Compton Scattering in Strong Magnetic Fields

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Compton Scattering in Strong Magnetic Fields

• Department of Physics
• National Tsing Hua University
• G.T. Chen
• 2006/5/4

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Outline

• Motivation
• Relativistic Landau Level
• Compton Scattering
• Results
• Discussion and Future Work

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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. ,AA ,2004
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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

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Motivation

• Compton Scattering

• Bremsstrahlung

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Relativistic Landau Level
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Relativistic Landau Level

• Dirac equation with magnetic field (
  )
• Choose Landau gauge

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Relativistic Landau Level

• Assume
• ?

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Relativistic Landau Level

• Energy eigenvalue
• or

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Compton Scattering
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Compton Scattering

• Feynman diagrams of Compton scattering

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Compton Scattering

• S-matrix
• and
• where

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Compton Scattering

• The differentiate cross section

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Compton Scattering

• Integrate final electron momentum

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Compton Scattering
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Compton Scattering

• Integrate over the final photon azimuth and
  average over initial yields

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Compton Scattering

• We assume the distribution of initial electrons
  is 1D relativistic thermal distribution
• K1modified Bessel fn. of the 2nd kind
• T the electron temperature parallel to the
  field

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Compton Scattering

• From the energy conservation and parallel
  momentum conservation, we have
• where

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Compton Scattering

• Redistribution function
• Apply into our case, because of the delta
  function of energy, the integration over momentum
  reduces to a summation.

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Compton Scattering

• Therefore, the Compton scattering differentiate
  cross section

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Compton Scattering

• 1

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Results
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Results

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• 2

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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 wgtwc
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Discussion Future Work

• Cold plasma ? hot plasma
• Vacuum polarization should be included

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Discussion Future Work

• Two photon process

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gtgtThank Youltlt
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Compton Scattering

• is the inverse of the half-life of the
  electron state j

H. Herold et al. ,AA, 1982
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Compton Scattering
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Compton Scattering
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