Jitter and Jitter Self-Compton processes for GRB High-energy Emission
- Author: Mao Jirong
- Organization: Mao Jirong
- Publish: Journal of Astronomy and Space Sciences Volume 30, Issue3, p141~144, 15 Sep 2013
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.
acceleration of particles , gamma-rays , radiation mechanisms , turbulence
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
is the frequency in the radiative field,
ωpeis the background plasma frequency, γis 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
The dispersion relation
q0 = q0( q) is in the fluid field, and the radiation field can be linked with the fluid field by the relation ω' = q0 - qv. We adopt the dispersion relation in the relativistic collisionless shocks presented by Milosavljevic et al. (2006). We find
. The relativistic electron frequency is
ωpe= (4 πe2 n/Г shme)1/2 = 9.8 × 109Г shs-1. where n = 3 × 1010cm-3 is the number density in the relativistic shock.
The stochastic magnetic field <
δB( q)> generated by the turbulent cascade can be given by
is decided by the turbulent cascades (She & Leveque 1994). The famous Kolmogorov number is
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
f( x) = x+2 x2ln x+ x2-2 x3 for 0 ？ x？ 1, f( x) = 0 for x？ 1, and x≡ v/4 γ2 v0. Thomson scattering section is σT= 8 πr02/3=6.65×10-25cm2. nph( v0) 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
γ≤ γnth and
γ？ γnth, where Cis the normalization constant, γnth is the connection number between the Maxwellian and power law components, and Θ = kT/ mec2 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
. The microemitter has the length scale of
ls= γctcool, where tcool = 6 πmec/ σTγB2 The total number of microemitters within the fireball shell is n= 4 πR2 δs/ ls3, where R~1013 cm is the fireball radius and δs= ctcool is the thick of the shell. The length scale of the turbulent eddy is leddy ~ R/Г. We can define a dimensionless scale as nl= leddy/ ls. Therefore, we sum up the contributions of the microemitters within the turbulent
eddy and obtain the total observed duration of GRB emission as
T= nlnPГ tcool.
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.
[Fig. 1.] Jet-in-jet Scenario.
[Fig. 2.] The multi-wavelength spectrum of GRB 100728A.