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Radiative Field (Hubeny & Mihalas Chapter 3)

This chapter explores the concept of specific intensity and its angular moments in the radiative field. It covers topics such as mean intensity, flux, radiation pressure, and the comparison to photon descriptions. The text is applicable to resolved objects and independent of distance.

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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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