Jitter and Jitter SelfCompton processes for GRB Highenergy Emission
 Author: Mao Jirong
 Organization: Mao Jirong
 Publish: Journal of Astronomy and Space Sciences Volume 30, Issue3, p141~144, 15 Sep 2013

ABSTRACT
We propose jitter radiation and jitter selfCompton process in this work. We apply our model to the study of GRB prompt emission and GeVemission. Our results can explain the multiwavelength spectrum of GRB 100728A very well.

KEYWORD
acceleration of particles , gammarays , radiation mechanisms , turbulence

1. INTRODUCTION
It is well accepted that the gammaray burst (GRB) prompt emission is original from synchrotron radiation. Synchrotron radiation is the radiation of relativistic electrons in an ordered and largescale magnetic field. If magnetic field is random and smallscale, 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 smallscale magnetic field (Mao & Wang 2011). Jitter photons can be scattered by those relativistic electrons. We call this phenomenon as “jitter selfCompton (JSC)” process. We apply this physical process to the study of GRB. The minijets 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
where
is the frequency in the radiative field,
ω_{pe} is the background plasma frequency,γ is the electron Lorentz factor, andw _{ω'} is the Fourier transform of the electron acceleration. We simplify the radiation feature in onedimensional case asThe 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 relationω ' =q _{0} q_{v} . We adopt the dispersion relation in the relativistic collisionless shocks presented by Milosavljevic et al. (2006). We find. The relativistic electron frequency is
ω_{pe} = (4πe ^{2}n /Г_{sh}m_{e} )^{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 bywhere
is decided by the turbulent cascades (She & Leveque 1994). The famous Kolmogorov number is
ξ_{p} =p /3.In general, our JSC calculation is as same as Synchrotron SelfCompton calculation. The JSC emission flux density in the unit of erg s^{1} cm^{3} Hz^{1} is
where
f (x ) =x +2x ^{2}lnx +x ^{2}2x ^{3} for 0 ？x ？ 1,f (x ) = 0 forx ？ 1, andx ≡v /4γ ^{2}v _{0}. Thomson scattering section isσ_{T} = 8πr _{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
for
γ ≤γ _{nth} andfor
γ ？γ _{nth}, whereC is the normalization constant,γ _{nth} is the connection number between the Maxwellian and power law components, and Θ =kT /m_{e}c ^{2} is a characteristic temperature.We further apply a “jetinjet” 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
. The microemitter has the length scale of
l_{s} =γct _{cool}, wheret _{cool} = 6πm_{e}c /σ_{T}γB ^{2} The total number of microemitters within the fireball shell isn = 4πR ^{2}δ_{s} /l_{s} ^{3}, whereR ~10^{13} cm is the fireball radius andδ_{s} =ct _{cool} is the thick of the shell. The length scale of the turbulent eddy isl _{eddy} ~R /Г. We can define a dimensionless scale asn_{l} =l _{eddy}/l_{s} . Therefore, we sum up the contributions of the microemitters within the turbulenteddy and obtain the total observed duration of GRB emission as
T =n_{l}nP Гt _{cool}.3. DISCUSSION AND CONCLUSION
We apply our model and reproduce the multiwavelength spectrum of GRB 100728A. The extremely powerful Xray flares and GeV emission of GRB 100728A were observed by the Swift/Xray 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.

[Fig. 1.] Jetinjet Scenario.

[Fig. 2.] The multiwavelength spectrum of GRB 100728A.