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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Altitude Differentiated Aerosol Extinction Over Tenerife (North Atlantic Coast) During ACE-2 by Means of Ground and Airborne Photometry and Lidar Measurements

Retrievals of spectral aerosol optical depths (tau(sub a)) by means of sun photometers have been undertaken in Tenerife (28 deg 16' N, 16 deg 36' W) during ACE-2 (June-July 1997). Five ground-based sites were located at four different altitudes in the marine boundary layer and in the free troposphere, from 0 to 3570 m asl. The goal of the investigation was to provide estimates of the vertical aerosol extinction over the island, both under clean and turbid conditions. Inversion of spectral tau(sub a) allowed to retrieve size distributions, from which the single scattering albedo omega(sub 0) and the asymmetry factor g could be estimated as a function of altitude. These parameters were combined to calculate aerosol forcing in the column. Emphasis is put on episodes of increased turbidity, which were observed at different locations simultaneously, and attributed to outbreaks of mineral dust from North Africa. Differentiation of tau(sub a) as a function of altitude provided the vertical profile of the extinction coefficient sigma(sub e). For dust outbreaks, aerosol extinction is concentrated in two distinct layers above and below the strong subsidence inversion around 1200 m asl. Vertical profiles of tau(sub a) and sigma(sub e) are shown for July 8. In some occasions, vertical profiles are compared to LIDAR observations, performed both at sea level and in the low free troposphere, and to airborne measurements of aerosol optical depths.

Formenti, P.↗
DOE OSTI2022

Microscopic-macroscopic level densities for low excitation energies

Level density ρ(E,Q) is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy E and additional integrals of motion Q , in line with several topics of the universal and fruitful activity of A. S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method, we obtain ρ ∝ I ν (S)/S ν , where I ν (S) is the modified Bessel function of the entropy S . For small shell-structure contribution, one finds ν = κ/2 + 1, where κ is the number of additional integrals of motion. This integer number is a dimension of Q, Q = { N, Z , …} for the case of two-component atomic nuclei, where N and Z are the numbers of neutrons and protons, respectively. For much larger shell structure contributions, one obtains ν = κ /2 + 2. The MMA level density ρ reaches the well-known Fermi gas asymptote for large excitation energies and the finite micro-canonical combinatoric limit for low excitation energies. Further, the additional integrals of motion can also be the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density ρ( E , Q) for a set of the integrals of motion Q = { N, Z }, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter K , which differs significantly from those of neutron resonances due to shell, isotopic asymmetry, and pairing effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Optical Activity of Chiral Excitons

Recent activity in the area of chiroptical phenomena has been focused on the connection between structural asymmetry, electron spin configuration and light/matter interactions in chiral semiconductors. In these systems, spin‐splitting phenomena emerge due to inversion symmetry breaking and the presence of extended electronic states, yet the connection to chiroptical phenomena is lacking. Here, in this study, we develop an analytical effective mass model of chiral excitons, parameterized by density functional theory. The model accounts for parity mixing of the band edge Bloch functions resulting from polar distortions, resulting in allowed magnetic dipole transitions. Through the study of a prototypical chiral 2D hybrid perovskite semiconductor, we show that circular dichroism of the chiral exciton and its interband continuum emerges from spin‐splitting via cross‐coupling of Rashba‐like and chiral/helical spin‐texture components. To demonstrate the generality of our approach, and as a counterpoint, we apply our model to describe chiroptical properties of three‐dimensionally confined excitons in perovskite nanocrystals that occur without chiral lattice distortions.

14 SOLAR ENERGY↗
NASA NTRS1982

Retrieval of aerosol optical characteristics from polarization measurements of reflected solar radiation above the oceans

The reflected near infrared solar radiation observed from space above the oceans is due mainly to the atmosphere scattering, as the ocean surface is nearly black. The molecular Rayleigh contribution is also minimized at infrared wavelengths and it can be evaluated. It is shown that the degree of polarization is much more sensitive to the aerosol properties than the radiance. Measurements of polarization at two wavelengths and with an angular scanning are simulated and an inversion algorithm is proposed. It aims at finding an 'equivalent aerosol model', which reproduces the optical thickness and the asymmetry factor of the actual aerosol at all wavelengths in the solar spectrum.

Santer, R.↗
NASA NTRS2001

Spatial orientation and balance control changes induced by altered gravitoinertial force vectors

To better understand the mechanisms of human adaptation to rotating environments, we exposed 19 healthy subjects and 8 vestibular-deficient subjects ("abnormal"; four bilateral and four unilateral lesions) to an interaural centripetal acceleration of 1 g (resultant 45 degrees roll-tilt of 1.4 g) on a 0.8-m-radius centrifuge for periods of 90 min. The subjects sat upright (body z-axis parallel to centrifuge rotation axis) in the dark with head stationary, except during 4 min of every 10 min, when they performed head saccades toward visual targets switched on at 3- to 5-s intervals at random locations (within +/- 30 degrees) in the earth-horizontal plane. Eight of the normal subjects also performed the head saccade protocol in a stationary chair adjusted to a static roll-tilt angle of 45 degrees for 90 min (reproducing the change in orientation but not the magnitude of the gravitoinertial force on the centrifuge). Eye movements, including voluntary saccades directed along perceived earth- and head-referenced planes, were recorded before, during, and immediately after centrifugation. Postural center of pressure (COP) and multisegment body kinematics were also gathered before and within 10 min after centrifugation. Normal subjects overestimated roll-tilt during centrifugation and revealed errors in perception of head-vertical provided by directed saccades. Errors in this perceptual response tended to increase with time and became significant after approximately 30 min. Motion-sickness symptoms caused approximately 25% of normal subjects to limit their head movements during centrifugation and led three normal subjects to stop the test early. Immediately after centrifugation, subjects reported feeling tilted 10 degrees in the opposite direction, which was in agreement with the direction of their earth-referenced directed saccades. Postural COP, segmental body motion amplitude, and hip-sway frequency increased significantly after centrifugation. These postural effects were short-lived, however, with a recovery time of several postural test trials (minutes). There were also asymmetries in the direction of postcentrifugation COP and head tilt which depended on the subject's orientation during the centrifugation adaptation period (left ear or right ear out). The amount of total head movements during centrifugation correlated poorly or inversely with postcentrifugation postural stability, and the most unstable subject made no head movements. There was no decrease in postural stability after static tilt, although these subjects also reported a perceived tilt briefly after return to upright, and they also had COP asymmetries. Abnormal subjects underestimated roll-tilt during centrifugation, and their directed saccades revealed permanent spatial distortions. Bilateral abnormal subjects started out with poor postural control, but showed no postural decrements after centrifugation, while unilateral abnormal subjects had varying degrees of postural decrement, both in their everyday function and as a result of experiencing the centrifugation. In addition, three unilateral, abnormal subjects, who rode twice in opposite orientations, revealed a consistent orthogonal pattern of COP offsets after centrifugation. These results suggest that both orientation and magnitude of the gravitoinertial vector are used by the central nervous system for calibration of multiple orientation systems. A change in the background gravitoinertial force (otolith input) can rapidly initiate postural and perceptual adaptation in several sensorimotor systems, independent of a structured visual surround.

Clinical Trial↗
NASA NTRS1984

Geologic studies of outer solar system satellites: Iapetus and Europa

A model of regolith evolution on bodies subjected to an asymmetric impact flux is presented. The general effect of an asymmetric impact flux is ballistic diffusion of regolith from areas of high impact flux to areas of lower flux. The effect is most pronounced on low gravity bodies where ejecta travel distances are large, and on bodies with strong flux asymmetries. It may be especially important on Iapetus, where retrograde debris from Phoebe striking the leading hemisphere may produce a flux asymmetry as large as 100 to 1 from apex to antapex. We find that the net amount of material transported by ballistic diffusion is inversely proportional to satellite density. Theoretical calculations and Voyager observations support the view that tidal heating is sufficient to maintain a liquid layer throughout the history of Europa. Photosynthetic, thermal, electrical, and chemical energy sources are considered. The calculations suggest that there may be regions on Europa, very limited in space and time, with physical conditions that are within the range of adaptation of life on Earth. Calculations for the electrical currents within Europa for a thick ice crust are very small.

Squyres, S. W.↗
DOE OSTI2023

Asymmetries in cloud microphysical properties ascribed to sea ice leads via water vapour transport in the central Arctic

To investigate the influence of sea ice openings like leads on wintertime Arctic clouds, the air mass transport is exploited as a heat and humidity feeding mechanism which can modify Arctic cloud properties. Cloud microphysical properties in the central Arctic are analysed as a function of sea ice conditions during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition in 2019–2020. The Cloudnet classification algorithm is used to characterize the clouds based on remote sensing observations and the atmospheric thermodynamic state from the observatory on board the research vessel (RV) Polarstern. To link the sea ice conditions around the observational site with the cloud observations, the water vapour transport (WVT) being conveyed towards RV Polarstern has been utilized as a mechanism to associate upwind sea ice conditions with the measured cloud properties. This novel methodology is used to classify the observed clouds as coupled or decoupled to the WVT based on the location of the maximum vertical gradient of WVT height relative to the cloud-driven mixing layer. Only a conical sub-sector of sea ice concentration (SIC) and the lead fraction (LF) centred on the RV Polarstern location and extending up to 50 km in radius and with an azimuth angle governed by the time-dependent wind direction measured at the maximum WVT is related to the observed clouds. We found significant asymmetries for cases when the clouds are coupled or decoupled to the WVT and selected by LF regimes. Liquid water path of low-level clouds is found to increase as a function of LF, while the ice water path does so only for deep precipitating systems. Clouds coupled to WVT are found to generally have a lower cloud base and larger thickness than decoupled clouds. Thermodynamically, for coupled cases the cloud-top temperature is warmer and accompanied by a temperature inversion at the cloud top, whereas the decoupled cases are found to be closely compliant with the moist adiabatic temperature lapse rate. The ice water fraction within the cloud layer has been found to present a noticeable asymmetry when comparing coupled versus decoupled cases. This novel approach of coupling sea ice to cloud properties via the WVT mechanism unfolds a new tool to study Arctic surface–atmosphere processes. With this formulation, long-term observations can be analysed to enforce the statistical significance of the asymmetries. Furthermore, our results serve as an opportunity to better understand the dynamic linkage between clouds and sea ice and to evaluate its representation in numerical climate models for the Arctic system.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

Integral functions of electron lateral distribution and their fluctuations in electron-photon cascades

Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.

Ivanenko, I. P.↗
DOE OSTI2021

Quenching of single-particle strengths in direct reactions

A discrepancy in the asymmetry dependence of spectroscopic factors extracted with different reaction probes calls into question whether the corresponding reaction models are properly understood. In this work, we present extracted spectroscopic factors from the Ar 46 , 34 ( p , d ) Ar 45 , 33 transfer reactions in inverse kinematics at a beam energy of 70 MeV/nucleon. The results are consistent with previous measurements of these reactions at a lower beam energy [Lee et al. , Phys. Rev. Lett. 104 , 112701 (2010) ], indicating that the transfer reaction is a reliable probe for the nuclear structure of exotic nuclei across a wide energy range. Results from a large body of transfer reaction measurements, ( p , p N ) measurements, and theoretical nuclear structure studies make a compelling case for much weaker asymmetry dependence than what is observed with single-nucleon knockout reactions on beryllium or carbon targets.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

LA17-V-InverseRadTransportProblem-PD2Kb. Final Project Report

In the inverse radiation transport problem, a radiation signal emanating from an unknown object is used to reconstruct geometric and material parameters of the object , e.g., the mass of special nuclear material (SNM), the isotopic composition of the SNM (e.g., the enrichment of 235U), the thickness of shielding, etc. The inverse radiation transport problem is one of the most fundamental and important in the emergency response mission, and has been addressed in previous NA-22 and NA-42/84 investments by using derivative-free optimization methods. Our project was aimed at (i) consolidating previous work by applying polynomial chaos expansion (PCE) for reducing significantly the number of forward model simulations required by derivative-free optimization methods; (ii) developing a general-purpose framework and stand-alone software for solving the inverse radiation transport problem by applying a new “predictive modeling” methodology (predictive modeling of coupled multi-physics systems, PM_CMPS) which enables the fusing of experimental and computational information; and (iii) developing several benchmarks (for unscattered gamma rays) for demonstrating the quantification of non-Gaussian features (e.g., skewness and kurtosis, which characterize asymmetries and long tails) of response distributions by deterministically and efficiently propagating parameter uncertainties (covariances and higher-order moments, where available) using high-order sensitivities computed by the recently developed comprehensive adjoint sensitivity analysis methodology (C-ASAM). With regard to (i), application of PCE, the most significant accomplishment of this project was an implementation of PCE into INVERSE that significantly reduced computation time for the DiffeRential Evolution Adaptive Metropolis (DREAM) and Differential Evolution (DE) methods. For inverse transport problems with measurements of neutron leakage, neutron multiplication, and neutron-induced gamma-rays, the solution times for the DREAM and DE methods were reduced by factors of 30-300, reducing run times from hours to minutes while maintaining the same accuracy as the standard (non-PCE) DREAM and DE. Speedups were further improved by exploring sparse grid quadrature sets using the Toolkit for Adaptive Stochastic Modeling and Non-Intrusive ApproximatioN (Tasmanian) toolset. An initial exploration of sparse grids indicated that further speedups factors of 5-10 are obtainable. The implementation of PCE in INVERSE is not in a form that users can easily access. With regard to (ii), solving the inverse problem using a predictive modeling paradigm, the most significant accomplishment of this project were the derivation and implementation of adjoint-based second derivatives in neutron and photon transport theory. There are two codes that compute these derivatives. SENSPG computes them for uncollided gamma rays and SENSMG computes them for neutron leakage. SENSMG is open-source code available on github. Other significant accomplishments included a stand-alone code, MULTI-PRED, that implements the predictive modeling paradigm, along with a detailed manual. The code was implemented in the existing INVERSE code for inverse problems, but a head-to-head comparison of inverse methods was not achieved. We also derived and implemented the capability to compute sensitivities for multiplicity measurements into the SENSMG code, and this capability was used in a data assimilation application, but it was not used for solving inverse problems. With regard to (iii), developing benchmarks to demonstrate the importance of high-order sensitivity and uncertainty analysis, the most significant accomplishment of this project were two test problems that showed how important second-order sensitivities are.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS2001

Motions and Initial Conditions in Star-Forming Dense Cores

Under this grant in the past year we have pursued spectral-line observations of star-forming regions over size scales from 0.01 pc to 0.5 pc. Our main goal has been to measure the systematic and turbulent motions of condensing and collapsing gas. In this area, our results include (1) in 67 starless dense cores, some 19 show clear evidence of spatially extended inward motions, with typical line-of-sight inward speed 0.05-0.09 km s(sup -1) and with typical plane-of-the-sky extent 0.1-0.3 pc, (2) In some 40 nearby regions with embedded groups and clusters, we see extended infall asymmetry in lines of CS and HCO(+) clearly in 4 regions and less clearly in 4 others, (3) Using finer resolution (15 arcsec or 0.01-0.02 pc) and lines tracing higher density, we see spatial concentration of infall asymmetry near the protostars in NGC 1333 IRS 4A and B, L483, and L1251B, and with still finer resolution (2 arcsec or 0.003 pc or 600 AU) we detect inverse P Cyg profiles, indicating absorption of continuum emission from the protostellar envelope by infalling gas in NGC 1333 IRS 4A and 4B. Further, at high resolution we identify regions of stellar mass and low turbulence ("kernels") which are good candidates to become the next generation of stars in embedded clusters. In addition we have completed a survey for the OH Zeeman effect in absorption against nearby H II regions, indicating that the large-scale magnetic field may be nearly critical if it typically threads a flattened structure. We have also developed a model of spatially extended infall motions based on dissipation of turbulence in a magnetized, selfgravitating layer. In the following we describe some of these results in more detail.

Myers, Philip C.↗
NASA NTRS1994

Asymmetry parameters of the phase function for densely packed scattering grains

Spatial correlation among densely packed particles can substantially change their single-scattering properties, thus making questionable the applicability of the independent scattering approximation in calculations of light scattering by planetary regoliths. The same problem arises in geophysics in light scattering computations for snow, frosts, and bare soil. In this paper, we use a dense-medium light-scattering theory based on the introduction of the static structure factor to calculate asymmetry parameters of the phase function for densely packed particles with real refractive indices 1.31 and 1.66, approximating water ice and soil particles, respectively, and imaginary refractive indices 0, 0.01, and 0.3. For sparsely distributed, independently scattering grains, the calculated asymmetry parameters are always positive and always larger than those for densely packed particles. For densely packed grains, the asymmetry parameters may be negative but only for radius-to-wavelength ratios from about 0.1 to about 0.4. With decreasing particle size, the calculated asymmetry parameters tend to zero independently of the compaction state. In the geometrical optics regime, the asymmetry parameters for densely packed scatterers are positive and very close to those for independently scattering grains. These results may have important implications for remote sensing of the Earth and solid planetary surfaces. In particular, it is demonstrated that negative asymmetry parameters derived with some approximate multiple-scattering theories may be physically irrelevant and can be the result of using an inaccurate bidirectional reflection function combined with the ill-conditionally of the inverse scattering problem.

Mishchenko, Michael I.↗
NASA NTRS1974

Analytical tools and isolation of TOF events

Analytical tools are presented in two reports. The first is a probability analysis of the orbital distribution of events in relation to dust flux density observed in Pioneer 8 and 9 distributions. A distinction is drawn between asymmetries caused by random fluctuations and systematic variations, by calculating the probability of any particular asymmetry. The second article discusses particle trajectories for a repulsive force field. The force on a particle due to solar radiation pressure is directed along the particle's radius vector, from the sun, and is inversely proportional to its distance from the sun. Equations of motion which describe both solar radiation pressure and gravitational attraction are presented.

Wolf, H.↗
NASA NTRS2011

On the Accuracy of Double Scattering Approximation for Atmospheric Polarization Computations

Interpretation of multi-angle spectro-polarimetric data in remote sensing of atmospheric aerosols require fast and accurate methods of solving the vector radiative transfer equation (VRTE). The single and double scattering approximations could provide an analytical framework for the inversion algorithms and are relatively fast, however accuracy assessments of these approximations for the aerosol atmospheres in the atmospheric window channels have been missing. This paper provides such analysis for a vertically homogeneous aerosol atmosphere with weak and strong asymmetry of scattering. In both cases, the double scattering approximation gives a high accuracy result (relative error approximately 0.2%) only for the low optical path - 10(sup -2) As the error rapidly grows with optical thickness, a full VRTE solution is required for the practical remote sensing analysis. It is shown that the scattering anisotropy is not important at low optical thicknesses neither for reflected nor for transmitted polarization components of radiation.

Korkin, Sergey V.↗
DOE OSTI2023

High Spatial Melt Rate Variability Near the Totten Glacier Grounding Zone Explained by New Bathymetry Inversion

Totten Glacier is a fast-moving East Antarctic outlet with the potential for significant future sea-level contributions. We deployed four autonomous phase-sensitive radars on its ice shelf to monitor ice-ocean interactions near its grounding zone and made active source seismic observations to constrain gravity-derived bathymetry models. We observe an asymmetry in basal melting with mean melt rates along the grounding zone differing by up to 20 m/a. Our new bathymetry model reveals that this melt rate asymmetry coincides with an asymmetry in water column thickness and that the low-melting ice-shelf portion is shielded from the main cavity circulation. A 2-year record yields year-to-year melt rate variability of 7–9 m/a with no seasonal cycle. Our results highlight the key role of bathymetry near grounding lines for accurate modeling of ice-shelf melt, and the importance of sustained multi-year monitoring, especially at ice-shelf cavities where the dominant melt rate drivers vary primarily inter-annually.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Spin–orbit torques in structures with asymmetric dusting layers

Current-induced spin–orbit torques (SOTs) in heavy metal/ferromagnet heterostructures have emerged as an efficient method for magnetization switching with applications in nonvolatile magnetic memory and logic devices. However, experimental realization of SOT switching of perpendicular magnetization requires an additional inversion symmetry breaking, calling for modifications of the conventional SOT heterostructures. In this work, we study SOTs and deterministic switching of perpendicular magnetization by inserting different asymmetric dusting layers at the heavy metal/ferromagnet interface. Similar to the previous works with lateral structural asymmetry, we study the emergence of current-induced perpendicular effective magnetic fields (H z eff ). By examining three different material combinations of heavy metal/dusting layers (W/IrMn, Pt/IrMn, and W/Ta), we shed light on the origins of H z eff ; we show that H z eff is generically created in all the studied asymmetric structures, has a close correlation with the interfacial magnetic anisotropy, and is independent of the signs of spin Hall angles of the materials. Furthermore, we show that the induction of H z eff enables field-free deterministic SOT switching of perpendicular magnetization. Our results can be used in designing SOT heterostructures for practical applications in nonvolatile technologies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

1612 MHz OH maser emission from axisymmetric circumstellar envelopes - Miras

Radiative transfer calculations are performed using a modified form of the Sobolev approximation to determine the inversion of the 1612 MHz line of OH in axisymmetric circumstellar envelopes around Miras. The mass loss is assumed to be occurring in the form of a smooth wind. Line profiles and maps are presented for three models of varying degrees of asymmetry and for various orientations of the envelopes. It is concluded that the axisymmetric models can reproduce many of the features of observed profiles and maps which both the standard, spherically symmetric model and the discrete emission model cannot easily explain. The model profiles reproduce all of the general features seen in the line profiles of real sources.

Collison, Alan J.↗
NASA NTRS2019

Detection of Nonthermal Hard X-Ray Emission from the “Fermi Bubble” in an External Galaxy

We report new Chandra hard X-ray (>2 keV) and Jansky Very Large Array C-band observations of the nuclear super bubble of NGC 3079, an analog of the “Fermi bubble” in our Milky Way. We detect extended hard X-ray emission on the southwest (SW)side of the galactic nucleus with coherent multiwavelength features in radio, Hα, and soft X-ray. The hard X-ray feature has a cone shape with possibly a weak cap, forming a bubble-like structure with a diameter of∼1.1 kpc. A similar extended feature, however, is not detected on the northeast (NE)side, which is brighter in all other wavelengths such as radio, Hα, and soft X-ray. Scattered photons from the nuclear region or other nearby point-like X-ray bright sources, inverse Compton emission from cosmic-ray(CR)electrons via interaction with the cosmic microwave background, or any individually faint stellar X-ray source populations, cannot explain the extended hard X-ray emission on the SW side and the strongly NE/SW asymmetry. A synchrotron emission model, plus a thermal component accounting for the excess at∼1 keV, can well characterize the broadband radio/hard X-ray spectra. The broadband synchrotron spectra do not show any significant cutoff, and even possibly slightly flatten at higher energy. This rule out a loss-limited scenario in the acceleration of the CR electrons in or around this superbubble. As the first detection of kiloparsec-scale extended hard X-ray emission associated with a galactic nuclear superbubble, the spatial and spectral properties of the multiwavelength emissions indicate that the CR leptons responsible for the broadband synchrotron emission from the SW bubble must be accelerated in situ, instead of transported from the nuclear region of the galaxy.

Jiang-Tao Li↗