sol3-f7 - Astro 405/505 fall semester 2007 Homework 3rd set...

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Astro 405/505, fall semester 2007 Homework, 3rd set, solutions. Problem 5: Radiation transport with lines Ray A carries the intensity B ν ( T c ) when leaving the central object, and that is essentially the observed intensity at the frequencies ν 1 , because absorption in the outer shell is negligible. At frequency ν 0 we observe B ν ( T s ) which is smaller than B ν ( T c ) for T s < T c , so we see an absorption line, vice versa an emission line. Ray B starts with zero intensity and we always observe an emission line. At ν 1 the intensity is essentially zero, whereas at the line frequency ν 0 the intensity reaches B ν ( T s ) . At ν 0 the intensity along A and B is thus the same. At ν 1 we only see the central object, i.e. ray A. Problem 6: Emission spectra, intensity and fux The source function is a constant and therefore the solution to the radiation transport equation would be S ν = A B ν 2 I ν = A B ν 2 (1 - exp(
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