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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 1,063 records · Page 59
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DOE OSTI2014

Spatially resolving the very high energy emission from MGRO J2019+37 with VERITAS

We present very high energy (VHE) imaging of MGRO J2019+37 obtained with the VERITAS observatory. The bright extended (∼2°) unidentified Milagro source is located toward the rich star formation region Cygnus-X. MGRO J2019+37 is resolved into two VERITAS sources. The faint, point-like source VER J2016+371 overlaps CTB 87, a filled-center remnant (SNR) with no evidence of a supernova remnant shell at the present time. Its spectrum is well fit in the 0.65-10 TeV energy range by a power-law model with photon index 2.3 ± 0.4. VER J2019+378 is a bright extended (∼1°) source that likely accounts for the bulk of the Milagro emission and is notably coincident with PSR J2021+3651 and the star formation region Sh 2–104. Its spectrum in the range 1-30 TeV is well fit with a power-law model of photon index 1.75 ± 0.3, among the hardest values measured in the VHE band, comparable to that observed near Vela-X. We explore the unusual spectrum and morphology in the radio and X-ray bands to constrain possible emission mechanisms for this source.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Synchrotron and inverse-Compton emissions from pairs formed in GRB afterglows (analytical treatment)

We calculate the synchrotron and inverse-Compton emissions from pairs formed in gamma-ray burst (GRB) afterglows from high-energy photons (above 100 MeV), assuming a power-law photon spectrum C {sub ν}∝ν{sup –2} and considering only the pairs generated from primary high-energy photons. The essential properties of these pairs (number, minimal energy, cooling energy, distribution with energy) and of their emission (peak flux, spectral breaks, spectral slope) are set by the observables GeV fluence Φ(t) = Ft and spectrum, and by the Lorentz factor, Γ, and magnetic field, B, of the source of high-energy photons, at observer time, t. Optical and X-ray pseudo light curves, F {sub ν}(Γ), are calculated for the given B; proper synchrotron self-Compton light curves are calculated by setting the dynamics Γ(t) of the high-energy photon source to be that of a decelerating, relativistic shock. It is found that the emission from pairs can accommodate the flux and decays of the optical flashes measured during the prompt (GRB) phase, but it decays faster than the X-ray plateaus observed during the delayed (afterglow) phase. The brightest pair optical emission is obtained for 100 < Γ < 500, and depends mostly on the GeV fluence, being independent of the source redshift. Emission from pairs formed during the GRB phase offers an alternate explanation to reverse-shock optical flashes. These two models may be distinguished based on their corresponding flux decay index-spectral slope relations, different correlations with the Large Area Telescope fluence, or through modeling of the afterglow multiwavelength data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

The extreme behavior of the radio-loud narrow-line Seyfert 1 galaxy J0849+5108

Simultaneous radio, optical (both photometry and polarimetry), X-ray, and γ-ray observations of the radio-loud narrow-line Seyfert 1 (RL-NLSy1) galaxy J0849+5108 are presented. A massive three-magnitude optical flare across five nights in 2013 April is detected, along with associated flux increases in the γ-ray, infrared, and radio regimes; no comparable event was detected in the X-rays, though this may be due to poor coverage. A spectral energy distribution (SED) for the object using quasi-simultaneous data centered on the optical flare is compared to the previously published SEDs for the object by D'Ammando et al. The flare event coincided with a high degree of optical polarization. High amplitude optical microvariability is clearly detected, and is found to be of comparable amplitude when the object is observed in both faint and bright states. The object is also seen to undergo rapid shifts in polarization in both degree and electric vector position angle within a single night. J0849+5108 appears to show even more extreme variability than that previously reported for the similar object J0948+0022. These observations appear to support the growing claim that some RL-NLSy1 galaxies constitute a sub-class of blazar-like active galactic nuclei.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

GRB 110731A: Early afterglow in stellar wind powered by a magnetized outflow

One of the most energetic gamma-ray bursts, GRB 110731A, was observed from an optical to GeV energy range. Previous analysis of the prompt phase revealed similarities between the Large Area Telescope (LAT) bursts observed by Fermi: (1) a delayed onset of the high-energy emission (>100 MeV), (2) a short-lasting bright peak at later times, and (3) a temporally extended component from this phase, lasting hundreds of seconds. Additionally to the prompt phase, multiwavelength observations over different epochs showed that the spectral energy distribution was better fitted by a wind afterglow model. We present a leptonic model based on an early afterglow that evolves in a stellar wind of its progenitor. We apply this model to interpret the temporally extended LAT emission and the brightest LAT peak exhibited by the prompt phase of GRB 110731A. Additionally, using the same set of parameters, we describe the multiwavelength afterglow observations. The origin of the temporally extended LAT, X-ray, and optical flux is explained through synchrotron radiation from the forward shock (FS) and the brightest LAT peak is described, evoking the synchrotron self-Compton emission from the reverse shock (RS). The bulk Lorentz factor required in this model (Γ ≃ 520) lies in the range of values demanded for most LAT-detected GRBs. We show that the strength of the magnetic field in the RS region is ∼50 times stronger than that in the FS region. This result suggests that, for GRB 110731A, the central engine is likely entrained with strong magnetic fields.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

High-latitude, transluscent molecular clouds as probes of local cosmic rays

We analyze the gamma ray emission from nine high latitude, translucent molecular clouds taken with the Fermi Large Area Telescope between 250 MeV and 10 GeV. Observations of gamma rays allow us to probe the density and spectrum of cosmic rays in the solar neighborhood. The clouds studied lie within ∼270 pc from the Sun and are selected from the Planck all-sky CO map. Gamma rays in this energy range mostly result from cosmic-ray interactions with the interstellar medium, which is traced with three components: H i, CO, and dark gas. Every cloud is detected and shows significant, extended gamma ray emission from molecular gas. The gamma ray emission is dominated by the CO-emitting gas in some clouds, but by the CO-dark gas in others. The average emissivity and gamma ray power law index from H i above 1 GeV shows no evidence of a systematic variation. The CO-to-H{sub 2} conversion factor shows no variation between clouds over this small spatial range, but shows significant variations within each cloud. The average CO-to-H{sub 2} conversion factor suggests that the CO-dark gas is molecular as opposed to optically thick H i.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A unified model of the Fermi bubbles, microwave haze, and polarized radio lobes: Reverse shocks in the galactic center’s giant outflows

The Galactic center’s giant outflows are manifest in three different, nonthermal phenomena: (1) the hard-spectrum, γ-ray “Fermi bubbles” emanating from the nucleus and extending to |b|∼50{sup ∘}; (2) the hard-spectrum, total-intensity microwave (∼20–40 GHz) “haze” extending to |b|∼35{sup ∘} in the lower reaches of the Fermi bubbles; and (3) the steep-spectrum, polarized, “S-PASS” radio (∼2–20 GHz) lobes that envelop the bubbles and extend to |b|∼60{sup ∘}. We find that the nuclear outflows inflate a genuine bubble in each Galactic hemisphere that has the classical structure, working outward, of reverse shock, contact discontinuity (CD), and forward shock. Expanding into the finite pressure of the halo and given appreciable cooling and gravitational losses, the CD of each bubble is now expanding only very slowly. We find observational signatures in both hemispheres of giant, reverse shocks at heights of ∼1 kpc above the nucleus; their presence ultimately explains all three of the nonthermal phenomena mentioned above. Synchrotron emission from shock-reaccelerated cosmic-ray electrons explains the spectrum, morphology, and vertical extent of the microwave haze and the polarized radio lobes. Collisions between shock-reaccelerated hadrons and denser gas in cooling condensations that form inside the CD account for most of the bubbles’ γ-ray emissivity. Inverse Compton emission from primary electrons contributes at the 10%–30% level. Our model suggests that the bubbles are signatures of a comparatively weak but sustained nuclear outflow driven by Galactic center star formation over ≳few × 10{sup 8} yr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

VISCOUS BOUNDARY LAYERS OF RADIATION-DOMINATED, RELATIVISTIC JETS. II. THE FREE-STREAMING JET MODEL

We analyze the interaction of a radiation-dominated jet and its surroundings using the equations of radiation hydrodynamics in the viscous limit. In a previous paper we considered the two-stream scenario, which treats the jet and its surroundings as distinct media interacting through radiation viscous forces. Here we present an alternative boundary layer model, known as the free-streaming jet model—where a narrow stream of fluid is injected into a static medium—and present solutions where the flow is ultrarelativistic and the boundary layer is dominated by radiation. It is shown that these jets entrain material from their surroundings and that their cores have a lower density of scatterers and a harder spectrum of photons, leading to observational consequences for lines of sight that look “down the barrel of the jet.” These jetted outflow models may be applicable to the jets produced during long gamma-ray bursts and super-Eddington phases of tidal disruption events.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

MULTITHERMAL REPRESENTATION OF THE KAPPA-DISTRIBUTION OF SOLAR FLARE ELECTRONS AND APPLICATION TO SIMULTANEOUS X-RAY AND EUV OBSERVATIONS

Acceleration of particles and plasma heating is one of the fundamental problems in solar flare physics. An accurate determination of the spectrum of flare-energized electrons over a broad energy range is crucial for our understanding of aspects such as the acceleration mechanism and the total flare energy. Recent years have seen a growing interest in the kappa-distribution as a representation of the total spectrum of flare-accelerated electrons. In this work we present the kappa-distribution as a differential emission measure. This allows for inferring the electron distribution from X-ray observations and EUV observations by simultaneously fitting the proposed function to RHESSI and SDO/AIA data. This yields the spatially integrated electron spectra of a coronal source from less than 0.1 keV up to several tens of keV. The method is applied to a single-loop GOES C4.1 flare. The results show that the total energy can only be determined accurately by combining RHESSI and AIA observations. Simultaneously fitting the proposed representation of the kappa-distribution reduces the electron number density in the analyzed flare by a factor of ∼30 and the total flare energy by a factor of ∼5 compared with the commonly used fitting of RHESSI spectra. The spatially integrated electron spectrum of the investigated flare between 0.043 and 24 keV is consistent with the combination of a low-temperature (∼2 MK) component and a hot (∼11 MK) kappa-like component with spectral index 4, reminiscent of solar wind distributions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

How bad or good are the external forward shock afterglow models of gamma-ray bursts?

The external forward shock models have been the standard paradigm to interpret the broadband afterglow data of gamma-ray bursts (GRBs). One prediction of the models is that some afterglow temporal breaks at different energy bands should be achromatic; that is, the break times should be the same in different frequencies. Multiwavelength observations in the Swift era have revealed chromatic afterglow behaviors at least in some GRBs, casting doubts on the external forward shock origin of GRB afterglows. In this paper, using a large sample of GRBs with both X-ray and optical afterglow data, we perform a systematic study to address the question: how bad or good are the external forward shock models? Our sample includes 85 GRBs up to 2014 March with well-monitored X-ray and optical light curves. Based on how well the data abide by the external forward shock models, we categorize them into five grades and three samples. The first two grades (Grade I and II) include 45 of 85 GRBs. They show evidence of, or are consistent with having, an achromatic break. The temporal and spectral behaviors in each afterglow segment are consistent with the predictions (the “closure relations”) of the forward shock models. These GRBs are included in the Gold sample. The next two grades (Grade III and IV) include 37 of 85 GRBs. They are also consistent with having an achromatic break, even though one or more afterglow segments do not comply with the closure relations. These GRBs are included in the Silver sample. Finally, Grade V (3/85) shows direct evidence of chromatic behaviors, suggesting that the external shock models are inconsistent with the data. These are included in the Bad sample. We further perform statistical analyses of various observational properties (temporal index α, spectral index β, break time t{sub b}) and model parameters (energy injection index q, electron spectral index p, jet opening angle θ{sub j}, radiative efficiency η{sub γ}, and so on) of the GRBs in the Gold sample, and derive constraints on the magnetization parameter ϵ{sub B} in the forward shock. Overall, we conclude that the simplest external forward shock models can account for the multiwavelength afterglow data of at least half of the GRBs. When more advanced modeling (e.g., long-lasting reverse shock, structured jets, arbitrary circumburst medium density profile) is invoked, up to >90% of the afterglows may be interpreted within the framework of the external shock models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

EVIDENCE OF CROSS-CORRELATION BETWEEN THE CMB LENSING AND THE γ-RAY SKY

We report the measurement of the angular power spectrum of cross-correlation between the unresolved component of the Fermi-LAT γ-ray sky maps and the cosmic microwave background lensing potential map reconstructed by the Planck satellite. The matter distribution in the universe determines the bending of light coming from the last scattering surface. At the same time, the matter density drives the growth history of astrophysical objects, including their capability at generating non-thermal phenomena, which in turn give rise to γ-ray emissions. The Planck lensing map provides information on the integrated distribution of matter, while the integrated history of γ-ray emitters is imprinted in the Fermi-LAT sky maps. We report here the first evidence of their correlation. We find that the multipole dependence of the cross-correlation measurement is in agreement with current models of the γ-ray luminosity function for active galactic nuclei and star-forming galaxies, with a statistical evidence of 3.0σ. Moreover, its amplitude can in general be matched only assuming that these extragalactic emitters are also the bulk contribution of the measured isotopic γ-ray background (IGRB) intensity. This leaves little room for a big contribution from galactic sources to the IGRB measured by Fermi-LAT, pointing toward direct evidence of the extragalactic origin of the IGRB.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

FIRST INTEGRAL OBSERVATIONS OF V404 CYGNI DURING THE 2015 OUTBURST: SPECTRAL BEHAVIOR IN THE 20–650 KeV ENERGY RANGE

In 2015 June, the source V404 Cygni (= GS2023+38) underwent an extraordinary outburst. We present the results obtained during the first revolution dedicated to this target by the INTEGRAL mission and focus on the spectral behavior in the hard X-ray domain, using both SPI and IBIS instruments. The source exhibits extreme variability and reaches fluxes of several tens of Crab. However, the emission between 20 and 650 keV can be understood in terms of two main components, varying on all the observable timescales, similar to what is observed in the persistent black hole system Cyg X-1. The low-energy component (up to ∼200 keV) presents a rather unusual shape, probably due to the intrinsic source variability. Nonetheless, a satisfactory description is obtained with a Comptonization model, if an unusually hot population of seed photons (kT{sub 0} ∼ 7 keV) is introduced. Above this first component, a clear excess extending up to 400–600 keV leads us to investigate a scenario where an additional (cutoff) power law could correspond to the contribution of the jet synchrotron emission, as proposed in Cyg X-1. A search for an annihilation feature did not provide any firm detection, with an upper limit of 2 × 10{sup −4} ph cm{sup −2} s{sup −1} (2σ) for a narrow line centered at 511 keV, on the averaged obtained spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

High-resolution measurements of Cl 15 + line shifts in hot, solid-density plasmas

The shifts of the 1s3p 1 P 1 → 1s 2 1 S 0 He-β transition of Cl 15+ were measured in hot (≥ 600 eV), dense (1–2 g/cm 3 ) plasmas generated by a (66–151)-J short-pulse laser beam at the Orion laser facility. The subpicosecond laser beam irradiated optically thin, KCl microdot targets buried in layers of plastic. The measured red shifts ranged from 4.8 ± 1.1 eV for unshocked to 5.9 ± 1.2 eV for shocked targets. Furthermore, these values are significantly smaller than recent predictions from a self-consistent-field ion-sphere model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Primary $\gamma$-ray intensities and $\gamma$-strength functions from discrete two-step $\gamma$-ray cascades in radiative proton-capture experiments

Background: Reaction rates of radiative capture reactions can play a crucial role in the nucleosynthesis of heavy nuclei in explosive stellar environments. These reaction rates depend strongly on $\gamma$-ray decay widths in the reaction products, which are, for nonresonant capture reactions at high excitation energies, derived from the $\gamma$-ray strength function and the nuclear level density. Recently, the ratio method was applied to primary $\gamma$ rays observed from ($\textit{d, p}$) reactions and nuclear resonance fluorescence measurements to extract the dipole strength in atomic nuclei and to test the generalized Brink-Axel hypothesis. Purpose: The purpose of this work is to apply the ratio method to primary $\gamma$-ray intensities of the 63,65 Cu($\textit{p},\gamma$) reactions to extract $\gamma$-ray strength information on the nuclei 64,66 Zn. Here, the impact of spin distribution, total $\gamma$-ray decay widths, level densities, and width fluctuations on the application of the ratio method will be discussed. Additionally, by comparing the relative $\gamma$-ray strength at different excitation energies, conclusions on the validity of the generalized Brink-Axel hypothesis can be made. Method: The radiative proton capture reaction measurements have been performed at the HORUS $\gamma$-ray spectrometer of the University of Cologne at one excitation energy for each reaction. Primary $\gamma$-ray intensities have been determined by normalizing secondary $\gamma$-ray transitions in two-step cascades using their absolute branching ratio. The ratio method was applied to the measured primary $\gamma$-ray intensities as well as to previous measurements by Erlandsson et al. at different excitation energies. Results: The relative strength function curve for 64 Zn from our measurement shows no significant deviation from the previous measurement at a different excitation energy. The same is true for 66 Zn where both measurements were at almost the same excitation energy. Absolute $\gamma$-strength function values have been obtained by normalizing the relative curves to quasiparticle random phase approximation calculations because of the absence of experimental data in the respective energy region. Conclusion: The generalized Brink-Axel hypothesis, i.e., the independence of the strength function on the excitation energy, seems to hold in the studied energy region and nuclei. The method to obtain primary $\gamma$-ray intensities from two-step cascade spectra was shown to be a valuable and sensitive tool although its uncertainties are connected to the knowledge of the low-energy level scheme of the investigated nucleus. The scaling in the ratio method should be taken with care, because the relative strength is not a simple sum of $f_{E1}$ and $f_{M1}$ but a somewhat complex linear combination dependent on the excitation energy of the nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

DISCOVERY OF γ -RAY EMISSION FROM THE RADIO-INTERMEDIATE QUASAR III ZW 2: VIOLENT JET ACTIVITY WITH INTRADAY γ -RAY VARIABILITY

III Zw 2 is the prototype of radio-intermediate quasars. Although there is the evidence of possessing strong jet, significant γ -ray emission has not been reported before. In this work, we carry out a detailed analysis of the latest Fermi -LAT Pass 8 data. No significant γ -ray signal has been detected in the time-averaged 7-year Fermi -LAT data of III Zw 2; however, we have identified two distinct γ -ray flares with isotropic luminosities of ∼10{sup 45} erg s{sup −1}. Multiwavelength data analysis (also including the optical photometric observations from Yunnan Observatories) are presented and the main finding is simultaneous optical and γ -ray flares of III Zw 2 appearing in 2009 November. Violent γ -ray variability with a doubling timescale of 2.5 hr was detected in another γ -ray flare in May 2010, for which the 3-hr γ -ray peak flux is ∼250 times of the average flux in 7 years. Rather similar behaviors are observed in blazars and the blazar model can reasonably reproduce the spectral energy distribution of III Zw 2 in a wide energy range, strongly suggesting that its central engine resembles that of blazars. In view of its core, which shares radio similarities with young radio sources, together with weak extended radio lobe emission, we suggest that III Zw 2 harbors a recurrent activity core and thus serves as a valuable target for investigating the fueling and triggering of the activity in radio-loud active galactic nuclei.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Gamma-Ray Observations of Tycho’s Supernova Remnant with VERITAS and Fermi

High-energy gamma-ray emission from supernova remnants (SNRs) has provided a unique perspective for studies of Galactic cosmic-ray acceleration. Tycho’s SNR is a particularly good target because it is a young, type Ia SNR that has been well-studied over a wide range of energies and located in a relatively clean environment. Since the detection of gamma-ray emission from Tycho’s SNR by VERITAS and Fermi -LAT, there have been several theoretical models proposed to explain its broadband emission and high-energy morphology. We report on an update to the gamma-ray measurements of Tycho’s SNR with 147 hr of VERITAS and 84 months of Fermi -LAT observations, which represent about a factor of two increase in exposure over previously published data. About half of the VERITAS data benefited from a camera upgrade, which has made it possible to extend the TeV measurements toward lower energies. The TeV spectral index measured by VERITAS is consistent with previous results, but the expanded energy range softens a straight power-law fit. At energies higher than 400 GeV, the power-law index is 2.92 ± 0.42{sub stat} ± 0.20{sub sys}. It is also softer than the spectral index in the GeV energy range, 2.14 ± 0.09{sub stat} ± 0.02{sub sys}, measured in this study using Fermi -LAT data. The centroid position of the gamma-ray emission is coincident with the center of the remnant, as well as with the centroid measurement of Fermi -LAT above 1 GeV. The results are consistent with an SNR shell origin of the emission, as many models assume. The updated spectrum points to a lower maximum particle energy than has been suggested previously.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The Maximum Isotropic Energy of Gamma-Ray Bursts

The most energetic gamma-ray bursts (GRBs) are remarkable sources releasing huge amounts of energy on short timescales. Their prompt emission, which usually lasts a few seconds, is so bright that it is visible across the whole observable universe. Studying these extreme events may provide clues on the nature of GRB progenitors and on the physical processes at work in relativistic jets. In this paper, we study the bright end of the isotropic energy distribution of long GRBs. We use two samples of long GRBs with redshift detected by Fermi/GBM or Konus-Wind, two instruments that measure the spectral shape and the energetics of the prompt emission accurately. We focus on GRBs within a range of redshifts z = 1–5, a volume that contains a large number of energetic GRBs, and we propose a simple method to reconstruct the bright end of the GRB energy distribution from the observed one. We find that the GRB energy distribution cannot be described by a simple power law but requires a strong cutoff above 1--3×10{sup 54} erg. We attribute this feature to an intrinsic limit on the energy per unit of solid angle radiated by GRBs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Fermi Bubble Edges: Spectrum and Diffusion Function

Current measurements of the γ-ray Fermi bubbles (FB) are based on model-dependent tracers, carry substantial systematic uncertainties, and contain some discrepancies between each other. We show that gradient filters pick out the FB edges, which are found to smoothly connect to the bipolar X-ray structure emanating from the Galactic center, thus supporting the interpretation of the FBs as a Galactic-scale phenomenon. The sharp edges facilitate a direct, model-free measurement of the peripheral FB spectrum. The result is strikingly similar to the full FB-integrated spectrum, softened by a power law of index η ≃ (0.2–0.3). This is naturally explained, in both hadronic and leptonic models, if cosmic rays are injected at the edge, and diffuse away preferentially at higher energies E. The inferred, averaged diffusion function in the (more plausible) leptonic model, D(E)≃10{sup 29.5}(E/10GeV){sup 0.48±0.02} cm{sup 2} s{sup −1}, is consistent with estimates for Kraichnan-like turbulence. Our results, in particular the minute spatial variations in η, indicate that the FB edge is a strong, Mach ≳5, forward shock.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Steep Decay Phase Shaped by the Curvature Effect. II. Spectral Evolution

We derive a simple analytical formula to describe the evolution of spectral index β in the steep decay phase shaped by the curvature effect with the assumption that the spectral parameters and Lorentz factor of the jet shell are the same for different latitudes. Here, the value of β is estimated in the 0.3−10 keV energy band. For a spherical thin shell with a cutoff power-law (CPL) intrinsic radiation spectrum, the spectral evolution can be read as a linear function of observer time. For the situation with the Band function intrinsic radiation spectrum, the spectral evolution may be complex. If the observed break energy of the radiation spectrum is larger than 10 keV, the spectral evolution is the same as that shaped by jet shells with a CPL spectrum. If the observed break energy is less than 0.3 keV, the value of β would be a constant. For others, the spectral evolution can be approximated as a logarithmal function of the observer time in general.

79 ASTRONOMY AND ASTROPHYSICS↗