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

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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

Originally I should report the results of the model using diffusion approximation, but there are still some problems.

Lun-Wen Yeh 2006.4.13

- 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.

The flat temperature profile at outer atmosphere

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

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.

The spherical symmetry geometries for the gray atmosphere.

Radiative equilibrium

LTE( if no scattering )

The plateau of temperature profile

rho~0.001-0.05 g/cm3

rho~0.002-0.01 g/cm3

rho~0.005-0.2 g/cm3

θB=0 degree

rho~0.001-2 g/cm3

rho~0.002-2 g/cm3

rho~0.3-1 g/cm3

rho~0.07-3 g/cm3

rho~1-3 g/cm3

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.

The additional opacity

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

Resonance frequency

( It is dependent on θ.)

Cutoff frequency

(It is independent of θ)

ωp

ωc

ωL

ωp

ωR

We define an angle-average optical depth:

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

The limb darkening and the magnetic beaming

frequency=1017 Hz

The spectra

θB=0o, O-mode

θB=0o, X-mode

θB=90o,ΦR=0o, O-mode

θB=90o,ΦR=0o, X-mode

The absorption features of both polarization modes

ωR

ωC

^__^

Thank you…………….