Far-infrared metallicity diagnostics: Application to local ultraluminous
  infrared galaxies
  The abundance of metals in galaxies is a key parameter which permits to
distinguish between different galaxy formation and evolution models. Most of
the metallicity determinations are based on optical line ratios. However, the
optical spectral range is subject to dust extinction and, for high-z objects (z
> 3), some of the lines used in optical metallicity diagnostics are shifted to
wavelengths not accessible to ground based observatories. For this reason, we
explore metallicity diagnostics using far-infrared (IR) line ratios which can
provide a suitable alternative in such situations. To investigate these far-IR
line ratios, we modeled the emission of a starburst with the photoionization
code CLOUDY. The most sensitive far-IR ratios to measure metallicities are the
[OIII]52$\mu$m and 88$\mu$m to [NIII]57$\mu$m ratios. We show that this ratio
produces robust metallicities in the presence of an AGN and is insensitive to
changes in the age of the ionizing stellar. Another metallicity sensitive ratio
is the [OIII]88$\mu$m/[NII]122$\mu$m ratio, although it depends on the
ionization parameter. We propose various mid- and far-IR line ratios to break
this dependency. Finally, we apply these far-IR diagnostics to a sample of 19
local ultraluminous IR galaxies (ULIRGs) observed with Herschel and Spitzer. We
find that the gas-phase metallicity in these local ULIRGs is in the range 0.7 <
Z_gas/Z_sun < 1.5, which corresponds to 8.5 < 12 + log (O/H) < 8.9. The
inferred metallicities agree well with previous estimates for local ULIRGs and
this confirms that they lie below the local mass-metallicity relation.
