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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 OSTI2012

CONSTRAINING THE BULK LORENTZ FACTOR OF GAMMA-RAY BURST OUTFLOW IN THE MAGNETIC-DOMINATED JET MODEL

Recent observations by the Fermi-LAT showed that there are delayed arrivals of GeV photons relative to the onset of MeV photons in some gamma-ray bursts (GRBs). In order to avoid a large optical depth, the minimal value of the Lorentz factor has been estimated to be higher than 1000 in some of the brightest bursts. In this paper, we present a detailed calculation of the time delay between the MeV and GeV photons in the framework of the magnetic-dominated jet model. We find that the time delay strongly depends on the saturated bulk Lorentz factor of the jet. Inspired by this fact, we use this model to calculate the Lorentz factors of the four brightest Fermi bursts. The results indicate that the Lorentz factors are much smaller than those obtained from the 'single-zone' scenario. The short burst GRB 090510 has a minimal Lorentz factor of 385, while the three long bursts, GRB 080916c, GRB 090902b, and GRB 090926, have almost the same Lorentz factors with an average value near 260. Another interesting result is that, for long bursts, GeV photons are emitted after the bulk Lorentz factor saturates. For the short GRB, however, MeV and GeV photons are emitted at the same phase, i.e., either in the expansion phase or in the coasting phase.

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 OSTI2015

CONSTRAINING THE LORENTZ FACTOR OF A RELATIVISTIC SOURCE FROM ITS THERMAL EMISSION

We propose a direct and simple method to measure the Lorentz factor of relativistically expanding objects such as gamma-ray bursts (GRBs). Only three measurements, i.e., the thermal component of the emission, the distance, and the variable timescale of the light curve, are used. When the uncertainties are considered, we will obtain a lower limit of the Lorentz factor instead. We apply this method to GRB 090618 and get a lower limit of 22 for the Lorentz factor. This method can be used for any relativistically moving objects, such as GRBs and soft gamma-ray repeaters.

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 OSTI2014

High energy emission of GRB 130821A: Constraining the density profile of the circum-burst medium as well as the initial Lorentz factor of the outflow

GRB 130821A was detected by Fermi-GBM/LAT, Konus-WIND, SPI-ACS/INTEGRAL, RHESSI and Mars Odyssey-HEND. Although the data of GRB 130821A are very limited, we show in this work that the high energy γ-ray emission (i.e., above 100 MeV) alone imposes tight constraint on the density profile of the circum-burst medium as well as the initial Lorentz factor of the outflow. The temporal behavior of the high energy γ-ray emission is consistent with the forward shock synchrotron radiation model, and the circum-burst medium likely has a constant-density profile. The Lorentz factor is about a few hundred, similar to other bright GRBs.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2012

LORENTZ-FACTOR-ISOTROPIC-LUMINOSITY/ENERGY CORRELATIONS OF GAMMA-RAY BURSTS AND THEIR INTERPRETATION

The bulk Lorentz factor of the gamma-ray burst (GRB) ejecta ({Gamma}{sub 0}) is a key parameter to understanding GRB physics. Liang et al. have discovered a correlation between {Gamma}{sub 0} and isotropic {gamma}-ray energy: {Gamma}{sub 0}{proportional_to}E{sup 0.25}{sub {gamma},iso,52}. By including more GRBs with updated data and more methods to derive {Gamma}{sub 0}, we confirm this correlation and obtain {Gamma}{sub 0} {approx_equal} 91E{sup 0.29}{sub {gamma},iso,52}. Evaluating the mean isotropic {gamma}-ray luminosities L{sub {gamma},iso} of the GRBs in the same sample, we discover an even tighter correlation {Gamma}{sub 0} {approx_equal} 249L{sup 0.30}{sub {gamma},iso,52}. We propose an interpretation to this later correlation. Invoking a neutrino-cooled hyperaccretion disk around a stellar mass black hole as the central engine of GRBs, we derive jet luminosity powered by neutrino annihilation and baryon loading from a neutrino-driven wind. Applying beaming correction, we finally derive {Gamma}{sub 0}{proportional_to}L{sup 0.22}{sub {gamma},iso}, which is consistent with the data. This suggests that the central engine of long GRBs is likely a stellar mass black hole surrounded by a hyper-accreting disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Estimates for Lorentz factors of gamma-ray bursts from early optical afterglow observations

The peak time of optical afterglow may be used as a proxy to constrain the Lorentz factor Γ of the gamma-ray burst (GRB) ejecta. We revisit this method by including bursts with optical observations that started when the afterglow flux was already decaying; these bursts can provide useful lower limits on Γ. Combining all analyzed bursts in our sample, we find that the previously reported correlation between Γ and the burst luminosity L {sub γ} does not hold. However, the data clearly show a lower bound Γ{sub min} that increases with L {sub γ}. We suggest an explanation for this feature: explosions with large jet luminosities and Γ < Γ{sub min} suffer strong adiabatic cooling before their radiation is released at the photosphere; they produce weak bursts, barely detectable with present instruments. To test this explanation, we examine the effect of adiabatic cooling on the GRB location in the L {sub γ} – Γ plane using a Monte Carlo simulation of the GRB population. Our results predict detectable on-axis 'orphan' afterglows. We also derive upper limits on the density of the ambient medium that decelerates the explosion ejecta. We find that the density in many cases is smaller than expected for stellar winds from normal Wolf-Rayet progenitors. The burst progenitors may be peculiar massive stars with weaker winds, or there might exist a mechanism that reduces the stellar wind a few years before the explosion.

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 OSTI2014

CONSTRAINTS ON THE MINIMUM ELECTRON LORENTZ FACTOR AND MATTER CONTENT OF JETS FOR A SAMPLE OF BRIGHT FERMI BLAZARS

We fit (quasi-)simultaneous multi-waveband spectral energy distributions for a sample of low-synchrotron-peaked (LSP) blazars with a one-zone leptonic model. The seed photons that predominantly come from the broad line region (BLR) and infrared (IR) molecular torus are considered in the context of an external Compton process. We find that modeling with IR seed photons is systematically better than that with BLR photons based on a χ{sup 2} test, which suggests that γ-ray-emitting regions are most likely found outside the BLR. The minimum electron Lorentz factor, γ{sub min}, is constrained from the modeling of these LSP blazars with good soft X-ray data (ranging from 5 to 160 with a median value of 55), which plays a key role in jet power estimation. Assuming a one-to-one ratio of protons to electrons, we find that the jet power for LSP blazars is systematically higher than that of FR II radio galaxies at a 151 MHz radio luminosity, L {sub 151} {sub MHz} even though FR IIs are regarded as the same as LSP blazars in a unification scheme except at the jet viewing angle. A possible reason for this is that there are some e {sup ±} pairs in the jets of these blazars. If this is the case, we find that the number density of e {sup ±} pairs should be several times higher than that of e {sup –}-p pairs by assuming the jet power is the same for LSP blazars and FR IIs at the given L {sub 151} {sub MHz}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

GRB 090510: A DISGUISED SHORT GAMMA-RAY BURST WITH THE HIGHEST LORENTZ FACTOR AND CIRCUMBURST MEDIUM

GRB 090510, observed by both Fermi and AGILE satellites, is the first bright short-hard gamma-ray burst (GRB) with an emission from the keV up to the GeV energy range. Within the Fireshell model, we interpret the faint precursor in the light curve as the emission at the transparency of the expanding e {sup +} e {sup -} plasma: the Proper-GRB. From the observed isotropic energy, we assume a total plasma energy E{sup tot}{sub e{sup +}e{sup -}}=(1.10{+-}0.06) Multiplication-Sign 10{sup 53} erg and derive a Baryon load B = (1.45 {+-} 0.28) Multiplication-Sign 10{sup -3} and a Lorentz factor at transparency {Gamma}{sub tr} = (6.7 {+-} 1.6) Multiplication-Sign 10{sup 2}. The main emission {approx}0.4 s after the initial spike is interpreted as the extended afterglow, due to the interaction of the ultrarelativistic baryons with the CircumBurst Medium (CBM). Using the condition of fully radiative regime, we infer a CBM average spherically symmetric density of (n{sub CBM}) = (1.85 {+-} 0.14) Multiplication-Sign 10{sup 3} particles cm{sup -3}, one of the highest found in the Fireshell model. The value of the filling factor, 1.5 Multiplication-Sign 10{sup -10}{<=}R{<=}3.8 Multiplication-Sign 10{sup -8}, leads to the estimate of filaments with densities n{sub fil} = n{sub CBM}/R approx. (10{sup 6}-10{sup 14}) particles cm{sup -3}. The sub-MeV and the MeV emissions are well reproduced. When compared to the canonical GRBs with (n{sub CBM}) Almost-Equal-To 1 particles cm{sup -3} and to the disguised short GRBs with (n{sub CBM}) Almost-Equal-To 10{sup -3} particles cm{sup -3}, the case of GRB 090510 leads to the existence of a new family of bursts exploding in an overdense galactic region with (n{sub CBM}) Almost-Equal-To 10{sup 3} particles cm{sup -3}. The joint effect of the high {Gamma}{sub tr} and the high density compresses in time and 'inflates' in intensity the extended afterglow, making it appear as a short burst, which we here define as a 'disguised short GRB by excess'. The determination of the above parameter values may represent an important step toward the explanation of the GeV emission.

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↗