exam1-06-sol

exam1-06-sol - into red giants so a steady state is not...

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Astro 346, Spring Semester 2006 Intermediate exam, solutions Problem 1: The lifetime of stars N = 0 . 7 2 M ¯ m p 1 . 6 · 10 57 δE = N 4 δm c 2 1 . 9 · 10 52 erg L M 4 L = 16 L ¯ τ = 0 . 1 δE L 10 9 years In the red-giant phase I use twice the amount of fuel (hydrogen) and radiate at 25 the rate compared with the main-sequence phase. The lifetime must therefore be a factor of 12 shorter. τ RG 8 · 10 7 years Red giants have a luminosity a factor of 25 higher, but live a factor of 12 shorter. In a steady state the relative contributions to the total luminosity of a galaxy scale as the the relative contributions to the total radiated energy, so red giants contribute twice as much as main sequence stars. However, stars of about one solar mass or less haven’t had time to turn
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Unformatted text preview: into red giants, so a steady state is not established and these stars presently only contribute radiation in the main-sequence phase. Problem 2: Angular momentum Angular momentum conservation for the initial state: ω i ’ ω ¯ R 2 ¯ R 2 i = 2 π P ¯ R 2 ¯ R 2 i ’ 2 . 5 · 10-22 rad / s The rotational velocity then follows as v φ = R i ω i ’ 1 . 7 · 10-3 cm / s The free-fall time scale is depending on the initial mass density as ρ = 3 M 4 π R 3 i ’ 1 . 4 · 10-24 g / cm 3 τ FF ’ ( G ρ )-1 / 2 ’ 3 · 10 15 s ’ 10 8 yrs...
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