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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Dipole-field sums and Lorentz factors for orthorhombic lattices, and implications for polarizable molecules

A method for computing the Lorentz tensor components in single crystals via rapidly convergent sums of Bessels functions is developed using the relationship between dipole-field sums and the tensor components. The Lorentz factors for simple, body-centered, and base-centered orthorhombic lattices are computed using this method, and the derivative Lorentz factors for simple orthorhombic lattices are also determined. Both the Lorentz factors and their derivatives are shown to be very sensitive to a lattice structure. The equivalent of the Clausius-Mossotti relation for general orthorhombic lattices is derived using the Lorentz-factor formalism, and the permanent molecular dipole moment is related to crystal polarization for the case of a ferroelectric of polarizable point dipoles. It is concluded that the polarization enhancement due to self-polarization familiar from classical theory may actually be a reduction in consequences of negative Lorentz factors in one or two lattice directions for noncubic crystals.

Purvis, C. K.↗
DOE OSTI2015

CONSTRAINTS ON THE BULK LORENTZ FACTORS OF GRB X-RAY FLARES

X-ray flares were discovered in the afterglow phase of gamma-ray bursts (GRBs) by the Swift satellite a decade ago and are known as a canonical component in GRB X-ray afterglows. In this paper, we constrain the Lorentz factors of GRB X-ray flares using two different methods. For the first method, we estimate the lower limit on the bulk Lorentz factor with the flare duration and jet break time. In the second method, the upper limit on the Lorentz factor is derived by assuming that the X-ray flare jet has undergone saturated acceleration. We also re-estimate the initial Lorentz factor with GRB afterglow onsets, and find the coefficient of the theoretical Lorentz factor is 1.67 rather than the commonly used 2 for the interstellar medium (ISM) and 1.44 for the wind case. We find that the correlation between the limited Lorentz factor and the isotropic radiation energy of X-ray flares in the ISM case is more consistent with that of prompt emission than the wind case in a statistical sense. For a comparison, the lower limit on the Lorentz factor is statistically larger than the extrapolation from prompt bursts in the wind case. Our results indicate that X-ray flares and prompt bursts are produced by the same physical mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Lorentz factor for time-of-flight neutron Bragg and total scattering

We report the three fundamental origins of the Lorentz factor for neutron time-of-flight powder diffraction are revisited. A detailed derivation of the Lorentz factor is presented in the context of diffuse scattering modelling in reciprocal space when perfect periodicity is assumed, and the total scattering pattern is constructed in its discrete form – the factor in this case becomes 1/Q 2 (or d 2 ). Discussion is also presented with respect to practical data reduction where a vanadium measurement is usually taken as the normalization factor (to account for various factors such as detector efficiency), and it is shown that the existence of the Lorentz factor is independent of such a normalization process.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Evaluating the Bulk Lorentz Factors of Outflow Material: Lessons Learned from the Extremely Energetic Outburst GRB 160625B

GRB 160625B is an extremely bright outburst with well-monitored afterglow emission. The geometry-corrected energy is high, up to ∼5.2 × 10{sup 52} erg or even ∼8 × 10{sup 52} erg, rendering it the most energetic GRB prompt emission recorded so far. We analyzed the time-resolved spectra of the prompt emission and found that in some intervals there were likely thermal-radiation components and the high energy emission was characterized by significant cutoff. The bulk Lorentz factors of the outflow material are estimated accordingly. We found out that the Lorentz factors derived in the thermal-radiation model are consistent with the luminosity-Lorentz factor correlation found in other bursts, as well as in GRB 090902B for the time-resolved thermal-radiation components, while the spectral cutoff model yields much lower Lorentz factors that are in tension with the constraints set by the electron pair Compton scattering process. We then suggest that these spectral cutoffs are more likely related to the particle acceleration process and that one should be careful in estimating the Lorentz factors if the spectrum cuts at a rather low energy (e.g., ∼tens of MeV). The nature of the central engine has also been discussed, and a stellar-mass black hole is favored.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Measuring the bulk Lorentz factors of gamma-ray bursts with Fermi

Gamma-ray bursts (GRBs) are powered by ultrarelativistic jets. Usually a minimum value of the Lorentz factor of the relativistic bulk motion is obtained based on the argument that the observed high-energy photons (≫MeV) can escape without suffering from absorption due to pair production. The exact value, rather than a lower limit, of the Lorentz factor can be obtained if the spectral cutoff due to such absorption is detected. With the good spectral coverage of the Large Area Telescope (LAT) on Fermi, measurements of such a cutoff become possible, and two cases (GRB 090926A and GRB 100724B) have been reported to have high-energy cutoffs or breaks. We systematically search for such high-energy spectral cutoffs/breaks from the LAT and the Gamma-ray Burst Monitor (GBM) observations of the prompt emission of GRBs detected since 2011 August. Six more GRBs are found to have cutoff-like spectral features at energies of ∼10–500 MeV. Assuming that these cutoffs are caused by pair-production absorption within the source, the bulk Lorentz factors of these GRBs are obtained. We further find that the Lorentz factors are correlated with the isotropic gamma-ray luminosity of the bursts, indicating that more powerful GRB jets move faster.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

The history of GRB outflows: ejection lorentz factor and radiation location of X-ray flares

We present time-resolved spectral analysis of the steep decay segments of 29 bright X-ray flares of gamma-ray bursts (GRBs) observed with the Swift/X-ray telescope, and model their light curves and spectral index evolution behaviors with the curvature effect model. Our results show that the observed rapid flux decay and strong spectral index evolution with time can be well fitted with this model, and the derived characteristic timescales (t {sub c}) are in the range of 23 ∼ 264 s. Using an empirical relation between the peak luminosity and the Lorentz factor derived from the prompt gamma-rays, we estimate the Lorentz factors of the flares (Γ{sub X}). We obtain Γ{sub X} = 17 ∼ 87 with a median value of 52, which is smaller than the initial Lorentz factors of prompt gamma-ray fireballs. With the derived t {sub c} and Γ{sub X}, we constrain the radiating regions of 13 X-ray flares, yielding R {sub X} = (0.2 ∼ 1.1) × 10{sup 16} cm, which are smaller than the radii of the afterglow fireballs at the peak times of the flares. A long evolution feature from prompt gamma-ray phase to the X-ray epoch is found by incorporating our results with a sample of GRBs whose initial Lorentz factors are available in the literature, i.e., Γ∝[t{sub p}/(1+z)]{sup −0.69±0.06}. These results may shed light on the long-term evolution of GRB central engines.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

An MAD explanation for the correlation between bulk Lorentz factor and minimum variability time-scale

Here we offer an explanation for the anticorrelation between the minimum variability time-scale (MTS) in the prompt emission light curve of gamma-ray bursts (GRBs) and the estimated bulk Lorentz factor of these GRBs, in the context of a magnetically arrested disc (MAD) model. In particular, we show that previously derived limits on the maximum available energy per baryon in a Blandford–Znajek jet leads to a relationship between the characteristic MAD time-scale in GRBs and the maximum bulk Lorentz factor: t MAD ∝ Γ -6 , somewhat steeper than (although within the error bars of) the fitted relationship found in the GRB data. Similarly, the MAD model also naturally accounts for the observed anticorrelation between MTS and gamma-ray luminosity L in the GRB data, and we estimate the accretion rates of the GRB disc (given these luminosities) in the context of this model. Finally, both these correlations (MTS-Γ and MTS-L) are also observed in the Active Galactic Nuclei (AGN) data, and we discuss the implications of our results in the context of both GRB and blazar systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Lorentz factor determination for local electric fields in semiconductor devices utilizing hyper-thin dielectrics

The local electric field (the field that distorts, polarizes, and weakens polar molecular bonds in dielectrics) has been investigated for hyper-thin dielectrics. Hyper-thin dielectrics are currently required for advanced semiconductor devices. In the work presented, it is shown that the common practice of using a Lorentz factor of L = 1/3, to describe the local electric field in a dielectric layer, remains valid for hyper-thin dielectrics. However, at the very edge of device structures, a rise in the macroscopic/Maxwell electric field E{sub diel} occurs and this causes a sharp rise in the effective Lorentz factor L{sub eff}. At capacitor and transistor edges, L{sub eff} is found to increase to a value 2/3 < L{sub eff} < 1. The increase in L{sub eff} results in a local electric field, at device edge, that is 50%–100% greater than in the bulk of the dielectric. This increase in local electric field serves to weaken polar bonds thus making them more susceptible to breakage by standard Boltzmann and/or current-driven processes. This has important time-dependent dielectric breakdown (TDDB) implications for all electronic devices utilizing polar materials, including GaN devices that suffer from device-edge TDDB.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Measuring ambient densities and Lorentz factors of gamma-ray bursts from GeV and optical observations

The Fermi satellite detected GeV flashes from cosmological gamma-ray bursts (GRBs). In two GRBs, an optical counterpart of the GeV flash was detected. Such flashes are predicted by the model of a blast wave running into a medium loaded with copious e{sup ±} pairs. Here we examine a sample of seven bursts with the best GeV+optical data and further test the model. We find that the observed light curves are in agreement with the theoretical predictions, which allows us to measure three parameters for each burst: the Lorentz factor of the explosion, its isotropic kinetic energy, and the external density. With the possible exception of GRB 090510 (the only short burst in the sample), the ambient medium is consistent with a wind from a Wolf–Rayet progenitor. The wind density parameter A=ρr{sup 2} varies in the sample around 10{sup 11} g cm{sup −1}. The initial Lorentz factor of the blast wave varies from 200 to 540, and correlates with the burst luminosity. Radiative efficiency of the prompt emission varies between 0.1 and 0.8. For the two bursts with a detected optical flash, GRB 120711A and GRB 130427A, we also estimate the magnetization of the external blast wave. Remarkably, despite its small number of free parameters, the model reproduces the entire optical light curve of GRB 120711A (with its sharp peak, fast decay, plateau, and break) as well as the GeV data. The spectra of GeV flashes are predicted to extend above 0.1 TeV, where they can be detected by ground-based Cherenkov telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Gamma-ray bursts: Temporal scales and the bulk Lorentz factor

For a sample of Swift and Fermi gamma-ray bursts, we show that the minimum variability timescale and the spectral lag of the prompt emission is related to the bulk Lorentz factor in a complex manner. For small Γ's, the variability timescale exhibits a shallow (plateau) region. For large Γ's, the variability timescale declines steeply as a function of Γ (δT∝Γ{sup −4.05±0.64}). Evidence is also presented for an intriguing correlation between the peak times, t{sub p}, of the afterglow emission and the prompt emission variability timescale.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A Peculiar GRB 110731A: Lorentz Factor, Jet Composition, Central Engine, and Progenitor

The jet compositions, central engines, and progenitors of gamma-ray bursts (GRBs) remain open questions in GRB physics. Applying broadband observations, including GRB prompt emission and afterglow properties derived from Fermi and Swift data, as well as from Keck host-galaxy observations, we address these questions for the peculiar, bright GRB 110731A. By using the pair-opacity method, we derive Γ{sub 0} > 190 during the prompt emission phase. Alternatively, we derive Γ{sub 0} ≈ 580 and Γ{sub 0} ≈ 154 by invoking the early-afterglow phase within the homogeneous density and wind cases, respectively. On the other hand, nondetection of a thermal component in the spectra suggests that the prompt emission is likely powered by dissipation of a Poynting-flux-dominated jet leading to synchrotron radiation in an optically thin region. The nondetection of a jet break in the X-ray and optical bands allows us to place a lower limit on the jet opening angle θ {sub j} > 5.°5. Within a millisecond magnetar central engine scenario, we derive the period P {sub 0} and polar magnetic field strength B {sub p}, which have extreme (but still allowed) values. The moderately short observed duration (7.3 s) and relatively large redshift (z = 2.83) place the burst as a “rest-frame short” GRB, so the progenitor of the burst is subject to debate. Its relatively large f{sub eff,z} parameter (ratio of the 1 s peak flux of a pseudo-GRB and the background flux) and a large physical offset from a potential host galaxy suggest that the progenitor of GRB 110731A may be a compact-star merger.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Kinematics of Parsec-scale Jets of Gamma-Ray Blazars at 43 GHz within the VLBA-BU-BLAZAR Program

We analyze the parsec-scale jet kinematics from 2007 June to 2013 January of a sample of γ-ray bright blazars monitored roughly monthly with the Very Long Baseline Array at 43 GHz. In a total of 1929 images, we measure apparent speeds of 252 emission knots in 21 quasars, 12 BL Lacertae objects (BLLacs), and 3 radio galaxies, ranging from 0.02c to 78c; 21% of the knots are quasi-stationary. Approximately one-third of the moving knots execute non-ballistic motions, with the quasars exhibiting acceleration along the jet within 5 pc (projected) of the core, and knots in BLLacs tending to decelerate near the core. Using the apparent speeds of the components and the timescales of variability from their light curves, we derive the physical parameters of 120 superluminal knots, including variability Doppler factors, Lorentz factors, and viewing angles. We estimate the half-opening angle of each jet based on the projected opening angle and scatter of intrinsic viewing angles of knots. We determine characteristic values of the physical parameters for each jet and active galactic nucleus class based on the range of values obtained for individual features. We calculate the intrinsic brightness temperatures of the cores, T{sub b,int}{sup core}, at all epochs, finding that the radio galaxies usually maintain equipartition conditions in the cores, while ∼30% of T{sub b,int}{sup core} measurements in the quasars and BLLacs deviate from equipartition values by a factor >10. This probably occurs during transient events connected with active states. In the Appendix, we briefly describe the behavior of each blazar during the period analyzed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Optical flashes from internal pairs formed in gamma-ray burst afterglows

We develop a numerical formalism for calculating the distribution with energy of the (internal) pairs formed in a relativistic source from unscattered MeV–TeV photons. For gamma-ray burst (GRB) afterglows, this formalism is more suitable if the relativistic reverse shock that energizes the ejecta is the source of the GeV photons. The number of pairs formed is set by the source GeV output (calculated from the Fermi-LAT fluence), the unknown source Lorentz factor, and the unmeasured peak energy of the LAT spectral component. We show synchrotron and inverse-Compton light curves expected from pairs formed in the shocked medium and identify some criteria for testing a pair origin of GRB optical counterparts. Pairs formed in bright LAT afterglows with a Lorentz factor in the few hundreds may produce bright optical counterparts (R<10) lasting for up to one hundred seconds. The number of internal pairs formed from unscattered seed photons decreases very strongly with the source Lorentz factor, thus bright GRB optical counterparts cannot arise from internal pairs if the afterglow Lorentz factor is above several hundreds.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2012

Constraining the High-Energy Emission from Gamma-Ray Bursts with Fermi

We examine 288 GRBs detected by the Fermi Gamma-ray Space Telescope's Gamma-ray Burst Monitor (GBM) that fell within the field-of-view of Fermi's Large Area Telescope (LAT) during the first 2.5 years of observations, which showed no evidence for emission above 100 MeV. We report the photon flux upper limits in the 0.1-10 GeV range during the prompt emission phase as well as for fixed 30 s and 100 s integrations starting from the trigger time for each burst. We compare these limits with the fluxes that would be expected from extrapolations of spectral fits presented in the first GBM spectral catalog and infer that roughly half of the GBM-detected bursts either require spectral breaks between the GBM and LAT energy bands or have intrinsically steeper spectra above the peak of the nuF(sub v) spectra (E(sub pk)). In order to distinguish between these two scenarios, we perform joint GBM and LAT spectral fits to the 30 brightest GBM-detected bursts and find that a majority of these bursts are indeed softer above E(sub pk) than would be inferred from fitting the GBM data alone. Approximately 20% of this spectroscopic subsample show statistically significant evidence for a cut-off in their high-energy spectra, which if assumed to be due to gamma gamma attenuation, places limits on the maximum Lorentz factor associated with the relativistic outflow producing this emission. All of these latter bursts have maximum Lorentz factor estimates that are well below the minimum Lorentz factors calculated for LAT-detected GRBs, revealing a wide distribution in the bulk Lorentz factor of GRB outflows and indicating that LAT-detected bursts may represent the high end of this distribution.

Gehrels, Neil↗
DOE OSTI2021

Fermi acceleration in relativistic collisionless plasma shocks correlates with anisotropic energy gains

Collisionless shocks generated by two colliding relativistic electron-positron plasma shells are studied using particle-in-cell simulations. Shocks are mediated by the Weibel instability (WI), and the kinetic energy of the fastest accelerated particles is found to be anisotropically modified by WI-induced electric fields. Specifically, we show that all particles interacting with the shock bifurcate into two groups based on their final relativistic Lorentz factor γ: slow (γ < γ bf ) and fast (γ < γ bf ), where γ bf is the bifurcation Lorentz factor that was found to be approximately twice the initial (upstream) Lorentz factor γ0. We have found that the kinetic energies of the slow particles are equally affected by the longitudinal and transverse components of the shock electric field, whereas the fast particles are primarily accelerated by the transverse field component.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Analysis of Two Models for the Angular Structure of the Outflows Producing the Swift/XRT “Larger-angle Emission” of Gamma-Ray Bursts

The quasi-instantaneous emission from a relativistic surface endowed with a Lorentz factor that decreases away from the outflow symmetry axis can naturally explain the three phases observed by Swift X-Ray Telescope (XRT) in gamma-ray bursts (GRBs) and their afterglows (GRB tail, afterglow plateau, and postplateau) based only on the angular change of the relativistic Doppler boost across the outflow surface. We develop further the analytical formalism of the “larger-angle emission” model for the case of “n-exponential” outflows (where the Lorentz factor Γ dependence of the angular location θ is Γ ~ exp{-(θ/θ c ) n }), and compare its ability to account for the X-ray emission of XRT afterglows relative to that of “power-law” outflows (Γ ∼ θ −g ). Power-law outflows yield longer afterglow plateaus, followed by slower postplateau flux decays than n-exponential outflows, features which may be used in identifying which type of angular structure is at work in a given afterglow. Identifying the Γ(θ) angular structure that accommodates XRT light curves is slightly complicated by the fact that the afterglow X-ray light curve is also determined by how two characteristics of the comoving-frame emission spectrum (peak energy $E'_p$ and peak intensity $i'_p$) change with the angular location or, equivalently, with the Lorentz factor. Here, we assume power-law Γ dependences of those spectral characteristics and find that, unlike power-law outflows, n-exponential outflows cannot account for plateaus with a temporal dynamical range larger than 100 (2 dex in logarithmic space). To capture all the information contained in XRT afterglow measurements (0.3–10 keV unabsorbed flux and effective spectral slope), we calculate 0.3 and 10 keV light curves using a broken-power-law emission spectrum of peak energy and low- and high-energy slopes that are derived from the effective slope measured by XRT. This economical peak energy determination is found to be consistent with the results of more expensive spectral fits. The angular distributions of the Lorentz factor, comoving frame peak energy, and peak intensity (Γ(θ), $E'_p$(θ), $i'_p$(θ)) constrain the (yet-to-be determined) convolution of various features of the production of relativistic jets by solar-mass black holes and of their propagation through the progenitor/circumburst medium, while the $E'_p$(Γ) and $i'_p$(Γ) dependences may constrain the GRB dissipation mechanism and the GRB emission process.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Energy Spectrum and Mass Composition of Ultra-high-energy Cosmic Rays Originating from Relativistic Jets of Nearby Radio Galaxies

Relativistic jets of radio galaxies (RGs) are possible sources of ultra-high-energy cosmic rays (UHECRs). Recent studies combining relativistic hydrodynamic simulations with Monte Carlo particle transport have demonstrated that UHECRs can be accelerated to energies beyond 10 20 eV through shocks, turbulence, and relativistic shear in jet-induced flows of Fanaroff–Riley type RGs. The resulting time-asymptotic UHECR spectrum is well modeled by a double power law with an “extended” exponential cutoff, primarily shaped by relativistic shear acceleration. In this study, we adopt this novel source spectrum and simulate the propagation of UHECRs from nearby RGs using the CRPropa code. We focus on Virgo A (Vir A), Centaurus A (Cen A), Fornax A (For A), and Cygnus A (Cyg A), expected to be the most prominent UHECR sources among RGs. We then analyze the energy spectrum and mass composition of UHECRs arriving at Earth. We find that, due to the extended high-energy tail in the source spectrum, UHECRs from Vir A, which has a higher Lorentz factor, exhibit a higher flux at the highest energies and a lighter mass composition at Earth compared to those from Cen A and For A with lower Lorentz factors. Despite Cyg A having an even higher Lorentz factor, the large distance limits its contribution. With a small number of nearby prominent RGs, our findings suggest that if RGs are the major sources of UHECRs, the energy spectrum and mass composition of observed UHECRs would exhibit hemispheric differences between the Northern and Southern skies at the highest energies.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

Gamma-ray burst spectral breaks and source beaming

The principal discovery of the Compton Gamma-Ray Observatory (GRO) concerning gamma-ray bursts is that these sources are isotropic but with a comparative deficiency of fainter sources, suggesting that they are probably cosmological in origin. If they are at such large distances from Earth then they are extremely luminous and compact. A consequence of this is that two-photon pair production attenuation of the gamma-ray continuum cannot be avoided unless the source radiation is substantially beamed. Most sources do not display gamma-ray turnovers although a few gamma-ray bursts (GRB) detected by GRO exhibit distinct spectral breaks in the MeV range. A derivation of the relationship defining of the degree of beaming in burst sources with spectral breaks due to gamma-gamma attenuation, as a function of source spectral index and break energy, is presented. It is found that sources at distances of approximately 1 Gpc must typically be beamed with bulk Lorentz factors of around 10(exp 3)-10(exp 4), indicating powerful bulk acceleration in bursts, although these Lorentz factors are reduced markedly for steep source spectra. Since the source spectra are not strongly Comptonized, such beaming will blueshift the gamma-gamma attenuation breaks to energies much higher than 1 MeV; an absolute lower bound to the source bulk Lorentz factor is determined from this additional constraint. This blueshifting suggests that those sources with MeV breaks may not be cosmological, or that their breaks are produced by a mechanism that dominates gamma-gamma attenuation at these energies.

Baring, Matthew G.↗