GRB Prompt Emission: Turbulence, Magnetic Field & Jitter Radiation

1. GRB Prompt Emission: Turbulence, Magnetic Field & Jitter Radiation Jirong Mao

2. Background • Relativistic electrons • Magnetic field • Synchrotron radiation

3. B for Synchrotron Radiation • B= constant Large scale external, homogenous and steady • Origin of B ?

4. Alternative Scenario • Small scale and random B? • Length scale • Skin length: lsk~c/wpe wpe is plasma frequency

5. Weibel Instability • Generation of random magnetic field: How to obtain mature B ? • Weibel instability ---- plasma velocity anisotropic distribution: initial perturbation (by relativistic shocks) -- electrons/positrons move oppositely -- perturbation current -- B production -- until certain balance

6. Turbulence Spectrum • Kolmogorov spectrum F(k): • Index is not universal

7. Stochastic Magnetic Field Production • Random magnetic field could be generated by turbulence:

8. Radiation (I) Radiation by a single relativistic particle in small scale B (Landau & Lifshitz 1971):

9. Radiation (II) • Space and temporal Fourier transform of Lorentz force(Fleishman 2006, Mao & Wang 2007): • Particularly, jitter radiation, 1D case

10. Radiation Spectral Index • K(q) ~<B^2> • spectral index • frequency depends on the relation

11. Magnetic Field of GRB

12. Particle Acceleration • Giannios & Spitkosky (2009) • turbulent acceleration (Honda 2005)

13. Maximum Acceleration • Stochastic acceleration Virtanen & Vainio (2005) • acceleration in random and small scale B field might be very effective • Mizuno et al. numerical simulation

14. Preliminary Results • Random & small scale B generated by turbulence • Jitter spectrum index determined by turbulent spectrum: results consistent with BASTE & Fermi • Acceleration is effective • Sironi, Nishikawa, numerical simulation

15. Turbulence Validation

16. Small-Scale Turbulent Dynamo • Schekochihin et al. (2004)

17. Small-Scale Turbulent Dynamo • Scale problem: sub-Larmor radius validation ? • B generation? • Particle acceleration? • Particle energy distribution? • ……

18. Wiggler Number & Deflection Angle

19. Relativistic electrons move in the external, homogenous and steady magnetic field (a) Relativistic electrons move in the random and small scale magnetic field (b) Medvedev 2000 Synchrotron vs. Jitter