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set4-f7 - Problem 8 Stellar emission The conditions in...

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Astro 405/505, fall semester 2007 Homework, 4th set, return before Friday, September 28, 4pm. Don’t forget to give your name. Problem 7: Radiation spectra under LTE A supernova remnant is observed with an angular diameter θ = 4 . 3 arcmin and a Fux at 100 MHz of F 100 = 1 . 6 · 10 - 19 erg / cm 2 / s / Hz Assume the emission is thermal and emitted under LTE conditions. a) What would be the temperature of the radiating material, if the emission were optically thick? (This is called the brightness temperature) b) At what frequency would the remnant have its radiation maximum, if the emission were optically thick? c) Given the above, what can you say about the ’temperature’ of the radiating material?
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Unformatted text preview: Problem 8: Stellar emission The conditions in stellar photospheres are often well represented by Local Thermodynamic Equilibrium (LTE). Neglecting scattering please derive a quantitative estimate for the angular distribution of the intensity, I ν , that would be seen by an outside observer. a) Assume the temperature T is constant, independent of the vertical optical depth, which itself is assumed independent of frequency. b) Assume the temperature is constant in each of three zones with values T ( τ z ) = T ≤ τ z ≤ τ 1 2 T τ 1 ≤ τ z ≤ τ 2 4 T τ 2 ≤ τ z...
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