2026ApJ...999...48F

The chemical abundance of the interstellar medium is a key tracer of galaxy evolution. Optical and ultraviolet emission lines are widely used to derive gas-phase metallicities, but suffer from uncertainties due to possible temperature fluctuations and extinction corrections. Far-infrared atomic fine-structure lines offer a promising alternative, penetrating dust without extinction correction and with minimal dependence on electron temperature. However, the far-infrared lacks useful hydrogen transitions and must be calibrated through other means, such as the N/O ratio. We use four far-infrared diagnostic emission lines, [O III]52μm, [N III]57 μm, [O III]88μm, and [N II]122 μm from archival Herschel/PACS and SOFIA/FIFI-LS data, coupled with a photoionization model to determine metallicity for a sample of local galaxies, ranging from dwarf irregular galaxies to ultraluminous infrared galaxies. We use a Bayesian framework, as well as simple emission-line ratios, to derive the O/H abundance ratio. The results are compared with results from optical diagnostics. After correcting for a slight difference between the calibrations used in the photoionization model used for the far-infrared emission lines, and the empirical calibration used for the optical emission lines, we find that far-infrared and optical diagnostics yield the same metallicity within the observational errors. Furthermore, we find no statistically significant difference between the N/O ratios derived from far-infrared emission lines and those derived using optical emission lines. Hence, the far-infrared methods provide robust metallicity estimates in the range 0.2 < Z/Z_⊙ < 1.0. We apply our far-infrared techniques to Atacama Large Millimeter/submillimeter Array data for the A1689-zD1 galaxy at z = 7.1. We find a low electron density consistent with findings for local low-metallicity galaxies. Assuming an ionization parameter similar to those found locally, we infer a gas-phase metallicity in the range 0.2-0.3 Z_⊙.