2. Radiation Field Basics I Specific Intensity Î© = dddd cos d tA I E

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ss’dEνp θ θ’ p’rdAdA’No sources or sinks of radiation. Pencil beam of radiation passingthrough dA at p and dA’ at p’. Radiant energy passing through bothareas is the same:' '= I cosθdAdtdνdΩ = dE= I cosθ'dA'dtdνdΩ'νSolid angle dΩ subtended by dA’ at p, dΩ’ subtended by dA at p’:dΩ = dA'cos' / r; d2θ Ω ='dAcosθ/ rν2νTherefore:'Iν= I νSpecific intensity independent of distance when no sources or sinks.Solar Limb DarkeningθAssume plane parallel atmosphereMeasure I at different positions on solar disk => get I(θ)
JJν=14IMean Intensity1dΩ =4π2πνπ 0 0πIνsinθdθdφJ ν is a very important quantity. It determines level populationsand ionization state throughout atmosphere. Like I ν , it is afunction of position. For a plane parallel atmosphere (no φdependence) with µ = cos θ:ν11 1( z)= Iν( z,θ )2πsinθdθ= Iν( z,µ )dµ4π2 −1We’ll later use moments of the radiation field. J ν is the 0 th momentMoment operator M operating on f :1( ) 1M n [ f ] = f µ n dµ2 −1R *θ *I *rWhat is J ν at distance r from a star with uniform specific intensityI * across its surface?I = I * for 0 < θ < θ * (µ * < µ < 1)I = 0 for θ > θ * (µ < µ * )JJ=12= I*1µ12I d=I (1 −µ 12 *µ* w is the dilution factor*2 2( 1−1−R*/ r ) = w I*)At large r, w = R 2 /4r 2
Page 1: 2. Radiation Field Basics I• Rutt
Page 5 and 6: The flux emitted by a star per unit
Page 7: For sufficiently small ∆V, the in

2. Radiation Field Basics I Specific Intensity Î© = dddd cos d tA I E

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