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h8s - Homework 8 Solutions 1 Show that a simple closed-box...

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Homework # 8 Solutions 1. Show that a simple closed-box model with instantaneous recycling results in the gas-phase metallicity increasing linearly with time. If this is true, what cosmic time does [Fe/H]=-3 correspond to? From the notes, we see that Z = Z 0 + (1 - R ) t , but only if the Schmidt law with N = 1 is assumed. Since Z ( T - 4 . 5 Gyr)) = Z , where T =today, Z ( T ) = Z + (4 . 5 Gyr) (1 - R ). If Z 0 = 0, Z ( T ) = Z T/ ( T - 4 . 5 Gyr) 1 . 6 Z . Then t = 7 . 5 Myr. Also show in this model that the distribution of stars in metallicity dN/d ln Z has a maximum where Z = p , the effective yield of heavy elements defined in the lecture notes. Since dN/d ln Z = M Ze - ( Z - Z 0 ) /p , where N is the number of stars in an interval of Z , the maximum will be at Z = p . 2. Explore the evolution of the solar neighborhood with a galactic chemical evo- lution model with instaneous recycling and infall which obeys f ( t ) = A ( 1 - t/τ f ) . Assume an infall timescale of τ f = 24 Gyr and initial densities Σ g (0)+Σ * (0) = Σ) T (0). Determine the value of A from the observed surface density Σ T ( T ) = 50 M pc - 2
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