Accurate oxygen abundance of interstellar gas in Mrk 71 from optical and infrared spectra

The heavy element content (`metallicity') of the Universe is a record of the total star formation history. Gas-phase metallicity in galaxies, as well as its evolution with time, is of particular interest as a tracer of accretion and outflow processes. However, metallicities from the widely used electron temperature (T<sub>e</sub>) method are typically approximately two times lower than the values based on the recombination line method. This `abundance discrepancy factor' is well known and is commonly ascribed to bias due to temperature fluctuations. We present a measurement of oxygen abundance in the nearby (3.4-Mpc) system, Markarian 71, using a combination of optical and far-infrared emission lines to measure and correct for temperature fluctuation effects. Our far-infrared result is inconsistent (>2σ significance) with the metallicity from recombination lines and, instead, indicates little to no bias in the standard T_e method, ruling out the long-standing hypothesis that the abundance discrepancy factor is explained by temperature fluctuations for this object. Our results provide a framework to accurately measure metallicity across cosmic history, including with recent data reaching within the first billion years, with the James Webb Space Telescope and the Atacama Large Millimeter Array.