GRB Prompt Emission: Turbulence, Magnetic Field & Jitter Radiation

Jirong Mao

Background

Relativistic electrons

Magnetic field

Synchrotron radiation

B for Synchrotron Radiation

B= constant Large scale

external, homogenous and steady

Origin of B ?

Alternative Scenario

Small scale and random B? Length scale

Skin length: lsk~c/wpe wpe is plasma frequency

skll )11.0(

Weibel Instability

Generation of random magnetic field: How to obtain mature B ? Weibel instability ---- plasma velocity anisotropic distribution: initial perturbation (by relativistic shocks) --

electrons/positrons move oppositely -- perturbation current -- B production -- until certain balance

Turbulence Spectrum

Kolmogorov spectrum F(k):

Index is not universal

3/5

kkF )(

Stochastic Magnetic Field Production

Random magnetic field could be generated by turbulence:

dkkFB )(2

Radiation (I)

Radiation by a single relativistic particle in small scale B (Landau & Lifshitz 1971):

)()2

1()(2 '

42'

2

2'

2

2/1

2'3

2

'

2

dwc

eI

Radiation (II)

Space and temporal Fourier transform of Lorentz force(Fleishman 2006, Mao & Wang 2007):

Particularly, jitter radiation, 1D case

))(()()()2

1())(( 000'

0

2/1

42'

2

2'2

'

'

232

4

2

qqqqKqvqdqdqdcm

eI

2222 / pe )/)(2/( 2222' pe

Radiation Spectral Index

K(q) ~<B^2> spectral index frequency depends on the relation

1 I

2/12222 )2//411( kcck pe

ck2

Magnetic Field of GRB

dkkBk

k

2

11 )/( tsheddy Rlk kk 2/1Pr

GB 6102.1 1

51332

62 )

10()

1()

100()

102.1(102.5

erg

E

s

t

G

BB

Particle Acceleration

Giannios & Spitkosky (2009)

turbulent acceleration (Honda 2005)

sc

U

cm

L

G

B

MeV

Etacc

1110

26

212 )1.0

()100.1

()102.1

()(104.1

sG

Btcool

26

14

8 )102.1

()108.1

(100.3

eVc

U

cm

LE )

1.0()

100.1()

108.1(107.4 2/1

102/1

414

4106.3/ epe mm

Maximum Acceleration

Stochastic acceleration Virtanen & Vainio (2005)

acceleration in random and small scale B field might be very effective

Mizuno et al. numerical simulation

122max 101.1/ mckeB

Preliminary Results

Random & small scale B generated by turbulence

Jitter spectrum index determined by turbulent spectrum: results consistent with BASTE & Fermi

Acceleration is effective

Sironi, Nishikawa, numerical simulation

Turbulence Validation

Small-Scale Turbulent Dynamo

Schekochihin et al. (2004)

Small-Scale Turbulent Dynamo

Scale problem: sub-Larmor radius validation ?

B generation? Particle acceleration? Particle energy distribution? ……

Wiggler Number & Deflection Angle

1/ 2 cmeBl ecol

2/ cmeBlK ecol

K1

Synchrotron vs. Jitter

Relativistic electrons move in the external, homogenous and steady magnetic field (a)

Relativistic electrons move in the random and small scale magnetic field (b)

Medvedev 2000

2mceFa

2mceFa