Transcript pptx

Radiation spectra
from relativistic electrons
moving in
turbulent magnetic fields
2011/3/5-7
Ｙｕｔｏ Ｔｅｒａｋｉ
&
Fumio Takahara
Theoretical Astrophysics Group
Osaka Univ., Japan
Raleigh
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The distribution of lower energy
spectral index of Band function
The number
of GRB
Standard scenario
Internal shock
Synchrotron radiation
Many GRB don’t suit
Synchrotron theory!

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(low energy
Spectral index)
2
3
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Kaneko et al 2006
BATSE
2
Weibel instability near the S.F.
Shock Front

B
PIC simulation by
Sironi & Spitkovsky ‘09
B 
Turbulent magnetic field
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B2
8
2
nme c
3
What decide spectrum shape ?
Synchrotron

B ・
Ｅ（ｔ）
ｔ
Beaming
 1/ 3
log F ( )
Observed pulse
e 
log 
Fourier transform spectrum
→synchrotron spectrum.
Synchrotron radiation or not
Electrons can trace gyro motion in
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rL

or not.
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Which is larger,
rL

or B
?
We focus on the Weibel instability.
B is the order of
c
B  
 peint
c
 pe .
int
The relative Lorentz factor of shells

Proportional coefficient
4ne 2
 pe 
Plasma frequency
 cold me
where
 cold Lorentz factor which generate
  10  B  0.1
the turbulent field
: typical value
from PIC.
2 cold B
B


 O(1)
rL 
int
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  1
  1
synchrotron radiation
Jitter radiation
 1
Intensive study is required !
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??
5
The missing link spectrum
dW
d

0
dW
d

br1
  1
5 / 3
 / g
dW
d
??
 1
 / g
 1/ 3
e 
 syn
 / g
  1
In this work, we reveal
this unknown spectrum.
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Model of turbulent fields
3D turbulent magnetic field
Kolmogorov type.
2
k
B (k )
kmin
 : mean value of B
 2  B 2 
Define  by
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max
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5 / 3
k
kmax
kmax  kmin 100
max  2 k
min
max 2 e


2
rL  k min me c
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E.O.M. and radiation spectrum.
Equation of motion
Example of trajectory
 3  5


dv
me
 e  B
dt
 5
and
  10
we calculate.
Radiation spectrum is calculated using
Lienard-Wiechert potential.

n
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Unit vector points observer
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t  Retarded time
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In case of
F ( )
  1(3D jitter radiation)
where


0
5 / 3
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Normalized by
e
g 
me c
Break1
F ( )  
 5
0
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Vertical axis: Flux
Horizontal axis:
Normalized frequency
F ( )  
5 / 3
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In case of
  0.5
where

0.02
  10

0.41
F ( )

Break 2
5 / 3
The low frequency region becomes hard.
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The spectrum in the case of   1
dW
d

1/ 2

0

5 / 3
 / g
br 2  syn
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br1   kmin c   syn
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1
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F ( )
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In case of
 3
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

0.44
!!
In this case
spectrum is harder than
synchrotron theory predict.
5 / 3
The value of  of near the
GRB internal shock front
  O (1)
Ｔhe harder spectral index of GRB prompt
emission than synchrotron is naturally explained.
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SUMMARY
• We calculate radiation spectra from electrons
moving in turbulent magnetic fields by using first
principle numerical simulation.
• The radiation spectrum in case of   1 was not
known precisely, we reveal it clearly.
• We get harder spectrum than synchrotron which
1



power index is up to
2 in the case of   3
which is in the range of predicted value of near
the GRB internal shock front by PIC simulations.
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