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Despite advances in observational data, theoretical models, and computationaltechniques to simulate key physical processes in the formation and evolution ofgalaxies, the stellar mass assembly of galaxies still remains an unsolvedproblem today. Optical spectroscopic measurements appear to show that thegas-phase metallicities of local ultra-luminous infrared galaxies (ULIRGs) aresignificantly lower than those of normal star-forming galaxies. This differencehas resulted in the claim that ULIRGs are fueled by metal-poor gas accretionfrom the outskirts\cite{Mannucci10}. Here we report on a new set of gas-phasemetallicity 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 insteadof the usual optical lines. Photoionization models have resulted in ametallicity diagnostic based on these three lines that break the electrondensity degeneracy and reduce the scatter of the correlation significantly.Using new data from SOFIA and archival data from Herschel Space Observatory, wefind that local ULIRGs lie on the mass-metallicity relation of star-forminggalaxies and have metallicities comparable to other galaxies with similarstellar masses and star formation rates. The lack of a departure suggests thatULIRGs follow the same mass assembly mechanism as luminous star-forminggalaxies and $\sim 0.3$ dex under-abundance in metallicities derived fromoptical lines is a result of heavily obscured metal-rich gas which has anegligible effect when using the FIR line diagnostics.

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