Jitter and Jitter Self-Compton processes for GRB High-energy Emission
Jitter and Jitter Self-Compton processes for GRB High-energy Emission
Journal of Astronomy and Space Sciences. 2013. Sep, 30(3): 141-144
Copyright ©2013, The Korean Space Science Society
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  • Received : November 11, 2012
  • Accepted : December 12, 2012
  • Published : September 15, 2013
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Jirong Mao
We propose jitter radiation and jitter self-Compton process in this work. We apply our model to the study of GRB prompt emission and GeV-emission. Our results can explain the multi-wavelength spectrum of GRB 100728A very well.
It is well accepted that the gamma-ray burst (GRB) prompt emission is original from synchrotron radiation. Synchrotron radiation is the radiation of relativistic electrons in an ordered and large-scale magnetic field. If magnetic field is random and small-scale, synchrotron radiation is not valid. In this work, we propose that random and smallscale magnetic field can be generated by turbulence. The socalled jitter radiation is the radiation of relativistic electrons in random and small-scale magnetic field (Mao & Wang 2011). Jitter photons can be scattered by those relativistic electrons. We call this phenomenon as “jitter self-Compton (JSC)” process. We apply this physical process to the study of GRB. The mini-jets in a bulk jet structure is also introduced as well (Mao & Wang 2012). We present our model below.
The radiation by a single relativistic electron in the smallscale magnetic field was studied by Landau & Lifshitz (1971). The radiation intensity, which is the energy per unit frequency per unit time is
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is the frequency in the radiative field, ωpe is the background plasma frequency, γ is the electron Lorentz factor, and w ω' is the Fourier transform of the electron acceleration. We simplify the radiation feature in one-dimensional case as
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The dispersion relation q 0 = q 0 ( q ) is in the fluid field, and the radiation field can be linked with the fluid field by the relation ω ' = q 0 - qv . We adopt the dispersion relation in the relativistic collisionless shocks presented by Milosavljevic et al. (2006). We find
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. The relativistic electron frequency is ωpe = (4 πe 2 n shme ) 1/2 = 9.8 × 10 9 Г sh s -1 . where n = 3 × 10 10 cm -3 is the number density in the relativistic shock.
The stochastic magnetic field < δB ( q )> generated by the turbulent cascade can be given by
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Jet-in-jet Scenario.
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is decided by the turbulent cascades (She & Leveque 1994). The famous Kolmogorov number is ξp = p /3.
In general, our JSC calculation is as same as Synchrotron Self-Compton calculation. The JSC emission flux density in the unit of erg s -1 cm -3 Hz -1 is
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where f ( x ) = x +2 x 2 ln x + x 2 -2 x 3 for 0 ˂ x ˂ 1, f ( x ) = 0 for x ˃ 1, and x v /4 γ 2 v 0 . Thomson scattering section is σT = 8 πr 0 2 /3=6.65×10 -25 cm 2 . n ph ( v 0 ) is the number density of seed photons, and it can be easily calculated from the jitter radiation.
The electron energy distribution is given by Giannios & Spitkovsky (2009) as
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for γ γ nth and
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for γ ˃ γ nth , where C is the normalization constant, γ nth is the connection number between the Maxwellian and power law components, and Θ = kT / mec 2 is a characteristic temperature.
We further apply a “jet-in-jet” scenario, as shown in Fig. 1 . Those microemitters radiating as minijets are within the bulk jet. The possibility of observing these minijets can be estimated by
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. The microemitter has the length scale of ls = γct cool , where t cool = 6 πmec / σTγB 2 The total number of microemitters within the fireball shell is n = 4 πR 2 δs / ls 3 , where R ~10 13 cm is the fireball radius and δs = ct cool is the thick of the shell. The length scale of the turbulent eddy is l eddy ~ R /Г. We can define a dimensionless scale as nl = l eddy / ls . Therefore, we sum up the contributions of the microemitters within the turbulent
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The multi-wavelength spectrum of GRB 100728A.
eddy and obtain the total observed duration of GRB emission as T = nlnP Г t cool .
We apply our model and reproduce the multi-wavelength spectrum of GRB 100728A. The extremely powerful X-ray flares and GeV emission of GRB 100728A were observed by the Swift/X-ray telescope and the Fermi/LAT, respectively. In this work, as shown in Fig. 2 , the emission of GRB 100728A can be well explained by the jitter radiation and JSC process.
This paper is supported by Grants-in-Aid for Foreign JSPSFellow (grant Number 24-02022).
Giannios D , Spitkovsky A (2009) Signatures of a Maxwelliancomponent in shock-accelerated electrons in GRBs MNRAS 400 330 - 336
Landau LD , Lifshitz EM 1971 The Classical Theory of Fields Pergamon Oxford
Mao J , Wang J (2011) Gamma-ray Burst Prompt Emission: JitterRadiation in Stochastic Magnetic Field Revisited, 2011 ApJ 731 26 - 31
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Milosavljevic M , Nakar E , Spitkovsky A (2006) Steady StateElectrostatic Layers from Weibel Instability inRelativistic Collisionless Shocks ApJ 637 765 - 773
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