On the far-infrared metallicity diagnostics: applications to high-redshift galaxies

In an earlier paper we modelled the far-infrared emission from a star-forming galaxy using the photoionization code CLOUDY and presented metallicity sensitive diagnostics based on farinfrared fine structure line ratios. Here, we focus on the applicability of the [OIII] 88 mu m/[N II] 122 mu m line ratio as a gas-phase metallicity indicator in high-redshift submillimetre luminous galaxies. The [O-III] 88 mu m/[N-II] 122 mu m ratio is strongly dependent on the ionization parameter (which is related to the total number of ionizing photons) and on the gas electron density. We demonstrate how the ratio of 88/122 mu m continuum flux measurements can provide a reasonable estimate of the ionization parameter, while the availability of the [N-II] 205 mu m line can constrain the electron density. Using the [O-III] 88 mu m/[N-II] 122 mu m line ratios from a sample of nearby normal and star-forming galaxies, we measure their gas-phase metallicities and find that their mass-metallicity relation is consistent with the one derived using optical emission lines. Using new, previously unpublished, Herschel spectroscopic observations of key far-infrared fine structure lines of the z similar to 3 galaxy HLSW-01 and additional published measurements of far-infrared fine structure lines of high-z submillimetre luminous galaxies, we derive gas-phasemetallicities using their [OIII] 88 mu m/[N-II] 122 mu mline ratio. We find that themetallicities of these z similar to 3 submm-luminous galaxies are consistent with solarmetallicities and that they appear to follow the mass-metallicity relation expected for z similar to 3 systems.