Advanced
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
This is an open Access article distributed under the terms of theCreative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which premits unrestrictednon-commercial use, distribution, and reproduction in any medium,provided the original work is properly cited.
  • Received : November 11, 2012
  • Accepted : December 12, 2012
  • Published : September 15, 2013
Download
PDF
e-PUB
PubReader
PPT
Export by style
Share
Article
Author
Metrics
Cited by
TagCloud
About the Authors
Jirong Mao
mao@yukawa.kyoto-u.ac.jp
Abstract
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.
Keywords
1. INTRODUCTION
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.
2. CALCULATION
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
Lager Image
where
Lager Image
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
Lager Image
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
Lager Image
. 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
Lager Image
Jet-in-jet Scenario.
Lager Image
where
Lager Image
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
Lager Image
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
Lager Image
for γ γ nth and
Lager Image
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
Lager Image
. 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
Lager Image
The multi-wavelength spectrum of GRB 100728A.
eddy and obtain the total observed duration of GRB emission as T = nlnP Г t cool .
3. DISCUSSION AND CONCLUSION
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.
Acknowledgements
This paper is supported by Grants-in-Aid for Foreign JSPSFellow (grant Number 24-02022).
References
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
Mao J , Wang J (2012) Jitter Self-Compton Process: GeV Emission ofGRB 100728A ApJ 748 135 - 141
Milosavljevic M , Nakar E , Spitkovsky A (2006) Steady StateElectrostatic Layers from Weibel Instability inRelativistic Collisionless Shocks ApJ 637 765 - 773
She ZS , Leveque E (1994) Universal scaling laws in fully developedturbulence PRL 72 336 - 339