1. Radiation spectra from relativistic electrons moving in turbulent magnetic fields Ｙｕｔｏ Ｔｅｒａｋｉ & Fumio Takahara Theoretical Astrophysics Group Osaka Univ., Japan 2011/3/5-71Raleigh

2. Kaneko et al 2006 BATSE The distribution of lower energy spectral index of Band function The number of GRB (low energy Spectral index) Many GRB don’t suit Synchrotron theory! Standard scenario Internal shock Synchrotron radiation 2011/3/5-72Raleigh

3. Weibel instability near the S.F. Shock Front Turbulent magnetic field PIC simulation by Sironi & Spitkovsky ‘09 2011/3/5-73Raleigh

4. What decide spectrum shape ? Beaming Ｅ（ｔ） ｔ Observed pulse Fourier transform spectrum → synchrotron spectrum. Synchrotron ・ Synchrotron radiation or not Electrons can trace gyro motion in or not. 2011/3/5-74Raleigh

5. Which is larger, or ? Intensive study is required ! is the order of. : typical value from PIC. where synchrotron radiation Jitter radiation Plasma frequency The relative Lorentz factor of shells Lorentz factor which generate the turbulent field Proportional coefficient We focus on the Weibel instability. 2011/3/5-75Raleigh

6. The missing link spectrum 2011/3/5-7Raleigh6 In this work, we reveal this unknown spectrum.

7. Model of turbulent fields 3D turbulent magnetic field Kolmogorov type. : mean value of B Define by 2011/3/5-77Raleigh

8. E.O.M. and radiation spectrum. Equation of motion Radiation spectrum is calculated using Lienard-Wiechert potential. Unit vector points observerRetarded time Example of trajectory and we calculate. 2011/3/5-78Raleigh

9. where Normalized by Break1 Vertical axis: Flux Horizontal axis: Normalized frequency Break1 (3D jitter radiation)In case of 2011/3/5-79Raleigh

10. Break 2 where The low frequency region becomes hard. In case of 2011/3/5-710Raleigh

11. The spectrum in the case of 2011/3/5-711Raleigh

12. In case of 2011/3/5-712Raleigh

13. Ｔ he harder spectral index of GRB prompt emission than synchrotron is naturally explained. The value of of near the GRB internal shock front ! In this case spectrum is harder than synchrotron theory predict. 2011/3/5-713Raleigh

14. SUMMARY We calculate radiation spectra from electrons moving in turbulent magnetic fields by using first principle numerical simulation. The radiation spectrum in case of was not known precisely, we reveal it clearly. We get harder spectrum than synchrotron which power index is up to in the case of which is in the range of predicted value of near the GRB internal shock front by PIC simulations. 2011/3/5-714Raleigh