# ps7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.901: Astrophysics I Fall Term 2002 PROBLEM SET 7 Due: Thursday, November 14, 2002 Reading: Carroll & Ostlie, Chapters 15. You may also find it useful to look at Chapters 2 and 3 of Black Holes, White Dwarfs, and Neutron Stars by Shapiro and Teukolsky, and Chapter 9 of Hansen and Kawaler. 1. Properties of a white dwarf. Carroll & Ostlie, Problem 15.1 2. Helium lines in white dwarfs. Carroll & Ostlie, Problem 15.2 3. Hydrogen content in white dwarfs. Carroll & Ostlie, Problem 15.3 4. White dwarf cooling. Carroll & Ostlie, Problem 15.8 5. Mass-radius relation for polytropic stars. In this problem, we return to polytropic stars, whose pressure and density are related as P = γ , where γ = 1+(1 /n ), K and n are constants, and n is the polytropic index. Recall that these stars satisfy the Lane-Emden equation. In lecture and in Problem Set 5, we showed that the radius of the star is R = 1 where a = ( n + 1) K 4 πG 1 / 2 ρ (1 n ) / 2 n c , and that the mass is M = 4 πa 3 ρ c - ξ 2 ξ = ξ 1 . (a) Show that the mass-radius relation for a polytropic star is

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