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### PSet5

Course: AST 871, Fall 2009
School: National Taiwan University
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Word Count: 315

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871, Astronomy Spring 2007, Problem Set 5 Due Tuesday, May 22 in class Problem 1: Given the tabulation of the Clayton, Cardelli &amp;Mathis interstellar extinction curve attached, renormalize the curve to plot A / AV as a function of 1/ for RV=3.1 and RV=5.0. Using this curve, and your retabulation, answer the following questions: a) Use your renormalized extinction curve to find the ratios: AH AH AH ABr...

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871, Astronomy Spring 2007, Problem Set 5 Due Tuesday, May 22 in class Problem 1: Given the tabulation of the Clayton, Cardelli &Mathis interstellar extinction curve attached, renormalize the curve to plot A / AV as a function of 1/ for RV=3.1 and RV=5.0. Using this curve, and your retabulation, answer the following questions: a) Use your renormalized extinction curve to find the ratios: AH AH AH ABr ABr ABr for each value of RV. Please specify how you did the interpolation of the extinction curve. You will need to look up the wavelengths of these 4 emission lines. b) In Case B recombination for an HII region with Te=104 K, the intrinsic line ratios are as follows: jH / jH = 2.87 jBr / jBr = 2.96 By comparing the observed line ratios to their Case B values, you can estimate the amount of extinction along the line of sight. Start by assuming that all of the extinction is in a simple foreground and screen, derive an expression for AV in terms of the observed and intrinsic emission-line ratios I(H)/I(H) and I(Br)/I(Br) for RV=3.1 c) The slab geometry is one in which the dust is uniformly mixed with the emission-line gas. The solution of the equation of radiative transfer in this case is 1 e I = I ,0 For this case, derive formulas for AV for the H/H and Br/Br emission line ratios (again for RV=3.1) d) Turning the problem around, make plots of the observed line ratios as a function of AV in the range 0<AV<30 for each of t...

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