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