwarf Galaxy in the Constellation Pegasus

We report the discovery of Pegasus IV, an ultra-faint dwarf galaxy found in archival data from the Dark Energy Camera processed by the DECam Local Volume Exploration Survey. Pegasus IV is a compact, ultra-faint stellar system ( pc; M $_{V}$ = −4.25 ± 0.2 mag) located at a heliocentric distance of . Based on spectra of seven nonvariable member stars observed with Magellan/IMACS, we confidently resolve Pegasus IV’s velocity dispersion, measuring km s$^{−1}$ (after excluding three velocity outliers); this implies a mass-to-light ratio of for the system. From the five stars with the highest signal-to-noise spectra, we also measure a systemic metallicity of [Fe/H] = dex, making Pegasus IV one of the most metal-poor ultra-faint dwarfs. We tentatively resolve a nonzero metallicity dispersion for the system. These measurements provide strong evidence that Pegasus IV is a dark-matter-dominated dwarf galaxy, rather than a star cluster. We measure Pegasus IV’s proper motion using data from Gaia Early Data Release 3, finding (μ $_{α*}$, μ $_{δ}$) = (0.33 ± 0.07, −0.21 ± 0.08) mas yr$^{−1}$. When combined with our measured systemic velocity, this proper motion suggests that Pegasus IV is on an elliptical, retrograde orbit, and is currently near its orbital apocenter. Lastly, we identify three potential RR Lyrae variable stars within Pegasus IV, including one candidate member located more than 10 half-light radii away from the system’s centroid. The discovery of yet another ultra-faint dwarf galaxy strongly suggests that the census of Milky Way satellites is still incomplete, even within 100 kpc.

79 ASTRONOMY AND ASTROPHYSICS↗

Revisiting the Supernova Engines in the 3C 397 and W49B Supernova Remnants

The nature of the supernova remnants (SNRs) 3C 397 and W49B has long been a subject of debate, with prior studies offering conflicting interpretations between thermonuclear and core-collapse scenarios. To help settle this debate, we present a systematic, spatially resolved, spectroscopic analysis of both remnants using XMM-Newton. By applying multicomponent thermal models, we derive key physical properties including elemental abundances, ejecta temperatures, ambient densities, and explosion energetics. We compare the inferred metal abundance ratios to a wide range of core-collapse and thermonuclear nucleosynthesis models, including new models whose explosion energies differ from the canonical value of 10 51 erg. We find that the observed Fe/Si and Ca/Si ratios in both SNRs are best matched by certain thermonuclear models. However, no model fully reproduces the complete set of observed abundance patterns. In 3C 397, high Fe enrichment and spatial abundance variations suggest interaction with a dense progenitor environment, and W49B’s composition is overall consistent with a thermonuclear origin; however, both require a low-energy (∼10 50 erg) supernova explosion. We additionally map the Fe Kα line centroid energies and find a spread, with W49B falling within the core-collapse region—highlighting both environmental complexity and the limitations of this diagnostic for supernova classification. Our results highlight the need for caution in relying on any single diagnostic or nucleosynthesis model for supernova typing, underscore the need for improved nucleosynthesis models, and motivate future high-resolution, high-throughput observations.

79 ASTRONOMY AND ASTROPHYSICS↗

A Universal Power-law Prescription for Variability from Synthetic Images of Black Hole Accretion Flows

We present a framework for characterizing the spatiotemporal power spectrum of the variability expected from the horizon-scale emission structure around supermassive black holes, and we apply this framework to a library of general relativistic magnetohydrodynamic (GRMHD) simulations and associated general relativistic ray-traced images relevant for Event Horizon Telescope (EHT) observations of Sgr A*. We find that the variability power spectrum is generically a red-noise process in both the temporal and spatial dimensions, with the peak in power occurring on the longest timescales and largest spatial scales. When both the time-averaged source structure and the spatially integrated light-curve variability are removed, the residual power spectrum exhibits a universal broken power-law behavior. On small spatial frequencies, the residual power spectrum rises as the square of the spatial frequency and is proportional to the variance in the centroid of emission. Beyond some peak in variability power, the residual power spectrum falls as that of the time-averaged source structure, which is similar across simulations; this behavior can be naturally explained if the variability arises from a multiplicative random field that has a steeper high-frequency power-law index than that of the time-averaged source structure. We briefly explore the ability of power spectral variability studies to constrain physical parameters relevant for the GRMHD simulations, which can be scaled to provide predictions for black holes in a range of systems in the optically thin regime. We present specific expectations for the behavior of the M87* and Sgr A* accretion flows as observed by the EHT.

79 ASTRONOMY AND ASTROPHYSICS↗

Upgrades of the ATLAS Zero Degree Calorimeter System for Run 3 at the Large Hadron Collider

Experimental studies of ultra-relativistic heavy ion collisions at the Large Hadron Collider (LHC) depend crucially on Zero Degree Calorimeters (ZDCs) that measure neutrons produced at near-beam rapidity in nucleus-nucleus collisions. In hadronic nuclear collisions these neutrons are mainly spectator neutrons, those that do not scatter from opposing nucleons during the collision. As a result, the ZDCs provide a vital probe of heavy ion collision geometry. The ZDCs are also essential in the study of ultra-peripheral collisions that are initiated by photons associated with the electric fields of one or both nuclei. Coherent photon emission typically leaves the photon emitter intact, making the observation of no ZDC signal, on one or both sides, a tag of such processes. The ATLAS ZDCs, built prior to Run 1 were substantially upgraded for LHC Run 3. The primary upgrades included replacement of the quartz Cherenkov radiator with $\text{H}_2$-doped fused silica rods; installation of fast air-core signal cables between the ZDC and the ATLAS USA15 cavern; new LED-based calibration system; and new electronics implemented for readout and fully-digital triggering. The ZDCs were also augmented with new "Reaction Plane Detectors" (RPDs) designed to measure the transverse centroid of multi-neutron showers to allow event-by-event reconstruction of the directed-flow plane in nuclear collisions. The Run~3 ZDC detectors, including the RPDs, are described in detail with emphasis on aspects that are new for Run~3.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Version 4 CALIPSO Imaging Infrared Radiometer ice and liquid water cloud microphysical properties – Part I: The retrieval algorithms

Following the release of the version 4 Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data products from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission, a new version (version 4; V4) of the CALIPSO Imaging Infrared Radiometer (IIR) Level 2 data products has been developed. The IIR Level 2 data products include cloud effective emissivities and cloud microphysical properties such as effective diameter and ice or liquid water path estimates. Dedicated retrievals for water clouds were added in V4, taking advantage of the high sensitivity of the IIR retrieval technique to small particle sizes. This paper (Part I) describes the improvements in the V4 algorithms compared to those used in the version 3 (V3) release, while results will be presented in a companion (Part II) paper. The IIR Level 2 algorithm has been modified in the V4 data release to improve the accuracy of the retrievals in clouds of very small (close to 0) and very large (close to 1) effective emissivities. To reduce biases at very small emissivities that were made evident in V3, the radiative transfer model used to compute clear-sky brightness temperatures over oceans has been updated and tuned for the simulations using Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) data to match IIR observations in clear-sky conditions. Furthermore, the clear-sky mask has been refined compared to V3 by taking advantage of additional information now available in the V4 CALIOP 5 km layer products used as an input to the IIR algorithm. After sea surface emissivity adjustments, observed and computed brightness temperatures differ by less than ±0.2 K at night for the three IIR channels centered at 08.65, 10.6, and 12.05 µm, and inter-channel biases are reduced from several tens of Kelvin in V3 to less than 0.1 K in V4. We have also improved retrievals in ice clouds having large emissivity by refining the determination of the radiative temperature needed for emissivity computation. The initial V3 estimate, namely the cloud centroid temperature derived from CALIOP, is corrected using a parameterized function of temperature difference between cloud base and top altitudes, cloud absorption optical depth, and CALIOP multiple scattering correction factor. As shown in Part II, this improvement reduces the low biases at large optical depths that were seen in V3 and increases the number of retrievals. As in V3, the IIR microphysical retrievals use the concept of microphysical indices applied to the pairs of IIR channels at 12.05 and 10.6 µm and at 12.05 and 08.65 µm. The V4 algorithm uses ice look-up tables (LUTs) built using two ice habit models from the recent “TAMUice2016” database, namely the single-hexagonal-column model and the eight-element column aggregate model, from which bulk properties are synthesized using a gamma size distribution. Four sets of effective diameters derived from a second approach are also reported in V4. Here, the LUTs are analytical functions relating microphysical index applied to IIR channels 12.05 and 10.6 µm and effective diameter as derived from in situ measurements at tropical and midlatitudes during the Tropical Composition, Cloud, and Climate Coupling (TC4) and Small Particles in Cirrus Science and Operations Plan (SPARTICUS) field experiments.

54 ENVIRONMENTAL SCIENCES↗

MPAS-Seaice (v1.0.0): sea-ice dynamics on unstructured Voronoi meshes

Abstract. We present MPAS-Seaice, a sea-ice model which uses the Model for Prediction Across Scales (MPAS) framework and spherical centroidal Voronoi tessellation (SCVT) unstructured meshes. As well as SCVT meshes, MPAS-Seaice can run on the traditional quadrilateral grids used by sea-ice models such as CICE. The MPAS-Seaice velocity solver uses the elastic–viscous–plastic (EVP) rheology and the variational discretization of the internal stress divergence operator used by CICE, but adapted for the polygonal cells of MPAS meshes, or alternatively an integral (“finite-volume”) formulation of the stress divergence operator. An incremental remapping advection scheme is used for mass and tracer transport. We validate these formulations with idealized test cases, both planar and on the sphere. The variational scheme displays lower errors than the finite-volume formulation for the strain rate operator but higher errors for the stress divergence operator. The variational stress divergence operator displays increased errors around the pentagonal cells of a quasi-uniform mesh, which is ameliorated with an alternate formulation for the operator. MPAS-Seaice shares the sophisticated column physics and biogeochemistry of CICE and when used with quadrilateral meshes can reproduce the results of CICE. We have used global simulations with realistic forcing to validate MPAS-Seaice against similar simulations with CICE and against observations. We find very similar results compared to CICE, with differences explained by minor differences in implementation such as with interpolation between the primary and dual meshes at coastlines. We have assessed the computational performance of the model, which, because it is unstructured, runs with 70 % of the throughput of CICE for a comparison quadrilateral simulation. The SCVT meshes used by MPAS-Seaice allow removal of equatorial model cells and flexibility in domain decomposition, improving model performance. MPAS-Seaice is the current sea-ice component of the Energy Exascale Earth System Model (E3SM).

58 GEOSCIENCES↗

rustpix

rustpix is a high-performance, open-source Rust library with first-class Python bindings (via PyO3) for processing pixel-detector data in neutron imaging. It targets time-stamping detectors such as Timepix3 (TPX3) at ORNL's Spallation Neutron Source (VENUS beamline), where each detected neutron deposits charge across a cluster of pixels within a very high-rate event stream (96M+ hits/sec). rustpix parses TPX3 event data in parallel using memory-mapped I/O, offers four interchangeable clustering algorithms (ABS adjacency-based search, DBSCAN, graph/union-find connected components, and a parallel grid method), and extracts weighted, super-resolved centroids to produce neutron-event lists. A streaming architecture lets it process files larger than available memory. rustpix is distributed as a pip-installable Python package (with NumPy integration), Rust crates, a command-line tool, and an interactive GUI; it writes HDF5, Apache Arrow, and CSV; and it is designed to extend to TPX4 and other detector types. Released as open-source under the MIT License.

Zhang, Chen [Oak Ridge National Laboratory (ORNL),↗

Package Data for CERF-Data Centers

This dataset contains sample input 100m resolution raster files for running the CERF-DC python package (see https://github.com/IMMM-SFA/cerf_data_centers) at the state level across the CONUS. Due to data availability constraints, some of the items included in this dataset are proxies or assumptions for siting factors used in the model. These are individually noted in the item descriptions and can be exchanged with more detailed information upon availability. Data Descriptions The following raster files are included in the data download: state_siting_region.tif — State areas identified by state FIPS code composite_siting_suitability.tif — Value of 1 indicates suitable siting location, 0 otherwise. The following areas are excluded from siting: Areas within 300m of a federal airport runway Waterbodies Areas with slope >16% Areas susceptible to sinkholes High coastal or inland flood risk areas Local, state, and federal parks, leisure areas, and cemeteries Areas >2 km away from electric substations Areas >5 km away from a municipal water supplier service area Areas >2 km away from high-speed fiber provider service territory Protected Areas Database of the United States (PAD-US) areas Railroads, major roadways, and minor roadways Military areas and training grounds Developed lands Areas >0.8 km (0.5 miles) from developed lands land_value_dollar_per_sqft.tif — USD per square foot (sqft) derived from USDA $/acre land cost personal_property_tax_rate.tif — Personal property tax rate by state. Uses an assumed 0.0125 personal property tax rate for states with personal property tax, 0 for states without personal property tax. real_property_tax_rate.tif — Real property tax rate. Based on county level residential real estate property tax rates. sales_tax_rate.tif — Sales tax rate by state. mechanical_cooling_fraction.tif — Fraction of year (values between 0 and 1, inclusive) that the data center would be cooled through mechanical processes based on local water stress and humidity levels. water_cooling_fraction.tif — Fraction of year (values between 0 and 1, inclusive) that the data center would be cooled through evaporative (water cooled) processes based on local water stress and humidity levels. distance_to_substation.tif — Distance to nearest substation in hundreds of meters (i.e., value of 1 equals a distance of 100m). Offshore areas have a value of 0. industrial_electricity_rates_dollar_per_kwh.tif — USD/kWh industrial electricity rates. Represents the average industrial rate across all utilities that operate within a given county. Values are derived from the US Utility Rate Database. commercial_electricity_rates_dollar_per_kwh.tif — USD/kWh commercial electricity rates. Represents the average commercial rate across all utilities that operate within a given county. Values are derived from the US Utility Rate Database. data_center_market_locations.tif — Grid cells with positive values represent the centroid of existing data center market clusters. The value of non-zero grid cells represents the number of data centers in the market cluster. All other grid cells have a value of 0. Geospatial Metadata CRS: Albers Equal Area Conic (ESRI:102003) Extent: -2415585.0000000023283064,-1441981.2605773280374706 : 2384414.9999999976716936,1708018.7394226719625294 Dimensions: X: 48000 Y: 31500 Bands: 1 Origin: -2415585.0000000023283064,1708018.7394226719625294 Pixel Size: 100,-100 Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. License This data is made available under a CCBY4.0 License Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Mongird, Kendall↗

Package Data for CERF-Data Centers

This dataset contains sample input 100m resolution raster files for running the CERF-DC python package (see https://github.com/IMMM-SFA/cerf_data_centers) at the state level across the CONUS. Due to data availability constraints, some of the items included in this dataset are proxies or assumptions for siting factors used in the model. These are individually noted in the item descriptions and can be exchanged with more detailed information upon availability. Data Descriptions The following raster files are included in the data download: state_siting_region.tif — State areas identified by state FIPS code composite_siting_suitability.tif — Value of 1 indicates suitable siting location, 0 otherwise. The following areas are excluded from siting: Areas within 300 m of a federal airport runway or within an airport area boundary Waterbodies Areas with slope >16% Areas susceptible to sinkholes High coastal or inland flood risk areas Local, state, and federal parks, leisure areas, and cemeteries Areas >2 km away from electric substations Areas >5 km away from a municipal water supplier service area Areas >2 km away from high-speed fiber provider service territory USGS Protected Areas Database of the United States (PAD-US) GAP status 1, 2, or 3 areas US National Parks Wetlands USFWS critical habitats BIA land areas Railroads, major roadways, and minor roadways Military areas and training grounds NLCD developed lands Areas >0.8 km (0.5 miles) from NLCD developed lands land_value_dollar_per_sqft.tif — USD per square foot (sqft) derived from USDA $/acre land cost personal_property_tax_rate.tif — Personal property tax rate by state. Uses an assumed 0.0125 personal property tax rate for states with personal property tax, 0 for states without personal property tax. real_property_tax_rate.tif — Real property tax rate. Based on county level residential real estate property tax rates. sales_tax_rate.tif — Sales tax rate by state. mechanical_cooling_fraction.tif — Fraction of year (values between 0 and 1, inclusive) that the data center would be cooled through mechanical processes based on local water stress and humidity levels. water_cooling_fraction.tif — Fraction of year (values between 0 and 1, inclusive) that the data center would be cooled through evaporative (water cooled) processes based on local water stress and humidity levels. distance_to_substation.tif — Distance to nearest substation in hundreds of meters (i.e., value of 1 equals a distance of 100m). Offshore areas have a value of 0. industrial_electricity_rates_dollar_per_kwh.tif — USD/kWh industrial electricity rates. Represents the average industrial rate across all utilities that operate within a given county. Values are derived from the US Utility Rate Database. commercial_electricity_rates_dollar_per_kwh.tif — USD/kWh commercial electricity rates. Represents the average commercial rate across all utilities that operate within a given county. Values are derived from the US Utility Rate Database. data_center_market_locations.tif — Grid cells with positive values represent the centroid of existing data center market clusters. The value of non-zero grid cells represents the number of data centers in the market cluster. All other grid cells have a value of 0. Geospatial Metadata CRS: Albers Equal Area Conic (ESRI:102003) Extent: -2415585.0000000023283064,-1441981.2605773280374706 : 2384414.9999999976716936,1708018.7394226719625294 Dimensions: X: 48000 Y: 31500 Bands: 1 Origin: -2415585.0000000023283064,1708018.7394226719625294 Pixel Size: 100,-100 Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. License This data is made available under a CCBY4.0 License Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Mongird, Kendall↗

Some recent observations and interpretation of the Jupiter decimeter emission

The decimetric emission consists partly of thermal radiation from the planetary disk and partly of nonthermal radiation from a region of larger angular extent and is thought to result from synchrotron emission by relativistic electrons in the magnetic field. Four topics relating to the decimetric emission are discussed. (1) A comparison is made of maps giving detailed brightness contours. One was obtained for epoch 1963.8 and was at a wavelength of 10.4 cm. The second was for epoch 1967.2 at 21.3 cm. (2) Interferometric data at 21.1 cm taken in April 1968 and May 1979 indicate that the emission centroid is fixed in Jupiter and rotates with it. (3) Circular polarization observations are described and are used to obtain a surface magnetic field strength at the equator between 3.2 and 15.2 gauss. (4) An upper limit on the Faraday rotation is used to set an upper limit on the density of thermal electrons surrounding Jupiter, and uncertainties in the results are discussed.

Berge, G. L.↗

A curve of growth determination of the f-values for the fourth positive system of CO and the Lyman-Birge-Hopfield system of N2.

The curve of growth method has been employed to determine f-values for the fourth positive system of CO and the magnetic dipole and electric quadrupole components of the Lyman-Birge-Hopfield system of N2. No significant dependence on r-centroid was found. The mean value of the ratio of the electric quadrupole to magnetic dipole f-values was 0.076.

Pilling, M. J.↗

Corkscrews and singularities in fruitflies - Resetting behavior of the circadian eclosion rhythm.

Description of experiments undertaken to define the phase-resetting behavior of the circadian rhythm of pupal eclosion in populations of fruitflies. An attempt is made to determine how and why the resetting response depends on the duration of a standard perturbation as well as on the time at which it is given. Plotting a three-dimensional graph of the measured emergence centroids vs the stimulus variables, the data are found to spiral up around a vertical rotation axis. Using a computer, a smooth surface, called the resetting surface, which approximately fits the helicoidal cloud of data points, is obtained and is shown to be best described as a vertical corkscrew linking together tilted planes. This corkscrew feature of the resetting surface is taken to indicate that there is an isolated perturbation following which there is either no circadian rhythm of emergence in the steady state, or one of unpredictable phase. A hypothesis concerning the clock dynamics underlying the eclosion rhythm is briefly sketched which encompasses the main features of known resetting data using single discrete pulses of any perturbing agent.

Winfree, A. T.↗

The extended X-ray source at M87.

It is shown that the X-ray source in Virgo must be intimately associated with the galaxy M87, as evidenced by the coincidence of the source centroid location with the galaxy. Although the presented results do not completely explain the origin of the X rays from the Virgo cluster, they do indicate that the bulk of the emission does not come from the nucleus or the jet, and they also indicate the presence of strong energy processes in a region surrounding M87. One view of the origin of these X rays is that they are due to relativistic electrons ejected from M87, and interacting with magnetic or radiation fields in intergalactic space by the synchrotron of inverse Compton process. The other view holds that the X rays could be due to thermal emission from a hot plasma.

Kellogg, E.↗

Moment expansion for ionospheric range error

On a plane earth, the ionospheric or tropospheric range error depends only on the total refractivity content or zeroth moment of the refracting layer and the elevation angle. On a spherical earth, however, the dependence is more complex; so for more accurate results it has been necessary to resort to complex ray-tracing calculations. A simple, high-accuracy alternative to the ray-tracing calculation is presented. By appropriate expansion of the angular dependence in the ray-tracing integral in a power series in height, an expression is obtained for the range error in terms of a simple function of elevation angle, E, at the expansion height and of the mth moment of the refractivity, N, distribution about the expansion height. The rapidity of convergence is heavily dependent on the choice of expansion height. For expansion heights in the neighborhood of the centroid of the layer (300-490 km), the expansion to N = 2 (three terms) gives results accurate to about 0.4% at E = 10 deg. As an analytic tool, the expansion affords some insight on the influence of layer shape on range errors in special problems.

Mallinckrodt, A.↗