Simulations: Anatoly Spitkovsky (Princeton)

1. Rice 05/15/07 GRBs + Lab. Weibel (shocks). Jitter radiation. Mikhail Medvedev (KU) 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)

2. Gamma-Ray Bursts ISM G1 G2

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

4. Why the Weibel

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

6. Weibel instability B J J t ~ (g/n)1/2 ms, l ~ 100 (gb/n)1/2 km (Medvedev & Loeb, 1999, ApJ) … current filamentation … x … B - field produced … z y 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 Need B >~ 10-11Gauss in order to obtain (sub)-micro-Gauss fields in clusters (Sigl, Miniati, Ensslin, 2004) (Bruggen, et al2005)

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

13. Observing the Weibel

14. Jitter Radiation Deflection parameter: d (Medvedev 2000, ApJ)

15. Jitter regime When d << 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) w┴(t) = random e- v = const (Medvedev, 2000, ApJ)

16. Jitter radiation. 3D model 2α ~ 4 2α-2β ~ -2.6 κ┴ Spectral power of radiation Electron’s acceleration spectrum B-field spectra in xy & z (Medvedev, ApJ, 2006)

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

18. Jitter vs Synchrotron spectra About 30% of BATSE GRBs and 50% of BSAX GRBs have photon soft indices a greater than –2/3, inconsistent with optically thin Synchrotron Shock Model Fn ~ na+1 (Medvedev, 2000) (Preece, et al., ApJS, 2000)

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

20. More spectra vs. viewing angle

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

22. Diagnostics of the Weibel

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

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

25. Spectrum vs. viewing angle ωpeak ω1 ω2 Spectrum vs. Θ ω1=0.03ωpeak ω2=0.1ωpeak Angle-dependent α(Θ) (Medvedev, ApJ, 2006)

26. 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 re=e2/mec2is 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.

27. Jitter radiation in Hercules (cont.) Now, some numbers. For one electron: Here, let's assume typical values: Magnetic field: B~10Mgauss; 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

28. 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

29. Are experiments and PIC simulations relevant?

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

31. Cooling & Weibel time-scales Synchrotron cooling time Electron/proton dynamical time R± Rph radiation from far downstream, if any Rint τcoolωpp=100 τcoolωpp=30 radiative shock τcoolωpp=1 radiative foreshock

32. Typical parameters GRB plasma laser plasma