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Model Spectra of Neutron Star Surface Thermal Emission – discuss some results

Model Spectra of Neutron Star Surface Thermal Emission – discuss some results. Originally I should report the results of the model using diffusion approximation, but there are still some problems. Lun-Wen Yeh 2006.4.13. outline. The flat temperature profile at outer atmosphere.

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Model Spectra of Neutron Star Surface Thermal Emission – discuss some results

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  1. Model Spectra of Neutron Star Surface Thermal Emission –discuss some results Originally I should report the results of the model using diffusion approximation, but there are still some problems. Lun-Wen Yeh 2006.4.13

  2. outline • The flat temperature profile at outer atmosphere. • The plateau of temperature profile. • The additional opacity. • The limb darkening and the magnetic beaming. • The spectra. • The absorption features of both polarization modes. Ps: All the following results are calculated in Teff=106K; B=1012 gauss or zero filed.

  3. The flat temperature profile at outer atmosphere

  4. This flat feature would extend to τ=0. That is because of the plane-parallel assumption.

  5. The gray atmosphere in the plane-parallel geometry Radiative equilibrium LTE( if no scattering ) f is Eddington factor which is ~ 1/3 at deep atmosphere and ~ 1 at outer atmosphere.

  6. The spherical symmetry geometries for the gray atmosphere. Radiative equilibrium LTE( if no scattering )

  7. The plateau of temperature profile

  8. rho~0.001-0.05 g/cm3

  9. rho~0.002-0.01 g/cm3

  10. rho~0.005-0.2 g/cm3

  11. θB=0 degree rho~0.001-2 g/cm3

  12. rho~0.002-2 g/cm3

  13. rho~0.3-1 g/cm3

  14. rho~0.07-3 g/cm3

  15. rho~1-3 g/cm3

  16. The plateau feature is because the photon-matter decoupling areas have stronger angle-dependence for the O-mode photons than the X-mode photons and most O-mode photons decouple than X-mode photons at more outer layer.

  17. The additional opacity

  18. In the cold plasma assumption the refractive index is Θ is the angle between the magnetic field and the direction of intensity. + is O-mode; - is X-mode

  19. Resonance frequency ( It is dependent on θ.) Cutoff frequency (It is independent of θ)

  20. ωp ωc ωL ωp ωR

  21. We define an angle-average optical depth: where i=1 for O-mode photons and i=2 for X-mode photons.

  22. The limb darkening and the magnetic beaming

  23. frequency=1017 Hz

  24. The spectra

  25. θB=0o, O-mode

  26. θB=0o, X-mode

  27. θB=90o,ΦR=0o, O-mode

  28. θB=90o,ΦR=0o, X-mode

  29. The absorption features of both polarization modes

  30. ωR ωC

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