the simplex $\chi^2$ minimization algorithm to simultaneously fit a flat continuum and Gaussian profile to each emission line. @Andrews13 found this to be a robust method consistent with other flux measurement techniques. Uncertainties are derived from the $\chi^2$ of the fit returned by *specfit*. We deredden the spectra using the extinction law from @Cardelli89 and the assumption of case B recombination (/= 2.86 for $T_e = 10^4$ K). @Andrews13 estimate the systematic error introduced by adopting a fixed / ratio to be $\lesssim 0.07$ dex. Finally, with the exception of \[\] $\lambda 3727$ Å, our diagnostic emission lines are anchored to nearby Balmer lines, and are thus insensitive to reddening.

Analysis {#sec:analysis}
========

Abundances {#sec:abund}
----------

We compute the chemical abundances of the stacks using the same procedure as @Andrews13; here we present a brief overview and direct the reader to that paper for further details.

We assume a simple two-zone model composed of a high ionization region (traced by \[\]) and a low ionization region (traced by \[\], \[\], and \[\]). Previous works have assumed simple relationships between the temperatures of the high and low ionization regions [the ${\hbox{$T_2-T_3$}}$ relation @Campbell86; @Garnett92; @Pagel92; @Izotov06; @Pilyugin09]. We assume a linear 