to the one third power, $\eta \propto 1/\sigma_h \propto M_h^{-1/3}$ [@Murray05; @Oppenheimer06]. Once the star formation has reached an equilibrium with the inflowing and outflowing gas, the metallicity is $Z = y/(1+\eta)$ where $y$ is the effective yield. In the limit that $\eta \gg 1$, the slope of the MZR is ultimately related to how ${\hbox{$M_{\star}$}}$ scales with $M_h$, since $\log(Z) \propto -\log(\eta) \propto \frac{1}{3} \log(M_h)$.

There is good observational evidence for a second parameter that affects the relationship between ${\hbox{$M_{\star}$}}$ and $Z$ such that galaxies with higher star formation rates have lower metallicities at fixed stellar mass [the ${\hbox{$M_{\star}$--$Z$--${\rm SFR}$}}$ relation; @Ellison08Apj; @Mannucci10; @LaraLopez10]. This relation is also apparent in high signal-to-noise ratio stacked spectra of SDSS galaxies [@Andrews13]. However, it has intriguingly not been seen in the CALIFA sample of 150 nearby galaxies studied with integral field spectroscopy by @Sanchez13.

The exact form of the SFR dependence is less clear, but if the fuel for star formation is lower metallicity gas accreted from the IGM, this would produce an anticorrelation between gas phase metallicity and SFR. The form of the secondary dependence of the MZR on SFR offers insights into several open questions, such as how star formation 