Chemical Abundances in Active Galaxies
  The Sloan Digital Sky Survey (SDSS) has proved to be a powerful resource for
understanding the physical properties and chemical composition of star-forming
galaxies in the local universe. The SDSS population of active galactic nuclei
(AGN) remains as of yet less explored in this capacity. To extend the rigorous
study of \ion{H}{ii} regions in the SDSS to AGN, we adapt methods for computing
direct-method chemical abundances for application to the narrow-line regions
(NLR) of AGN. By accounting for triply-ionized oxygen, we are able to more
completely estimate the total oxygen abundance. We find a strong correlation
between electron temperature and oxygen abundance due to collisional cooling by
metals. Furthermore, we find that nitrogen and oxygen abundances in AGN are
strongly correlated. From the metal-temperature relation and the coupling of
nitrogen and oxygen abundances, we develop a new, empirically and physically
motivated method for determining chemical abundances from the strong emission
lines commonly employed in flux-ratio diagnostic diagrams (BPT diagrams). Our
approach, which for AGN reduces to a single equation based on the BPT line
ratios, consistently recovers direct-method abundances over a 1.5 dex range in
oxygen abundance with an rms uncertainty of 0.18 dex. We have determined
metallicities for thousands of AGN in the SDSS, and in the process have
discovered an ionization-related discriminator for Seyfert and LINER galaxies.
