1. Compton Scattering in Strong Magnetic Fields Department of Physics National Tsing Hua University G.T. Chen 2006/5/4

2. Outline  Motivation  Relativistic Landau Level  Compton Scattering  Results  Discussion and Future Work

3. Motivation  The isolated neutron star 1E1207.4-5209 Four absorption features are seen in the pn spectrum at the harmonically spaced energies of ~0.7kev, ~1.4kev, ~2.1kev, ~2.8kev A. De Luca et al.,A&A,2004

4. Motivation  Using three independent statistical analyses indicated that there is no third or four line. (Kaya Mori et al.,ApJ,2005)  Spectral lines: observed timing : B ~ 2.6 x10 12 G observed timing : B ~ 2.6 x10 12 G cyclotron lines: B~ 8 x10 10 G (electron) cyclotron lines: B~ 8 x10 10 G (electron) B~ 1.6 x10 14 G (proton) B~ 1.6 x10 14 G (proton)  We attempt to construct a model finding  We attempt to construct a model finding the origin of these lines the origin of these lines

5. Motivation  Compton Scattering  Bremsstrahlung Z

6. Relativistic Landau Level

7.  Dirac equation with magnetic field: ( )  Choose Landau gauge

8. Relativistic Landau Level  Assume  ………

9. Relativistic Landau Level  Energy eigenvalue or or

10. Compton Scattering

11.  Feynman diagrams of Compton scattering : Compton Scattering

12.  S-matrix: and and where where

13. Compton Scattering  The differentiate cross section

14. Compton Scattering  Integrate final electron momentum

15. Compton Scattering

16.  Integrate over the final photon azimuth and average over initial yields

17. Compton Scattering  We assume the distribution of initial electrons is 1D relativistic thermal distribution K 1 =modified Bessel fn. of the 2nd kind T = the electron temperature parallel to the field

18. Compton Scattering  From the energy conservation and parallel momentum conservation, we have where where

19. Compton Scattering  Redistribution function: Apply into our case, because of the delta function of energy, the integration over momentum reduces to a summation. Apply into our case, because of the delta function of energy, the integration over momentum reduces to a summation.

20. Compton Scattering  Therefore, the Compton scattering differentiate cross section

21. Compton Scattering 1111

22. Results

23. Results 11221122

29. Discussion & Future Work  The relativistic calculation is given major correction  The appearance of higher harmonics  The appearance of higher harmonics  The energy shift of the resonance  The decrease below the Thomson value at w>w c

30. Discussion & Future Work  Cold plasma  hot plasma  Vacuum polarization should be included

31. Discussion & Future Work  Two photon process

32. >>Thank You >Thank You<<

33. Compton Scattering  is the inverse of the half-life of the electron state j’’ H. Herold et al.,A&A, 1982

34. Compton Scattering

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