On the far-infrared metallicity diagnostics: applications to
  high-redshift galaxies
  In an earlier paper we modeled the far-infrared emission from a star-forming
galaxy using the photoionisation 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/[NII]122 microns line ratio as a
gas phase metallicity indicator in high redshift submillimetre luminous
galaxies. The [OIII]88/[NII]122 microns 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/$122
continuum flux measurements can provide a reasonable estimate of the ionization
parameter while the availability of the [NII]205 microns line can constrain the
electron density. Using the [OIII]88/[NII]122 microns 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unpublished, Herschel spectroscopic observations of key far-infrared fine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~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/[NII]122 microns line
ratio. We find that the metallicities of these z~3 submm luminous galaxies are
consistent with solar metallicities and that they appear to follow the
mass-metallicity relation expected for z~3 systems.
