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Radiative Field (Hubeny & Mihalas Chapter 3)

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

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Radiative Field (Hubeny & Mihalas Chapter 3)

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  1. Radiative Field(Hubeny & Mihalas Chapter 3) Specific IntensityI and its angular moments:Mean Intensity JFlux HRadiation Pressure K

  2. Specific Intensity I

  3. Specific Intensity • Vector • Units: • for one dimensional casewhere z is height in atmospheremeasured positive upwards • Applied to resolved objects • Independent of distance

  4. Compare to Photon Description

  5. Mean Intensity J • Scalar: z I

  6. J and Energy Density

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

  8. Flux F

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

  10. Surface and Observed Flux

  11. Surface and Observed Flux

  12. Integrated Flux andStellar Effective Temperature • monochromatic • bolometric • Stefan’s law • relation

  13. Radiation Pressure Tensor

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

  15. Mean Radiation Pressure

  16. K in1-D Case: see hand out

  17. Isotropic case (deep in star)

  18. Plane wave (outer atmosphere) • Variable Eddington factor = K / Jchanges from 1/3 (deep) to 1(outer)

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