Model Spectra of Neutron Star Surface Thermal Emission Department of Physics National Tsing Hua University Lun-Wen Yeh

Structure of neutron star Radiation transfer equation Temperature correction Flux ≠const Flux = const Spectrum P(τ) ρ(τ) T(τ)

Assumptions  Plane-parallel atmosphere( local model)  Radiative equilibrium( energy transported solely by radiation )  Equation of state is ideal gas( ionized H)  Neglect conduction and convection  Hydrostatics  No magnetic field  The physical properties independent of time

Structure of NS  Gray atmosphere  Equation of state  Oppenheimer-Volkoff

Structure of NS  Rosseland mean

Radiation transfer equation Absorption Spontaneous emissionInduced emission Scattering

Radiation transfer equation Diffusion approimation

Feautrier method Mean intensity like Flux like

Feautrier method Surface normal n

Feautrier method

d=2,3,……,D-2,D-1 μ=1,2,……M

Feautrier method I 1 I 2 I 3.. I 1 I 2 I 3.. I 1 I 2 I 3.. d=1 d=2 d=3…..

Test Feautrier method Scattering

Test Feautrier method Scattering and free-free absorption

46~91 4.9% 91~ % 901~ %

46~ % 91~ % 901~ %

46~ % 91~ % 901~ %

46~91 4.2% 91~ % 901~ %

Future work  Run my program with many directions, and carry out temperature-correction.  Add magnetic filed in local model