# Galaxies Lecture 15

### Leaky Box Model

• Leaky Box Model
• Gas leaves system via galactic winds from SNe
${d \over dt}{M_{tot}}=-C{d \over dt}{M_{s}}\,\!$ Where $M_{s}$ is the mass in stars, and $M_{tot}$ is the mass in stars and gas.

• Going through the same reasoning as before, we find:
{\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.
${d \over dt}{M_{tot}}\neq 0\,\!$ but $dM_{s}+dM_{g}=0$ .

• Working through this model, we find that:
$M_{s}(Z Note the log (as opposed to exponential) dependence.

• Choosing $Z={\frac {1}{3}}Z_{0}$ , and using $M_{g}=0.1M_{s}$ , we find:
${{M_{s}(Z<{\frac {1}{3}}Z_{0}) \over M_{s}}=0.04}\,\!$ This solves the G dwarf problem.