Metallicity diagnostics with infrared fine-structure lines

Although measuring the gas metallicity in galaxies at various redshifts is crucial to constrain galaxy evolutionary scenarios, only rest-frame optical emission lines have been generally used to measure the metallicity. This has prevented us to accurately measure the metallicity of dust-obscured galaxies, and accordingly to understand the chemical evolution of dusty populations, such as ultraluminous infrared galaxies. Here we propose diagnostics of the gas metallicity based on infrared fine-structure emission lines, which are nearly unaffected by dust extinction even the most obscured systems. Specifically, we focus on fine-structure lines arising mostly from HII regions, not in photo-dissociation regions, to minimize the dependence and uncertainties of the metallicity diagnostics from various physical parameters. Based on photoionization models, we show that the emission-line flux ratio of ([OIII]51.80+[OIII]88.33)/[NIII]57.21 is an excellent tracer of the gas metallicity. The individual line ratios [OIII]51.80/[NIII]57.21 or [OIII]88.33/[NIII]57.21 can also be used as diagnostics of the metallicity, but they are more strongly dependent on the gas density. The line ratios [OIII]88.33/[OIII]51.80 and [NII]121.7/[NIII]57.21 can be used to measure and, therefore, account for the dependences on the gas density and ionization parameter, respectively. We show that these diagnostic fine-structure lines are detectable with Herschel in luminous infrared galaxies out z similar to 0.4. Metallicity measurements with these fine-structure lines will be feasible at relatively high redshift (z similar to 1 or more) with SPICA, the future infrared space observatory.