radiation spectra from relativistic electrons moving in turbulent magnetic fields
DESCRIPTION
Radiation spectra from relativistic electrons moving in turbulent magnetic fields. Yuto Teraki & Fumio Takahara Theoretical A strophysics Group Osaka Univ., Japan. The distribution of lower energy spectral index of Band function. Line of Death. The number of GRB. Standard scenario. - PowerPoint PPT PresentationTRANSCRIPT
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
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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 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
321
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