Jitter and Jitter Self-Compton processes for GRB High-energy Emission

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  • 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.


  • KEYWORD

    acceleration of particles , gamma-rays , radiation mechanisms , turbulence

  • 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

    image

    where

    image

    is the frequency in the radiative field, ωpe is the background plasma frequency, γ is the electron Lorentz factor, and wω' is the Fourier transform of the electron acceleration. We simplify the radiation feature in one-dimensional case as

    image

    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

    image

    . The relativistic electron frequency is ωpe = (4πe2nshme)1/2 = 9.8 × 109Гshs-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

    image

    where

    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

    image

    where f(x) = x+2x2lnx+x2-2x3 for 0 ? x ? 1, f(x) = 0 for x ? 1, and xv/4γ2v0. Thomson scattering section is σT = 8πr02/3=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

    image

    for γγnth and

    image

    for γγnth, where C is 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

    image

    . The microemitter has the length scale of ls = γctcool, where tcool = 6πmec/σTγB2 The total number of microemitters within the fireball shell is n = 4πR2δs/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 = nlnPГtcool.

    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.

  • 1. Giannios D, Spitkovsky A (2009) Signatures of a Maxwellian component in shock-accelerated electrons in GRBs [MNRAS] Vol.400 P.330-336 google doi
  • 2. Landau LD, Lifshitz EM 1971 The Classical Theory of Fields google
  • 3. Mao J, Wang J (2011) Gamma-ray Burst Prompt Emission: Jitter Radiation in Stochastic Magnetic Field Revisited, 2011 [ApJ] Vol.731 P.26-31 google doi
  • 4. Mao J, Wang J (2012) Jitter Self-Compton Process: GeV Emission of GRB 100728A [ApJ] Vol.748 P.135-141 google doi
  • 5. Milosavljevic M, Nakar E, Spitkovsky A (2006) Steady State Electrostatic Layers from Weibel Instability in Relativistic Collisionless Shocks [ApJ] Vol.637 P.765-773 google doi
  • 6. She ZS, Leveque E (1994) Universal scaling laws in fully developed turbulence [PRL] Vol.72 P.336-339 google doi
  • [Fig. 1.] Jet-in-jet Scenario.
    Jet-in-jet Scenario.
  • [Fig. 2.] The multi-wavelength spectrum of GRB 100728A.
    The multi-wavelength spectrum of GRB 100728A.