1. 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)

2. Gamma-Ray Bursts   ISM

3. …by analogy with Quasar Jets (Marshall, et al 2002) Quasar: 3C 273 X-ray image: Chandra UV optical radio

4. Why the Weibel

5. Conditions at a shock Anisotropic distribution of particles (counter-propagating streams) at the shock front p e-e- shock ISM ISM Reflected Component

6. Weibel instability … current filamentation … x y z J J B … B - field produced … (Medvedev & Loeb, 1999, ApJ)  n) 1/2 ms,  n) 1/2 km shock plane

7. Relativistic e-ion shock (2D) (Figures – thanks to Anatoly Spitkovsky)

8. Magnetizing the Universe

9. Cluster collision

10. Fact: B-fields do exist  Faraday rotation  Synchrotron emission  radio halos  relic radio sources  radio emission from shocks (Ensslin, Vogt, Pfrommer, 2003)

11. Cosmo LCDM+MHD simulation (Sigl, Miniati, Ensslin, 2004) (Bruggen, et al2005) B >~ 10 -11 Gauss Need B >~ 10 -11 Gauss in order to obtain (sub)-micro-Gauss fields in clusters

12. Biermann Battery at Reionization (Gnedin, Ferrara, Zweibel, 2000) BB is not enough: generated fields orders of magnitude too weak: B <~10 -17 G | (grad n) x (grad T) |>0

13. Large Scale Structure shocks shocks 3D Nonrelativistic Weibel v/c~0.1; M~20 (Ryu, et al 2003) (Medvedev, Silva, Kamionkowski 2006)

14. Observing the Weibel

15. Jitter Radiation (Medvedev 2000, ApJ) Deflection parameter: 

16. 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) = r 0 + c t  particle experiences random acceleration w ┴ (t) e-e- v = const w ┴ (t) = random (Medvedev, 2000, ApJ)

17. 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┴κ┴

18. Some GRB spectra Time-resolved spectra synch. limit (Kaneko, et al 2006)

19. 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)

20. Beppo-SAX spectra GRB 970111 soft photon index violates synchrotron limit for the entire burst In a sample of 8 GRBs (2-700keV) 50% violate synchrotron limit (Frontera, et al., ApJ, 2000)

21. Radiation vs Θ B-field is anisotropic: B  =(B x, B y ) is random, B z =0 (Medvedev, Silva, Kamionkowski 2006; Medvedev 2006) n z x v Θ observer

22. More spectra vs. viewing angle

23. Modeling spectral evolution slope ~0.8 flux α slope~0.8

24. Diagnostics of the Weibel

25. Hercules experiment (Thanks to Paul Drake, 2006)

26. Weibel diagnostics (Medvedev 2006) v n z x Θ detector electron radiation beam

27. Angle-dependent α(Θ) (Medvedev, ApJ, 2006) Spectrum vs. viewing angle ω 2 =0.1ω peak ω 1 =0.03ω peak ω1ω1 ω2ω2 ω peak Spectrum vs. Θ

28. 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: where r e =e 2 /m e c 2 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.

29. Jitter radiation in Hercules (cont.) Now, some numbers. For one electron: 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 10 9 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 10 6 electrons

30. Feasibility of Jitter diagnostics Total power of jitter radiation: dW/dt ~ 2 x 10 3 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: E ph ~ ħ(ω pe γ 2 ) ~ 4 x 10 -16 J ~ 2.5 keV. Estimate total amount of photons. Duration of pulse t pulse ~ 20fs ~2 x 10 -14 s. The number of photons emitted is, (dW/dt)*t pulse /E ph : N phot ~ 10 5

31. Are experiments and PIC simulations relevant?

32. Relativistic e-ion shock (2D) (Figures – thanks to Anatoly Spitkovsky)

33. Cooling & Weibel time-scales Synchrotron cooling time Electron/proton dynamical time τ cool ω pp =1 τ cool ω pp =30 τ cool ω pp =100 R ph R±R±R±R± R int radiative foreshock radiative shock radiation from far downstream, if any

34. Model constraints realistic possible internal shocks external shocks

35. Typical parameters n ~ 7 x 10 15 cm -3 (L 52 Γ i / Γ 2 2 R 12 2 )n ~ 10 19 cm -3 B ~ 16 MG (√(L 52 ε B ) Γ i / Γ 2 R 12 )B ~ 10 MG ion skin ~ 0.3 cm (Γ 2 R 12 / √L 52 )electron skin ~ 2 microns Weibel on: ions, γ ~ fewelectrons, γ ~ 200 Radiation electrons: γ ~ few 1000γ ~ 200 Photon E ~ 100 keV – 1 MeVE ~ 2.5 keV GRB plasma laser plasma