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ps3_oct2011

ps3_oct2011 - Ge 133 Problem Set 3 due Oct 27th A The goal...

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Ge 133 - Problem Set # 3, due Oct. 27 th A) The goal of this problem is to understand Spectral Energy Distributions (SEDs), the spectra emitted by a star plus a disk. Using some simple assumptions, you’ll generate your own model SED. For this problem, assume the star has the properties adopted by Chiang & Goldreich (an effective temperature of 4000 K, a mass of 0.5 solar masses, and a radius of 2.5 solar radii). For the disk, assume an opaque disk extending from the stellar surface out to 100 AU. We will also assume that the dust in the disk radiates as a perfect blackbody. For this problem, use the following form of the blackbody equation: B λ ( T ) = 2 πhc 2 ( λ ) 5 1 e hc/ ( λkT ) - 1 [erg / s / cm 2 / cm] where everything is in cgs units. (1) Equation (4) of Chiang & Goldreich tells you what the temperature versus radius is for a flat, geometri- cally thin disk. Calculate this flat disk temperature at a distance of 1 AU and compare it to what you know about the Earth. Why do these numbers differ? (2) Real disks are flared, and for the interior, optically thick part of the disk the temperaure can be approximated as T(interior) 150/R 3 / 7 K, where R=distance from the central star (in AU). Assuming that we are viewing the star and disk from directly above (i.e. along the pole) at a distance of 10 parsecs (a parsec is 3 × 10 18

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