# Galaxies Lecture 15

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### Leaky Box Model

• Leaky Box Model
• Gas leaves system via galactic winds from SNe
${\displaystyle {d \over dt}{M_{tot}}=-C{d \over dt}{M_{s}}\,\!}$

Where ${\displaystyle M_{s}}$ is the mass in stars, and ${\displaystyle M_{tot}}$ is the mass in stars and gas.

• Going through the same reasoning as before, we find:
{\displaystyle {\begin{aligned}M_{g}(t)&={M_{g}(0) \over 1+C}e^{-{(1+C)Z \over \rho }}\\M_{s}(t)&={M_{tot}(0) \over 1+C}e^{-{(1+C)Z \over \rho }}\\\end{aligned}}\,\!}
• This can explain the G dwarf problem if 90% of gas is blown out of the galaxy. This doesn’t match observations for the Milky Way, but it does work for dwarf irregulars.
• Accreting Box Model
• For large spirals, gas only accounts for a small amount of the total mass. Some infalling gas immediately turns into stars.
${\displaystyle {d \over dt}{M_{tot}}\neq 0\,\!}$

but ${\displaystyle dM_{s}+dM_{g}=0}$.

• Working through this model, we find that:
${\displaystyle M_{s}(Z

Note the log (as opposed to exponential) dependence.

• Choosing ${\displaystyle Z={\frac {1}{3}}Z_{0}}$, and using ${\displaystyle M_{g}=0.1M_{s}}$, we find:
${\displaystyle {{M_{s}(Z<{\frac {1}{3}}Z_{0}) \over M_{s}}=0.04}\,\!}$

This solves the G dwarf problem.