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sol2-f5

# sol2-f5 - Astro 405/505 fall semester 2005 Homework 2nd set...

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Astro 405/505, fall semester 2005 Homework, 2nd set, solutions Problem 3: Radiation spectra under LTE The supernova remnant subtends a solid angle element d Ω = 1 . 2 · 10 - 6 sr. The intensity therefore is I ν = F ν d Ω = 1 . 3 · 10 - 13 erg / cm 2 / s / Hz / sr which we need to compare with the Planckian, because that is the solution of the radiation transport equation for LTE and large optical depth. B ν ( T ) = 2 h ν 3 c 2 1 exp kT - 1 B 100 ( T ) = (1 . 5 · 10 - 23 cgs) 1 exp kT - 1 I ν = B 100 ( T ) requires kT or, more precisely, kT = (8 . 7 · 10 9 ) T 4 · 10 7 K The radiation maximum occurs at about 3 kT or about 2 · 10 18 Hz. The emission is not necessarily optically thick, in which case the radiating material can only be hotter than calculated here. Problem 4: Time-dependent line profiles The problem is similar to that discussed in class except that now we would wish to calculate rates, i.e. also temporal probabilities. The ansatz would be P ( E γ , t obs ) dE γ dt obs = P ( v ) dv P (Ω) dφ d cos θ P ( t ) dt

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sol2-f5 - Astro 405/505 fall semester 2005 Homework 2nd set...

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