Gas Phase Metallicities of Local Ultra-Luminous Infrared Galaxies Follow Normal Star-Forming Galaxies

Despite advances in observational data, theoretical models, and computational techniques to simulate key physical processes in the formation and evolution of galaxies, the stellar mass assembly of galaxies still remains an unsolved problem today. Optical spectroscopic measurements appear to show that the gas-phase metallicities of local ultra-luminous infrared galaxies (ULIRGs) are significantly lower than those of normal star-forming galaxies. This difference has resulted in the claim that ULIRGs are fueled by metal-poor gas accretion from the outskirts\cite{Mannucci10}. Here we report on a new set of gas-phase metallicity measurements making use of the far-infrared spectral lines of [O{\sc iii}]52 $\mu$m, [O{\sc iii}]88 $\mu$m, and [N{\sc iii}]57 $\mu$m instead of the usual optical lines. Photoionization models have resulted in a metallicity diagnostic based on these three lines that break the electron density degeneracy and reduce the scatter of the correlation significantly. Using new data from SOFIA and archival data from Herschel Space Observatory, we find that local ULIRGs lie on the mass-metallicity relation of star-forming galaxies and have metallicities comparable to other galaxies with similar stellar masses and star formation rates. The lack of a departure suggests that ULIRGs follow the same mass assembly mechanism as luminous star-forming galaxies and $\sim 0.3$ dex under-abundance in metallicities derived from optical lines is a result of heavily obscured metal-rich gas which has a negligible effect when using the FIR line diagnostics.