Model spectra of neutron star surface thermal emission discuss some results
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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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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

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.


Model spectra of neutron star surface thermal emission discuss some results

The flat temperature profile at outer atmosphere


Model spectra of neutron star surface thermal emission discuss some results

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


Model spectra of neutron star surface thermal emission discuss some results

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.


Model spectra of neutron star surface thermal emission discuss some results

The spherical symmetry geometries for the gray atmosphere.

Radiative equilibrium

LTE( if no scattering )


Model spectra of neutron star surface thermal emission discuss some results

The plateau of temperature profile


Model spectra of neutron star surface thermal emission discuss some results

rho~0.001-0.05 g/cm3


Model spectra of neutron star surface thermal emission discuss some results

rho~0.002-0.01 g/cm3


Model spectra of neutron star surface thermal emission discuss some results

rho~0.005-0.2 g/cm3


Model spectra of neutron star surface thermal emission discuss some results

θB=0 degree

rho~0.001-2 g/cm3


Model spectra of neutron star surface thermal emission discuss some results

rho~0.002-2 g/cm3


Model spectra of neutron star surface thermal emission discuss some results

rho~0.3-1 g/cm3


Model spectra of neutron star surface thermal emission discuss some results

rho~0.07-3 g/cm3


Model spectra of neutron star surface thermal emission discuss some results

rho~1-3 g/cm3


Model spectra of neutron star surface thermal emission discuss some results

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.


Model spectra of neutron star surface thermal emission discuss some results

The additional opacity


Model spectra of neutron star surface thermal emission discuss some results

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


Model spectra of neutron star surface thermal emission discuss some results

Resonance frequency

( It is dependent on θ.)

Cutoff frequency

(It is independent of θ)


Model spectra of neutron star surface thermal emission discuss some results

ωp

ωc

ωL

ωp

ωR


Model spectra of neutron star surface thermal emission discuss some results

We define an angle-average optical depth:

where i=1 for O-mode photons and i=2 for X-mode photons.


Model spectra of neutron star surface thermal emission discuss some results

The limb darkening and the magnetic beaming


Model spectra of neutron star surface thermal emission discuss some results

frequency=1017 Hz


Model spectra of neutron star surface thermal emission discuss some results

The spectra


Model spectra of neutron star surface thermal emission discuss some results

θB=0o, O-mode


Model spectra of neutron star surface thermal emission discuss some results

θB=0o, X-mode


Model spectra of neutron star surface thermal emission discuss some results

θB=90o,ΦR=0o, O-mode


Model spectra of neutron star surface thermal emission discuss some results

θB=90o,ΦR=0o, X-mode


Model spectra of neutron star surface thermal emission discuss some results

The absorption features of both polarization modes


Model spectra of neutron star surface thermal emission discuss some results

ωR

ωC


Model spectra of neutron star surface thermal emission discuss some results

^__^

Thank you…………….


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