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

Unresolved SourcesRelate energy observed to ν at stellar surface:Energy received per detector area, from anulus: df ν= Iνdωdω = solid angle of anulusAnulus area (r = R * sin θ):θdS = 2πr dr= 2πµ dµR *rdSfνdω = dS /D 2Integrate over ω:2R *2= 2π( R*/ D)I(R*, µ , ν ) µ ¤dµ02= ( R / D)R , ν )1 2α*Rα¢¡* = angular diameter=*,ν )4Unresolved => measure fluxInverse square law. Know α * , get absolute flux at star*£¡1*Energy DensityThe energy flow in a beam of radiation isdVds = c dtnθdAdEν= I cosθdAdtdνdΩThe flow has velocity c (photons) andtravels a distance ds in time dt = ds/cthrough volume dV = dA ds cos θ. Thus,each beam carries dE ν = (1/c) I ν dΩ dV.If multiple beams pass through a smallvolume ∆V, integration over ∆V and overall beam directions gives the radiantenergy E ν dν contained in ∆V acrossbandwidth dν as:1νd ν ¥ ¥ E = IνdVdΩdνc ∆VΩν