Far-Infrared Line Diagnostics: Improving N/O Abundance Estimates for Dusty Galaxies

The nitrogen-to-oxygen (N/O) abundance ratio is an important diagnostic of galaxy evolution because the ratio is closely tied to the growth of metallicity and the star formation history in galaxies. Estimates for the N/O are traditionally made with optical lines that could suffer from extinction and excitation effects, so the N/O is arguably measured better through far-infrared (far-IR) fine-structure lines. Here we show that the [N iii]57 mu m/[O iii]52 mu m line ratio, denoted N3O3, is a physically robust probe of N/O. This parameter is insensitive to gas temperature and only weakly dependent on electron density. Although it has a dependence on the hardness of the ionizing radiation field, we show that it is well corrected when the [Ne iii]15.5 mu m/[Ne ii]12.8 mu m line ratio is included. We verify the method, and characterize its intrinsic uncertainties by comparing the results to photoionization models. We then apply our method to a sample of nearby galaxies using new observations obtained with SOFIA/FIFI-LS in combination with available Herschel/PACS data, and the results are compared with optical N/O estimates. We find evidence for a systematic offset between the far-IR and optically derived N/O. We argue that the likely reason is that our far-IR method is biased toward younger and denser H ii regions, while the optical methods are biased toward older H ii regions as well as diffuse ionized gas. This work provides a local template for studies of the abundance of interstellar medium in the early Universe.