Upload
graham-harding
View
46
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Rice 05/15/07. GRBs + Lab. Weibel (shocks). Jitter radiation. Mikhail Medvedev (KU). Simulations: Anatoly Spitkovsky (Princeton) - PowerPoint PPT Presentation
Citation preview
Rice 05/15/07
Simulations: Anatoly Spitkovsky (Princeton)
Luis Silva and the Plasma Simulation Group (Portugal)
Ken Nishikawa (U. Alabama, Huntsville)
Aake Nordlund and his group (Niels Bohr Institute, Copenhagen, Denmark)
Experiment: Paul Drake and Hercules Exp. Team (U.Michigam)
Mikhail Medvedev (KU)Mikhail Medvedev (KU)
Gamma-Ray Bursts
ISM
…by analogy with Quasar Jets
(Marshall, et al 2002)
Quasar: 3C 273
X-ray image: Chandra
UV
optical
radio
Why the WeibelWhy the Weibel
Conditions at a shock
Anisotropic distribution of
particles (counter-propagating
streams) at the shock front
p
e-
shock ISM
ISM Reflected
Component
Weibel instability
… current filamentation …x
y
z
J
J
B… B - field produced …
(Medvedev & Loeb, 1999, ApJ)
n)1/2 ms, n)1/2 kmshock plane
Relativistic e-ion shock (2D)
(Figures – thanks to Anatoly Spitkovsky)
Magnetizing the UniverseMagnetizing the Universe
Cluster collision
Fact: B-fields do exist
Faraday rotationSynchrotron emission
radio halos relic radio sourcesradio emission from shocks
(Ensslin, Vogt, Pfrommer, 2003)
Cosmo LCDM+MHD simulation
(Sigl, Miniati, Ensslin, 2004)
(Bruggen, et al2005)
Need B >~ 10 B >~ 10-11-11GaussGauss in order to obtain (sub)-micro-Gauss fields in clusters
Large Scale Structure shocks
shocks
3D Nonrelativistic Weibelv/c~0.1; M~20
(Ryu, et al 2003) (Medvedev, Silva, Kamionkowski 2006)
Observing Observing
the Weibelthe Weibel
Jitter Radiation
(Medvedev 2000, ApJ)
2)/1( mceB
anglengbeamiangledeflection
Deflection parameter:
Jitter regime
When 1, one can assume that particle is highly relativistic ɣ>>1
particle’s trajectory is piecewise-linear particle velocity is nearly constant r(t) = r0 + c t
particle experiences random acceleration w┴(t)
e-
v = const
w┴(t) = random
(Medvedev, 2000, ApJ)
Jitter radiation. 3D model
Spectral power of radiation
B-field spectra in xy & z
(Medvedev, ApJ, 2006)
Electron’s acceleration
spectrum
2α ~ 4
2α-2β ~ -2.6
κ┴
Some GRB spectra
Time-resolved spectra
synch. limit
(Kaneko, et al 2006)
Jitter vs Synchrotron spectra
About 30% of BATSE GRBs and 50% of BSAX GRBs have photon soft indices
greater than –2/3, inconsistent with optically thin Synchrotron Shock Model
F ~
(Preece, et al., ApJS, 2000)
(Medvedev, 2000)
Radiation vs ΘB-field is anisotropic:B=(Bx , By) is random,
Bz=0
(Medvedev, Silva, Kamionkowski 2006; Medvedev 2006)
n
z
xv Θ
observer
More spectra vs. viewing angle
Radiation Spectra for Varying θ
-18
-17.5
-17
-16.5
-16
-15.5
-15
-14.5
-14
-13.5
-13
-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1
Log ω
Log (dW
/dω
)
10
20
30
40
50
60
70
80
Modeling spectral evolution
slope ~0.8
flux
α
slope~0.8
Diagnostics of Diagnostics of
the Weibelthe Weibel
Hercules experiment
(Thanks to Paul Drake, 2006)
Weibel diagnostics
(Medvedev 2006)
v
n
z
xΘ
detector
electron radiation beam
Angle-dependent α(Θ)
(Medvedev, ApJ, 2006)
Spectrum vs. viewing angle
ω2=0.1ωpeak
ω1=0.03ωpeak
ω1 ω2
ωpeak
Spectrum vs. Θ
Jitter radiation in Hercules
To estimate the overall energetics of radiation emitted in the experiment, we compute the total power of jitter radiation, averaged over angles, emitted by a relativistic electron with the Lorentz factor γ in the magnetic field of strength B. Interestingly, it turns out to be identical to that of synchrotron radiation:
,3
2 222 cBrdt
dWe
where re=e2/mec2 is the classical electron radius. Note that the spectrum
and angular dependence different in the jitter and synchrotron regimes. Note also that since the emitting electron is relativistic, most of the radiation goes into a cone of opening angle ~1/γ about its direction of propagation. The observed power is smaller when the system (Weibel filaments) is observed from angles greater than ~1/γ with respect to the electron beam direction. Here we do not consider the angular dependence, but can be accurately calculated later, when needed.
Jitter radiation in Hercules (cont.)
Now, some numbers. For one electron:
,)()/(10568.1 2215 gaussBsergdt
dW
Here, let's assume typical values:Magnetic field: B~10 Mgauss;Electron energy: ~100MeV γ~200
These yield the emitted power per electron of about:
dW/dt ~ 6 x 10-4 Watt.
In order to calculate the total emitted energy, one needs to multiply by the total number of emitting electrons. The charge in the beam is 0.5 nC, which is about 3 x 109 electrons. However, the beam diverges by about 1 degree so that at a distance of 6 mm the beam is about 100 µm in extent. If it interacts with a 3 µm structure (perhaps a bit of an underestimate), then only about 0.1% of the electrons interact with the structure, N ~ 3 x 106 electrons
Feasibility of Jitter diagnostics
Total power of jitter radiation:
dW/dt ~ 2 x 103 Watt.
This should be a good approximation for emission power within the beaming cone of ~1/γ. A more accurate estimate of emitted power as a function of angle can be done.
Photon energy:
Eph~ ħ(ωpeγ2) ~ 4 x 10-16 J ~ 2.5 keV.
Estimate total amount of photons.
Duration of pulse tpulse~ 20fs ~2 x 10-14 s. The number of photons emitted is, (dW/dt)*tpulse/Eph :
Nphot ~ 105
Are experiments andAre experiments and
PIC simulations relevant?PIC simulations relevant?
Relativistic e-ion shock (2D)
(Figures – thanks to Anatoly Spitkovsky)
Cooling & Weibel time-scales
Synchrotron cooling time
Electron/proton dynamical time
ττcoolcool ωωpppp=1=1
ττcoolcool ωωpppp=30=30
ττcoolcool ωωpppp=100=100
RRphph
RR±±
RRintint
radiative foreshockradiative foreshock
radiative shockradiative shock
radiation from far radiation from far downstream, if anydownstream, if any
Typical parameters
n ~ 7 x 1015 cm-3 (L52 Γi / Γ22 R12
2) n ~ 1019 cm-3
B ~ 16 MG (√(L52 εB) Γi / Γ2 R12) B ~ 10 MG
ion skin ~ 0.3 cm (Γ2 R12 / √L52) electron skin ~ 2 microns
Weibel on: ions, γ ~ few electrons, γ ~ 200
Radiation electrons: γ ~ few 1000 γ ~ 200
Photon E ~ 100 keV – 1 MeV E ~ 2.5 keV
GRB plasma laser plasma