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Unformatted text preview: AST 3722C - Spring 2008 Homework #7 – Due before class March 25 Instructions: Solve each part of each problem below. Where math is involved, and unless otherwise indicated, show your work. • 1. (1 point.) The star β Cyg is actually a double star. (a) Let subscripts 1 and 2 refer to the two stars. In B-band, the stars have magnitudes m B 1 = 4 . 171 and m B 2 = 5 . 027. Which star is fainter and by what factor in flux density? (b) In V-band, the stars have magnitudes m V 1 = 3 . 085 and m V 2 = 5 . 088. Which star is fainter and by what factor in flux density? (c) Use these numbers to figure out and explain which is the bluer (hotter) star, 1 or 2? • 2. (3 points.) Suppose you are looking at a star – call it “A” – that provides a flux density F A ( λ ) such that: F A ( λ ) = C A × parenleftBigg 1 μ m λ parenrightBigg 3 . 97 , where λ is the wavelength and C A is a constant with dimension power per area per wavelength interval. Nearby, a new object has appeared in the sky – call it “B” – and very conveniently you can take pictures of B while A is in the same FOV. You observe the two objects at several wavelengths and measure the following differences in magnitudes between A and B: Wavelength m A − m B ( μ m) (mag) 1.2 μ m-10.058 1.6 μ m-5.730 2.2 μ m-2.282 3.6 μ m 1.115 5.0 μ m 2.498 8.9 μ m 3.904 9.7 μ m 4.040 10.6 μ m 4.166 11.7 μ m 4.291 12.5 μ m 4.366 18.7 μ m 4.714 20.6 μ m 4.776 (Of course there are uncertainties on these magnitudes but ignore those for now.) (a) Calculate F B , object B’s flux density, at all 12 wavelengths in terms of C A . (b) Make a semilog plot of wavelength versus F B . Since C A is in all values of F B , you can assume C A = 1 (in proper units), or anything you want for that matter. You should see that the plotted points more or less trace out a Planck function....
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- Spring '09
- Astronomy, Hubble Space Telescope, Globular cluster, µm µm µm