Radiation spectra from relativistic electrons

moving in turbulent magnetic fields

Ｙｕｔｏ Ｔｅｒａｋｉ&

Fumio TakaharaTheoretical Astrophysics Group

Osaka Univ., Japan2011/3/5-7 1Raleigh

Kaneko et al 2006BATSE

Line of Death

32

The distribution of lower energy spectral index of Band function

The numberof GRB

(low energy Spectral index)

Many GRB don’t suitSynchrotron theory!

Standard scenario Internal shock

Synchrotron radiation

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Weibel instability near the S.F.

Shock Front

Turbulent magnetic field

PIC simulation 　 bySironi & Spitkovsky ‘09

B

2

2

8cnm

B

eB

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What decide spectrum shape ?

Beaming

Ｅ（ｔ）

ｔ

3/1 e

Observed pulse Fourier transform spectrum→synchrotron spectrum.

)(log F

log

　　　　

Synchrotron

・B

Synchrotron radiation or notElectrons can trace gyro motion in or not.

Lr

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Which is larger, orLr ?

Intensive study is required !

B

is the order of .

)1(2

int

Or

Bcold

L

B

10 1.0B : typical valuefrom PIC.

int

peB

c

where

pe

c

11

　 synchrotron radiationJitter radiation

B

ecold

pe mne

24 Plasma frequency

int

cold

The relative Lorentz factor of shells

Lorentz factor which generate the turbulent field

Proportional coefficient

1 ??

We focus on the Weibel instability.

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The missing link spectrum

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ddW

g /

3/1ed

dW

g /1br

03/5

ddW

g /

??11 1

In this work, we reveal this unknown spectrum.

syn

Model of turbulent fields3D turbulent magnetic field Kolmogorov type.

k

)(2 kB

maxkmink

3/5k

2min

max 2cme

kr eL

100minmax kk

minmax

2k

22 B: mean value of B

maxDefine by

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E.O.M. and radiation spectrum.Equation of motion

Bedtvdme

Radiation spectrum is calculated usingLienard-Wiechert potential.

nUnit vector points observer tRetarded time

53Example of trajectory

5 10and we calculate.

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5

　where

1

cme

eg

Normalized by

Break1

03/5)(F

Vertical axis: FluxHorizontal axis: Normalized frequency

Break1 3/5)( F

(3D jitter radiation)

0)( F

In case of

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1041.002.0

3/5Break 2

where

)(F

5.0

The low frequency region becomes hard.

In case of

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ddW

g /

02/1 3/5

synbr 2

The spectrum in the case of

synbr ck 1min

21

1

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3In case of)(F

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3/5

Ｔ he harder spectral index of GRB prompt emission than synchrotron is naturally explained.

)1(O　The value of of near the GRB internal shock front

44.0 ! !In this case spectrum is harder than synchrotron theory predict.

Ｃｏｎｓｉｓｔｅｎｔ

2011/3/5-7 13Raleigh

SUMMARY• We calculate radiation spectra from electrons

moving in turbulent magnetic fields by using first principle numerical simulation.

• The radiation spectrum in case of was not known precisely, we reveal it clearly.

• We get harder spectrum than synchrotron which power index is up to in the case of which is in the range of predicted value of near the GRB internal shock front by PIC simulations.

1

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