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# Sol4 - AST371 Introduction to Astrophysics(Fall 2006 HW4...

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AST371: Introduction to Astrophysics (Fall 2006) HW4 – Solutions 1) a)

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b) In this figure the horizontal axis is the time (in units of the period), and the vertical axis is the bolometric magnitude. Notice that the magnitude is shown “backwards,” so that points on the light curve with higher magnitude is shown closer to the bottom. The primary minimum is the one that goes deeper, i.e., the one on the right. The secondary minimum is on the left.
c) m 1 = - 2.457487 m 2 = - 1.545881 m 3 = - 1.991399 F 2 F 1 =10 2 5 m 1 - m 2 ( ) F 3 F 1 =10 2 5 m 1 - m 3 ( ) F 1 - F 2 F 1 - F 3 = 1- F 2 F 1 1- F 3 F 1 = 1- 10 2 5 m 1 - m 2 ( ) 1- 10 2 5 m 1 - m 3 ( ) = = 1- 0.431873 1- 0.650975 =1.628 T 1 T 2 = F 1 - F 2 F 1 - F 3 1 4 =1.1296 The temperature ratio of the data given is 15200 / 13700 = 1.1095, better than 2% agreement. Our model and calculation is a very simplistic. E.g., we assumed perfect black bodies, and ignored tidal deformations.

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2) a) Main sequence stars are in red circles; the blue line has a slope of 4, and the dashed magenta line has a slope of 3.5. Overall, 4 seems to be a reasonable approximation.
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