Compton Scattering in Strong Magnetic Fields

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 x1012 G cyclotron lines: B~ 8 x1010 G (electron) B~ 1.6 x1014 G (proton)  We attempt to construct a model finding the origin of these lines

5. Z Motivation • Compton Scattering • Bremsstrahlung

6. Relativistic Landau Level

7. Relativistic Landau Level • Dirac equation with magnetic field: ( ) • Choose Landau gauge

8. Relativistic Landau Level • Assume  ………

9. Relativistic Landau Level • Energy eigenvalue or

10. Compton Scattering

11. Compton Scattering • Feynman diagrams of Compton scattering :

12. Compton Scattering • S-matrix: and where

13. Compton Scattering • The differentiate cross section

14. Compton Scattering • Integrate final electron momentum

15. Compton Scattering

16. Compton Scattering • 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 K1=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

19. Compton Scattering • Redistribution function: 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

22. Results

23. Results • 1 • 2

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

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

31. Discussion & Future Work • Two photon process

32. >>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

36. Compton Scattering

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