Yuki Takeuchi

1. FUNDAMENTAL OD RADIATIVE TRANSFER

Ch1.1 The spectrum correspond to waves which have various wavelength and frequency. λν=c Temperature and energy E=hν T=E/k

ch1.2 Flux = the measure of energy of all rays passing through a given area dAdt. Flux from isotropic source = assuming there are two spherical sources S and S' with radii r and r'. by conservation of energy, energy passing both elements are the same; F(r)*4πr^2 = F(r')*4πr'^2. => F= const/r^2 if S' is fixed.

ch1.3 radiation is the energy carried by individual rays, but we need to consider the energy carried by sets of rays rather than individual ray because single ray essentially does not carry energy.

Specific Intensity = describes the rate of radiative transfer of energy at a specific point P.

Net Flux = integration of flux over solid angle with direction n. F = ∫IcosθdΩ

Momentum flux = momentum flux along ray at angle θ is dF/c. and integrate it over solid angle.

Specific Energy Density = the energy per unit volume per unit frequency range. Total radiation density = integrating specific density over all frequency. Radiation Pressure P = 1/3 u which is also useful for thermodynamics of blackbody radiation.

Ch1.4Radiative Transfer Emission => dI = jds Spontaneous emission coefficient: dE = jdVdΩdt Monochromatic emission coefficient: dE = jdVdΩdtdν (where j_ν = 1/4pi P)

• spontaneous emission can be defined as emissivity ε.

So, spontaneous emission can be dE = ερdVdtdν(dΩ/4π) then, compare those dE to get j = ερ/4pi

Absorption => dI = -αIds derivation is similar to emission above

Radiative transfer equation can be obtained by combining emission and absorption. => (dI/ds)=-αI+j Case.1) Emission only α=0 Case.2) Absorption Only j = 0

Also, transfer equation can be simpler by introducing optical depth τ =>(dI/dτ)=-I+S where S = j/α

Ch1.5

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to be continued...