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Using new , previously unpublished , Herschel spectroscopic observations of key far-infrared fine structure lines of the z \sim 3 galaxy HLSW-01 and additional published measurements of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