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

Background  Relativistic electrons  Magnetic field  Synchrotron radiation

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

Alternative Scenario  Small scale and random B?  Length scale  Skin length: l sk ~c/w pe w pe is plasma frequency

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

Turbulence Spectrum  Kolmogorov spectrum F(k):  Index is not universal

Stochastic Magnetic Field Production  Random magnetic field could be generated by turbulence:

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

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

Radiation Spectral Index  K(q) ~  spectral index  frequency depends on the relation

Magnetic Field of GRB 

Particle Acceleration  Giannios & Spitkosky (2009)  turbulent acceleration (Honda 2005)

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

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

Turbulence Validation

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

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

Wiggler Number & Deflection Angle

Synchrotron vs. Jitter  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