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Model Spectra of Neutron Star Surface Thermal Emission

Model Spectra of Neutron Star Surface Thermal Emission. Soccer 2005.10.20. Assumptions. Plane-parallel atmosphere( local model). Radiative equilibrium( energy transported solely by radiation ) . Hydrostatics. The composition of the atmosphere is fully ionized ideal hydrogen gas.

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Model Spectra of Neutron Star Surface Thermal Emission

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  1. Model Spectra of Neutron Star Surface Thermal Emission Soccer 2005.10.20

  2. Assumptions • Plane-parallel atmosphere( local model). • Radiative equilibrium( energy transported solely by radiation ) . • Hydrostatics. • The composition of the atmosphere is fully ionized ideal hydrogen gas. • B~1012 gauss, T~ 106K, g*~1014cm/s2. • All physical quantities are independent of time

  3. Oppenheimer-Volkoff The Structure of neutron star atmosphere P(τ) ρ(τ) T(τ) Feautrier or Improved Feautrier Flux = const Radiation transfer equation Spectrum Flux ≠const Unsold Lucy process Temperature correction

  4. The structure of neutron star atmosphere • Gray atmosphere • Equation of state • Oppenheimer-Volkoff We adopted the Thomson depth,

  5. Radiation transfer equation: Spontaneous emission Absorption Scattering Induced emission ň

  6. Electromagnetic wave in magnetized plasma We considered fully ionized hydrogen gas in homogenous magnetic field. The equation of motion of the gas is Assuming cold plasma that is neglect the thermal motions of gas.

  7. Assuming neutral plasma that is J0=0 and neglecting the volume magnetic moment we have M=0. From the above formulas we can get the dielectric tensor for cold plasma. If w>>wci, w>>wpi, we can neglect ion component. The dielectric tensor describes the properties of the plasma in the magnetic field.

  8. From Maxwell equations we can solve index of reflection( a complex number). B z k θ y x

  9. Solving above equation we obtain N2 for X-mode and O-mode. Plus sign for X-mode ; minus sign for O-mode.

  10. Then we can solve Ex, Ey, Ez in the coordinate that the magnetic field is parallel to z-axis. Define e+=(Ex+iEy)/21/2 e-=(Ex-iEy)/21/2 ez=Ez. Here |e+|2 +|e-|2 +|ez|2=1 B z k θ y x

  11. The Thomson scattering opacity The free-free opacity

  12. Radiation transfer equation: Absorption Spontaneous emission Induced emission Scattering ň

  13. z I B n θR θB Θ is the angle between B and I. ΦR y x

  14. Boundary condition: Use diffusion approximation for inner boundary. Ii(τ1,-μR)=0 Ii(τD, μR)=(B(τD)+ μR∂B(τD)/∂τ)/2 τ1,τ2,τ3, . . . . . . . . . . . . . . . . . . . . . . . . . . .,τD

  15. Feautrier method

  16. Combine above two equation and use matrix form for two modes. Boundary conditions: PD=B/2 P1=R1 We can solve P and then obtain R and intensity I immediately.

  17. Unsold-Lucy Process(Mihalas , 1st edition ,1970) flux temperature tau tau temperature flux log(tau) tau

  18. ∫ dΩ ∫μRdΩ

  19. Assume: J(τ)~3K(τ) , J(0)~2H(0) Combine above two equation, we have

  20. 1.The following results are in the condition of θB=0 that is surface normal parallel to magnetic field. 2.Dellogtau=0.01, dellogfre=0.1, number of direction in hemisphere is 25. 3.The magnetic filed=1012 Gauss, Teff=106 K, g*=1e14 cm/s2. 4.Only the radiation damping term was adopted in opacities.

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