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We present an analysis of Mg II $\lambda2798$ and Fe II UV emission lines forarchival Sloan Digital Sky Survey (SDSS) quasars to explore diagnostics of themagnesium-to-iron abundance ratio in a broad-line region cloud. Our sampleconsists of 17,432 quasars selected from the SDSS Data Release 7 with aredshift range of $0.72 < z < 1.63$. A strong anticorrelation between Mg IIequivalent width (EW) and the Eddington ratio is found, while only a weakpositive correlation is found between Fe II EW and the Eddington ratio. Toinvestigate the origin of these differing behaviors of Mg II and Fe II emissionlines, we have performed photoionization calculations using the Cloudy code,where constraints from recent reverberation mapping studies are considered. Wefind from calculations that (i) Mg II and Fe II emission lines are created atdifferent regions in a photoionized cloud, and (ii) their EW correlations withthe Eddington ratio can be explained by just changing the cloud gas density.These results indicate that the Mg II/Fe II flux ratio, which has been used asa first-order proxy for the Mg/Fe abundance ratio in chemical evolution studieswith quasar emission lines, depends largely on the cloud gas density. Bycorrecting this density dependence, we propose new diagnostics of the Mg/Feabundance ratio for a broad line region cloud. Comparing the derived Mg/Feabundance ratios with chemical evolution models, we suggest that$\alpha$-enrichment by mass loss from metal-poor intermediate-mass starsoccurred at $z\sim2$ or earlier.

Chemical evolution of the Universe at 0.7 < z < 1.6 derived from abundance diagnostics of the broad-line region of quasars