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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Kinetic beaming in radiative relativistic magnetic reconnection: a mechanism for rapid gamma-ray flares in jets

ABSTRACT Rapid gamma-ray flares pose an astrophysical puzzle, requiring mechanisms both to accelerate energetic particles and to produce fast observed variability. These dual requirements may be satisfied by collisionless relativistic magnetic reconnection. On the one hand, relativistic reconnection can energize gamma-ray emitting electrons. On the other hand, as previous kinetic simulations have shown, the reconnection acceleration mechanism preferentially focuses high energy particles – and their emitted photons – into beams, which may create rapid blips in flux as they cross a telescope’s line of sight. Using a series of 2D pair-plasma particle-in-cell simulations, we explicitly demonstrate the critical role played by radiative (specifically inverse Compton) cooling in mediating the observable signatures of this ‘kinetic beaming’ effect. Only in our efficiently cooled simulations do we measure kinetic beaming beyond one light crossing time of the reconnection layer. We find a correlation between the cooling strength and the photon energy range across which persistent kinetic beaming occurs: stronger cooling coincides with a wider range of beamed photon energies. We also apply our results to rapid gamma-ray flares in flat-spectrum radio quasars, suggesting that a paradigm of radiatively efficient kinetic beaming constrains relevant emission models. In particular, beaming-produced variability may be more easily realized in two-zone (e.g. spine-sheath) set-ups, with Compton seed photons originating in the jet itself, rather than in one-zone external Compton scenarios.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2003

Improving the Accuracy of Lunar Laser Ranging Tests of Gravitational Theory: Modeling and Future Directions

Accurate analysis of precision ranges to the Moon have provided several tests of gravitational theory: the equivalence principle, geodetic precession, PPN parameters beta and gamma, and the constancy of the gravitational constant G. Other possible tests include the inverse square law at 20,000 km length scales and the PPN parameter 1. The uncertainties of these tests have decreased as data accuracies have improved and data time span has lengthened. We are exploring the modeling improvements necessary to proceed from cm to mm range accuracies. Looking to future exploration, what characteristics are desired for the next generation of ranging devices, what fundamental questions can be investigated, and what are the challenges for modeling and data analysis?

Williams, James G.↗
DOE OSTI2026

Stable and tunable MeV $$\gamma$$-ray generation via dual-laser inverse Thomson scattering from a laser-plasma accelerator

Abstract Inverse Thomson scattering from laser-plasma accelerators offers a pathway to compact, tunable MeV $$\gamma$$ -ray sources for reduced-dose radiography and enhanced performance in nuclear resonance fluorescence (NRF)-based isotope identification. However, photon yield and spectral quality are often limited by constraints on interaction geometry and scatter-laser tunability. Here we demonstrate a MeV $$\gamma$$ -ray source based on a dual-laser inverse Thomson scattering configuration driven by a 100-TW laser-plasma accelerator. Electron beams tunable from 122 to 204 MeV with $$<5$$ mrad divergence and $$<1$$ mrad pointing stability generate $$\gamma$$ rays with peak energies from 276 keV to 1.2 MeV and yields up to $$2\times 10^{7}$$ photons per shot. By independently controlling the interaction position and the scatter-pulse duration, we experimentally match the scatter pulse to the walk-off-limited interaction length. Extending the scatter pulse to 200 fs increases photon production by approximately $$15\%$$ while maintaining operation in the linear Thomson regime, thereby preserving narrow spectral bandwidth and controlled radiation divergence. Radiographic characterization demonstrates MeV-level penetration and $$\approx 0.1$$ mm spatial resolution, while stable operation is sustained over multi-hour timescales across multiple days. These results show that interaction-length optimization provides a scalable strategy for improving photon yield, spectral control, and operational stability in compact laser-plasma-accelerator-driven $$\gamma$$ -ray sources.

Tsai, Hai-En↗
NASA NTRS1998

New Mission Concept Study: Energetic X-Ray Imaging Survey Telescope (EXIST)

This Report summarizes the activity carried out under the New Mission Concept (NMC) study for a mission to conduct a sensitive all-sky imaging survey in the hard x-ray (HX) band (approximately 10-600 keV). The Energetic X-ray Imaging Survey Telescope (EXIST) mission was originally proposed for this NMC study and was then subsequently proposed for a MIDEX mission as part of this study effort. Development of the EXIST (and related) concepts continues for a future flight proposal. The hard x-ray band (approximately 10-600 keV) is nearly the final band of the astronomical spectrum still without a sensitive imaging all-sky survey. This is despite the enormous potential of this band to address a wide range of fundamental and timely objectives - from the origin and physical mechanisms of cosmological gamma-ray bursts (GRBs) to the processes on strongly magnetic neutron stars that produce soft gamma-repeaters and bursting pulsars; from the study of active galactic nuclei (AGN) and quasars to the origin and evolution of the hard x-ray diffuse background; from the nature and number of black holes and neutron stars and the accretion processes onto them to the extreme non-thermal flares of normal stars; and from searches for expected diffuse (but relatively compact) nuclear line (Ti-44) emission in uncatalogued supernova remnants to diffuse non-thermal inverse Compton emission from galaxy clusters. A high sensitivity all-sky survey mission in the hard x-ray band, with imaging to both address source confusion and time-variable background radiations, is very much needed.

Source record↗
NASA NTRS2019

The Orbital Variation of Non-Thermal X-Ray Emission from eta Carinae

The collision of strong stellar winds in massive binary systems creates powerful shocks,which accelerates a small amount of particles to relativistic energies at the shock interface.This process is important in fundamental astrophysics in two ways;i) some particles may contribute to cosmic-rays observed around the Earth, whose origin is not well known, andii) it provides a good laboratory for particle acceleration physics as the shock occurs steadily in a predictable environment.Some relativistic particles collide with stellar photons or ambient material near the binary systemand emit non-thermal X-rays and gamma-rays, which are good probes of particle acceleration.This emission had been searched for decades but not found convincingly without sensitive high-energy telescopes.The NuSTAR telescope observed the enigmatic supermassive binary system eta Carinae multiple times after 2014 and found conclusive evidence of non-thermal emission from the star in the extremely hard X-ray band.This emission is prominent between 20-50 keV, below which thermal emission from shock colliding plasma dominates.It is relatively stable throughout the binary orbit, but it disappears near periastron when the wind colliding activity shuts off.This variation indicates that the non-thermal X-ray emission originates from the head-on wind-wind collision.The flat spectrum is consistent with inverse-Compton of stellar UV photons by accelerated electrons.The spectrum smoothly connects to a gamma-ray spectrum of a Fermi source detected around eta Carinae,suggesting that acceleration occurs up to the GeV energy.This result provide the strongest evidence so far that particle acceleration occurs at the wind colliding shock of a massive colliding wind binary system.

Hamaguchi, Kenji↗
NASA NTRS1999

Multiwavelength Observations of Mkn 501 During the 1997 High State

During the observation period 1977, the close Blazar Mkn 501 showed extremely strong emission and high variability. We examine multiwavelength aspects of this event using Radio optical, soft and hard X-ray and TeV data. We concentrate on the medium-timescale variability of the broadband spectra averaged over 1-week intervals. We confirm the previously found correlation between soft and hard X-ray emission and the at TeV energies while the source shows only minor variability at radio and optical wavelengths. The non-linear correlation between hard X-ray and TeV fluxes is consistent with a simple analytic estimate based on an SSC model in which Klein-Nishina effects are important for the highest-energy electrons in the jet and flux; variations are caused by variations of the electron density and/or the spectral index of the electron injection spectrum. The time-averaged spectra are fitted with an SSC dominated leptonic jet model using the full Klein-Nishina cross section and following the self-consistent evolution of relativistic particles along the jet accounting for gamma gamma absorption and pair production within the source as well as due to the intergalactic infrared red background radiation. The contribution from external inverse-Compton scattering is tightly constrained by the low maximum EGRET flux and found co be negligible.

Petry, D.↗
DOE OSTI2023

Dark matter halo mass functions and density profiles from mass and energy cascade

Abstract Halo abundance and structure play a central role for modeling structure formation and evolution. Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of −4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time $$\tau _g$$ τ g . First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with $$\tau _g\propto m_h^{-\lambda }$$ τ g ∝ m h - λ , where $$m_h$$ m h is the halo mass and $$\lambda$$ λ is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different $$\lambda$$ λ for haloes below and above a critical mass scale $$m_h^*$$ m h ∗ , i.e. a double- $$\lambda$$ λ halo mass function. Second, a double- $$\gamma$$ γ density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time $$\tau _g \propto \Phi (r)^{-1} \propto r^{-\gamma }$$ τ g ∝ Φ ( r ) - 1 ∝ r - γ , where $$\Phi$$ Φ is the gravitational potential and r is the particle distance to halo center. Theory predicts $$\gamma =2/3$$ γ = 2 / 3 that leads to a cuspy density profile with an inner slope of −4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the $$-4/3$$ - 4 / 3 scaling law ( $$\rho _h \propto r^{-4/3}$$ ρ h ∝ r - 4 / 3 ) on small scales. Theory predicts the halo number density scales with halo mass as $$\propto m_h^{-1.9}$$ ∝ m h - 1.9 , while the halo mass density scales as $$\propto m_h^{4/9}$$ ∝ m h 4 / 9 . Results were compared against the Illustris simulations. This new perspective provides a theory for nearly universal halo mass functions and density profiles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

On the gamma-ray emission from the core of the Sagittarius dwarf galaxy

ABSTRACT We use Fermi-LAT data to analyse the faint gamma-ray source located at the centre of the Sagittarius (Sgr) dwarf spheroidal galaxy. In the 4FGL-DR3 catalogue, this source is associated with the globular cluster, M54. We investigate the spectral energy distribution and spatial extension of this source, with the goal of testing two hypotheses: (1) the emission is due to millisecond pulsars within M54, or (2) the emission is due to annihilating dark matter from the Sgr halo. For the pulsar interpretation, we consider a two-component model which describes both the lower-energy magnetospheric emission and possible high-energy emission arising from inverse Compton scattering. We find that this source has a point-like morphology at low energies, consistent with magnetospheric emission, and find no evidence for a higher-energy component. For the dark matter interpretation, we find the signal favours a dark matter mass of mχ = 29.6 ± 5.8 GeV and an annihilation cross section of $\sigma v = (2.1 \pm 0.59) \times 10^{-26} \, \text{cm}^3$ s−1 for the $b \bar{b}$ channel (or mχ = 8.3 ± 3.8 GeV and $\sigma v = (0.90 \pm 0.25) \times 10^{-26} \, \text{cm}^3$ s−1 for the τ+τ− channel), when adopting a J-factor of $J=10^{19.6} \, \text{GeV}^2 \, \text{cm}^{-5}$. This parameter space is consistent with gamma-ray constraints from other dwarf galaxies and with dark matter interpretations of the Galactic Centre Gamma-Ray Excess.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Clustering and Cliques in Preferential Attachment Random Graphs with Edge Insertion

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability 1 – f(t). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation –$\gamma$, where $\gamma$ $\in$ [0, 1). Finally, we also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Gamma guidance of trajectories for coplanar, aeroassisted orbital transfer

The optimization and guidance of trajectories for coplaner, aeroassisted orbital transfer (AOT) from high Earth orbit (HEO) to low Earth orbit (LEO) are examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that at most three impulses are employed: one at HEO exit, one at atmospheric exit, and one at LEO entry. It is also assumed that, during the atmospheric pass, the trajectory is controlled via the lift coefficient. The presence of upper and lower bounds on the lift coefficient is considered. First, optimal trajectories are computed by minimizing the total velocity impulse (hence, the propellant consumption) required for AOT transfer. The sequential gradient-restoration algorithm (SGRA) is used for optimal control problems. The optimal trajectory is shown to include two branches: a relatively short descending flight branch (branch 1) and a long ascending flight branch (branch 2). Next, attention is focused on guidance trajectories capable of approximating the optimal trajectories in real time, while retaining the essential characteristics of simplicity, ease of implementation, and reliability. For the atmospheric pass, a feedback control scheme is employed and the lift coefficient is adjusted according to a two-stage gamma guidance law. Further improvements are possible via a modified gamma guidance which is more stable with respect to dispersion effects arising from navigation errors, variations of the atmospheric density, and uncertainties in the aerodynamic coefficients than gamma guidance trajectory. A byproduct of the studies on dispersion effects is the following design concept. For coplaner aeroassisted orbital transfer, the lift-range-to-weight ratio appears to play a more important role than the lift-to-drag ratio. This is because the lift-range-to-weight ratio controls mainly the minimum altitude (hence, the peak heating rate) of the guidance trajectory; on the other hand, the lift-to-drag ratio controls mainly the duration of the atmospheric pass of the guidance trajectory.

Miele, A.↗
NASA NTRS2016

CGRO/BATSE Data Support the New Paradigm For GRB Prompt Emission and the New L-i(nTh)-E-peak,i(nTh,rest) Relation

The paradigm for gamma-ray burst (GRB) prompt emission is changing. Since early in the Compton Gamma RayObservatory (CGRO) era, the empirical Band function has been considered a good description of the keV-MeV-gamma-ray prompt emission spectra despite the fact that its shape was very often inconsistent with the theoretical predictions, especially those expected in pure synchrotron emission scenarios. We have recently established a new observational model analyzing data of the NASA Fermi Gamma-ray Space Telescope. In this model, GRB prompt emission would be a combination of three main emission components: (i) a thermal-like component that we have interpreted so far as emission from the jet photosphere, (ii) a non-thermal component that we have interpreted so far as either synchrotron radiation from the propagating and accelerated charged particles within the jet or reprocessed jet photospheric emission, and (iii) an additional non-thermal (cutoff) power law (PL) extending from low to high energies in gamma-rays and most likely of inverse Compton origin. In this article we reanalyze some of the bright GRBs, namely GRBs 941017, 970111, and 990123, observed with the Burst And Transient Source Experiment (BATSE) on board CGRO with the new model. We conclude that BATSE data for these three GRBs are fully consistent with the recent results obtained with Fermi: some bright BATSE GRBs exhibit three separate components during the prompt phase with similar spectral parameters as those reported from Fermi data. In addition, the analysis of the BATSE GRBs with the new prompt emission model results in a relation between the time-resolved energy flux of the non-thermal component, F(in)(Th), and its corresponding nuFnu spectral peak energy,Epeak,inTh (i.e., FinThEpeak,inTh ), which has a similar index when fitted to a PL as the one initially derived from Fermi data. For GRBs with known redshifts (z) this results in a possible universal relation between the luminosity of the non-thermal component, LinTh, and its corresponding nuFnu spectral peak energy in the rest frame, Epeak,iNT,rest (i.e.,LinThEpeak,iNT,rest). We estimated the redshifts of GRBs 941017 and 970111 using GRB 990123 with z = 1.61as a reference. The estimated redshift for GRB 941017 is typical for long GRBs and the estimated redshift for GRB970111 is right in the range of the expected values for this burst.

acceleration of particles – black hole physics â↗
NASA NTRS1989

The probability of detecting absorption features in gamma-ray burst spectra

It has recently been suggested that several mechanisms for the primary release of energy in gamma-ray bursts may result in the excitation of magnetospheric plasma oscillations (MPO) above the polar cap of a neutron star. The basic MPO idea is refined by determining the soft photon source (which damps the particle motion via inverse Compton scattering interactions) self-consistently by means of a Monte Carlo simulation for the deposition of back-scattered gamma-ray energy below the stellar photosphere. The observed fraction of bursts displaying low-energy absorption features may be understood in the context of a model wherein the overall spectrum changes with inclination angle due to the superposition of several components with different angular distributions. GRB spectra should display these cyclotron lines about 18 percent of the time, which is consistent with the KONUS and Ginga sets of data.

Melia, F.↗
DOE OSTI2021

Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using a cylindrical-harmonics expansion

Inertial confinement fusion capsule implosions produce neutron, gamma-ray, and x-ray emission, which are recorded by a variety of detectors, both time integrated and time resolved, to determine the performance of the implosion. Further, two-dimensional emission images from multiple directions can now be combined to infer three-dimensional structures in the implosion, such as the distribution of thermonuclear fuel density, carbon ablator, and impurities. Because of the cost and complexity of the imaging systems, however, only a few measurements can be made, so reconstructions of the source must be made from a limited number of views. Here, a cylindrical-harmonics decomposition technique to reconstruct the three-dimensional object from two views in the same symmetry plane is presented. In the limit of zero order, this method recovers the Abel inversion method. The detailed algorithms used for this characterization and the resulting reconstructed neutron source from an experiment collected at the National Ignition Facility are presented.

47 OTHER INSTRUMENTATION↗
NASA NTRS1993

Diffuse gamma-ray emission from pulsars in the Large Magellanic Cloud

We investigate the contribution of pulsars to the diffuse gamma-ray emission from the LMC. The pulsar birth rate in the LMC is a factor of about 10 lower than that of the Galaxy and the distance to pulsars in the LMC is about 5-10 times larger than to Galactic pulsars. The resulting total integrated photon flux from LMC pulsars is thus reduced by a factor of about 100 to 1000. However, the surface brightness is not reduced by the same amount because of the much smaller angular extent of the LMC in comparison to the diffuse glow from the Galactic plane. We show that gamma-ray emission due to pulsars born in the LMC could produce gamma-ray fluxes that are larger than the inverse Compton component from relativistic cosmic-ray electrons and a significant fraction of the extragalactic isotropic background or the diffuse Galactic background in that direction. The diffuse pulsar glow above 100 MeV should therefore be included in models of high-energy emission from the LMC. For a gamma-ray beaming fraction of order unity the detected emissions from the LMC constrain the pulsar birth rate to less than one per 50 yr. This limit is about one order of magnitude above the supernova rate inferred from the historic record or from the star-formation rate.

Hartmann, Dieter H.↗
NASA NTRS1983

The Spectral Properties of Gamma-ray Bursts: a Review of Recent Development

Developments in the spectroscopy of gamma ray bursts (GRB) are reviewed. The general question of the validity of the spectral results, particularly with regard to features in the spectrum, is discussed. Confirmations of these spectral features are summarized. Results from the KONUS experiments on Venera 13 and 14 are reviewed. The status of models of the continuum spectrum is summarized. A number of different radiation mechanisms appear capable of fitting the data. These include thermal bremsstrahlung, thermal synchrotron and inverse Compton. Rapid variability of the spectra shape on time scales 76] 0.25 sec. was reported. The characteristic energy of the spectrum was observed to vary over nearly an order of magnitude during individual events. A strong correlation between spectral hardness and luminosity was found. Low-energy (50 keV) absorption features and high-energy (400 keV) emission features continue to appear in GRB spectra. Understanding the origin of these lines in the context of the existing continuum models remains a difficult problem.

Teegarden, B. J.↗
NASA NTRS2013

mBAND Analysis of Early and Late Damages in the Chromosome of Human Lymphocytes after Exposures to Gamma Rays and Fe Ions

Stable type chromosome aberrations that survive multiple generations of cell division include translocation and inversions. An efficient method to detect an inversion is multi-color banding fluorescent in situ hybridization (mBAND) which allows identification of both inter- and intrachromosome aberrations simultaneously. Post irradiation, chromosome aberrations may also arise after multiple cell divisions as a result of genomic instability. To investigate the stable or late-arising chromosome aberrations induced after radiation exposure, we exposed human lymphocytes to gamma rays and Fe ions ex vivo, and cultured the cells for multiple generations. Chromosome aberrations were analyzed in cells collected at first mitosis and at several time intervals during the culture period post irradiation. With gamma irradiation, about half of the damages observed at first mitosis remained after 7 day- and 14 day- culture, suggesting the transmissibility of damages to the surviving progeny. At the doses that produced similar frequencies of gamma-induced chromosome aberrations as observed at first mitosis, a significantly lower yield of aberrations remained at the same population doublings after Fe ion exposure. At these equitoxic doses, more complex type aberrations were observed for Fe ions, indicating that Fe ion-induced initial chromosome damages are more severe and may lead to cell death. Detailed analysis of breaks participating in total chromosome exchanges within the first cell cycle post irradiation revealed a common hotspot located in the 3p21 region, which is a known fragile site corresponding to the band 6 in the mBand analysis. The breakpoint distribution in chromosomes collected at 7 days, but not at 14 days, post irradiation appeared similar to the distribution in cells collected within the first cell cycle post irradiation. The breakpoint distribution for human lymphocytes after radiation exposure was different from the previously published distribution for human mammary epithelial cells, indicating that interphase chromatin folding structures play a role in the distribution of radiation-induced breaks.

Sunagawa, Mayumi↗
NASA NTRS1992

Radiative instabilities and 1000 second fluctuations in astrophysical masers

A stability analysis for small (linear) perturbations is presented for the radiation in astrophysical masers treated in the usual, linear maser approximation. Instabilities that oscillate with a period of about L/c, where L is the length of the maser are found. They occur (1) when the maser is partly but not heavily saturated, (2) when the decay rate Gamma for the molecular states is near c/L, and (3) when the product of the brightness temperature T sub 0 of the incident radiation and the angle for the beaming is less than a critical value that depends upon the particular masing transition. A fourth parameter, the fractional inversion in the pumping multiplied by (T sub 0/frequency), determines the importance of spontaneous emission which can eliminate the instabilities. These instabilities are a likely cause for the fluctuations in the radiation from the 18 cm OH masers that have been reported to occur on time scales as short as 1000 s. The calculations are applicable to other types of astrophysical masers as well, and suggest that spontaneous emission will prevent similar instabilities in the H2O and SiO masers.

Scappaticci, Gerardo A.↗
NASA NTRS1994

Convective solar nebula

Analyzing turbulent flows with rotation, Dubrulle and Valdettaro have concluded that some new effects come into play and may modify the standard picture we have concerning turbulence. In that respect the value of the Rossby number is of crucial importance since it will determine the transition between regimes where rotation is or is not important. With rotation there will be a tendency to constrain the motion to the plane perpendicular to the rotation axis and as a consequence the horizontal scale will increase as compared to the longitudinal one, which means that the turnover time in this direction will increase. The net effect is that the energy cascade down process is hindered by rotation. As a matter of fact, when rotation is present one observes two cascades: an enstrophy (vorticity) cascade from large scales to small scales; and an inverse energy cascade from small scales to large scales. Since the first process is not efficient on transporting energy to the dissipation range, what we see is energy storage in the large structures at the expense of the small structures. This kind of behavior has been confirmed experimentally. For a very large gamma we obtain, in the inertial range, a spectrum of k(exp -3) instead of the usual Kilmogorov's k(exp -5/3) spectrum. In reality, when rotation is dominant, energy gets stored in inertial waves that propagate it essentially in the longitudinal direction. In that case, we can no longer assign just one viscosity to the fluid and, what is most important, the concept of viscosity loses its meaning since we no longer have local transport of energy. Such results, however, were derived considering a hot disk, in which opacity is mainly given by electron scattering. In the present work we have applied the formulation developed in the previous work for the description of the viscous-stage solar nebula.

Meirellesfilho, C.↗