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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 Mikhail Medvedev (KU) (KU)

Simulations: Anatoly Spitkovsky (Princeton)

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Rice 05/15/07. GRBs + Lab. Weibel (shocks). Jitter radiation. Mikhail Medvedev (KU). Simulations: Anatoly Spitkovsky (Princeton) - PowerPoint PPT Presentation

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Page 1: Simulations: Anatoly Spitkovsky  (Princeton)

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)

Page 2: Simulations: Anatoly Spitkovsky  (Princeton)

Gamma-Ray Bursts

ISM

Page 3: Simulations: Anatoly Spitkovsky  (Princeton)

…by analogy with Quasar Jets

(Marshall, et al 2002)

Quasar: 3C 273

X-ray image: Chandra

UV

optical

radio

Page 4: Simulations: Anatoly Spitkovsky  (Princeton)

Why the WeibelWhy the Weibel

Page 5: Simulations: Anatoly Spitkovsky  (Princeton)

Conditions at a shock

Anisotropic distribution of

particles (counter-propagating

streams) at the shock front

p

e-

shock ISM

ISM Reflected

Component

Page 6: Simulations: Anatoly Spitkovsky  (Princeton)

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

Page 7: Simulations: Anatoly Spitkovsky  (Princeton)

Relativistic e-ion shock (2D)

(Figures – thanks to Anatoly Spitkovsky)

Page 8: Simulations: Anatoly Spitkovsky  (Princeton)

Magnetizing the UniverseMagnetizing the Universe

Page 9: Simulations: Anatoly Spitkovsky  (Princeton)

Cluster collision

Page 10: Simulations: Anatoly Spitkovsky  (Princeton)

Fact: B-fields do exist

Faraday rotationSynchrotron emission

radio halos relic radio sourcesradio emission from shocks

(Ensslin, Vogt, Pfrommer, 2003)

Page 11: Simulations: Anatoly Spitkovsky  (Princeton)

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

Page 12: Simulations: Anatoly Spitkovsky  (Princeton)

Large Scale Structure shocks

shocks

3D Nonrelativistic Weibelv/c~0.1; M~20

(Ryu, et al 2003) (Medvedev, Silva, Kamionkowski 2006)

Page 13: Simulations: Anatoly Spitkovsky  (Princeton)

Observing Observing

the Weibelthe Weibel

Page 14: Simulations: Anatoly Spitkovsky  (Princeton)

Jitter Radiation

(Medvedev 2000, ApJ)

2)/1( mceB

anglengbeamiangledeflection

Deflection parameter:

Page 15: Simulations: Anatoly Spitkovsky  (Princeton)

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)

Page 16: Simulations: Anatoly Spitkovsky  (Princeton)

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┴

Page 17: Simulations: Anatoly Spitkovsky  (Princeton)

Some GRB spectra

Time-resolved spectra

synch. limit

(Kaneko, et al 2006)

Page 18: Simulations: Anatoly Spitkovsky  (Princeton)

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)

Page 19: Simulations: Anatoly Spitkovsky  (Princeton)

Radiation vs ΘB-field is anisotropic:B=(Bx , By) is random,

Bz=0

(Medvedev, Silva, Kamionkowski 2006; Medvedev 2006)

n

z

xv Θ

observer

Page 20: Simulations: Anatoly Spitkovsky  (Princeton)

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

Page 21: Simulations: Anatoly Spitkovsky  (Princeton)

Modeling spectral evolution

slope ~0.8

flux

α

slope~0.8

Page 22: Simulations: Anatoly Spitkovsky  (Princeton)

Diagnostics of Diagnostics of

the Weibelthe Weibel

Page 23: Simulations: Anatoly Spitkovsky  (Princeton)

Hercules experiment

(Thanks to Paul Drake, 2006)

Page 24: Simulations: Anatoly Spitkovsky  (Princeton)

Weibel diagnostics

(Medvedev 2006)

v

n

z

detector

electron radiation beam

Page 25: Simulations: Anatoly Spitkovsky  (Princeton)

Angle-dependent α(Θ)

(Medvedev, ApJ, 2006)

Spectrum vs. viewing angle

ω2=0.1ωpeak

ω1=0.03ωpeak

ω1 ω2

ωpeak

Spectrum vs. Θ

Page 26: Simulations: Anatoly Spitkovsky  (Princeton)

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.

Page 27: Simulations: Anatoly Spitkovsky  (Princeton)

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

Page 28: Simulations: Anatoly Spitkovsky  (Princeton)

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

Page 29: Simulations: Anatoly Spitkovsky  (Princeton)

Are experiments andAre experiments and

PIC simulations relevant?PIC simulations relevant?

Page 30: Simulations: Anatoly Spitkovsky  (Princeton)

Relativistic e-ion shock (2D)

(Figures – thanks to Anatoly Spitkovsky)

Page 31: Simulations: Anatoly Spitkovsky  (Princeton)

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

Page 32: Simulations: Anatoly Spitkovsky  (Princeton)

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