Homework # 8, due 26 Apr
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?
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.
2. Explore the evolution of the solar neighborhood with a galactic chemical evolution model with instaneous recycling and infall
which obeys
f (t) = A 1 − t/τf .
Assume an infall timescale of τf = 24 Gyr. Determine the value
of A from the observed surface density ΣT (T ) = 50 M pc−2
of stars and gas at the present time T = 12 Gyr in the Galactic
plane in the solar neighborhood.
Assuming the Schmidt SFR Ψ = νΣg , determine the value of
ν that will give the present gas fraction Σg (T )/ΣT (T ) = 0.24 at
the present time. Hint: Note that
d αt df
−αt
+ αf = e
fe
dt
dt
if α is a constant.
3. Explain why the value of [O/Fe] observed in stars is both greater
than 0 and does not vary with [Fe/H] for metal-deficient stars for
[Fe/H]< −1.5, but decreases with increasing metallicity for more
metal-rich stars. When [Fe/H]=0, what value should [O/Fe] have?
4. Do problem 4.13 in the text.