Radiative Field (Hubeny & Mihalas Chapter 3)

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Presentation transcript:

Radiative Field (Hubeny & Mihalas Chapter 3) Specific Intensity I and its angular moments: Mean Intensity J Flux H Radiation Pressure K

Specific Intensity I

Specific Intensity Vector Units: for one dimensional case where z is height in atmosphere measured positive upwards Applied to resolved objects Independent of distance

Compare to Photon Description

Mean Intensity J Scalar: z I

J and Energy Density

Total Energy Density Total energy density across spectrum Thermal equilibrium (deep in star) J=B

Flux F

Flux in 1-D Atmosphere Defined only in z direction Astrophysical flux (see Kurucz 1979) Eddington flux

Surface and Observed Flux

Surface and Observed Flux

Integrated Flux and Stellar Effective Temperature monochromatic bolometric Stefan’s law relation

Radiation Pressure Tensor

Physical Meaning: Photon Distribution Function # photons/sec passing unit area oriented with normal in i direction E/c =momentum/photon

Mean Radiation Pressure

K in1-D Case: see hand out

Isotropic case (deep in star)

Plane wave (outer atmosphere) Variable Eddington factor = K / J changes from 1/3 (deep) to 1(outer)