Joint Optical and Infrared Observations of N and O Reveal the Dust-Obscured Gas in Haro 3

Accurate chemical compositions of star-forming regions are a critical diagnostic tool to characterize the star formation history and gas flows which regulate galaxy formation. However, the abundance discrepancy factor (ADF) between measurements from the "direct" optical electron temperature ($T_e$) method and from the recombination lines (RL) represents $\sim0.2$ dex systematic uncertainty in oxygen abundance. The degree of uncertainty for other elements is unknown. We conduct a comprehensive analysis of O$^{++}$ and N$^+$ ion abundances using optical and far-infrared spectra of a star-forming region within the nearby dwarf galaxy Haro 3, which exhibits a typical ADF. Assuming homogeneous conditions, the far-IR emission indicates an O abundance which is higher than the $T_e$ method and consistent with the RL value, as would be expected from temperature fluctuations, whereas the far-IR N abundance is too large to be explained by temperature fluctuations. A two-phase analytical model reveals that differential dust obscuration associated with temperature inhomogeneity is likely required to explain all the emission line ratios, and that the total oxygen metallicity of two phases is consistent with the RL metallicity. Our findings underscore the critical importance of resolving the cause of abundance discrepancies and understanding the biases between different metallicity methods. This work represents a promising methodology, and we identify further approaches to address the current dominant uncertainties.