Research Paper J. Astron. Space Sci. 30(3), 141-143 (2013) http://dx.doi.org/10.5140/JASS.2013.30.3.141

Jitter and Jitter Self-Compton processes for GRB High-energy Emission Jirong Mao† Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea Yunnan Observatory, Chinese Academy of Sciences, Kunming, China Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming, China

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: 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.

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

(2)

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 . We adopt the dispersion relation in the relativistic collisionless shocks presented by Milosavljevic et al. (2006).

2. CALCULATION

We find frequency is

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

. The relativistic electron , where n =

3×1010cm-3 is the number density in the relativistic shock. The stochastic magnetic field generated by the turbulent cascade can be given by

Received Nov 20, 2012 Revised Dec 25, 2012 Accepted Dec 30, 2012 †Corresponding Author E-mail: [email protected] Tel: +82-42-865-3332, Fax: +82-42-861-5610

This is an open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http:// creativecommons.org/licenses/by-nc/3.0/) which premits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Copyright © The Korean Space Science Society

(1)

141

http://janss.kr plSSN: 2093-5587 elSSN: 2093-1409

5×10−10 10

−10

Fig. 1. Jet-in-jet Scenario.

2×10−10

flux (erg cm−2 s−1)

10−9

2×10−9

J. Astron. Space Sci. 30(3), 141-143 (2013)

~

~

(3) 1

where 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

(4)

105

106

107

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.

(5)

ACKNOWLEDGMENTS

and

(6)

This paper is supported by Grants-in-Aid for Foreign JSPS Fellow (grant Number 24-02022).

, where C is the normalization constant, is the for connection number between the Maxwellian and power law is a characteristic temperature. components, and 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 . The can be estimated by , where microemitter has the length scale of The total number of microemitters within , where ~ is the fireball the fireball shell is is the thick of the shell. The length radius and ~ . We can define a scale of the turbulent eddy is . Therefore, we sum up the dimensionless scale as contributions of the microemitters within the turbulent

http://dx.doi.org/10.5140/JASS.2013.30.3.141

1000 104 energy (keV)

eddy and obtain the total observed duration of GRB . emission as

for for x>1, and . Thomson scattering section is . 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

100

Fig. 2. The multi-wavelength spectrum of GRB 100728A.

where

10

REFERENCES Giannios D, Spitkovsky A, Signatures of a Maxwellian component in shock-accelerated electrons in GRBs, MNRAS, 400, 330-336 (2009). http://dx.doi.org/10.1111/ j.1365-2966.2009.15454.x Landau LD, Lifshitz EM, The Classical Theory of Fields (Pergamon, Oxford, 1971). Mao J, Wang J, Gamma-ray Burst Prompt Emission: Jitter Radiation in Stochastic Magnetic Field Revisited, 2011, ApJ, 731, 26-31(2011). http://dx.doi.org/10.1088/0004637X/731/1/26

142

Jirong Mao Jitter & Jitter self-Compton process for GRB emission

Mao J, Wang J, Jitter Self-Compton Process: GeV Emission of GRB 100728A, ApJ, 748, 135-141 (2012). http://dx.doi. org/10.1088/0004-637X/748/2/135 Milosavljevic M, Nakar E, Spitkovsky A, Steady State Electrostatic Layers from Weibel Instability in Relativistic Collisionless Shocks, ApJ, 637, 765-773 (2006). http://dx.doi.org/10.1086/498445 She ZS, Leveque E, Universal scaling laws in fully developed turbulence, PRL, 72, 336-339 (1994). http://dx.doi. org/10.1103/PhysRevLett.72.336

143

http://janss.kr

Jitter and Jitter Self-Compton processes for GRB High-energy Emission Jirong Mao† Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea Yunnan Observatory, Chinese Academy of Sciences, Kunming, China Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming, China

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: 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.

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

(2)

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 . We adopt the dispersion relation in the relativistic collisionless shocks presented by Milosavljevic et al. (2006).

2. CALCULATION

We find frequency is

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

. The relativistic electron , where n =

3×1010cm-3 is the number density in the relativistic shock. The stochastic magnetic field generated by the turbulent cascade can be given by

Received Nov 20, 2012 Revised Dec 25, 2012 Accepted Dec 30, 2012 †Corresponding Author E-mail: [email protected] Tel: +82-42-865-3332, Fax: +82-42-861-5610

This is an open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http:// creativecommons.org/licenses/by-nc/3.0/) which premits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Copyright © The Korean Space Science Society

(1)

141

http://janss.kr plSSN: 2093-5587 elSSN: 2093-1409

5×10−10 10

−10

Fig. 1. Jet-in-jet Scenario.

2×10−10

flux (erg cm−2 s−1)

10−9

2×10−9

J. Astron. Space Sci. 30(3), 141-143 (2013)

~

~

(3) 1

where 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

(4)

105

106

107

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.

(5)

ACKNOWLEDGMENTS

and

(6)

This paper is supported by Grants-in-Aid for Foreign JSPS Fellow (grant Number 24-02022).

, where C is the normalization constant, is the for connection number between the Maxwellian and power law is a characteristic temperature. components, and 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 . The can be estimated by , where microemitter has the length scale of The total number of microemitters within , where ~ is the fireball the fireball shell is is the thick of the shell. The length radius and ~ . We can define a scale of the turbulent eddy is . Therefore, we sum up the dimensionless scale as contributions of the microemitters within the turbulent

http://dx.doi.org/10.5140/JASS.2013.30.3.141

1000 104 energy (keV)

eddy and obtain the total observed duration of GRB . emission as

for for x>1, and . Thomson scattering section is . 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

100

Fig. 2. The multi-wavelength spectrum of GRB 100728A.

where

10

REFERENCES Giannios D, Spitkovsky A, Signatures of a Maxwellian component in shock-accelerated electrons in GRBs, MNRAS, 400, 330-336 (2009). http://dx.doi.org/10.1111/ j.1365-2966.2009.15454.x Landau LD, Lifshitz EM, The Classical Theory of Fields (Pergamon, Oxford, 1971). Mao J, Wang J, Gamma-ray Burst Prompt Emission: Jitter Radiation in Stochastic Magnetic Field Revisited, 2011, ApJ, 731, 26-31(2011). http://dx.doi.org/10.1088/0004637X/731/1/26

142

Jirong Mao Jitter & Jitter self-Compton process for GRB emission

Mao J, Wang J, Jitter Self-Compton Process: GeV Emission of GRB 100728A, ApJ, 748, 135-141 (2012). http://dx.doi. org/10.1088/0004-637X/748/2/135 Milosavljevic M, Nakar E, Spitkovsky A, Steady State Electrostatic Layers from Weibel Instability in Relativistic Collisionless Shocks, ApJ, 637, 765-773 (2006). http://dx.doi.org/10.1086/498445 She ZS, Leveque E, Universal scaling laws in fully developed turbulence, PRL, 72, 336-339 (1994). http://dx.doi. org/10.1103/PhysRevLett.72.336

143

http://janss.kr