A novel approach to correcting Tₑ-based mass-metallicity relations

Deriving oxygen abundances from the electron temperature (hereafter the Tₑ-method) is the gold-standard for extragalactic metallicity studies. However, unresolved temperature fluctuations within individual HII regions and across different HII regions throughout a galaxy can bias metallicity estimates low, with a magnitude that depends on the underlying and typically unknown temperature distribution. Using a toy model, we confirm that computing Tₑ-based metallicities using the temperature derived from the O III λ4363/λ5007 or O II λλ7320, 7330 / O II λλ3727 ratio ('ratio temperature'; T ₑ₀ₓ₈₎) results in an underprediction of metallicity when temperature fluctuations are present. In contrast, using the unobservable 'line temperatures' (T ₋₈₍₄) that provide the mean electron and ion density-weighted emissivity yield an accurate metallicity estimate. To correct this bias in low-mass galaxies, we demonstrate an example calibration of a relation between Tᵣatio and Tₗine based on a high-resolution (4. 5 pc) RAMSES-RTZ simulation of a dwarf galaxy that self-consistently models the formation of multiple HII regions and ion temperature distribution in a galactic context. Applying this correction to the low-mass end of the mass-metallicity relation shifts its normalization up by 0. 18 dex on average and flattens its slope from 0. 87 to 0. 58, highlighting the need for future studies to account for, and correct, this bias.