Journal articles: 'Lorentz gamma factor'

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Ghirlanda, G., F. Nappo, G. Ghisellini, A. Melandri, G. Marcarini, L. Nava, O. S. Salafia, S. Campana, and R. Salvaterra. "Bulk Lorentz factors of gamma-ray bursts." Astronomy & Astrophysics 609 (January 2018): A112. http://dx.doi.org/10.1051/0004-6361/201731598.

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Knowledge of the bulk Lorentz factor Γ0 of gamma-ray bursts (GRBs) allows us to compute their comoving frame properties shedding light on their physics. Upon collisions with the circumburst matter, the fireball of a GRB starts to decelerate, producing a peak or a break (depending on the circumburst density profile) in the light curve of the afterglow. Considering all bursts with known redshift and with an early coverage of their emission, we find 67 GRBs (including one short event) with a peak in their optical or GeV light curves at a time tp. For another 106 GRBs we set an upper limit tpUL. The measure of tp provides the bulk Lorentz factor Γ0 of the fireball before deceleration. We show that tp is due to the dynamics of the fireball deceleration and not to the passage of a characteristic frequency of the synchrotron spectrum across the optical band. Considering the tp of 66 long GRBs and the 85 most constraining upper limits, we estimate Γ0 or a lower limit Γ0LL. Using censored data analysis methods, we reconstruct the most likely distribution of tp. All tp are larger than the time Tp,γ when the prompt γ-ray emission peaks, and are much larger than the time Tph when the fireball becomes transparent, that is, tp>Tp,γ>Tph. The reconstructed distribution of Γ0 has median value ~300 (150) for a uniform (wind) circumburst density profile. In the comoving frame, long GRBs have typical isotropic energy, luminosity, and peak energy ⟨ Eiso ⟩ = 3(8) × 1050 erg, ⟨ Liso ⟩ = 3(15) × 1047 erg s-1, and ⟨ Epeak ⟩ = 1(2) keV in the homogeneous (wind) case. We confirm that the significant correlations between Γ0 and the rest frame isotropic energy (Eiso), luminosity (Liso), and peak energy (Ep) are not due to selection effects. When combined, they lead to the observed Ep−Eiso and Ep−Liso correlations. Finally, assuming a typical opening angle of 5 degrees, we derive the distribution of the jet baryon loading which is centered around a few 10-6M⊙.

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Ioka, K. "Very High Lorentz Factor Fireballs and Gamma-Ray Burst Spectra." Progress of Theoretical Physics 124, no. 4 (October 1, 2010): 667–710. http://dx.doi.org/10.1143/ptp.124.667.

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Granot, J., and P. Kumar. "Distribution of gamma-ray burst ejecta energy with Lorentz factor." Monthly Notices of the Royal Astronomical Society: Letters 366, no. 1 (February 1, 2006): L13—L16. http://dx.doi.org/10.1111/j.1745-3933.2005.00121.x.

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Sonbas, E., G. A. MacLachlan, K. S. Dhuga, P. Veres, A. Shenoy, and T. N. Ukwatta. "GAMMA-RAY BURSTS: TEMPORAL SCALES AND THE BULK LORENTZ FACTOR." Astrophysical Journal 805, no. 2 (May 22, 2015): 86. http://dx.doi.org/10.1088/0004-637x/805/2/86.

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LIANG, EN-WEI, HOUJUN LÜ, SHUANG-XI YI, BING ZHANG, BIN-BIN ZHANG, and JIN ZHANG. "DISCERNING EMISSION COMPONENTS IN EARLY AFTERGLOW DATA AND CONSTRAINING THE INITIAL LORENTZ FACTOR OF LONG GRB FIREBALL." International Journal of Modern Physics D 20, no. 10 (September 2011): 1955–59. http://dx.doi.org/10.1142/s0218271811020007.

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We prove that both the canonical and single power-law decay X-ray afterglow lightcurves of gamma-ray bursts (GRBs) observed with the Swift X-ray telescope may be an emission component radiated by external shocks prior to the GRB trigger. Our systematical analysis on both the early optical and X-ray afterglow data also indicates that they might be from different components. The detected optical emission possibly is dominated by the afterglow of the GRB fireball. The X-ray afterglows may be detected for some GRBs, but most of the detected X-rays for most GRBs are likely dominated by the prior X-ray component. With the deceleration feature in the early optical afterglow data, we estimate the initial Lorentz factors of the GRBs and discover a tight relation of the Lorentz factor to the isotropic gamma-ray energy.

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Baring, Matthew G. "Gamma-Ray Burst Spectral Breaks and Source Beaming." International Astronomical Union Colloquium 142 (1994): 899–903. http://dx.doi.org/10.1017/s0252921100078283.

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AbstractThe principal discovery of the ComptonGamma-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 GRB detected byGROexhibit 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 toγ-γattenuation, as a function of source spectral index and break energy, is presented. It is found that sources at distances of ~1 Gpc must typically be beamed with bulk Lorentz factors of around 103-104, 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 γ-γ 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 γ-γ attenuation at these energies.Subject headings:gamma-rays: bursts — radiation mechanisms: nonthermal

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Zhang, Hai-Ming, Da-Bin Lin, Ting-Ting Lin, Bao-Rong Liu, Xiao-Li Huang, Shu-Qing Zhong, Rui-Jing Lu, and En-Wei Liang. "Lorentz Factor Evolution Patterns within Relativistic Jets of GRBs and AGNs." Proceedings of the International Astronomical Union 12, S324 (September 2016): 78–81. http://dx.doi.org/10.1017/s1743921317001260.

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AbstractThe Lorentz factor (Γ) is an important parameter related to the relativistic jet physics. We study the evolution patterns of Γ within gamma-ray burst (GRB) and active galactic nuclear jets for individual GRB 090168, GRB 140508A, and 3C 454.3. By estimating the Γ values for well-separated pulses in GRBs 090618 and 140508A with an empirical relation derived from typical GRBs, we find that the Γ evolution pattern in the two GRBs are different. The increasing-to-coasting evolution pattern of Γ in GRB 090618 likely indicates that the GRB fireball is still being accelerated in the prompt phase. The clear decrease evolution pattern of Γ in GRB 140508A suggests the deceleration of the fireball components. By deriving the Γ value through fitting their spectral energy distribution in different flares of 3C 454.3, a pattern of Γ-tracking-γ-ray flux is clearly found, likely indicating that the observed gamma-ray flares are being due to the Doppler boosting effect to the jet emission.

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Matsumoto, Tatsuya, Shigeo S. Kimura, Kohta Murase, and Peter Mészáros. "Linking extended and plateau emissions of short gamma-ray bursts." Monthly Notices of the Royal Astronomical Society 493, no. 1 (February 11, 2020): 783–91. http://dx.doi.org/10.1093/mnras/staa305.

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ABSTRACT Some short gamma-ray bursts (SGRBs) show a longer lasting emission phase, called extended emission (EE) lasting ${\sim}10^{2\!-\!3}\, \rm s$, as well as a plateau emission (PE) lasting ${\sim}10^{4\!-\!5}\, \rm s$. Although a long-lasting activity of the central engines is a promising explanation for powering both emissions, their physical origin and their emission mechanisms are still uncertain. In this work, we study the properties of the EEs and their connection with the PEs. First, we constrain the minimal Lorentz factor Γ of the outflows powering EEs, using compactness arguments and find that the outflows should be relativistic, Γ ≳ 10. We propose a consistent scenario for the PEs, where the outflow eventually catches up with the jet responsible for the prompt emission, injecting energy into the forward shock formed by the prior jet, which naturally results in a PE. We also derive the radiation efficiency of EEs and the Lorentz factor of the outflow within our scenario for 10 well-observed SGRBs accompanied by both EE and PE. The efficiency has an average value of ${\sim}3\, {{\ \rm per\ cent}}$ but shows a broad distribution ranging from ∼0.01 to ${\sim}100{{\ \rm per\ cent}}$. The Lorentz factor is ∼20–30, consistent with the compactness arguments. These results suggest that EEs are produced by a slower outflow via more inefficient emission than the faster outflow that causes the prompt emission with a high radiation efficiency.

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Salvati, M., M. Spada, and F. Pacini. "Rapid Variability of Gamma-Ray Blazars." Highlights of Astronomy 11, no. 2 (1998): 816–19. http://dx.doi.org/10.1017/s1539299600018864.

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This paper is devoted to a discussion of the rapid variability observed in γ-ray blazars. We do this in the framework of a widely accepted scenario, according to which the blazar emission arises from a jet, i.e. a continuous flow of relativistic fluid, with perturbations occasionally superimposed. The jet is assumed to have a bulk Lorentz factor Γ ≫ 1, and length z and radius r such that r ã z/Γ.

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STERN, B. E., and J. POUTANEN. "GAMMA-RAY EMISSION OF RELATIVISTIC JETS AS A SUPERCRITICAL PROCESS." International Journal of Modern Physics D 17, no. 09 (September 2008): 1611–17. http://dx.doi.org/10.1142/s0218271808013212.

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Supercriticality of the same kind as that in a nuclear pile can take place in high-energy astrophysical objects producing a number of impressive effects. For example, it could cause an explosive release of the energy of a cloud of ultrarelativistic protons into radiation. More certainly, supercriticality should be responsible for energy dissipation of very energetic relativistic fluids such as ultrarelativistic shocks in gamma-ray bursts and jets in active galactic nuclei (AGNs). In this case, the photon breeding process operates. It is a kind of converter mechanism with the high-energy photons and e+e- pairs converting into each other via pair production and inverse Compton scattering. Under certain conditions, which should be satisfied in powerful AGNs, the photon breeding mechanism becomes supercritical: the high-energy photons breed exponentially until their feedback on the fluid changes its velocity pattern. Then the system comes to a self-adjusting near-critical steady state. Monte-Carlo simulations with detailed treatment of particle propagation and interactions demonstrate that a jet with a Lorentz factor Γ ≈ 20 can radiate away up to a half of its total energy, and for Γ = 40 the radiation efficiency can be up to 80 per cent. Outer layers of the jet decelerate down to a moderate Lorentz factor 2–4, while the spine of the jet has a final Lorentz factor in the range 10–20 independent of the initial Γ. Such sharp deceleration under the impact of radiation must cause a number of interesting phenomena such as formation of internal shocks and an early generation of turbulence.

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Katz, J. I. "The FRB–SGR connection." Monthly Notices of the Royal Astronomical Society 499, no. 2 (October 2, 2020): 2319–26. http://dx.doi.org/10.1093/mnras/staa3042.

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ABSTRACT The discovery that the Galactic Soft Gamma Repeater (SGR) 1935+2154 emitted Fast Radio Burst (FRB) 200428 simultaneous with a gamma-ray flare, demonstrated the common source and association of these phenomena. If FRB radio emission is the result of coherent curvature radiation, the net charge of the radiating ‘bunches’ or waves may be inferred from the radiated fields, independent of the mechanism by which the bunches are produced. A statistical argument indicates that the radiating bunches must have a Lorentz factor ⪆ 10. The observed radiation frequencies indicate that their phase velocity (pattern speed) corresponds to Lorentz factors ⪆ 100. Coulomb repulsion implies that the electrons making up these bunches have yet larger Lorentz factors, limited by their incoherent curvature radiation. These electrons also Compton scatter the soft gamma-rays of the SGR. In FRB 200428, the power they radiated coherently at radio frequencies exceeded that of Compton scattering, but in more luminous SGR outbursts, Compton scattering dominates, precluding the acceleration of energetic electrons. This explains the absence of a FRB associated with the giant 2004 December 27 outburst of SGR 1806−20. SGR with luminosity ≳ 1042 erg s–1 are predicted not to emit FRB, while those of lesser luminosity can do so. ‘Superbursts’ like FRB 200428 are produced when narrowly collimated FRB are aligned with the line of sight; they are unusual, but not rare, and ‘cosmological’ FRB may be superbursts.

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DERISHEV, E. V. "LIMITS TO THE PHYSICAL PARAMETERS IN EXTRAGALACTIC GAMMA-RAY SOURCES." International Journal of Modern Physics D 18, no. 10 (October 2009): 1523–27. http://dx.doi.org/10.1142/s0218271809015448.

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We examine several constraints on the physical parameters in active galactic nuclei and gamma-ray burst, originating from the assumption that these sources are efficient in converting their energy into gamma-rays. It is shown that in most cases these constraints may be reformulated in terms of bounds on the jet Lorentz factor, for which both the lower and the upper limits can be evaluated.

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Saikia, Dipok. "Lorentz gamma factor from vacuum to medium and Minkowski momentum of a photon." AIP Advances 8, no. 8 (August 2018): 085026. http://dx.doi.org/10.1063/1.5043496.

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Lü, Jing, Yuan-Chuan Zou, Wei-Hua Lei, Bing Zhang, Qingwen Wu, Ding-Xiong Wang, En-Wei Liang, and Hou-Jun Lü. "LORENTZ-FACTOR–ISOTROPIC-LUMINOSITY/ENERGY CORRELATIONS OF GAMMA-RAY BURSTS AND THEIR INTERPRETATION." Astrophysical Journal 751, no. 1 (May 3, 2012): 49. http://dx.doi.org/10.1088/0004-637x/751/1/49.

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Zdziarski, Andrzej A., Alexandra J. Tetarenko, and Marek Sikora. "Jet Parameters in the Black Hole X-Ray Binary MAXI J1820+070." Astrophysical Journal 925, no. 2 (February 1, 2022): 189. http://dx.doi.org/10.3847/1538-4357/ac38a9.

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Abstract We study the jet in the hard state of the accreting black hole (BH) binary MAXI J1820+070. From the available radio-to-optical spectral and variability data, we put strong constraints on the jet parameters. We find while it is not possible to uniquely determine the jet Lorentz factor from the spectral and variability properties alone, we can estimate the jet opening angle (≈1.°5 ± 1°), the distance at which the jet starts emitting synchrotron radiation (∼3 × 1010 cm), and the magnetic field strength there (∼104 G), with relatively low uncertainty, as they depend weakly on the bulk Lorentz factor. We find the breaks in the variability power spectra from radio to submillimeter wavelength are consistent with variability damping over the timescale equal to the travel time along the jet at any Lorentz factor. This factor can still be constrained by the electron–positron pair-production rate within the jet base, which we calculate based on the observed X-ray/soft-gamma-ray spectrum, and the jet power, required to be less than the accretion power. The minimum (∼1.5) and maximum (∼4.5) Lorentz factors correspond to the dominance of pairs and ions, and the minimum and maximum jet power, respectively. We estimate the magnetic flux threading the BH and find the jet can be powered by the Blandford–Znajek mechanism in a magnetically arrested flow accretion flow. We point out the similarity of our derived formalism to that of core shifts, observed in extragalactic radio sources.

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MÉSZÁROS, PETER. "THE PROMPT AND HIGH ENERGY EMISSION OF GAMMA RAY BURSTS." International Journal of Modern Physics D 18, no. 10 (October 2009): 1551–55. http://dx.doi.org/10.1142/s0218271809015540.

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I discuss some recent results on the prompt emission of gamma-ray bursts, in particular the jet and radiation properties of the naked-eye burst GRB 080319b, based on Swift and related observations. I then discuss the recent observations by the Fermi satellite of GRB 080916C, the resulting constraints for the bulk Lorentz factor determinations, and the highest lower limit on the quantum gravity energy scale obtained so far.

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LI, ZHUO. "ON GRB PHYSICS REVEALED BY FERMI/LAT." International Journal of Modern Physics: Conference Series 23 (January 2013): 223–27. http://dx.doi.org/10.1142/s2010194513011343.

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We discuss the implications of Fermi/LAT observations on several aspects of gamma-ray burst (GRB) physics, including the radiation process, the emission sites, the bulk Lorentz factor, and the pre-shock magnetic field: (1) MeV-range emission favors synchrotron process but the highest energy (> 10 GeV) emission may not be synchrotron origin, more likely inverse Compton origin; (2) GRB should have multi-zone emission region, with MeV emission produced at smaller radii while optical and > 100 MeV emission at larger radii; (3) the bulk Lorentz factor can be a few 100's, much lower than 103, in multi-zone model; (4) the upstream magnetic field of afterglow shock is strongly amplified to be at least in mG scale.

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MIZUNO, YOSUKE, BING ZHANG, BRUNO GIACOMAZZO, KEN-ICHI NISHIKAWA, PHILIP E. HARDEE, SHIGEHIRO NAGATAKI, and DIETER H. HARTMANN. "MAGNETOHYDRODYNAMIC EFFECTS IN RELATIVISTIC EJECTA." International Journal of Modern Physics D 19, no. 06 (June 2010): 991–96. http://dx.doi.org/10.1142/s0218271810017044.

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We study the problem of deceleration of an arbitrarily magnetized relativistic ejecta in a static unmagnetized medium and its connection to the physics of gamma-ray bursts (GRBs). By computing exact solutions of the Riemann problem describing this scenario, we find that with the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization parameter σ (the Poynting-to-kinetic flux ratio). The reverse shock becomes a rarefaction wave when σ exceeds a critical value defined by the balance between magnetic pressure in the ejecta and thermal pressure in the forward shock. In the rarefaction wave regime, the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value due to the strong magnetic pressure in the ejecta. We discuss the implications for models of GRBs.

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Sari, R. "Gamma-ray Bursts and Afterglow." Symposium - International Astronomical Union 195 (2000): 329–38. http://dx.doi.org/10.1017/s0074180900163107.

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The origin of GRBs has been a mystery for almost 30 years. Their sources emit a huge amount of energy on short time scales, and the process involves extreme relativistic motion with a bulk Lorentz factor of at least a few hundred. In the last two years, “afterglow” emission in X-ray, optical, IR, and radio was detected. The afterglow can be measured up to months and even years after the few-seconds GRB. We review the theories for the γ-ray emission and its afterglow, and show that these are strongly supported by observations. A recent detection of optical emission simultaneous with the GRB agrees well with theoretical predictions and further constrains the free parameters of the models. We discuss the evidence that some of the bursts are jets and discuss the prospects of polarization measurements.

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Ziaeepour, Houri. "Properties of jet and surrounding material of GW/GRB 170817A." Monthly Notices of the Royal Astronomical Society 490, no. 2 (October 3, 2019): 2822–37. http://dx.doi.org/10.1093/mnras/stz2735.

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ABSTRACT We use published data in radio, optical, and X-ray bands to analyse and model afterglows of GW/GRB 170817A. Our analysis is based on a phenomenological gamma-ray burst generator model, which we previously used to study the prompt gamma-ray emission of this important transient. We find a multicomponent model and a few of its variants that are consistent with broad-band ∼1 yr observations of afterglows, once the contribution of kilonova in optical/IR band is taken into account. Considering beaming and off-axis view of relativistic outflows, we interpret the components of the model as approximately presenting the profile of a relativistic structured jet with a rapidly declining Lorentz factor from our line of sight, where it had a Lorentz factor of $\mathcal {O}(100)$, to outer boundaries, where it became a mildly relativistic cocoon with a relative velocity to light of ∼0.4–0.97. Properties of the ultra-relativistic core of the jet obtained here are consistent with conclusions from analysis of the prompt gamma-ray emission. In particular, our results show that after prompt internal shocks the remnant of the jet retained in some extent its internal collimation and coherence. Slow rise of the afterglows can be associated to low density of circumburst material and low column density of the jet. The long distance of external shocks from the merger, which could have been in part responsible for extensive thinning of the jet through expansion and energy dissipation before occurrence of external shocks, is responsible for the peak of emission being at ≳110 d after the merger. We discuss implications of these observations for origin and properties of circumburst material around binary neutron stars. This analysis confirms our previous results showing that an outflow with a Lorentz factor of ∼2–5 cannot explain observed afterglows without an additional X-ray source or significant absorption of optical/IR photons.

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Zou, Yuan-Chuan, and Tsvi Piran. "Lorentz factor constraint from the very early external shock of the gamma-ray burst ejecta." Monthly Notices of the Royal Astronomical Society 402, no. 3 (March 1, 2010): 1854–62. http://dx.doi.org/10.1111/j.1365-2966.2009.15863.x.

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Jin, Zhi-Ping, Yi-Zhong Fan, and Da-Ming Wei. "THE BULK LORENTZ FACTOR OF OUTFLOW POWERING X-RAY FLARE IN GAMMA-RAY BURST AFTERGLOW." Astrophysical Journal 724, no. 2 (November 9, 2010): 861–65. http://dx.doi.org/10.1088/0004-637x/724/2/861.

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Nava, L., R. Desiante, F. Longo, A. Celotti, N. Omodei, G. Vianello, E. Bissaldi, and T. Piran. "Constraints on the bulk Lorentz factor of gamma-ray burst jets fromFermi/LAT upper limits." Monthly Notices of the Royal Astronomical Society 465, no. 1 (October 27, 2016): 811–19. http://dx.doi.org/10.1093/mnras/stw2771.

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Chen, Ye, Ruo-Yu Liu, and Xiang-Yu Wang. "Constraints onthe bulk Lorentz factor of gamma-ray burstswith the detection rate by Fermi LAT." Monthly Notices of the Royal Astronomical Society 478, no. 1 (May 4, 2018): 749–57. http://dx.doi.org/10.1093/mnras/sty1171.

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Lazzati, D., G. Ghisellini, and A. Celotti. "Constraints on the bulk Lorentz factor in the internal shock scenario for gamma-ray bursts." Monthly Notices of the Royal Astronomical Society 309, no. 2 (October 21, 1999): L13—L17. http://dx.doi.org/10.1046/j.1365-8711.1999.02970.x.

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Han, Song, Xinyu Li, Luyao Jiang, Zhiping Jin, Haoning He, Yuanzhu Wang, and Daming Wei. "GRB 181110A: Constraining the Jet Structure, Circumburst Medium and the Initial Lorentz Factor." Universe 8, no. 4 (April 18, 2022): 248. http://dx.doi.org/10.3390/universe8040248.

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The afterglow data of gamma ray bursts (GRBs) can be used to constrain the physical properties of the fireball (e.g., the jet structure and opening angle) and the circumburst medium. With the peak time of the early afterglow light curve being taken as the deceleration time, one can estimate the initial Lorentz factor of the fireball. In this work, we perform a comprehensive analysis on the prompt emission and the afterglow data of GRB 181110A, where a clear peak is detected by Swift UVOT and XRT in optical to X-ray bands. Prompt emission spectral analysis shows that the spectrum of GRB 181110A is soft, and both hard-to-soft and intensity-tracking spectral evolution are found. By fitting the afterglow light curve and building spectral energy distribution, we find that the standard external forward shock model with a constant circumburst medium is favored, and the jet structure of GRB 181110A tends to be uniform rather than structured. With the peak time of early afterglow emission, we estimate the initial fireball Lorentz factor of GRB 181110A to be Γ0=169−40+92. We also compare GRB 181110A with other typical long GRBs in a statistical context.

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Sarin, N., R. Hamburg, E. Burns, G. Ashton, P. D. Lasky, and G. P. Lamb. "Low-efficiency long gamma-ray bursts: a case study with AT2020blt." Monthly Notices of the Royal Astronomical Society 512, no. 1 (March 8, 2022): 1391–99. http://dx.doi.org/10.1093/mnras/stac601.

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ABSTRACT The Zwicky Transient Facility recently announced the detection of an optical transient AT2020blt at redshift z = 2.9, consistent with the afterglow of an on-axis gamma-ray burst. However, no prompt emission was observed. We analyse AT2020blt with detailed models, showing the data are best explained as the afterglow of an on-axis long gamma-ray burst, ruling out other hypotheses such as a cocoon and a low-Lorentz factor jet. We search Fermi data for prompt emission, setting deeper upper limits on the prompt emission than in the original detection paper. Together with KONUS-Wind observations, we show that the gamma-ray efficiency of AT2020blt is $\lesssim 0.3\!-\!4.5{{\ \rm per\, cent}}$. We speculate that AT2020blt and AT2021any belong to the low-efficiency tail of long gamma-ray burst distributions that are beginning to be readily observed due to the capabilities of new observatories like the Zwicky Transient Facility.

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Zhang, Bing, Shiho Kobayashi, and Peter Meszaros. "Gamma‐Ray Burst Early Optical Afterglows: Implications for the Initial Lorentz Factor and the Central Engine." Astrophysical Journal 595, no. 2 (October 2003): 950–54. http://dx.doi.org/10.1086/377363.

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Chang, Zhe, Hai-Nan Lin, and Yunguo Jiang. "CONSTRAINING THE BULK LORENTZ FACTOR OF GAMMA-RAY BURST OUTFLOW IN THE MAGNETIC-DOMINATED JET MODEL." Astrophysical Journal 759, no. 2 (October 29, 2012): 129. http://dx.doi.org/10.1088/0004-637x/759/2/129.

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Muccino, M., R. Ruffini, C. L. Bianco, L. Izzo, A. V. Penacchioni, and G. B. Pisani. "GRB 090510: A DISGUISED SHORT GAMMA-RAY BURST WITH THE HIGHEST LORENTZ FACTOR AND CIRCUMBURST MEDIUM." Astrophysical Journal 772, no. 1 (July 5, 2013): 62. http://dx.doi.org/10.1088/0004-637x/772/1/62.

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Li, Zhuo, Z. G. Dai, and T. Lu. "e±-rich GRB Fireball and Infrared Flashes." Symposium - International Astronomical Union 214 (2003): 331–32. http://dx.doi.org/10.1017/s0074180900194677.

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Gamma-ray bursts (GRBs) are believed to originate from ultra-relativistic fireballs, with initial Lorentz factor η ∼ 102 − 103. However very high energy photons may still suffer from γγ interaction. We show here that in a wide range of model parameters, the resulting pairs may dominate electrons associated with the fireball baryons. This may provide an explanation for the rarity of prompt optical detections. A rapid response to the GRB trigger at the IR band would detect such a strong flash.

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VERGANI, S. D., D. MALESANI, and E. MOLINARI. "THE INTERPLAY OF PROMPT AND AFTERGLOW EMISSION IN GRB 060418." International Journal of Modern Physics D 17, no. 09 (September 2008): 1343–49. http://dx.doi.org/10.1142/s0218271808012899.

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We present observations of the early afterglow emission of GRB 060418. Thanks to the simultaneous coverage at optical, X-ray and gamma-ray wavelengths, we can detect and separate the external shock emission (visible in the optical and late X-ray data) and the central engine activity (early X and gamma rays). The two components are clearly distinguished based on temporal and spectral properties. The detection of the afterglow onset (in the optical) allows the determination of the fundamental fireball properties, namely its bulk Lorentz factor and total energy. The early time X-ray flare closely resembles the prompt emission gamma-ray pulses in its temporal profile, being wider at low energies and showing lags between the hard and soft bands. This provides a strong suggestion that X-ray flares are a continuation of the prompt emission.

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Gottlieb, Ore, Amir Levinson, and Ehud Nakar. "High efficiency photospheric emission entailed by formation of a collimation shock in gamma-ray bursts." Monthly Notices of the Royal Astronomical Society 488, no. 1 (July 4, 2019): 1416–26. http://dx.doi.org/10.1093/mnras/stz1828.

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ABSTRACT The primary dissipation mechanism in jets of gamma-ray bursts (GRBs), and the high efficiency of the prompt emission are long-standing issues. One possibility is strong collimation of a weakly magnetized relativistic jet by the surrounding medium, which can considerably enhance the efficiency of the photospheric emission. We derive a simple analytic criterion for the radiative efficiency of a collimated jet showing that it depends most strongly on the baryon loading. We confirm this analytic result by 3D numerical simulations, and further find that mixing of jet and cocoon material at the collimation throat leads to a substantial stratification of the outflow as well as sporadic loading, even if the injected jet is uniform and continuous. One consequence of this mixing is a strong angular dependence of the radiative efficiency. Another is large differences in the Lorentz factor of different fluid elements that lead to formation of internal shocks. Our analysis indicates that in both long and short GRBs a prominent photospheric component cannot be avoided when observed within an angle of a few degrees to the axis, unless the asymptotic Lorentz factor is limited by baryon loading at the jet base to Γ∞ < 100 (with a weak dependence on outflow power). Photon generation by newly created pairs behind the collimation shock regulates the observed temperature at $\sim 50~\theta _0^{-1}$ keV, where θ0 is the initial jet opening angle, in remarkable agreement with the observed peak energies of prompt emission spectra. Further consequences for the properties of the prompt emission are discussed at the end.

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Salafia, O. S., C. Barbieri, S. Ascenzi, and M. Toffano. "Gamma-ray burst jet propagation, development of angular structure, and the luminosity function." Astronomy & Astrophysics 636 (April 2020): A105. http://dx.doi.org/10.1051/0004-6361/201936335.

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The fate and observable properties of gamma-ray burst jets crucially depend on their interaction with the progenitor material that surrounds the central engine. We present a semi-analytical model of this interaction (which builds upon several previous analytical and numerical works) aimed at predicting the angular distribution of jet and cocoon energy and Lorentz factor after breakout given the properties of the ambient material and of the jet at launch. Using this model, we constructed synthetic populations of structured jets, assuming either a collapsar (for long gamma-ray bursts – LGRBs) or a binary neutron star merger (for short gamma-ray bursts – SGRBs) as progenitor. We assumed all progenitors to be identical, and we allowed little variability in the jet properties at launch: our populations therefore feature a quasi-universal structure. These populations are able to reproduce the main features of the observed LGRB and SGRB luminosity functions, although several uncertainties and caveats have yet to be addressed. We make our simulated populations publicly available.

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Huang, Xiao-Li, Hai-Ming Zhang, Shu-Qing Zhong, and En-Wei Liang. "Doppler Boosting Effect on the Jet Radiation of Gamma-Ray Bursts and Active Galactic Nuclei." Proceedings of the International Astronomical Union 12, S324 (September 2016): 82–84. http://dx.doi.org/10.1017/s1743921317001090.

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AbstractHigh energy photon radiations of gamma-ray bursts (GRBs) and active galactic nuclei (AGNs) are dominated by their jet radiations. It was suggested that relativistic jets powered by different mass-scale black holes may share the same physical laws. A tight relation among the peak luminosity, the peak photon energy in the νfν spectrum, and the initial Lorentz factor is found for GRBs. With samples of GeV-TeV BL Lacs, FSRQs, and NLS1 galaxies, we show that these sources do not follow this relation. This may be attributed to the jet geometry and continuous/episodic jet as well as radiation physics for different kinds of sources.

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Sato, Yuri, Kaori Obayashi, Ryo Yamazaki, Kohta Murase, and Yutaka Ohira. "Off-axis jet scenario for early afterglow emission of low-luminosity gamma-ray burst GRB 190829A." Monthly Notices of the Royal Astronomical Society 504, no. 4 (May 7, 2021): 5647–55. http://dx.doi.org/10.1093/mnras/stab1273.

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ABSTRACT Recently, ground-based Imaging Atmospheric Cherenkov Telescopes have reported the detection of very-high-energy (VHE) gamma-rays from some gamma-ray bursts (GRBs). One of them, GRB 190829A, was triggered by the Swift satellite, and about 2 × 104 s after the burst onset the VHE gamma-ray emission was detected by H.E.S.S. with ∼5σ significance. This event had unusual features of having much smaller isotropic equivalent gamma-ray energy than typical long GRBs and achromatic peaks in X-ray and optical afterglow at about 1.4 × 103 s. Here, we propose an off-axis jet scenario that explains these observational results. In this model, the relativistic beaming effect is responsible for the apparently small isotropic gamma-ray energy and spectral peak energy. Using a jetted afterglow model, we find that the narrow jet, which has the initial Lorentz factor of 350 and the initial jet opening half-angle of 0.015 rad, viewed off-axis can describe the observed achromatic behaviour in the X-ray and optical afterglow. Another wide, baryon-loaded jet is necessary for the later-epoch X-ray and radio emissions. According to our model, the VHE gamma rays observed by H.E.S.S. at 2 × 104 s may come from the narrow jet through the synchrotron self-Compton process.

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Aoi, Junichi, Kohta Murase, Keitaro Takahashi, Kunihito Ioka, and Shigehiro Nagataki. "CAN WE PROBE THE LORENTZ FACTOR OF GAMMA-RAY BURSTS FROM GeV-TeV SPECTRA INTEGRATED OVER INTERNAL SHOCKS?" Astrophysical Journal 722, no. 1 (September 21, 2010): 440–51. http://dx.doi.org/10.1088/0004-637x/722/1/440.

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Ziaeepour, Houri. "Binary Neutron Star (BNS) Merger: What We Learned from Relativistic Ejecta of GW/GRB 170817A." Physics 1, no. 2 (July 17, 2019): 194–228. http://dx.doi.org/10.3390/physics1020018.

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Gravitational Waves (GW) from coalescence of a Binary Neutron Star (BNS) and its accompanying short Gamma-Ray Burst (GRB) GW/GRB 170817A confirmed the presumed origin of these puzzling transients and opened up the way for relating properties of short GRBs to those of their progenitor stars and their surroundings. Here we review an extensive analysis of the prompt gamma-ray and late afterglows of this event. We show that a fraction of polar ejecta from the merger had been accelerated to ultra-relativistic speeds. This structured jet had an initial Lorentz factor of about 260 in our direction, which was O ( 10 ∘ ) from the jet’s axis, and was a few orders of magnitude less dense than in typical short GRBs. At the time of arrival to circum-burst material the ultra-relativistic jet had a close to Gaussian profile and a Lorentz factor ≳ 130 in its core. It had retained in some extent its internal collimation and coherence, but had extended laterally to create mildly relativistic lobes—a cocoon. Its external shocks on the far from center inhomogeneous circum-burst material and low density of colliding shells generated slowly rising afterglows, which peaked more than 100 days after the prompt gamma-ray. The circum-burst material was somehow correlated with the merger. As non-relativistic outflows or tidally ejected material during BNS merger could not have been arrived to the location of the external shocks before the relativistic jet, circum-burst material might have contained recently ejected materials from resumption of internal activities, faulting and mass loss due to deformation and breaking of stars crusts by tidal forces during latest stages of their inspiral but well before their merger. By comparing these findings with the results of relativistic Magneto-Hydro-Dynamics (MHD) simulations and observed gravitational waves we conclude that progenitor neutron stars were most probably old, had close masses and highly reduced magnetic fields.

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Iwamoto, Masanori, Takanobu Amano, Yosuke Matsumoto, Shuichi Matsukiyo, and Masahiro Hoshino. "Particle Acceleration by Pickup Process Upstream of Relativistic Shocks." Astrophysical Journal 924, no. 2 (January 1, 2022): 108. http://dx.doi.org/10.3847/1538-4357/ac38aa.

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Abstract Particle acceleration at magnetized purely perpendicular relativistic shocks in electron–ion plasmas is studied by means of two-dimensional particle-in-cell simulations. Magnetized shocks with the upstream bulk Lorentz factor γ 1 ≫ 1 are known to emit intense electromagnetic waves from the shock front, which induce electrostatic plasma waves (wakefield) and transverse filamentary structures in the upstream region via stimulated/induced Raman scattering and filamentation instability, respectively. The wakefield and filaments inject a fraction of the incoming particles into a particle acceleration process, in which particles are once decoupled from the upstream bulk flow by the wakefield, and are picked up again by the flow. The picked-up particles are accelerated by the motional electric field. The maximum attainable Lorentz factor is estimated as γ max , e ∼ α γ 1 3 for electrons and γ max , i ∼ ( 1 + m e γ 1 / m i ) γ 1 2 for ions, where α ∼ 10 is determined from our simulation results. α can increase up to γ 1 for a weakly magnetized shock if γ 1 is sufficiently large. This result indicates that highly relativistic astrophysical shocks such as external shocks of gamma-ray bursts can be an efficient particle accelerator.

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Chen, Qiang, and Xue-Wen Liu. "An energy-conserving dynamical model of GRB afterglows from magnetized forward and reverse shocks." Monthly Notices of the Royal Astronomical Society 504, no. 2 (April 5, 2021): 1759–71. http://dx.doi.org/10.1093/mnras/stab946.

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ABSTRACT In the dynamical models of gamma-ray burst (GRB) afterglows, the uniform assumption of the shocked region is known as provoking total energy conservation problem. In this work, we consider shocks originating from magnetized ejecta and extend the energy-conserving hydrodynamical model of Yan, Wei & Fan to the MHD limit by applying the magnetized jump conditions from Zhang & Kobayashi. Compared with the non-conservative models, our Lorentz factor of the whole shocked region is larger by a factor ${\lesssim}\sqrt{2}$. The total pressure of the forward shocked region is higher than the reversed shocked region, in the relativistic regime with a factor of about 3 in our interstellar medium (ISM) cases while ejecta magnetization degree σ < 1, and a factor of about 2.4 in the wind cases. For σ ≤ 1, the non-conservative model loses 32–42 per cent of its total energy for ISM cases, and for wind cases 25–38 per cent, which happens specifically in the forward shocked region, making the shock synchrotron emission from the forward shock less luminous than expected. Once the energy conservation problem is fixed, the late-time light curves from the forward shock become nearly independent of the ejecta magnetization. The reverse shocked region does not suffer from the energy conservation problem since the changes of the Lorentz factor are recompensed by the changes of the shocked particle number density. The early light curves from the reverse shock are sensitive to the magnetization of the ejecta, thus are an important probe of the magnetization degree.

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Vieyro, F. L., V. Bosch-Ramon, and N. Torres-Albà. "Non-thermal emission produced by the interaction of a jet with a supernova remnant." International Journal of Modern Physics D 27, no. 10 (July 2018): 1844021. http://dx.doi.org/10.1142/s0218271818440212.

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Core-collapse supernovae (SNe) are found in galaxies with ongoing star-formation. If a starburst galaxy hosts an active galactic nucleus (AGN) with a relativistic jet, the SN could take place inside the jet. The collision of the SN ejecta with the jet flow leads to the formation of a shock, where particles could be accelerated up to relativistic energies, and produce gamma-ray emission. In this work, we analyze the dynamical evolution of the SN within the jet, and compute the non-thermal radiation expected from the interaction. The evolution of the SN Lorentz factor and radius regulates the intensity of the non-thermal emission. The SN can achieve a relativistic regime for powerful jets, resulting in emission significantly enhanced by Doppler boosting for blazar sources. The interaction of SNe with jets of moderate luminosity can result in steady, unbeamed gamma-ray emission, that might be detectable for sources in the local universe.

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JANIUK, AGNIESZKA, and MONIKA MOSCIBRODZKA. "ACCRETION AND OUTFLOW FROM A MAGNETIZED, NEUTRINO COOLED TORUS AROUND THE GAMMA RAY BURST CENTRAL ENGINE." International Journal of Modern Physics: Conference Series 08 (January 2012): 352–55. http://dx.doi.org/10.1142/s2010194512004874.

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Gamma Ray Bursts (GRB) are the extremely energetic transient events, visible from the most distant parts of the Universe. They are most likely powered by accretion on the hyper-Eddington rates that proceeds onto a newly born stellar mass black hole. This central engine gives rise to the most powerful, high Lorentz factor jets that are responsible for energetic gamma ray emission. We investigate the accretion flow evolution in GRB central engine, using the 2D MHD simulations in General Relativity. We compute the structure and evolution of the extremely hot and dense torus accreting onto the fast spinning black hole, which launches the magnetized jets. We calculate the chemical structure of the disk and account for neutrino cooling. Our preliminary runs apply to the short GRB case (remnant torus accreted after NS-NS or NS-BH merger). We estimate the neutrino luminosity of such an event for chosen disk and central BH mass.

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Lin, Da-Bin, Rui-Jing Lu, Shen-Shi Du, Tong Liu, Xiang-Gao Wang, and En-Wei Liang. "Lorentz Factor Evolution of an Expanding Jet Shell Observed in a Gamma-Ray Burst: Case Study of GRB 160625B." Astrophysical Journal 883, no. 2 (October 3, 2019): 187. http://dx.doi.org/10.3847/1538-4357/ab3a56.

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KHANGULYAN, D. V., F. A. AHARONIAN, S. V. BOGOVALOV, A. V. KOLDOBA, and G. V. USTYUGOVA. "HYDRODYNAMICS OF INTERACTION OF PULSAR AND STELLAR WINDS AND ITS IMPACT ON THE HIGH ENERGY RADIATION OF BINARY PULSAR SYSTEMS." International Journal of Modern Physics D 17, no. 10 (September 2008): 1909–15. http://dx.doi.org/10.1142/s021827180801356x.

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The hydrodynamics of the interaction of pulsar and stellar winds in binary systems harboring a pulsar and its impact on the nonthermal radiation of the binary pulsar PSR B1259-63/SS2883 is discussed. The collision of an ultrarelativistic pulsar wind with a nonrelativistic stellar outflow results in significant bulk acceleration of the shocked material from the pulsar wind. Already at distances comparable to the size of the binary system, the Lorentz factor of the shocked flow can be as large as γ ~ 4. This results in significant anisotropy of the inverse Compton radiation of accelerated electrons. Because of the Doppler boosting of the produced radiation, one should expect a variable gamma-ray signal from the system. In particular, this effect may naturally explain the reported tendency of a decrease of TeV gamma-ray flux close to the periastron. The modeling of the interaction of pulsar and stellar winds allows self-consistent calculations of adiabatic losses. Our results show that adiabatic losses dominate over the radiative losses. These results have direct impact on the orbital variability of radio, X-ray and gamma-ray signals detected from the binary pulsar PSR B1259-63/SS2883.

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Liang, En-Wei, Shuang-Xi Yi, Jin Zhang, Hou-Jun Lü, Bin-Bin Zhang, and Bing Zhang. "CONSTRAINING GAMMA-RAY BURST INITIAL LORENTZ FACTOR WITH THE AFTERGLOW ONSET FEATURE AND DISCOVERY OF A TIGHT Γ0-Eγ,isoCORRELATION." Astrophysical Journal 725, no. 2 (December 6, 2010): 2209–24. http://dx.doi.org/10.1088/0004-637x/725/2/2209.

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Yassine, M., F. Piron, R. Mochkovitch, and F. Daigne. "Time evolution of the spectral break in the high-energy extra component of GRB 090926A." Astronomy & Astrophysics 606 (October 2017): A93. http://dx.doi.org/10.1051/0004-6361/201630353.

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Aims. The prompt light curve of the long GRB 090926A reveals a short pulse ~10 s after the beginning of the burst emission, which has been observed by the Fermi observatory from the keV to the GeV energy domain. During this bright spike, the high-energy emission from GRB 090926A underwent a sudden hardening above 10 MeV in the form of an additional power-law component exhibiting a spectral attenuation at a few hundreds of MeV. This high-energy break has been previously interpreted in terms of gamma-ray opacity to pair creation and has been used to estimate the bulk Lorentz factor of the outflow. In this article, we report on a new time-resolved analysis of the GRB 090926A broadband spectrum during its prompt phase and on its interpretation in the framework of prompt emission models. Methods. We characterized the emission from GRB 090926A at the highest energies with Pass 8 data from the Fermi Large Area Telescope (LAT), which offer a greater sensitivity than any data set used in previous studies of this burst, particularly in the 30−100 MeV energy band. Then, we combined the LAT data with the Fermi Gamma-ray Burst Monitor (GBM) in joint spectral fits to characterize the time evolution of the broadband spectrum from keV to GeV energies. We paid careful attention to the systematic effects that arise from the uncertainties on the LAT response. Finally, we performed a temporal analysis of the light curves and we computed the variability timescales from keV to GeV energies during and after the bright spike. Results. Our analysis confirms and better constrains the spectral break, which has been previously reported during the bright spike. Furthermore, it reveals that the spectral attenuation persists at later times with an increase of the break characteristic energy up to the GeV domain until the end of the prompt phase. We discuss these results in terms of keV−MeV synchroton radiation of electrons accelerated during the dissipation of the jet energy and inverse Compton emission at higher energies. We interpret the high-energy spectral break as caused by photon opacity to pair creation. Requiring that all emissions are produced above the photosphere of GRB 090926A, we compute the bulk Lorentz factor of the outflow, Γ. The latter decreases from 230 during the spike to 100 at the end of the prompt emission. Assuming, instead, that the spectral break reflects the natural curvature of the inverse Compton spectrum, lower limits corresponding to larger values of Γ are also derived. Combined with the extreme temporal variability of GRB 090926A, these Lorentz factors lead to emission radii R ~ 1014 cm, which are consistent with an internal origin of both the keV−MeV and GeV prompt emissions.

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Xingxing, Hu, Takata Jumpei, and Tang Qingwen. "GeV emission of gamma-ray binary with pulsar scenario." Monthly Notices of the Royal Astronomical Society 494, no. 3 (April 13, 2020): 3699–711. http://dx.doi.org/10.1093/mnras/staa985.

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ABSTRACT We study GeV emission from gamma-ray binaries by assuming that the compact object is a young pulsar. We assume that the relativistic unshocked pulsar wind with a Lorentz factor of 104–5 can produce the GeV emission by the inverse-Compton scattering process in the dense soft-photon field of the companion star. The travel distance of the unshocked pulsar wind that moves toward the observer depends on the orbital phase of the pulsar. We discuss that the orbital modulation of the GeV emission is a result of combination of the effects of the travel distance of the unshocked pulsar wind and of the anisotropic soft-photon field of the companion star. In this paper, we study how the effect of the travel distance of the unshocked pulsar wind affects to the orbital modulation of GeV emission. We apply our scenario to two gamma-ray binaries, LMC P3 and 4FGL J1405.1−6119. We find that with the suggested system parameters of LMC P3, the observed amplitude of the orbital modulation and the peak width are more consistent with the model light curve by taking into account the effect of the travel distance. For LMC P3, we analyse the GeV spectrum with 8-yr Fermi-LAT data and discuss the broadband emission process in X-ray to TeV energy bands. We predict a possible system geometry for 4FGL J1405.1−6119 by fitting the GeV light curve.

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Pe'er, Asaf, Felix Ryde, Ralph A. M. J. Wijers, Peter Mészáros, and Martin J. Rees. "A New Method of Determining the Initial Size and Lorentz Factor of Gamma-Ray Burst Fireballs Using a Thermal Emission Component." Astrophysical Journal 664, no. 1 (June 27, 2007): L1—L4. http://dx.doi.org/10.1086/520534.

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POUTANEN, J., and B. E. STERN. "PHOTON BREEDING MECHANISM IN RELATIVISTIC JETS: ASTROPHYSICAL IMPLICATIONS." International Journal of Modern Physics D 17, no. 09 (September 2008): 1619–28. http://dx.doi.org/10.1142/s0218271808013224.

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Photon breeding in relativistic jets involves multiplication of high-energy photons propagating from the jet into the external environment and back, with the conversion into electron-positron pairs. The exponential growth of the energy density of these photons is a supercritical process powered by the bulk energy of the jet. The efficient deceleration of the jet outer layers creates a structured jet morphology with a fast spine and slow sheath. In initially fast and high-power jets even the spine can be decelerated efficiently leading to very high radiative efficiencies of conversion of the jet bulk energy into radiation. The decelerating, structured jets have angular distribution of radiation significantly broader than that predicted by a simple blob model with a constant Lorentz factor. This reconciles the discrepancy between the high Doppler factors determined by the fits to the spectra of TeV blazars and the low apparent velocities observed at VLBI scales as well as the low jet Lorentz factors required by the observed statistics and luminosity ratio of Fanaroff-Riley I radio galaxies and BL Lac objects. Photon breeding produces a population of high-energy leptons in agreement with the constraints on the electron injection function required by spectral fits of the TeV blazars. Relativistic pairs created outside the jet and emitting gamma-rays by the inverse Compton process might explain the relatively high level of TeV emission from the misaligned jet in the radio galaxies. The mechanism reproduces basic spectral features observed in blazars including the blazar sequence (shift of the spectral peaks towards lower energies with increasing luminosity). The mechanism is very robust and can operate in various environments characterized by the high photon density.

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Sobacchi, E., and Y. E. Lyubarsky. "Magnetic energy dissipation and origin of non-thermal spectra in radiatively efficient relativistic sources." Monthly Notices of the Royal Astronomical Society 491, no. 3 (November 27, 2019): 3900–3907. http://dx.doi.org/10.1093/mnras/stz3313.

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ABSTRACT The dissipation of turbulent magnetic fields is an appealing scenario to explain the origin of non-thermal particles in high-energy astrophysical sources. However, it has been suggested that the particle distribution may effectively thermalize when the radiative (synchrotron and/or Inverse Compton) losses are severe. Inspired by recent particle-in-cell simulations of relativistic turbulence, which show that electrons are impulsively heated in intermittent current sheets by a strong electric field aligned with the local magnetic field, we instead argue that in plasmas where the particle number density is dominated by the pairs (electron–positron and electron–positron–ion plasmas): (i) as an effect of fast cooling and of different injection times, the electron energy distribution is dne/dγ ∝ γ−2 for γ ≲ γheat (the Lorentz factor γheat being close to the equipartition value), while the distribution steepens at higher energies; (ii) since the time-scales for the turbulent fields to decay and for the photons to escape are of the same order, the magnetic and the radiation energy densities in the dissipation region are comparable; (iii) if the mass energy of the plasma is dominated by the ion component, the pairs with a Lorentz factor smaller than a critical one (of the order of the proton-to-electron mass ratio) become isotropic, while the pitch angle remains small otherwise. The outlined scenario is consistent with the typical conditions required to reproduce the spectral energy distribution of blazars, and allows one to estimate the magnetization of the emission site. Finally, we show that turbulence within the Crab Nebula may power the observed gamma-ray flares if the pulsar wind is nearly charge separated at high latitudes.

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Journal articles on the topic 'Lorentz gamma factor'

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