Model Spectra of Neutron Model Spectra of Neutron Star Surface Thermal Star Surface Thermal EmissionEmission
Department of Physics
National Tsing Hua University
Lun-Wen Yeh 2004.5.6
Structure of neutron star
Radiation transfer equation
Temperature correction
Flux ≠const
Flux = constSpectrum
P(τ) ρ(τ) T(τ)
AssumptionsAssumptions Plane-parallel atmosphere( local model)Plane-parallel atmosphere( local model)
Radiative equilibrium( energy transported solely by radiation ) Radiative equilibrium( energy transported solely by radiation )
Equation of state is ideal gas( ionized H) Equation of state is ideal gas( ionized H)
Neglect conduction and convectionNeglect conduction and convection
HydrostaticsHydrostatics
No magnetic fieldNo magnetic field
The physical properties independent of timeThe physical properties independent of time
Structure of NSStructure of NS
Gray atmosphere Gray atmosphere
Equation of stateEquation of state
Oppenheimer-VolkoffOppenheimer-VolkoffkT
mP p
2
Structure of NSStructure of NS
Rosseland meanRosseland mean
Radiation transfer equationRadiation transfer equationAbsorption Spontaneous emission Induced emission
Scattering
Radiation transfer Radiation transfer equationequation
Diffusion approimation
Feautrier methodFeautrier methodMean intensity like
Flux like
1
0
2
1
2
i1
2
j
2
ij
R
SCi
ii
1
0
2
1
2
i1
2
j
2
ij
R
SCi
ii
j
j
),(g)(P),(g)(P2163
S)(Id
)(dI
),(g)(P),(g)(P2163
S)(Id
)(dI
Feautrier methodFeautrier method
Surface normal n
Feautrier methodFeautrier method
ddddddd SPAPBPC 11
Feautrier methodFeautrier method
ddddddd SPAPBPC 11
d=2,3,……,D-2,D-1
μ=1,2,……M
Feautrier methodFeautrier method
I1
I2
I3
..
..
..
I1
I2
I3
..
..
..
I1
I2
I3
..
..
..
d=1 d=2 d=3…..
Test Feautrier methodTest Feautrier method
Scattering
Test Feautrier methodTest Feautrier method
Scattering and free-free absorption
46~91 4.9%
91~901 4.1%
901~9001 0.39%
46~91 0.29%
91~901 0.17%
901~9001 0.0079%
46~91 0.19%
91~901 0.065%
901~9001 0.0058%
46~91 4.2%
91~901 3.6%
901~9001 0.30%
Future workFuture work
Run my program with many directions , Run my program with many directions , and carry out temperature-correction.and carry out temperature-correction.
Add magnetic filed in local model Add magnetic filed in local model
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